57268

File Attachment

Coverjpg

Edward L Wolf

Nanophysics of Solar and

Renewable Energy

Related Titles

Wengenmayr R Buumlhrke T (eds)

Renewable Energy

Sustainable Energy Concepts for the Future

2012

ISBN 978-3-527-41108-5

Vogel W Kalb H

Large-Scale Solar Thermal Power

Technologies Costs and Development

2010

ISBN 978-3-527-40515-2

Quaschning V

Renewable Energy and Climate Change

2010

ISBN 978-0-470-74707-0

Wolf E L

Quantum Nanoelectronics

An Introduction to Electronic Nanotechnology

and Quantum Computing

2009

ISBN 978-3-527-40749-1

Wuumlrfel P

Physics of Solar Cells

From Basic Principles to Advanced Concepts

2009

ISBN 978-3-527-40857-3

Freris L Infield D

Renewable Energy in Power Systems

2008

ISBN 978-0-470-01749-4

De Vos A

Thermodynamics of Solar EnergyConversion

2008

ISBN 978-3-527-40841-2

Wolf E L

Nanophysics and Nanotechnology

An Introduction to Modern Concepts

in Nanoscience

2006

ISBN 978-3-527-40651-7

Edward L Wolf

Nanophysics of Solar andRenewable Energy

The Author

Prof Edward L WolfPolytechnic Institute of the New York UniversityBrooklyn USAemail ewolfpolyedu

Cover picturePictures clockwiseThe sunphotographed by NASAs SOHO spacecraft NASA 2004

The flexible solar module(Credit Copyright Fraunhofer ISE)

Pillared graphene consists of CNTs and graphenesheets combined to form a 3D network nanostructure SPIE 2009George Dimitrakakis Emmanuel Tylianakis andGeorge Froudakis Designing novel carbon nanos-tructures for hydrogen storage SPIE Newsroom doi101117212009021451

Solar panelsPart of the Solar Farm at PTLEN IndustriIndonesias largest solar cell producer and importerThis 900 square meter farm generates enough elec-tricity to power their solar factory and the employeescafetariaPhotograph by Chandra Marsono 2008

All books published by Wiley-VCH are carefullyproduced Nevertheless authors editors and pub-lisher do not warrant the information contained inthese books including this book to be free of errorsReaders are advised to keep in mind that statementsdata illustrations procedural details or other itemsmay inadvertently be inaccurate

Library of Congress Card No applied for

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from theBritish Library

Bibliographic information published bythe Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publica-tion in the Deutsche Nationalbibliografie detailedbibliographic data are available on the Internet athttpdnbd-nbde

2012 Wiley-VCH Verlag amp Co KGaABoschstr 12 69469 Weinheim Germany

All rights reserved (including those of translationinto other languages) No part of this book may bereproduced in any form ndash by photoprinting micro-film or any other means ndash nor transmitted or trans-lated into a machine language without writtenpermission from the publishers Registered namestrademarks etc used in this book even when notspecifically marked as such are not to be consideredunprotected by law

Composition Thomson Digital Noida India

Printing and Binding Markono Print Media Pte LtdSingapore

Cover Design Schulz Grafik-Design Fuszliggoumlnheim

Print ISBN 978-3-527-41052-1 (HC)978-3-527-41046-0 (SC)

ePDF ISBN 978-3-527-64631-9ePub ISBN 978-3-527-64630-2mobi ISBN 978-3-527-64629-6oBook ISBN 978-3-527-64628-9

Printed in SingaporePrinted on acid-free paper

In Memory of Ned

Edward OrsquoBrien Wolf

1973ndash2011

Contents

Preface XIII

1 A Survey of Long-Term Energy Resources 111 Introduction 1111 Direct Solar Influx 61111 Properties of the Sun 61112 An Introduction to Fusion Reactions on the Sun 101113 Distribution of Solar Influx for Conversion 13112 Secondary Solar-Driven Sources 141121 Flow Energy 141122 Hydroelectric Power 181123 Ocean Waves 20113 Earth-Based Long-Term Energy Resources 221131 Lunar Ocean Tidal Motion 221132 Geothermal Energy 241133 The Earths Deuterium and its Potential 25114 Plan of This Book 26

2 Physics of Nuclear Fusion the Source of allSolar-Related Energy 27

21 Introduction Protons in the Suns Core 2822 Schrodingers Equation for the Motion of Particles 30221 Time-Dependent Equation 32222 Time-Independent Equation 32223 Bound States Inside a One-Dimensional Potential

Well E gt 0 3323 Protons and Neutrons and Their Binding 3524 Gamows Tunneling Model Applied to Fusion

in the Suns Core 3525 A Survey of Nuclear Properties 43

VII

3 Atoms Molecules and Semiconductor Devices 4931 Bohrs Model of the Hydrogen Atom 4932 Charge Motion in Periodic Potential 5233 Energy Bands and Gaps 53331 Properties of a Metal Electrons in an Empty Box (I) 5734 Atoms Molecules and the Covalent Bond 60341 Properties of a Metal Electrons in an Empty Box (II) 66342 Hydrogen Molecule Ion H2

thorn 6935 Tetrahedral Bonding in Silicon and Related Semiconductors 71351 Connection with Directed or Covalent Bonds 72352 Bond Angle 7236 Donor and Acceptor Impurities Charge Concentrations 73361 Hydrogenic Donors and Excitons in Semiconductors Direct

and Indirect Bandgaps 75362 Carrier Concentrations in Semiconductors 76363 The Degenerate Metallic Semiconductor 7937 The PN Junction Diode IndashV Characteristic Photovoltaic Cell 8038 Metals and Plasmas 84

4 Terrestrial Approaches to Fusion Energy 8741 Deuterium Fusion Demonstration Based on Field Ionization 88411 Electric Field Ionization of Deuterium (Hydrogen) 9442 Deuterium Fusion Demonstration Based on Muonic Hydrogen 96421 Catalysis of DD Fusion by Mu Mesons 10143 Deuterium Fusion Demonstration in Larger Scale Plasma

Reactors 102431 Electrical Heating of the Plasma 103432 Scaling the Fusion Power Density from that in the Sun 104433 Adapt DD Plasma Analysis to DT Plasma as in ITER 104434 Summary a Correction and Further Comments 110

5 Introduction to Solar Energy Conversion 11551 Sun as an Energy Source Spectrum on Earth 11552 Heat Engines and Thermodynamics Carnot Efficiency 11753 Solar Thermal Electric Power 11954 Generations of Photovoltaic Solar Cells 12255 Utilizing Solar Power with Photovoltaics the Rooftops of

New York versus Space Satellites 12556 The Possibility of Space-Based Solar Power 126

6 Solar Cells Based on Single PN Junctions 13361 Single-Junction Cells 133611 Silicon Crystalline Cells 136612 GaAs Epitaxially Grown Solar Cells 141613 Single-Junction Limiting Conversion Efficiency 141

VIII Contents

62 Thin-Film Solar Cells versus Crystalline Cells 14563 CIGS (CuIn1xGaxSe2) Thin-Film Solar Cells 147631 Printing Cells onto Large-Area Flexible Substrates 14764 CdTe Thin-Film Cells 15165 Dye-Sensitized Solar Cells 153651 Principle of Dye Sensitization to Extend Spectral Range

to the Red 154652 Questions of Efficiency 15566 Polymer Organic Solar Cells 155661 A Basic Semiconducting Polymer Solar Cell 156

7 Multijunction and Energy Concentrating Solar Cells 15771 Tandem Cells Premium and Low Cost 158711 GaAs-based Tandem Single-Crystal Cells a Near Text-Book

Example 158712 A Smaller Scale Concentrator Technology Built

on Multijunction Cells 162713 Low-Cost Tandem Technology Advanced Tandem Semiconducting

Polymer Cells 1637131 Band-Edge Energies in the Multilayer Tandem Semiconductor

Polymer Structure 1657132 Performance of the Advanced Polymer Tandem Cell 166714 Low-Cost Tandem Technology Amorphous SiliconH-Based

Solar Cells 16672 Organic Molecules as Solar Concentrators 16973 Spectral Splitting Cells 17174 Summary and Comments on Efficiency 17275 A Niche Application of Concentrating Cells on Pontoons 172

8 Third-Generation Concepts Survey of Efficiency 17581 Intermediate Band Cells 17582 Impact Ionization and Carrier Multiplication 177821 Electrons and Holes in a 3D lsquolsquoQuantum Dotrsquorsquo 18083 Ferromagnetic Materials for Solar Conversion 18284 Efficiencies Three Generations of Cells 185

9 Cells for Hydrogen Generation Aspects of Hydrogen Storage 18791 Intermittency of Renewable Energy 18792 Electrolysis of Water 18793 Efficient Photocatalytic Dissociation of Water into Hydrogen

and Oxygen 188931 Tandem Cell as Water Splitter 190932 Possibility of a Mass Production Tandem Cell

Water-Splitting Device 191933 Possibilities for Dual-Purpose Thin-Film Tandem Cell Devices 193

Contents IX

94 The lsquolsquoArtificial Leafrsquorsquo of Nocera 19395 Hydrogen Fuel Cell Status 19496 Storage and Transport of Hydrogen as a Potential Fuel 19597 Surface Adsorption for Storing Hydrogen in High Density 196971 Titanium-Decorated Carbon Nanotube Cloth 19998 Economics of Hydrogen 200981 Further Aspects of Storage and Transport of Hydrogen 200982 Hydrogen as Potential Intermediate in US Electricity

Distribution 201

10 Large-Scale Fabrication Learning Curves and EconomicsIncluding Storage 203

101 Fabrication Methods Vary but Exhibit Similar Learning Curves 203102 Learning Strategies for Module Cost 205103 Thin-Film Cells Nanoinks for Printing Solar Cells 207104 Large-Scale Scenario Based on Thin-Film CdTe or CIGS Cells 2091041 Solar Influx Cell Efficiency and Size of Solar Field Required

to Meet Demand 2101042 Economics of lsquolsquoPrinting Pressrsquorsquo CIGS or CdTe Cell Production

to Satisfy US Electric Demand 2111043 Projected Total Capital Need Conditions for Profitable

Private Investment 212105 Comparison of Solar Power versus Wind Power 214106 The Importance of Storage and Grid Management to

Large-Scale Utilization 2151061 Batteries from LeadndashAcid to Lithium to Sodium Sulfur 2171062 Basics of Lithium Batteries 2181063 NiMH 220

11 Prospects for Solar and Renewable Power 223111 Rapid Growth in Solar and Wind Power 223112 Renewable Energy Beyond Solar and Wind 225113 The Legacy World Developing Countries and the

Third World 226114 Can Energy Supply Meet Demand in the Longer Future 2271141 The lsquolsquoOil Bubblersquorsquo 2271142 The lsquolsquoEnergy Miraclersquorsquo 229

Appendix A Exercises 231Exercises to Chapter 1 231Exercises to Chapter 2 232Exercises to Chapter 3 233Exercises to Chapter 4 234Exercises to Chapter 5 236Exercises to Chapter 6 236

X Contents

Exercises to Chapter 7 237Exercises to Chapter 8 238Exercises to Chapter 9 238Exercises to Chapter 10 238Exercises to Chapter 11 239

Glossary of Abbreviations 241

References 245

Index 251

Contents XI

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

Edward L Wolf

Nanophysics of Solar and

Renewable Energy

Related Titles

Wengenmayr R Buumlhrke T (eds)

Renewable Energy

Sustainable Energy Concepts for the Future

2012

ISBN 978-3-527-41108-5

Vogel W Kalb H

Large-Scale Solar Thermal Power

Technologies Costs and Development

2010

ISBN 978-3-527-40515-2

Quaschning V

Renewable Energy and Climate Change

2010

ISBN 978-0-470-74707-0

Wolf E L

Quantum Nanoelectronics

An Introduction to Electronic Nanotechnology

and Quantum Computing

2009

ISBN 978-3-527-40749-1

Wuumlrfel P

Physics of Solar Cells

From Basic Principles to Advanced Concepts

2009

ISBN 978-3-527-40857-3

Freris L Infield D

Renewable Energy in Power Systems

2008

ISBN 978-0-470-01749-4

De Vos A

Thermodynamics of Solar EnergyConversion

2008

ISBN 978-3-527-40841-2

Wolf E L

Nanophysics and Nanotechnology

An Introduction to Modern Concepts

in Nanoscience

2006

ISBN 978-3-527-40651-7

Edward L Wolf

Nanophysics of Solar andRenewable Energy

The Author

Prof Edward L WolfPolytechnic Institute of the New York UniversityBrooklyn USAemail ewolfpolyedu

Cover picturePictures clockwiseThe sunphotographed by NASAs SOHO spacecraft NASA 2004

The flexible solar module(Credit Copyright Fraunhofer ISE)

Pillared graphene consists of CNTs and graphenesheets combined to form a 3D network nanostructure SPIE 2009George Dimitrakakis Emmanuel Tylianakis andGeorge Froudakis Designing novel carbon nanos-tructures for hydrogen storage SPIE Newsroom doi101117212009021451

Solar panelsPart of the Solar Farm at PTLEN IndustriIndonesias largest solar cell producer and importerThis 900 square meter farm generates enough elec-tricity to power their solar factory and the employeescafetariaPhotograph by Chandra Marsono 2008

All books published by Wiley-VCH are carefullyproduced Nevertheless authors editors and pub-lisher do not warrant the information contained inthese books including this book to be free of errorsReaders are advised to keep in mind that statementsdata illustrations procedural details or other itemsmay inadvertently be inaccurate

Library of Congress Card No applied for

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from theBritish Library

Bibliographic information published bythe Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publica-tion in the Deutsche Nationalbibliografie detailedbibliographic data are available on the Internet athttpdnbd-nbde

2012 Wiley-VCH Verlag amp Co KGaABoschstr 12 69469 Weinheim Germany

All rights reserved (including those of translationinto other languages) No part of this book may bereproduced in any form ndash by photoprinting micro-film or any other means ndash nor transmitted or trans-lated into a machine language without writtenpermission from the publishers Registered namestrademarks etc used in this book even when notspecifically marked as such are not to be consideredunprotected by law

Composition Thomson Digital Noida India

Printing and Binding Markono Print Media Pte LtdSingapore

Cover Design Schulz Grafik-Design Fuszliggoumlnheim

Print ISBN 978-3-527-41052-1 (HC)978-3-527-41046-0 (SC)

ePDF ISBN 978-3-527-64631-9ePub ISBN 978-3-527-64630-2mobi ISBN 978-3-527-64629-6oBook ISBN 978-3-527-64628-9

Printed in SingaporePrinted on acid-free paper

In Memory of Ned

Edward OrsquoBrien Wolf

1973ndash2011

Contents

Preface XIII

1 A Survey of Long-Term Energy Resources 111 Introduction 1111 Direct Solar Influx 61111 Properties of the Sun 61112 An Introduction to Fusion Reactions on the Sun 101113 Distribution of Solar Influx for Conversion 13112 Secondary Solar-Driven Sources 141121 Flow Energy 141122 Hydroelectric Power 181123 Ocean Waves 20113 Earth-Based Long-Term Energy Resources 221131 Lunar Ocean Tidal Motion 221132 Geothermal Energy 241133 The Earths Deuterium and its Potential 25114 Plan of This Book 26

2 Physics of Nuclear Fusion the Source of allSolar-Related Energy 27

21 Introduction Protons in the Suns Core 2822 Schrodingers Equation for the Motion of Particles 30221 Time-Dependent Equation 32222 Time-Independent Equation 32223 Bound States Inside a One-Dimensional Potential

Well E gt 0 3323 Protons and Neutrons and Their Binding 3524 Gamows Tunneling Model Applied to Fusion

in the Suns Core 3525 A Survey of Nuclear Properties 43

VII

3 Atoms Molecules and Semiconductor Devices 4931 Bohrs Model of the Hydrogen Atom 4932 Charge Motion in Periodic Potential 5233 Energy Bands and Gaps 53331 Properties of a Metal Electrons in an Empty Box (I) 5734 Atoms Molecules and the Covalent Bond 60341 Properties of a Metal Electrons in an Empty Box (II) 66342 Hydrogen Molecule Ion H2

thorn 6935 Tetrahedral Bonding in Silicon and Related Semiconductors 71351 Connection with Directed or Covalent Bonds 72352 Bond Angle 7236 Donor and Acceptor Impurities Charge Concentrations 73361 Hydrogenic Donors and Excitons in Semiconductors Direct

and Indirect Bandgaps 75362 Carrier Concentrations in Semiconductors 76363 The Degenerate Metallic Semiconductor 7937 The PN Junction Diode IndashV Characteristic Photovoltaic Cell 8038 Metals and Plasmas 84

4 Terrestrial Approaches to Fusion Energy 8741 Deuterium Fusion Demonstration Based on Field Ionization 88411 Electric Field Ionization of Deuterium (Hydrogen) 9442 Deuterium Fusion Demonstration Based on Muonic Hydrogen 96421 Catalysis of DD Fusion by Mu Mesons 10143 Deuterium Fusion Demonstration in Larger Scale Plasma

Reactors 102431 Electrical Heating of the Plasma 103432 Scaling the Fusion Power Density from that in the Sun 104433 Adapt DD Plasma Analysis to DT Plasma as in ITER 104434 Summary a Correction and Further Comments 110

5 Introduction to Solar Energy Conversion 11551 Sun as an Energy Source Spectrum on Earth 11552 Heat Engines and Thermodynamics Carnot Efficiency 11753 Solar Thermal Electric Power 11954 Generations of Photovoltaic Solar Cells 12255 Utilizing Solar Power with Photovoltaics the Rooftops of

New York versus Space Satellites 12556 The Possibility of Space-Based Solar Power 126

6 Solar Cells Based on Single PN Junctions 13361 Single-Junction Cells 133611 Silicon Crystalline Cells 136612 GaAs Epitaxially Grown Solar Cells 141613 Single-Junction Limiting Conversion Efficiency 141

VIII Contents

62 Thin-Film Solar Cells versus Crystalline Cells 14563 CIGS (CuIn1xGaxSe2) Thin-Film Solar Cells 147631 Printing Cells onto Large-Area Flexible Substrates 14764 CdTe Thin-Film Cells 15165 Dye-Sensitized Solar Cells 153651 Principle of Dye Sensitization to Extend Spectral Range

to the Red 154652 Questions of Efficiency 15566 Polymer Organic Solar Cells 155661 A Basic Semiconducting Polymer Solar Cell 156

7 Multijunction and Energy Concentrating Solar Cells 15771 Tandem Cells Premium and Low Cost 158711 GaAs-based Tandem Single-Crystal Cells a Near Text-Book

Example 158712 A Smaller Scale Concentrator Technology Built

on Multijunction Cells 162713 Low-Cost Tandem Technology Advanced Tandem Semiconducting

Polymer Cells 1637131 Band-Edge Energies in the Multilayer Tandem Semiconductor

Polymer Structure 1657132 Performance of the Advanced Polymer Tandem Cell 166714 Low-Cost Tandem Technology Amorphous SiliconH-Based

Solar Cells 16672 Organic Molecules as Solar Concentrators 16973 Spectral Splitting Cells 17174 Summary and Comments on Efficiency 17275 A Niche Application of Concentrating Cells on Pontoons 172

8 Third-Generation Concepts Survey of Efficiency 17581 Intermediate Band Cells 17582 Impact Ionization and Carrier Multiplication 177821 Electrons and Holes in a 3D lsquolsquoQuantum Dotrsquorsquo 18083 Ferromagnetic Materials for Solar Conversion 18284 Efficiencies Three Generations of Cells 185

9 Cells for Hydrogen Generation Aspects of Hydrogen Storage 18791 Intermittency of Renewable Energy 18792 Electrolysis of Water 18793 Efficient Photocatalytic Dissociation of Water into Hydrogen

and Oxygen 188931 Tandem Cell as Water Splitter 190932 Possibility of a Mass Production Tandem Cell

Water-Splitting Device 191933 Possibilities for Dual-Purpose Thin-Film Tandem Cell Devices 193

Contents IX

94 The lsquolsquoArtificial Leafrsquorsquo of Nocera 19395 Hydrogen Fuel Cell Status 19496 Storage and Transport of Hydrogen as a Potential Fuel 19597 Surface Adsorption for Storing Hydrogen in High Density 196971 Titanium-Decorated Carbon Nanotube Cloth 19998 Economics of Hydrogen 200981 Further Aspects of Storage and Transport of Hydrogen 200982 Hydrogen as Potential Intermediate in US Electricity

Distribution 201

10 Large-Scale Fabrication Learning Curves and EconomicsIncluding Storage 203

101 Fabrication Methods Vary but Exhibit Similar Learning Curves 203102 Learning Strategies for Module Cost 205103 Thin-Film Cells Nanoinks for Printing Solar Cells 207104 Large-Scale Scenario Based on Thin-Film CdTe or CIGS Cells 2091041 Solar Influx Cell Efficiency and Size of Solar Field Required

to Meet Demand 2101042 Economics of lsquolsquoPrinting Pressrsquorsquo CIGS or CdTe Cell Production

to Satisfy US Electric Demand 2111043 Projected Total Capital Need Conditions for Profitable

Private Investment 212105 Comparison of Solar Power versus Wind Power 214106 The Importance of Storage and Grid Management to

Large-Scale Utilization 2151061 Batteries from LeadndashAcid to Lithium to Sodium Sulfur 2171062 Basics of Lithium Batteries 2181063 NiMH 220

11 Prospects for Solar and Renewable Power 223111 Rapid Growth in Solar and Wind Power 223112 Renewable Energy Beyond Solar and Wind 225113 The Legacy World Developing Countries and the

Third World 226114 Can Energy Supply Meet Demand in the Longer Future 2271141 The lsquolsquoOil Bubblersquorsquo 2271142 The lsquolsquoEnergy Miraclersquorsquo 229

Appendix A Exercises 231Exercises to Chapter 1 231Exercises to Chapter 2 232Exercises to Chapter 3 233Exercises to Chapter 4 234Exercises to Chapter 5 236Exercises to Chapter 6 236

X Contents

Exercises to Chapter 7 237Exercises to Chapter 8 238Exercises to Chapter 9 238Exercises to Chapter 10 238Exercises to Chapter 11 239

Glossary of Abbreviations 241

References 245

Index 251

Contents XI

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

Related Titles

Wengenmayr R Buumlhrke T (eds)

Renewable Energy

Sustainable Energy Concepts for the Future

2012

ISBN 978-3-527-41108-5

Vogel W Kalb H

Large-Scale Solar Thermal Power

Technologies Costs and Development

2010

ISBN 978-3-527-40515-2

Quaschning V

Renewable Energy and Climate Change

2010

ISBN 978-0-470-74707-0

Wolf E L

Quantum Nanoelectronics

An Introduction to Electronic Nanotechnology

and Quantum Computing

2009

ISBN 978-3-527-40749-1

Wuumlrfel P

Physics of Solar Cells

From Basic Principles to Advanced Concepts

2009

ISBN 978-3-527-40857-3

Freris L Infield D

Renewable Energy in Power Systems

2008

ISBN 978-0-470-01749-4

De Vos A

Thermodynamics of Solar EnergyConversion

2008

ISBN 978-3-527-40841-2

Wolf E L

Nanophysics and Nanotechnology

An Introduction to Modern Concepts

in Nanoscience

2006

ISBN 978-3-527-40651-7

Edward L Wolf

Nanophysics of Solar andRenewable Energy

The Author

Prof Edward L WolfPolytechnic Institute of the New York UniversityBrooklyn USAemail ewolfpolyedu

Cover picturePictures clockwiseThe sunphotographed by NASAs SOHO spacecraft NASA 2004

The flexible solar module(Credit Copyright Fraunhofer ISE)

Pillared graphene consists of CNTs and graphenesheets combined to form a 3D network nanostructure SPIE 2009George Dimitrakakis Emmanuel Tylianakis andGeorge Froudakis Designing novel carbon nanos-tructures for hydrogen storage SPIE Newsroom doi101117212009021451

Solar panelsPart of the Solar Farm at PTLEN IndustriIndonesias largest solar cell producer and importerThis 900 square meter farm generates enough elec-tricity to power their solar factory and the employeescafetariaPhotograph by Chandra Marsono 2008

All books published by Wiley-VCH are carefullyproduced Nevertheless authors editors and pub-lisher do not warrant the information contained inthese books including this book to be free of errorsReaders are advised to keep in mind that statementsdata illustrations procedural details or other itemsmay inadvertently be inaccurate

Library of Congress Card No applied for

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from theBritish Library

Bibliographic information published bythe Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publica-tion in the Deutsche Nationalbibliografie detailedbibliographic data are available on the Internet athttpdnbd-nbde

2012 Wiley-VCH Verlag amp Co KGaABoschstr 12 69469 Weinheim Germany

All rights reserved (including those of translationinto other languages) No part of this book may bereproduced in any form ndash by photoprinting micro-film or any other means ndash nor transmitted or trans-lated into a machine language without writtenpermission from the publishers Registered namestrademarks etc used in this book even when notspecifically marked as such are not to be consideredunprotected by law

Composition Thomson Digital Noida India

Printing and Binding Markono Print Media Pte LtdSingapore

Cover Design Schulz Grafik-Design Fuszliggoumlnheim

Print ISBN 978-3-527-41052-1 (HC)978-3-527-41046-0 (SC)

ePDF ISBN 978-3-527-64631-9ePub ISBN 978-3-527-64630-2mobi ISBN 978-3-527-64629-6oBook ISBN 978-3-527-64628-9

Printed in SingaporePrinted on acid-free paper

In Memory of Ned

Edward OrsquoBrien Wolf

1973ndash2011

Contents

Preface XIII

1 A Survey of Long-Term Energy Resources 111 Introduction 1111 Direct Solar Influx 61111 Properties of the Sun 61112 An Introduction to Fusion Reactions on the Sun 101113 Distribution of Solar Influx for Conversion 13112 Secondary Solar-Driven Sources 141121 Flow Energy 141122 Hydroelectric Power 181123 Ocean Waves 20113 Earth-Based Long-Term Energy Resources 221131 Lunar Ocean Tidal Motion 221132 Geothermal Energy 241133 The Earths Deuterium and its Potential 25114 Plan of This Book 26

2 Physics of Nuclear Fusion the Source of allSolar-Related Energy 27

21 Introduction Protons in the Suns Core 2822 Schrodingers Equation for the Motion of Particles 30221 Time-Dependent Equation 32222 Time-Independent Equation 32223 Bound States Inside a One-Dimensional Potential

Well E gt 0 3323 Protons and Neutrons and Their Binding 3524 Gamows Tunneling Model Applied to Fusion

in the Suns Core 3525 A Survey of Nuclear Properties 43

VII

3 Atoms Molecules and Semiconductor Devices 4931 Bohrs Model of the Hydrogen Atom 4932 Charge Motion in Periodic Potential 5233 Energy Bands and Gaps 53331 Properties of a Metal Electrons in an Empty Box (I) 5734 Atoms Molecules and the Covalent Bond 60341 Properties of a Metal Electrons in an Empty Box (II) 66342 Hydrogen Molecule Ion H2

thorn 6935 Tetrahedral Bonding in Silicon and Related Semiconductors 71351 Connection with Directed or Covalent Bonds 72352 Bond Angle 7236 Donor and Acceptor Impurities Charge Concentrations 73361 Hydrogenic Donors and Excitons in Semiconductors Direct

and Indirect Bandgaps 75362 Carrier Concentrations in Semiconductors 76363 The Degenerate Metallic Semiconductor 7937 The PN Junction Diode IndashV Characteristic Photovoltaic Cell 8038 Metals and Plasmas 84

4 Terrestrial Approaches to Fusion Energy 8741 Deuterium Fusion Demonstration Based on Field Ionization 88411 Electric Field Ionization of Deuterium (Hydrogen) 9442 Deuterium Fusion Demonstration Based on Muonic Hydrogen 96421 Catalysis of DD Fusion by Mu Mesons 10143 Deuterium Fusion Demonstration in Larger Scale Plasma

Reactors 102431 Electrical Heating of the Plasma 103432 Scaling the Fusion Power Density from that in the Sun 104433 Adapt DD Plasma Analysis to DT Plasma as in ITER 104434 Summary a Correction and Further Comments 110

5 Introduction to Solar Energy Conversion 11551 Sun as an Energy Source Spectrum on Earth 11552 Heat Engines and Thermodynamics Carnot Efficiency 11753 Solar Thermal Electric Power 11954 Generations of Photovoltaic Solar Cells 12255 Utilizing Solar Power with Photovoltaics the Rooftops of

New York versus Space Satellites 12556 The Possibility of Space-Based Solar Power 126

6 Solar Cells Based on Single PN Junctions 13361 Single-Junction Cells 133611 Silicon Crystalline Cells 136612 GaAs Epitaxially Grown Solar Cells 141613 Single-Junction Limiting Conversion Efficiency 141

VIII Contents

62 Thin-Film Solar Cells versus Crystalline Cells 14563 CIGS (CuIn1xGaxSe2) Thin-Film Solar Cells 147631 Printing Cells onto Large-Area Flexible Substrates 14764 CdTe Thin-Film Cells 15165 Dye-Sensitized Solar Cells 153651 Principle of Dye Sensitization to Extend Spectral Range

to the Red 154652 Questions of Efficiency 15566 Polymer Organic Solar Cells 155661 A Basic Semiconducting Polymer Solar Cell 156

7 Multijunction and Energy Concentrating Solar Cells 15771 Tandem Cells Premium and Low Cost 158711 GaAs-based Tandem Single-Crystal Cells a Near Text-Book

Example 158712 A Smaller Scale Concentrator Technology Built

on Multijunction Cells 162713 Low-Cost Tandem Technology Advanced Tandem Semiconducting

Polymer Cells 1637131 Band-Edge Energies in the Multilayer Tandem Semiconductor

Polymer Structure 1657132 Performance of the Advanced Polymer Tandem Cell 166714 Low-Cost Tandem Technology Amorphous SiliconH-Based

Solar Cells 16672 Organic Molecules as Solar Concentrators 16973 Spectral Splitting Cells 17174 Summary and Comments on Efficiency 17275 A Niche Application of Concentrating Cells on Pontoons 172

8 Third-Generation Concepts Survey of Efficiency 17581 Intermediate Band Cells 17582 Impact Ionization and Carrier Multiplication 177821 Electrons and Holes in a 3D lsquolsquoQuantum Dotrsquorsquo 18083 Ferromagnetic Materials for Solar Conversion 18284 Efficiencies Three Generations of Cells 185

9 Cells for Hydrogen Generation Aspects of Hydrogen Storage 18791 Intermittency of Renewable Energy 18792 Electrolysis of Water 18793 Efficient Photocatalytic Dissociation of Water into Hydrogen

and Oxygen 188931 Tandem Cell as Water Splitter 190932 Possibility of a Mass Production Tandem Cell

Water-Splitting Device 191933 Possibilities for Dual-Purpose Thin-Film Tandem Cell Devices 193

Contents IX

94 The lsquolsquoArtificial Leafrsquorsquo of Nocera 19395 Hydrogen Fuel Cell Status 19496 Storage and Transport of Hydrogen as a Potential Fuel 19597 Surface Adsorption for Storing Hydrogen in High Density 196971 Titanium-Decorated Carbon Nanotube Cloth 19998 Economics of Hydrogen 200981 Further Aspects of Storage and Transport of Hydrogen 200982 Hydrogen as Potential Intermediate in US Electricity

Distribution 201

10 Large-Scale Fabrication Learning Curves and EconomicsIncluding Storage 203

101 Fabrication Methods Vary but Exhibit Similar Learning Curves 203102 Learning Strategies for Module Cost 205103 Thin-Film Cells Nanoinks for Printing Solar Cells 207104 Large-Scale Scenario Based on Thin-Film CdTe or CIGS Cells 2091041 Solar Influx Cell Efficiency and Size of Solar Field Required

to Meet Demand 2101042 Economics of lsquolsquoPrinting Pressrsquorsquo CIGS or CdTe Cell Production

to Satisfy US Electric Demand 2111043 Projected Total Capital Need Conditions for Profitable

Private Investment 212105 Comparison of Solar Power versus Wind Power 214106 The Importance of Storage and Grid Management to

Large-Scale Utilization 2151061 Batteries from LeadndashAcid to Lithium to Sodium Sulfur 2171062 Basics of Lithium Batteries 2181063 NiMH 220

11 Prospects for Solar and Renewable Power 223111 Rapid Growth in Solar and Wind Power 223112 Renewable Energy Beyond Solar and Wind 225113 The Legacy World Developing Countries and the

Third World 226114 Can Energy Supply Meet Demand in the Longer Future 2271141 The lsquolsquoOil Bubblersquorsquo 2271142 The lsquolsquoEnergy Miraclersquorsquo 229

Appendix A Exercises 231Exercises to Chapter 1 231Exercises to Chapter 2 232Exercises to Chapter 3 233Exercises to Chapter 4 234Exercises to Chapter 5 236Exercises to Chapter 6 236

X Contents

Exercises to Chapter 7 237Exercises to Chapter 8 238Exercises to Chapter 9 238Exercises to Chapter 10 238Exercises to Chapter 11 239

Glossary of Abbreviations 241

References 245

Index 251

Contents XI

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

Edward L Wolf

Nanophysics of Solar andRenewable Energy

The Author

Prof Edward L WolfPolytechnic Institute of the New York UniversityBrooklyn USAemail ewolfpolyedu

Cover picturePictures clockwiseThe sunphotographed by NASAs SOHO spacecraft NASA 2004

The flexible solar module(Credit Copyright Fraunhofer ISE)

Pillared graphene consists of CNTs and graphenesheets combined to form a 3D network nanostructure SPIE 2009George Dimitrakakis Emmanuel Tylianakis andGeorge Froudakis Designing novel carbon nanos-tructures for hydrogen storage SPIE Newsroom doi101117212009021451

Solar panelsPart of the Solar Farm at PTLEN IndustriIndonesias largest solar cell producer and importerThis 900 square meter farm generates enough elec-tricity to power their solar factory and the employeescafetariaPhotograph by Chandra Marsono 2008

All books published by Wiley-VCH are carefullyproduced Nevertheless authors editors and pub-lisher do not warrant the information contained inthese books including this book to be free of errorsReaders are advised to keep in mind that statementsdata illustrations procedural details or other itemsmay inadvertently be inaccurate

Library of Congress Card No applied for

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from theBritish Library

Bibliographic information published bythe Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publica-tion in the Deutsche Nationalbibliografie detailedbibliographic data are available on the Internet athttpdnbd-nbde

2012 Wiley-VCH Verlag amp Co KGaABoschstr 12 69469 Weinheim Germany

All rights reserved (including those of translationinto other languages) No part of this book may bereproduced in any form ndash by photoprinting micro-film or any other means ndash nor transmitted or trans-lated into a machine language without writtenpermission from the publishers Registered namestrademarks etc used in this book even when notspecifically marked as such are not to be consideredunprotected by law

Composition Thomson Digital Noida India

Printing and Binding Markono Print Media Pte LtdSingapore

Cover Design Schulz Grafik-Design Fuszliggoumlnheim

Print ISBN 978-3-527-41052-1 (HC)978-3-527-41046-0 (SC)

ePDF ISBN 978-3-527-64631-9ePub ISBN 978-3-527-64630-2mobi ISBN 978-3-527-64629-6oBook ISBN 978-3-527-64628-9

Printed in SingaporePrinted on acid-free paper

In Memory of Ned

Edward OrsquoBrien Wolf

1973ndash2011

Contents

Preface XIII

1 A Survey of Long-Term Energy Resources 111 Introduction 1111 Direct Solar Influx 61111 Properties of the Sun 61112 An Introduction to Fusion Reactions on the Sun 101113 Distribution of Solar Influx for Conversion 13112 Secondary Solar-Driven Sources 141121 Flow Energy 141122 Hydroelectric Power 181123 Ocean Waves 20113 Earth-Based Long-Term Energy Resources 221131 Lunar Ocean Tidal Motion 221132 Geothermal Energy 241133 The Earths Deuterium and its Potential 25114 Plan of This Book 26

2 Physics of Nuclear Fusion the Source of allSolar-Related Energy 27

21 Introduction Protons in the Suns Core 2822 Schrodingers Equation for the Motion of Particles 30221 Time-Dependent Equation 32222 Time-Independent Equation 32223 Bound States Inside a One-Dimensional Potential

Well E gt 0 3323 Protons and Neutrons and Their Binding 3524 Gamows Tunneling Model Applied to Fusion

in the Suns Core 3525 A Survey of Nuclear Properties 43

VII

3 Atoms Molecules and Semiconductor Devices 4931 Bohrs Model of the Hydrogen Atom 4932 Charge Motion in Periodic Potential 5233 Energy Bands and Gaps 53331 Properties of a Metal Electrons in an Empty Box (I) 5734 Atoms Molecules and the Covalent Bond 60341 Properties of a Metal Electrons in an Empty Box (II) 66342 Hydrogen Molecule Ion H2

thorn 6935 Tetrahedral Bonding in Silicon and Related Semiconductors 71351 Connection with Directed or Covalent Bonds 72352 Bond Angle 7236 Donor and Acceptor Impurities Charge Concentrations 73361 Hydrogenic Donors and Excitons in Semiconductors Direct

and Indirect Bandgaps 75362 Carrier Concentrations in Semiconductors 76363 The Degenerate Metallic Semiconductor 7937 The PN Junction Diode IndashV Characteristic Photovoltaic Cell 8038 Metals and Plasmas 84

4 Terrestrial Approaches to Fusion Energy 8741 Deuterium Fusion Demonstration Based on Field Ionization 88411 Electric Field Ionization of Deuterium (Hydrogen) 9442 Deuterium Fusion Demonstration Based on Muonic Hydrogen 96421 Catalysis of DD Fusion by Mu Mesons 10143 Deuterium Fusion Demonstration in Larger Scale Plasma

Reactors 102431 Electrical Heating of the Plasma 103432 Scaling the Fusion Power Density from that in the Sun 104433 Adapt DD Plasma Analysis to DT Plasma as in ITER 104434 Summary a Correction and Further Comments 110

5 Introduction to Solar Energy Conversion 11551 Sun as an Energy Source Spectrum on Earth 11552 Heat Engines and Thermodynamics Carnot Efficiency 11753 Solar Thermal Electric Power 11954 Generations of Photovoltaic Solar Cells 12255 Utilizing Solar Power with Photovoltaics the Rooftops of

New York versus Space Satellites 12556 The Possibility of Space-Based Solar Power 126

6 Solar Cells Based on Single PN Junctions 13361 Single-Junction Cells 133611 Silicon Crystalline Cells 136612 GaAs Epitaxially Grown Solar Cells 141613 Single-Junction Limiting Conversion Efficiency 141

VIII Contents

62 Thin-Film Solar Cells versus Crystalline Cells 14563 CIGS (CuIn1xGaxSe2) Thin-Film Solar Cells 147631 Printing Cells onto Large-Area Flexible Substrates 14764 CdTe Thin-Film Cells 15165 Dye-Sensitized Solar Cells 153651 Principle of Dye Sensitization to Extend Spectral Range

to the Red 154652 Questions of Efficiency 15566 Polymer Organic Solar Cells 155661 A Basic Semiconducting Polymer Solar Cell 156

7 Multijunction and Energy Concentrating Solar Cells 15771 Tandem Cells Premium and Low Cost 158711 GaAs-based Tandem Single-Crystal Cells a Near Text-Book

Example 158712 A Smaller Scale Concentrator Technology Built

on Multijunction Cells 162713 Low-Cost Tandem Technology Advanced Tandem Semiconducting

Polymer Cells 1637131 Band-Edge Energies in the Multilayer Tandem Semiconductor

Polymer Structure 1657132 Performance of the Advanced Polymer Tandem Cell 166714 Low-Cost Tandem Technology Amorphous SiliconH-Based

Solar Cells 16672 Organic Molecules as Solar Concentrators 16973 Spectral Splitting Cells 17174 Summary and Comments on Efficiency 17275 A Niche Application of Concentrating Cells on Pontoons 172

8 Third-Generation Concepts Survey of Efficiency 17581 Intermediate Band Cells 17582 Impact Ionization and Carrier Multiplication 177821 Electrons and Holes in a 3D lsquolsquoQuantum Dotrsquorsquo 18083 Ferromagnetic Materials for Solar Conversion 18284 Efficiencies Three Generations of Cells 185

9 Cells for Hydrogen Generation Aspects of Hydrogen Storage 18791 Intermittency of Renewable Energy 18792 Electrolysis of Water 18793 Efficient Photocatalytic Dissociation of Water into Hydrogen

and Oxygen 188931 Tandem Cell as Water Splitter 190932 Possibility of a Mass Production Tandem Cell

Water-Splitting Device 191933 Possibilities for Dual-Purpose Thin-Film Tandem Cell Devices 193

Contents IX

94 The lsquolsquoArtificial Leafrsquorsquo of Nocera 19395 Hydrogen Fuel Cell Status 19496 Storage and Transport of Hydrogen as a Potential Fuel 19597 Surface Adsorption for Storing Hydrogen in High Density 196971 Titanium-Decorated Carbon Nanotube Cloth 19998 Economics of Hydrogen 200981 Further Aspects of Storage and Transport of Hydrogen 200982 Hydrogen as Potential Intermediate in US Electricity

Distribution 201

10 Large-Scale Fabrication Learning Curves and EconomicsIncluding Storage 203

101 Fabrication Methods Vary but Exhibit Similar Learning Curves 203102 Learning Strategies for Module Cost 205103 Thin-Film Cells Nanoinks for Printing Solar Cells 207104 Large-Scale Scenario Based on Thin-Film CdTe or CIGS Cells 2091041 Solar Influx Cell Efficiency and Size of Solar Field Required

to Meet Demand 2101042 Economics of lsquolsquoPrinting Pressrsquorsquo CIGS or CdTe Cell Production

to Satisfy US Electric Demand 2111043 Projected Total Capital Need Conditions for Profitable

Private Investment 212105 Comparison of Solar Power versus Wind Power 214106 The Importance of Storage and Grid Management to

Large-Scale Utilization 2151061 Batteries from LeadndashAcid to Lithium to Sodium Sulfur 2171062 Basics of Lithium Batteries 2181063 NiMH 220

11 Prospects for Solar and Renewable Power 223111 Rapid Growth in Solar and Wind Power 223112 Renewable Energy Beyond Solar and Wind 225113 The Legacy World Developing Countries and the

Third World 226114 Can Energy Supply Meet Demand in the Longer Future 2271141 The lsquolsquoOil Bubblersquorsquo 2271142 The lsquolsquoEnergy Miraclersquorsquo 229

Appendix A Exercises 231Exercises to Chapter 1 231Exercises to Chapter 2 232Exercises to Chapter 3 233Exercises to Chapter 4 234Exercises to Chapter 5 236Exercises to Chapter 6 236

X Contents

Exercises to Chapter 7 237Exercises to Chapter 8 238Exercises to Chapter 9 238Exercises to Chapter 10 238Exercises to Chapter 11 239

Glossary of Abbreviations 241

References 245

Index 251

Contents XI

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

The Author

Prof Edward L WolfPolytechnic Institute of the New York UniversityBrooklyn USAemail ewolfpolyedu

Cover picturePictures clockwiseThe sunphotographed by NASAs SOHO spacecraft NASA 2004

The flexible solar module(Credit Copyright Fraunhofer ISE)

Pillared graphene consists of CNTs and graphenesheets combined to form a 3D network nanostructure SPIE 2009George Dimitrakakis Emmanuel Tylianakis andGeorge Froudakis Designing novel carbon nanos-tructures for hydrogen storage SPIE Newsroom doi101117212009021451

Solar panelsPart of the Solar Farm at PTLEN IndustriIndonesias largest solar cell producer and importerThis 900 square meter farm generates enough elec-tricity to power their solar factory and the employeescafetariaPhotograph by Chandra Marsono 2008

All books published by Wiley-VCH are carefullyproduced Nevertheless authors editors and pub-lisher do not warrant the information contained inthese books including this book to be free of errorsReaders are advised to keep in mind that statementsdata illustrations procedural details or other itemsmay inadvertently be inaccurate

Library of Congress Card No applied for

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from theBritish Library

Bibliographic information published bythe Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publica-tion in the Deutsche Nationalbibliografie detailedbibliographic data are available on the Internet athttpdnbd-nbde

2012 Wiley-VCH Verlag amp Co KGaABoschstr 12 69469 Weinheim Germany

All rights reserved (including those of translationinto other languages) No part of this book may bereproduced in any form ndash by photoprinting micro-film or any other means ndash nor transmitted or trans-lated into a machine language without writtenpermission from the publishers Registered namestrademarks etc used in this book even when notspecifically marked as such are not to be consideredunprotected by law

Composition Thomson Digital Noida India

Printing and Binding Markono Print Media Pte LtdSingapore

Cover Design Schulz Grafik-Design Fuszliggoumlnheim

Print ISBN 978-3-527-41052-1 (HC)978-3-527-41046-0 (SC)

ePDF ISBN 978-3-527-64631-9ePub ISBN 978-3-527-64630-2mobi ISBN 978-3-527-64629-6oBook ISBN 978-3-527-64628-9

Printed in SingaporePrinted on acid-free paper

In Memory of Ned

Edward OrsquoBrien Wolf

1973ndash2011

Contents

Preface XIII

1 A Survey of Long-Term Energy Resources 111 Introduction 1111 Direct Solar Influx 61111 Properties of the Sun 61112 An Introduction to Fusion Reactions on the Sun 101113 Distribution of Solar Influx for Conversion 13112 Secondary Solar-Driven Sources 141121 Flow Energy 141122 Hydroelectric Power 181123 Ocean Waves 20113 Earth-Based Long-Term Energy Resources 221131 Lunar Ocean Tidal Motion 221132 Geothermal Energy 241133 The Earths Deuterium and its Potential 25114 Plan of This Book 26

2 Physics of Nuclear Fusion the Source of allSolar-Related Energy 27

21 Introduction Protons in the Suns Core 2822 Schrodingers Equation for the Motion of Particles 30221 Time-Dependent Equation 32222 Time-Independent Equation 32223 Bound States Inside a One-Dimensional Potential

Well E gt 0 3323 Protons and Neutrons and Their Binding 3524 Gamows Tunneling Model Applied to Fusion

in the Suns Core 3525 A Survey of Nuclear Properties 43

VII

3 Atoms Molecules and Semiconductor Devices 4931 Bohrs Model of the Hydrogen Atom 4932 Charge Motion in Periodic Potential 5233 Energy Bands and Gaps 53331 Properties of a Metal Electrons in an Empty Box (I) 5734 Atoms Molecules and the Covalent Bond 60341 Properties of a Metal Electrons in an Empty Box (II) 66342 Hydrogen Molecule Ion H2

thorn 6935 Tetrahedral Bonding in Silicon and Related Semiconductors 71351 Connection with Directed or Covalent Bonds 72352 Bond Angle 7236 Donor and Acceptor Impurities Charge Concentrations 73361 Hydrogenic Donors and Excitons in Semiconductors Direct

and Indirect Bandgaps 75362 Carrier Concentrations in Semiconductors 76363 The Degenerate Metallic Semiconductor 7937 The PN Junction Diode IndashV Characteristic Photovoltaic Cell 8038 Metals and Plasmas 84

4 Terrestrial Approaches to Fusion Energy 8741 Deuterium Fusion Demonstration Based on Field Ionization 88411 Electric Field Ionization of Deuterium (Hydrogen) 9442 Deuterium Fusion Demonstration Based on Muonic Hydrogen 96421 Catalysis of DD Fusion by Mu Mesons 10143 Deuterium Fusion Demonstration in Larger Scale Plasma

Reactors 102431 Electrical Heating of the Plasma 103432 Scaling the Fusion Power Density from that in the Sun 104433 Adapt DD Plasma Analysis to DT Plasma as in ITER 104434 Summary a Correction and Further Comments 110

5 Introduction to Solar Energy Conversion 11551 Sun as an Energy Source Spectrum on Earth 11552 Heat Engines and Thermodynamics Carnot Efficiency 11753 Solar Thermal Electric Power 11954 Generations of Photovoltaic Solar Cells 12255 Utilizing Solar Power with Photovoltaics the Rooftops of

New York versus Space Satellites 12556 The Possibility of Space-Based Solar Power 126

6 Solar Cells Based on Single PN Junctions 13361 Single-Junction Cells 133611 Silicon Crystalline Cells 136612 GaAs Epitaxially Grown Solar Cells 141613 Single-Junction Limiting Conversion Efficiency 141

VIII Contents

62 Thin-Film Solar Cells versus Crystalline Cells 14563 CIGS (CuIn1xGaxSe2) Thin-Film Solar Cells 147631 Printing Cells onto Large-Area Flexible Substrates 14764 CdTe Thin-Film Cells 15165 Dye-Sensitized Solar Cells 153651 Principle of Dye Sensitization to Extend Spectral Range

to the Red 154652 Questions of Efficiency 15566 Polymer Organic Solar Cells 155661 A Basic Semiconducting Polymer Solar Cell 156

7 Multijunction and Energy Concentrating Solar Cells 15771 Tandem Cells Premium and Low Cost 158711 GaAs-based Tandem Single-Crystal Cells a Near Text-Book

Example 158712 A Smaller Scale Concentrator Technology Built

on Multijunction Cells 162713 Low-Cost Tandem Technology Advanced Tandem Semiconducting

Polymer Cells 1637131 Band-Edge Energies in the Multilayer Tandem Semiconductor

Polymer Structure 1657132 Performance of the Advanced Polymer Tandem Cell 166714 Low-Cost Tandem Technology Amorphous SiliconH-Based

Solar Cells 16672 Organic Molecules as Solar Concentrators 16973 Spectral Splitting Cells 17174 Summary and Comments on Efficiency 17275 A Niche Application of Concentrating Cells on Pontoons 172

8 Third-Generation Concepts Survey of Efficiency 17581 Intermediate Band Cells 17582 Impact Ionization and Carrier Multiplication 177821 Electrons and Holes in a 3D lsquolsquoQuantum Dotrsquorsquo 18083 Ferromagnetic Materials for Solar Conversion 18284 Efficiencies Three Generations of Cells 185

9 Cells for Hydrogen Generation Aspects of Hydrogen Storage 18791 Intermittency of Renewable Energy 18792 Electrolysis of Water 18793 Efficient Photocatalytic Dissociation of Water into Hydrogen

and Oxygen 188931 Tandem Cell as Water Splitter 190932 Possibility of a Mass Production Tandem Cell

Water-Splitting Device 191933 Possibilities for Dual-Purpose Thin-Film Tandem Cell Devices 193

Contents IX

94 The lsquolsquoArtificial Leafrsquorsquo of Nocera 19395 Hydrogen Fuel Cell Status 19496 Storage and Transport of Hydrogen as a Potential Fuel 19597 Surface Adsorption for Storing Hydrogen in High Density 196971 Titanium-Decorated Carbon Nanotube Cloth 19998 Economics of Hydrogen 200981 Further Aspects of Storage and Transport of Hydrogen 200982 Hydrogen as Potential Intermediate in US Electricity

Distribution 201

10 Large-Scale Fabrication Learning Curves and EconomicsIncluding Storage 203

101 Fabrication Methods Vary but Exhibit Similar Learning Curves 203102 Learning Strategies for Module Cost 205103 Thin-Film Cells Nanoinks for Printing Solar Cells 207104 Large-Scale Scenario Based on Thin-Film CdTe or CIGS Cells 2091041 Solar Influx Cell Efficiency and Size of Solar Field Required

to Meet Demand 2101042 Economics of lsquolsquoPrinting Pressrsquorsquo CIGS or CdTe Cell Production

to Satisfy US Electric Demand 2111043 Projected Total Capital Need Conditions for Profitable

Private Investment 212105 Comparison of Solar Power versus Wind Power 214106 The Importance of Storage and Grid Management to

Large-Scale Utilization 2151061 Batteries from LeadndashAcid to Lithium to Sodium Sulfur 2171062 Basics of Lithium Batteries 2181063 NiMH 220

11 Prospects for Solar and Renewable Power 223111 Rapid Growth in Solar and Wind Power 223112 Renewable Energy Beyond Solar and Wind 225113 The Legacy World Developing Countries and the

Third World 226114 Can Energy Supply Meet Demand in the Longer Future 2271141 The lsquolsquoOil Bubblersquorsquo 2271142 The lsquolsquoEnergy Miraclersquorsquo 229

Appendix A Exercises 231Exercises to Chapter 1 231Exercises to Chapter 2 232Exercises to Chapter 3 233Exercises to Chapter 4 234Exercises to Chapter 5 236Exercises to Chapter 6 236

X Contents

Exercises to Chapter 7 237Exercises to Chapter 8 238Exercises to Chapter 9 238Exercises to Chapter 10 238Exercises to Chapter 11 239

Glossary of Abbreviations 241

References 245

Index 251

Contents XI

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

In Memory of Ned

Edward OrsquoBrien Wolf

1973ndash2011

Contents

Preface XIII

1 A Survey of Long-Term Energy Resources 111 Introduction 1111 Direct Solar Influx 61111 Properties of the Sun 61112 An Introduction to Fusion Reactions on the Sun 101113 Distribution of Solar Influx for Conversion 13112 Secondary Solar-Driven Sources 141121 Flow Energy 141122 Hydroelectric Power 181123 Ocean Waves 20113 Earth-Based Long-Term Energy Resources 221131 Lunar Ocean Tidal Motion 221132 Geothermal Energy 241133 The Earths Deuterium and its Potential 25114 Plan of This Book 26

2 Physics of Nuclear Fusion the Source of allSolar-Related Energy 27

21 Introduction Protons in the Suns Core 2822 Schrodingers Equation for the Motion of Particles 30221 Time-Dependent Equation 32222 Time-Independent Equation 32223 Bound States Inside a One-Dimensional Potential

Well E gt 0 3323 Protons and Neutrons and Their Binding 3524 Gamows Tunneling Model Applied to Fusion

in the Suns Core 3525 A Survey of Nuclear Properties 43

VII

3 Atoms Molecules and Semiconductor Devices 4931 Bohrs Model of the Hydrogen Atom 4932 Charge Motion in Periodic Potential 5233 Energy Bands and Gaps 53331 Properties of a Metal Electrons in an Empty Box (I) 5734 Atoms Molecules and the Covalent Bond 60341 Properties of a Metal Electrons in an Empty Box (II) 66342 Hydrogen Molecule Ion H2

thorn 6935 Tetrahedral Bonding in Silicon and Related Semiconductors 71351 Connection with Directed or Covalent Bonds 72352 Bond Angle 7236 Donor and Acceptor Impurities Charge Concentrations 73361 Hydrogenic Donors and Excitons in Semiconductors Direct

and Indirect Bandgaps 75362 Carrier Concentrations in Semiconductors 76363 The Degenerate Metallic Semiconductor 7937 The PN Junction Diode IndashV Characteristic Photovoltaic Cell 8038 Metals and Plasmas 84

4 Terrestrial Approaches to Fusion Energy 8741 Deuterium Fusion Demonstration Based on Field Ionization 88411 Electric Field Ionization of Deuterium (Hydrogen) 9442 Deuterium Fusion Demonstration Based on Muonic Hydrogen 96421 Catalysis of DD Fusion by Mu Mesons 10143 Deuterium Fusion Demonstration in Larger Scale Plasma

Reactors 102431 Electrical Heating of the Plasma 103432 Scaling the Fusion Power Density from that in the Sun 104433 Adapt DD Plasma Analysis to DT Plasma as in ITER 104434 Summary a Correction and Further Comments 110

5 Introduction to Solar Energy Conversion 11551 Sun as an Energy Source Spectrum on Earth 11552 Heat Engines and Thermodynamics Carnot Efficiency 11753 Solar Thermal Electric Power 11954 Generations of Photovoltaic Solar Cells 12255 Utilizing Solar Power with Photovoltaics the Rooftops of

New York versus Space Satellites 12556 The Possibility of Space-Based Solar Power 126

6 Solar Cells Based on Single PN Junctions 13361 Single-Junction Cells 133611 Silicon Crystalline Cells 136612 GaAs Epitaxially Grown Solar Cells 141613 Single-Junction Limiting Conversion Efficiency 141

VIII Contents

62 Thin-Film Solar Cells versus Crystalline Cells 14563 CIGS (CuIn1xGaxSe2) Thin-Film Solar Cells 147631 Printing Cells onto Large-Area Flexible Substrates 14764 CdTe Thin-Film Cells 15165 Dye-Sensitized Solar Cells 153651 Principle of Dye Sensitization to Extend Spectral Range

to the Red 154652 Questions of Efficiency 15566 Polymer Organic Solar Cells 155661 A Basic Semiconducting Polymer Solar Cell 156

7 Multijunction and Energy Concentrating Solar Cells 15771 Tandem Cells Premium and Low Cost 158711 GaAs-based Tandem Single-Crystal Cells a Near Text-Book

Example 158712 A Smaller Scale Concentrator Technology Built

on Multijunction Cells 162713 Low-Cost Tandem Technology Advanced Tandem Semiconducting

Polymer Cells 1637131 Band-Edge Energies in the Multilayer Tandem Semiconductor

Polymer Structure 1657132 Performance of the Advanced Polymer Tandem Cell 166714 Low-Cost Tandem Technology Amorphous SiliconH-Based

Solar Cells 16672 Organic Molecules as Solar Concentrators 16973 Spectral Splitting Cells 17174 Summary and Comments on Efficiency 17275 A Niche Application of Concentrating Cells on Pontoons 172

8 Third-Generation Concepts Survey of Efficiency 17581 Intermediate Band Cells 17582 Impact Ionization and Carrier Multiplication 177821 Electrons and Holes in a 3D lsquolsquoQuantum Dotrsquorsquo 18083 Ferromagnetic Materials for Solar Conversion 18284 Efficiencies Three Generations of Cells 185

9 Cells for Hydrogen Generation Aspects of Hydrogen Storage 18791 Intermittency of Renewable Energy 18792 Electrolysis of Water 18793 Efficient Photocatalytic Dissociation of Water into Hydrogen

and Oxygen 188931 Tandem Cell as Water Splitter 190932 Possibility of a Mass Production Tandem Cell

Water-Splitting Device 191933 Possibilities for Dual-Purpose Thin-Film Tandem Cell Devices 193

Contents IX

94 The lsquolsquoArtificial Leafrsquorsquo of Nocera 19395 Hydrogen Fuel Cell Status 19496 Storage and Transport of Hydrogen as a Potential Fuel 19597 Surface Adsorption for Storing Hydrogen in High Density 196971 Titanium-Decorated Carbon Nanotube Cloth 19998 Economics of Hydrogen 200981 Further Aspects of Storage and Transport of Hydrogen 200982 Hydrogen as Potential Intermediate in US Electricity

Distribution 201

10 Large-Scale Fabrication Learning Curves and EconomicsIncluding Storage 203

101 Fabrication Methods Vary but Exhibit Similar Learning Curves 203102 Learning Strategies for Module Cost 205103 Thin-Film Cells Nanoinks for Printing Solar Cells 207104 Large-Scale Scenario Based on Thin-Film CdTe or CIGS Cells 2091041 Solar Influx Cell Efficiency and Size of Solar Field Required

to Meet Demand 2101042 Economics of lsquolsquoPrinting Pressrsquorsquo CIGS or CdTe Cell Production

to Satisfy US Electric Demand 2111043 Projected Total Capital Need Conditions for Profitable

Private Investment 212105 Comparison of Solar Power versus Wind Power 214106 The Importance of Storage and Grid Management to

Large-Scale Utilization 2151061 Batteries from LeadndashAcid to Lithium to Sodium Sulfur 2171062 Basics of Lithium Batteries 2181063 NiMH 220

11 Prospects for Solar and Renewable Power 223111 Rapid Growth in Solar and Wind Power 223112 Renewable Energy Beyond Solar and Wind 225113 The Legacy World Developing Countries and the

Third World 226114 Can Energy Supply Meet Demand in the Longer Future 2271141 The lsquolsquoOil Bubblersquorsquo 2271142 The lsquolsquoEnergy Miraclersquorsquo 229

Appendix A Exercises 231Exercises to Chapter 1 231Exercises to Chapter 2 232Exercises to Chapter 3 233Exercises to Chapter 4 234Exercises to Chapter 5 236Exercises to Chapter 6 236

X Contents

Exercises to Chapter 7 237Exercises to Chapter 8 238Exercises to Chapter 9 238Exercises to Chapter 10 238Exercises to Chapter 11 239

Glossary of Abbreviations 241

References 245

Index 251

Contents XI

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

Contents

Preface XIII

1 A Survey of Long-Term Energy Resources 111 Introduction 1111 Direct Solar Influx 61111 Properties of the Sun 61112 An Introduction to Fusion Reactions on the Sun 101113 Distribution of Solar Influx for Conversion 13112 Secondary Solar-Driven Sources 141121 Flow Energy 141122 Hydroelectric Power 181123 Ocean Waves 20113 Earth-Based Long-Term Energy Resources 221131 Lunar Ocean Tidal Motion 221132 Geothermal Energy 241133 The Earths Deuterium and its Potential 25114 Plan of This Book 26

2 Physics of Nuclear Fusion the Source of allSolar-Related Energy 27

21 Introduction Protons in the Suns Core 2822 Schrodingers Equation for the Motion of Particles 30221 Time-Dependent Equation 32222 Time-Independent Equation 32223 Bound States Inside a One-Dimensional Potential

Well E gt 0 3323 Protons and Neutrons and Their Binding 3524 Gamows Tunneling Model Applied to Fusion

in the Suns Core 3525 A Survey of Nuclear Properties 43

VII

3 Atoms Molecules and Semiconductor Devices 4931 Bohrs Model of the Hydrogen Atom 4932 Charge Motion in Periodic Potential 5233 Energy Bands and Gaps 53331 Properties of a Metal Electrons in an Empty Box (I) 5734 Atoms Molecules and the Covalent Bond 60341 Properties of a Metal Electrons in an Empty Box (II) 66342 Hydrogen Molecule Ion H2

thorn 6935 Tetrahedral Bonding in Silicon and Related Semiconductors 71351 Connection with Directed or Covalent Bonds 72352 Bond Angle 7236 Donor and Acceptor Impurities Charge Concentrations 73361 Hydrogenic Donors and Excitons in Semiconductors Direct

and Indirect Bandgaps 75362 Carrier Concentrations in Semiconductors 76363 The Degenerate Metallic Semiconductor 7937 The PN Junction Diode IndashV Characteristic Photovoltaic Cell 8038 Metals and Plasmas 84

4 Terrestrial Approaches to Fusion Energy 8741 Deuterium Fusion Demonstration Based on Field Ionization 88411 Electric Field Ionization of Deuterium (Hydrogen) 9442 Deuterium Fusion Demonstration Based on Muonic Hydrogen 96421 Catalysis of DD Fusion by Mu Mesons 10143 Deuterium Fusion Demonstration in Larger Scale Plasma

Reactors 102431 Electrical Heating of the Plasma 103432 Scaling the Fusion Power Density from that in the Sun 104433 Adapt DD Plasma Analysis to DT Plasma as in ITER 104434 Summary a Correction and Further Comments 110

5 Introduction to Solar Energy Conversion 11551 Sun as an Energy Source Spectrum on Earth 11552 Heat Engines and Thermodynamics Carnot Efficiency 11753 Solar Thermal Electric Power 11954 Generations of Photovoltaic Solar Cells 12255 Utilizing Solar Power with Photovoltaics the Rooftops of

New York versus Space Satellites 12556 The Possibility of Space-Based Solar Power 126

6 Solar Cells Based on Single PN Junctions 13361 Single-Junction Cells 133611 Silicon Crystalline Cells 136612 GaAs Epitaxially Grown Solar Cells 141613 Single-Junction Limiting Conversion Efficiency 141

VIII Contents

62 Thin-Film Solar Cells versus Crystalline Cells 14563 CIGS (CuIn1xGaxSe2) Thin-Film Solar Cells 147631 Printing Cells onto Large-Area Flexible Substrates 14764 CdTe Thin-Film Cells 15165 Dye-Sensitized Solar Cells 153651 Principle of Dye Sensitization to Extend Spectral Range

to the Red 154652 Questions of Efficiency 15566 Polymer Organic Solar Cells 155661 A Basic Semiconducting Polymer Solar Cell 156

7 Multijunction and Energy Concentrating Solar Cells 15771 Tandem Cells Premium and Low Cost 158711 GaAs-based Tandem Single-Crystal Cells a Near Text-Book

Example 158712 A Smaller Scale Concentrator Technology Built

on Multijunction Cells 162713 Low-Cost Tandem Technology Advanced Tandem Semiconducting

Polymer Cells 1637131 Band-Edge Energies in the Multilayer Tandem Semiconductor

Polymer Structure 1657132 Performance of the Advanced Polymer Tandem Cell 166714 Low-Cost Tandem Technology Amorphous SiliconH-Based

Solar Cells 16672 Organic Molecules as Solar Concentrators 16973 Spectral Splitting Cells 17174 Summary and Comments on Efficiency 17275 A Niche Application of Concentrating Cells on Pontoons 172

8 Third-Generation Concepts Survey of Efficiency 17581 Intermediate Band Cells 17582 Impact Ionization and Carrier Multiplication 177821 Electrons and Holes in a 3D lsquolsquoQuantum Dotrsquorsquo 18083 Ferromagnetic Materials for Solar Conversion 18284 Efficiencies Three Generations of Cells 185

9 Cells for Hydrogen Generation Aspects of Hydrogen Storage 18791 Intermittency of Renewable Energy 18792 Electrolysis of Water 18793 Efficient Photocatalytic Dissociation of Water into Hydrogen

and Oxygen 188931 Tandem Cell as Water Splitter 190932 Possibility of a Mass Production Tandem Cell

Water-Splitting Device 191933 Possibilities for Dual-Purpose Thin-Film Tandem Cell Devices 193

Contents IX

94 The lsquolsquoArtificial Leafrsquorsquo of Nocera 19395 Hydrogen Fuel Cell Status 19496 Storage and Transport of Hydrogen as a Potential Fuel 19597 Surface Adsorption for Storing Hydrogen in High Density 196971 Titanium-Decorated Carbon Nanotube Cloth 19998 Economics of Hydrogen 200981 Further Aspects of Storage and Transport of Hydrogen 200982 Hydrogen as Potential Intermediate in US Electricity

Distribution 201

10 Large-Scale Fabrication Learning Curves and EconomicsIncluding Storage 203

101 Fabrication Methods Vary but Exhibit Similar Learning Curves 203102 Learning Strategies for Module Cost 205103 Thin-Film Cells Nanoinks for Printing Solar Cells 207104 Large-Scale Scenario Based on Thin-Film CdTe or CIGS Cells 2091041 Solar Influx Cell Efficiency and Size of Solar Field Required

to Meet Demand 2101042 Economics of lsquolsquoPrinting Pressrsquorsquo CIGS or CdTe Cell Production

to Satisfy US Electric Demand 2111043 Projected Total Capital Need Conditions for Profitable

Private Investment 212105 Comparison of Solar Power versus Wind Power 214106 The Importance of Storage and Grid Management to

Large-Scale Utilization 2151061 Batteries from LeadndashAcid to Lithium to Sodium Sulfur 2171062 Basics of Lithium Batteries 2181063 NiMH 220

11 Prospects for Solar and Renewable Power 223111 Rapid Growth in Solar and Wind Power 223112 Renewable Energy Beyond Solar and Wind 225113 The Legacy World Developing Countries and the

Third World 226114 Can Energy Supply Meet Demand in the Longer Future 2271141 The lsquolsquoOil Bubblersquorsquo 2271142 The lsquolsquoEnergy Miraclersquorsquo 229

Appendix A Exercises 231Exercises to Chapter 1 231Exercises to Chapter 2 232Exercises to Chapter 3 233Exercises to Chapter 4 234Exercises to Chapter 5 236Exercises to Chapter 6 236

X Contents

Exercises to Chapter 7 237Exercises to Chapter 8 238Exercises to Chapter 9 238Exercises to Chapter 10 238Exercises to Chapter 11 239

Glossary of Abbreviations 241

References 245

Index 251

Contents XI

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

3 Atoms Molecules and Semiconductor Devices 4931 Bohrs Model of the Hydrogen Atom 4932 Charge Motion in Periodic Potential 5233 Energy Bands and Gaps 53331 Properties of a Metal Electrons in an Empty Box (I) 5734 Atoms Molecules and the Covalent Bond 60341 Properties of a Metal Electrons in an Empty Box (II) 66342 Hydrogen Molecule Ion H2

thorn 6935 Tetrahedral Bonding in Silicon and Related Semiconductors 71351 Connection with Directed or Covalent Bonds 72352 Bond Angle 7236 Donor and Acceptor Impurities Charge Concentrations 73361 Hydrogenic Donors and Excitons in Semiconductors Direct

and Indirect Bandgaps 75362 Carrier Concentrations in Semiconductors 76363 The Degenerate Metallic Semiconductor 7937 The PN Junction Diode IndashV Characteristic Photovoltaic Cell 8038 Metals and Plasmas 84

4 Terrestrial Approaches to Fusion Energy 8741 Deuterium Fusion Demonstration Based on Field Ionization 88411 Electric Field Ionization of Deuterium (Hydrogen) 9442 Deuterium Fusion Demonstration Based on Muonic Hydrogen 96421 Catalysis of DD Fusion by Mu Mesons 10143 Deuterium Fusion Demonstration in Larger Scale Plasma

Reactors 102431 Electrical Heating of the Plasma 103432 Scaling the Fusion Power Density from that in the Sun 104433 Adapt DD Plasma Analysis to DT Plasma as in ITER 104434 Summary a Correction and Further Comments 110

5 Introduction to Solar Energy Conversion 11551 Sun as an Energy Source Spectrum on Earth 11552 Heat Engines and Thermodynamics Carnot Efficiency 11753 Solar Thermal Electric Power 11954 Generations of Photovoltaic Solar Cells 12255 Utilizing Solar Power with Photovoltaics the Rooftops of

New York versus Space Satellites 12556 The Possibility of Space-Based Solar Power 126

6 Solar Cells Based on Single PN Junctions 13361 Single-Junction Cells 133611 Silicon Crystalline Cells 136612 GaAs Epitaxially Grown Solar Cells 141613 Single-Junction Limiting Conversion Efficiency 141

VIII Contents

62 Thin-Film Solar Cells versus Crystalline Cells 14563 CIGS (CuIn1xGaxSe2) Thin-Film Solar Cells 147631 Printing Cells onto Large-Area Flexible Substrates 14764 CdTe Thin-Film Cells 15165 Dye-Sensitized Solar Cells 153651 Principle of Dye Sensitization to Extend Spectral Range

to the Red 154652 Questions of Efficiency 15566 Polymer Organic Solar Cells 155661 A Basic Semiconducting Polymer Solar Cell 156

7 Multijunction and Energy Concentrating Solar Cells 15771 Tandem Cells Premium and Low Cost 158711 GaAs-based Tandem Single-Crystal Cells a Near Text-Book

Example 158712 A Smaller Scale Concentrator Technology Built

on Multijunction Cells 162713 Low-Cost Tandem Technology Advanced Tandem Semiconducting

Polymer Cells 1637131 Band-Edge Energies in the Multilayer Tandem Semiconductor

Polymer Structure 1657132 Performance of the Advanced Polymer Tandem Cell 166714 Low-Cost Tandem Technology Amorphous SiliconH-Based

Solar Cells 16672 Organic Molecules as Solar Concentrators 16973 Spectral Splitting Cells 17174 Summary and Comments on Efficiency 17275 A Niche Application of Concentrating Cells on Pontoons 172

8 Third-Generation Concepts Survey of Efficiency 17581 Intermediate Band Cells 17582 Impact Ionization and Carrier Multiplication 177821 Electrons and Holes in a 3D lsquolsquoQuantum Dotrsquorsquo 18083 Ferromagnetic Materials for Solar Conversion 18284 Efficiencies Three Generations of Cells 185

9 Cells for Hydrogen Generation Aspects of Hydrogen Storage 18791 Intermittency of Renewable Energy 18792 Electrolysis of Water 18793 Efficient Photocatalytic Dissociation of Water into Hydrogen

and Oxygen 188931 Tandem Cell as Water Splitter 190932 Possibility of a Mass Production Tandem Cell

Water-Splitting Device 191933 Possibilities for Dual-Purpose Thin-Film Tandem Cell Devices 193

Contents IX

94 The lsquolsquoArtificial Leafrsquorsquo of Nocera 19395 Hydrogen Fuel Cell Status 19496 Storage and Transport of Hydrogen as a Potential Fuel 19597 Surface Adsorption for Storing Hydrogen in High Density 196971 Titanium-Decorated Carbon Nanotube Cloth 19998 Economics of Hydrogen 200981 Further Aspects of Storage and Transport of Hydrogen 200982 Hydrogen as Potential Intermediate in US Electricity

Distribution 201

10 Large-Scale Fabrication Learning Curves and EconomicsIncluding Storage 203

101 Fabrication Methods Vary but Exhibit Similar Learning Curves 203102 Learning Strategies for Module Cost 205103 Thin-Film Cells Nanoinks for Printing Solar Cells 207104 Large-Scale Scenario Based on Thin-Film CdTe or CIGS Cells 2091041 Solar Influx Cell Efficiency and Size of Solar Field Required

to Meet Demand 2101042 Economics of lsquolsquoPrinting Pressrsquorsquo CIGS or CdTe Cell Production

to Satisfy US Electric Demand 2111043 Projected Total Capital Need Conditions for Profitable

Private Investment 212105 Comparison of Solar Power versus Wind Power 214106 The Importance of Storage and Grid Management to

Large-Scale Utilization 2151061 Batteries from LeadndashAcid to Lithium to Sodium Sulfur 2171062 Basics of Lithium Batteries 2181063 NiMH 220

11 Prospects for Solar and Renewable Power 223111 Rapid Growth in Solar and Wind Power 223112 Renewable Energy Beyond Solar and Wind 225113 The Legacy World Developing Countries and the

Third World 226114 Can Energy Supply Meet Demand in the Longer Future 2271141 The lsquolsquoOil Bubblersquorsquo 2271142 The lsquolsquoEnergy Miraclersquorsquo 229

Appendix A Exercises 231Exercises to Chapter 1 231Exercises to Chapter 2 232Exercises to Chapter 3 233Exercises to Chapter 4 234Exercises to Chapter 5 236Exercises to Chapter 6 236

X Contents

Exercises to Chapter 7 237Exercises to Chapter 8 238Exercises to Chapter 9 238Exercises to Chapter 10 238Exercises to Chapter 11 239

Glossary of Abbreviations 241

References 245

Index 251

Contents XI

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

62 Thin-Film Solar Cells versus Crystalline Cells 14563 CIGS (CuIn1xGaxSe2) Thin-Film Solar Cells 147631 Printing Cells onto Large-Area Flexible Substrates 14764 CdTe Thin-Film Cells 15165 Dye-Sensitized Solar Cells 153651 Principle of Dye Sensitization to Extend Spectral Range

to the Red 154652 Questions of Efficiency 15566 Polymer Organic Solar Cells 155661 A Basic Semiconducting Polymer Solar Cell 156

7 Multijunction and Energy Concentrating Solar Cells 15771 Tandem Cells Premium and Low Cost 158711 GaAs-based Tandem Single-Crystal Cells a Near Text-Book

Example 158712 A Smaller Scale Concentrator Technology Built

on Multijunction Cells 162713 Low-Cost Tandem Technology Advanced Tandem Semiconducting

Polymer Cells 1637131 Band-Edge Energies in the Multilayer Tandem Semiconductor

Polymer Structure 1657132 Performance of the Advanced Polymer Tandem Cell 166714 Low-Cost Tandem Technology Amorphous SiliconH-Based

Solar Cells 16672 Organic Molecules as Solar Concentrators 16973 Spectral Splitting Cells 17174 Summary and Comments on Efficiency 17275 A Niche Application of Concentrating Cells on Pontoons 172

8 Third-Generation Concepts Survey of Efficiency 17581 Intermediate Band Cells 17582 Impact Ionization and Carrier Multiplication 177821 Electrons and Holes in a 3D lsquolsquoQuantum Dotrsquorsquo 18083 Ferromagnetic Materials for Solar Conversion 18284 Efficiencies Three Generations of Cells 185

9 Cells for Hydrogen Generation Aspects of Hydrogen Storage 18791 Intermittency of Renewable Energy 18792 Electrolysis of Water 18793 Efficient Photocatalytic Dissociation of Water into Hydrogen

and Oxygen 188931 Tandem Cell as Water Splitter 190932 Possibility of a Mass Production Tandem Cell

Water-Splitting Device 191933 Possibilities for Dual-Purpose Thin-Film Tandem Cell Devices 193

Contents IX

94 The lsquolsquoArtificial Leafrsquorsquo of Nocera 19395 Hydrogen Fuel Cell Status 19496 Storage and Transport of Hydrogen as a Potential Fuel 19597 Surface Adsorption for Storing Hydrogen in High Density 196971 Titanium-Decorated Carbon Nanotube Cloth 19998 Economics of Hydrogen 200981 Further Aspects of Storage and Transport of Hydrogen 200982 Hydrogen as Potential Intermediate in US Electricity

Distribution 201

10 Large-Scale Fabrication Learning Curves and EconomicsIncluding Storage 203

101 Fabrication Methods Vary but Exhibit Similar Learning Curves 203102 Learning Strategies for Module Cost 205103 Thin-Film Cells Nanoinks for Printing Solar Cells 207104 Large-Scale Scenario Based on Thin-Film CdTe or CIGS Cells 2091041 Solar Influx Cell Efficiency and Size of Solar Field Required

to Meet Demand 2101042 Economics of lsquolsquoPrinting Pressrsquorsquo CIGS or CdTe Cell Production

to Satisfy US Electric Demand 2111043 Projected Total Capital Need Conditions for Profitable

Private Investment 212105 Comparison of Solar Power versus Wind Power 214106 The Importance of Storage and Grid Management to

Large-Scale Utilization 2151061 Batteries from LeadndashAcid to Lithium to Sodium Sulfur 2171062 Basics of Lithium Batteries 2181063 NiMH 220

11 Prospects for Solar and Renewable Power 223111 Rapid Growth in Solar and Wind Power 223112 Renewable Energy Beyond Solar and Wind 225113 The Legacy World Developing Countries and the

Third World 226114 Can Energy Supply Meet Demand in the Longer Future 2271141 The lsquolsquoOil Bubblersquorsquo 2271142 The lsquolsquoEnergy Miraclersquorsquo 229

Appendix A Exercises 231Exercises to Chapter 1 231Exercises to Chapter 2 232Exercises to Chapter 3 233Exercises to Chapter 4 234Exercises to Chapter 5 236Exercises to Chapter 6 236

X Contents

Exercises to Chapter 7 237Exercises to Chapter 8 238Exercises to Chapter 9 238Exercises to Chapter 10 238Exercises to Chapter 11 239

Glossary of Abbreviations 241

References 245

Index 251

Contents XI

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

94 The lsquolsquoArtificial Leafrsquorsquo of Nocera 19395 Hydrogen Fuel Cell Status 19496 Storage and Transport of Hydrogen as a Potential Fuel 19597 Surface Adsorption for Storing Hydrogen in High Density 196971 Titanium-Decorated Carbon Nanotube Cloth 19998 Economics of Hydrogen 200981 Further Aspects of Storage and Transport of Hydrogen 200982 Hydrogen as Potential Intermediate in US Electricity

Distribution 201

10 Large-Scale Fabrication Learning Curves and EconomicsIncluding Storage 203

101 Fabrication Methods Vary but Exhibit Similar Learning Curves 203102 Learning Strategies for Module Cost 205103 Thin-Film Cells Nanoinks for Printing Solar Cells 207104 Large-Scale Scenario Based on Thin-Film CdTe or CIGS Cells 2091041 Solar Influx Cell Efficiency and Size of Solar Field Required

to Meet Demand 2101042 Economics of lsquolsquoPrinting Pressrsquorsquo CIGS or CdTe Cell Production

to Satisfy US Electric Demand 2111043 Projected Total Capital Need Conditions for Profitable

Private Investment 212105 Comparison of Solar Power versus Wind Power 214106 The Importance of Storage and Grid Management to

Large-Scale Utilization 2151061 Batteries from LeadndashAcid to Lithium to Sodium Sulfur 2171062 Basics of Lithium Batteries 2181063 NiMH 220

11 Prospects for Solar and Renewable Power 223111 Rapid Growth in Solar and Wind Power 223112 Renewable Energy Beyond Solar and Wind 225113 The Legacy World Developing Countries and the

Third World 226114 Can Energy Supply Meet Demand in the Longer Future 2271141 The lsquolsquoOil Bubblersquorsquo 2271142 The lsquolsquoEnergy Miraclersquorsquo 229

Appendix A Exercises 231Exercises to Chapter 1 231Exercises to Chapter 2 232Exercises to Chapter 3 233Exercises to Chapter 4 234Exercises to Chapter 5 236Exercises to Chapter 6 236

X Contents

Exercises to Chapter 7 237Exercises to Chapter 8 238Exercises to Chapter 9 238Exercises to Chapter 10 238Exercises to Chapter 11 239

Glossary of Abbreviations 241

References 245

Index 251

Contents XI

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

Exercises to Chapter 7 237Exercises to Chapter 8 238Exercises to Chapter 9 238Exercises to Chapter 10 238Exercises to Chapter 11 239

Glossary of Abbreviations 241

References 245

Index 251

Contents XI

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

Preface

This book is a text on aspects of solar and renewable energy conversion based onquantum physics or lsquolsquonanophysicsrsquorsquo We take a broader view of renewable energythan is common including deuterium-based fusion energy as approached throughTokamak-type fusion reactorsWe use the physics of the sun to introduce the ideas ofquantum mechanics

Our book may be regarded as a vehicle for teaching modern and solid-statephysics taking examples from the contemporary energy arena We assume thatthe reader understands elementary college physics and related college-level mathe-matics chemistry and computer science Exercises are provided for each of the 11chapters of the book

We omit nuclear fission power on the basis that it is available engineering as wellas that the supplies of uranium are limited

A second view of the book is as explaining and assessing opportunities forlsquolsquonanophysicsrsquorsquo -based technology toward solving the worlds looming energy pro-blem Earth has a population of 7 billion and rising we are at 1 billion autos headedtoward 2 billion with rising demand in developing nations But oil will sharply risein price on a scale of 30 years the timescale on which the easily accessible oil will beused There is definitely a problem to be solved even without involving questions ofclimate change

Fusion reactors are not usually regarded as lsquolsquonanotechnologyrsquorsquo but certainly arebased on the nanophysics or quantum physics of nuclear reactions Schrodingersequation was used by George Gamow to explain radioactive decay which is aninverse process to fusion The sun would not operate without quantum mechanicaltunneling of protons through Coulomb barriers The lsquolsquoTokamakrsquorsquo class of toroidalfusion reactors (as represented by ITER the international fusion energy project inCadarache France) is the culmination of decades of fusion research with a hugeaccumulated literature The complexity of this literature may have discouraged textbook writers from dealing with the subject even though the basis of the toroidalreactor is easily understood

It is an elementary exercise in plasma physics to find that plasma containment inorbits of particles around magnetic field lines and Faradays law of magneticinduction can lead to I2R heating of a gas (plasma) of fusible ions having smallheat capacity at temperatures much higher than that in the sun up to 150million K

XIII

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

A temperature of 15 million Kelvins (core of the sun) is sufficient for protonndashprotonfusion powering our whole existence only because of the high density on the orderof 150 gcc (150 times the density of water) of hydrogen at the suns core Thisdensity at 15 106 K is unachievable terrestrially but higher temperatures areavailable at lower densities on the order of 1020 particlesm3The physics of solar cells and photocatalytic production of hydrogen from water is

introduced in stages from atoms to covalent bonds to semiconductors to PNjunctions We emphasize durable thin-film solar cells that can be produced onroller-carried aluminum foil substrates in air by printing stoichiometric nanoparti-cles We mention in passing that First Solar has a billion-dollar contract to build a 2gigawatt solar cell facility in InnerMongolia On the other hand we do not attempt totreat laser-based methods of terrestrial fusion even though they may have promiseA hindrance to interdisciplinary endeavors is the existence of compartmented

literatures such as the overwhelming literature of the Tokomak reactor or the detailsof particle physics which attest to the accumulation of knowledge but have someeffect of putting walls around the knowledge The successful worker must have theenergy and audacity to plunge in to extract what is needed overcoming barriers innames in notation and in choice of units which sometimes obscure simplebasic factsThe author has benefited from teaching three classes of engineering and science

graduate and undergraduate students in lsquolsquoPhysics of Alternative Energyrsquorsquo at NYUPoly In particular he has benefited from class notes taken by Manasa Medikonda inSpring 2010 Students who have helped in this process include Angelantonio TafuniKarandeep Singh Mingbo Xu Paul-Henry Volmar Nikita Supronova and DiegoDelAntonio Dell Jones of Regenesis Power is thanked for information on the lowerright cover photo of the 2MWsolar cell installation at Florida Gulf Coast Universityand Dr Karl-Heinz Haas of Fraunhofer Institute for Solar Energy is thanked forinformation on the upper right cover photo of a dye-sensitized flexible solar celldeveloped at Freiburg The author thanks Prof Lorcan Folan andMs DeShane Lyewin the Applied Physics Office for help in several ways The assistance of EdmundImmergut Consulting Editor and of Vera Palmer and UlrikeWerner at Wiley-VCHis gratefully acknowledged Manasa Medikonda Mahbubur Rahman and AnkitaShah have been very helpful in preparing the manuscript Carol Wolf PhD inmathematics and Prof of Computer Science has been a constant source of supportin this project

Brooklyn NY Edward L WolfJuly 2012

XIV Preface

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

1A Survey of Long-Term Energy Resources

11Introduction

All energy resources on earth have come from the sun including the fossil fueldeposits that power our civilization at present Plants grew by photosynthesis startingin the carboniferous era about 300million years ago and the decay of some of theseinstead of oxidizing back into the atmosphere occurred underground in oxygen-freezones These anaerobic decays did not release the carbon but reduced some of theoxygen leading to the present deposits of oil gas and coal These deposits are nowbeing depleted on a 100-year timescale and will not be replaced Once theseaccumulated deposits are depleted no quick replenishment is possible The energyusage will have to reduce to what will be available in the absence of the huge depositsThe words sustainable and renewable apply to this vision of the future

There is clear evidence that the amount of available oil is limited and is distributedonly to depths of a fewmiles The geology of oil very clearly indicates limited suppliesIt is agreed that the continental US oil supplies havemostly been depleted Deffeyes(Deffeyes K (2001) Hubberts Peak (Princeton Univ Press Princeton) authori-tatively and clearly explains that liquid oil was formed over geologic time in favoredlocations and only in a window of depths between 7500 and 15 000 feet roughly15ndash3 miles (At depths more than 3miles the temperature is too high to form liquidoil from biological residues and natural gas forms) The limited depth and theextremely long time needed to form oil from decaying organic matter (it only occursin particular anaerobic oxygen-free locations otherwise the carbon is released asgaseous carbon dioxide) support the nearly obvious conclusion that the worldsaccessible oil is going to run out certainly on a timescale of 100 years

Furthermore scientists increasingly agree that accelerated oxidation of the coaland oil that remain as implied by the present energy use trajectory of advanced andemerging economies is fouling the atmosphere Increased combustion contributesto changes in the composition of the rather slim atmosphere of the earth in a way thatwill alter the energy balance and raise the temperature on the earths surfaceDramatic loss of glaciers is widely noted in Switzerland in the Andes Mountainsand in the polar icecaps which relates to sea-level rises

Nanophysics of Solar and Renewable Energy First Edition Edward L Wolf 2012 Wiley-VCH Verlag GmbH amp Co KGaA Published 2012 by Wiley-VCH Verlag GmbH amp Co KGaA

j1

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

New sources of energy to replace depleting oil and gas are needed The new energysources will stimulate changes in related technology An increasing premium willprobably be placed on new sources and methods of use that limit emission of gasesthat tend to trap heat in the earths atmosphere New emphasis is surely to be placedon efficiency in areas of energy generation and use Conservation and efficiency areadmired goals that are being reaffirmed

All energy comes from the sun from the direct radiation from the indirectlyresulting winds and related hydroelectric and wave energy possibilities Thesesources are considered renewable always available Fuels resulting from long erasof sunlight including deposits of coal oil and natural gas are nonrenewable Theseresources are depleting on time scales of decades to centuries Solar radiation is therenewable energy source that is most obviously an opportunity at present to fill theshortfall in energy

Solar energy while the basic source of all energy on earth presently provides onlya tiny fraction of utilized energy supply Global energy usage (global powerconsumption from all sources) has been estimated as available from the solarradiation falling on 1 of the earths desert areas Hence from a rational andtechnical point of view there need never be a lack of energy In recent years the oilprice has been on the order of $100 per barrel with predictions of prices muchhigher than the recent peak of $147 per barrel in the span of several years From thegeological point of view the worlds supply of oil is finite and there is someconsensus that in the past 100 years nearly half of it has been used A long-termenergy perspectivemust be based on long-term resources and oil is not a long-termresource on a 100-year basis

Solar energy conversion has aspects in which electronic processes are importantand for that reason this is a major topic in our book Direct photovoltaic conversionof light photons into electronndashhole pairs and into electrons traversing an externalcircuit is one topic of interest The second topic direct absorption of photons to splitwater into hydrogen and oxygen will be discussed Other permanent energysources which are by-products of solar energy for instance windpower hydro-power and power extracted from ocean waves do not depend in any strong way onthemicroscopic and nanoscopic physical processes that are the focus of our book Akey part of our book along this vein is on nuclear fusion energy a proven resourceon the sun whose reactions are well understood We will look carefully at severalapproaches to using the effectively infinite supply of deuterium in the ocean Weneed technology on earth to convert the deuterium to helium as occurs on the sunthe supply of deuterium if converted to energywould supply the energy needs of ourcivilization for millions of years

There are some who raise alarm at the dangerous suggestions that our energy-dependent civilization could be reorganized to run only on the renewable forms ofenergy These observers overlap those who deny that the existing supplies of oil andcoal are strictly limited andwho refuse to address the future beyond such depletions

The strong basis for such a fear is the overwhelming dependence at present on thefossil fuels oil coal and natural gas with small amounts of hydroelectric powerand nuclear power On charts the present consumption levels from solar power

2j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

windpower geothermal power wave and tidal power are too small to be seen on thesame scales

Energy can be expressed as power times time one kWh (kilowatt hour) is1000 3600frac14 36 106 Jfrac14 36 106Ws The BTU British thermal unit is1054 J and the less familiar Quadfrac14 1015 BTU is thus 1054 1018 J It is statedbelow that the US energy consumption was 9482 Quads in 2009 In terms ofaverage power since a year is 365 24 3600 sfrac14 315 107 s this 317 TW (Thisamounts to about 216 of global power while one may note that US population of311 million is only 44 of the global population at 7 billion)

According to the BP Statistical Review of World Energy June 2010 the worldsequivalent total power consumption in 2008was 147 TW (see Figure 11) The largestsources in order are oil coal and natural gas with hydroelectric accounting for11 TWand nuclear about 07 TW about 73 and 45 respectively Renewable powersuch as solar andwind are not tabulated byBP but are clearly almost negligible on thepresent scale of fossil fuel power consumptions

More details of the 2009 power consumption in theUnited States breaking out therenewable energy portions are shown in Figure 12

Although the renewable energy portions are at present small they are clearly inrapid growth To get an idea of the growth we find from reasonable sources

Figure 11 Global consumed power (based onBP Statistical Review of World Energy June2010) The smallest band is nuclear about066 TW and next smallest is hydroelectricabout 107 TW (This is also referred to as TPEStotal primary energy supply) The largest in orderare oil coal and natural gas accounting for

about 882 of all energy consumption Astuteobservers agree that the three leading sourcesshown here are likely to significantly decrease inthe next century as prices rise due to depletionof easily available sources

11 Introduction j3

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

(Renewables 2011 Global Status Report httpwwwren21netPortals97docu-mentsGSRGSR2011_Master18pdf see also httpwwwapsorgunitsgerameet-ingsmarch10uploadCarlsonAPS3-14-10pdf and Global Trends in RenewableEnergy Investment 2011 (Bloomberg New Energy Finance) available at httpfs-unep-centreorgpublicationsglobal-trends-renewable-energy-investment-2011)estimates that in 2010 installed windpower capacity worldwide is 198GW andgrowing at 30 per year If this rate continues (which is not assured) it will beless than 20 years from 2010 until windpower reaches 5 TW the present power fromcoal This can thus be crudely extrapolated to happen by 2030 In a similar vein in2010 installed photovoltaic PV capacity is 40GWand increasing at 43 per year Onthis basis it will take 135 years from 2010 to reach 5 TW thus estimated in 2024

These are long extrapolations inherently uncertain in their accuracy One mayquestion that a 5 TW level fromwindpower is attainable from the point of view of landarea and suitable sites apart from capital investment grid linkage and storage issuesThe limiting capacities are not easy to estimate However one detailed study ofChina [1] based onwindspeed data predicted that installation of 15MW turbines onmainland China could provide up to 247 PWh of electricity annually which worksout to an average power of 282 TW This suggests that 5 TWwind capacity worldwidemay be achievable On the other hand theNew York Times [2] has recently publishedan analysis of power investment in China and finds that coal is by far the largest andmost rapidly growing source of energy and that windpower capacity is scarcelyincreasing

Estimates of the power potentially available fromdirect photovoltaic conversion arestraightforward To reach 5 TW assuming an average power density of 205Wm2

with 10 efficient solar cells requires an area (5 1012205)m2frac14 244 1011m2

Figure 12 Energy consumed in United Statesin 2009 totals to 9482Quadsfrac14 999 1019 JOfthis figure 816 (7745 Quads) is classified asrenewable as broken out on the right In therenewable category wind accounts for 9 thus

only 07 of the total US power consumption(US Energy Information AdministrationRenewable Energy Consumption and ElectricityPreliminary Statistics 2009)

4j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

that would be 4938 kmon a side This area compared to the area of the Sahara desert9 106 km2 is 27

Adetailed plan for providing renewable power to Europe has been given byCzischThis comprehensive plan finds that transmission lines are essential to a plan that canpower all of Europe at similar to present rates without coal or oil as source (httpwwwisetuni-kasseldeabtw3-wprojekteWWEC2004pdfDrGCzisch Low costbut totally renewable electricity supply for a huge supply area a europeantrans-european example (httpwww2fz-juelichdeiefief-stedatapoolsteforumCzisch-Textpdf))

The data in Figures 11 and 12 should be regarded as accurate numbers and thistotal consumption is reasonably extrapolated to double by 2050 and triple by 2100 Tomake a difference in the global energy pattern any new source has to be on the scaleof 1ndash5 TW on a long timescale The total geothermal power at the earths surface isestimated as 12 TW only a small portion extractable It is said that total untappedhydroelectric capacity is 05 TW and total power from waves and tides is less than2TW These latter estimates are not so certain See Basic Research Needs for SolarEnergy Utilization Report of the Basic Energy Sciences Workshop on Solar EnergyUtilization April 18ndash21 2005 US Department of Energy

An overview of the potential renewable energy sources in the global environmenthas been offered by Richter The numbers in Table 11 are totals and do not indicatewhat fractions may be extractable

These numbers do not reflect any estimate of what portion may be extractableThus Figure 11 indicates 107 TW global hydroelectric power which is far short of7 TW in this table for river flow energy and elsewhere it is estimated that untappedhydroelectric power is only 05 TW Such an estimate probably does not consider thepotential for water turbines analogous to wind turbines in worldwide rivers (basedon Table 81 Richter [3])

Our interest is in the science and technology of long-term solutions to energyproduction with emphasis on the aspects that are addressed by nanophysics orquantum physics Quantum physics is needed to understand the energy release inthe sun and in nuclear fusion reactors such as Tokamaks on earth and also tounderstand photovoltaic cells and related devices It seems sensible to describe these

Table 11 Global natural power sources in terawatts (adapted from Ref [3])

Average global power consumed 2008 147Solar input onto land massa) 30 500Wind 840Ocean waves 56Ocean tides 35Geothermal world potential 322Global photosynthesis 91River flow energy 7

a) Solar input onto land area assuming 205Wm2

11 Introduction j5

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

processes as nanophysics the physics that applies on the size scale of atoms andsmall nuclei such as protons deuterons and 3He Needed also are basic aspects ofmaterials including plasmas and semiconductors Our hope is to provide a basicpicture based on Schrodingers equation with enough details to account for nuclearfusion reactions in plasmas and photovoltaic cells in semiconductors Fromour pointof view oil gas coal and nuclear fission materials are not renewable sources ofenergy because of the short timescales for their depletion We focus on the energythat comes from the sun directly as radiation and indirectly on earth in the form ofwinds waves and hydroelectric power

Beyond this we consider the vast amounts of deuterium in the oceans as asustainable source of energy once we learn how to make fusion reactors work onearth The heat energy in the earth geothermal energy is renewable but its overlapwith nanophysics is not large In a similar vein the energy of tidal motions which isextracted from the orbital energy of themoon around the earth is a long-term sourcebut it is not strongly related to nanophysics

The main opportunities for nanophysics are in photovoltaic cells and relateddevices aspects of energy storage and in various approaches toward fusion based ondeuterium and possibly lithium We want to learn about the nanophysical nuclearfusion energy generation in the sun for its own importance as an existence proof forfusion and also as a guide to how controlled fusionmight be accomplished on earth

111Direct Solar Influx

The primary energy source for earth over billions of years has been the radiation fromthe sun The properties of the sun including its composition and energy generationmechanisms are now known as a result of years of research Our purpose here is tosummarize modern knowledge of the sun with the intention of showing how theenergy production of the sun requires a quantummechanical view of the interactionsof particles such as protons and neutrons at small distance scales The Schrodingerequation needed for understanding the rather simple tunneling processes thatmustoccur in the sun will be used later to get a working understanding of atomsmolecules and solids such as semiconductors

1111 Properties of the SunThemass of the sun isMfrac14 199 1030 kg its radiusRsfrac14 0696 106 km at distanceDes about 93 million miles (1496 108 km) from earth The suns composition bymass is approximately 735hydrogen and 249helium plus a distribution of lightelements up to carbon The suns surface temperature is 5778ndash5973K while thesuns core temperature is estimated as 157 106K (Much of the data for the sunhave been taken from Principles of Stellar Evolution and Nucleosynthesis byDonald D Clayton (University of Chicago 1983) and Sun Fact Sheet by D RWilliams (NASA 2004))

We are interested in the energy input to the earth by electromagnetic radiationtraveling at the speed of light from the sun A measurement is shown in Figure 13

6j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

obtained in the near vacuum above the earths atmosphere The curve closely fits thePlanck radiation law

uethnTHORN frac14 frac128phn3=c3frac12expethhn=kBTTHORN11 eth11THORNwhere hfrac14 66 1034 J s kBfrac14 138 1023 JK is Boltzmanns constant and theKelvin temperatureT is 5973K This is the Planck thermal energy density units Joulesper (Hzm3) describing the spectrum of black body radiation as a function of thefrequency n in Hertz Equation 11 is the product of the number of electromagneticmodes per Hertz and per cubic meter at frequency n the energy per mode and thechance that themode is occupied The powerdensity is obtained bymultiplying by c4where cfrac14 2998 108ms is the speed of light The Planck function is alternativelyexpressed in terms of wavelength through the relation nfrac14 cl

Integrating this energy density over frequency and multiplying by c4 leads to theStefanndashBoltzmann law for the radiation energy per unit time and per unit area from asurface at temperature T which is

dU=dt frac14 Uc=4 frac14 sSBT4 sSB frac14 2p5kB

4=eth15 h3 c2THORN frac14 567 108 W=m2K4

eth12THORN

Thewavelength distribution of black body radiation peaks at wavelength lm suchthat lmTfrac14 constantfrac14 29mmK The value of lmfrac14 486 nm for the solar spectrum

Figure 13 Directly measured solar energyspectrum from200 to 2400nm froma satellite-carried spectrometer just above the earthsatmosphere The units are related to energymWm2 nm and the area under this curve

should be close to 1366Wm2 Note that thepeak here is close to 486 nm corresponding to ablack body at 5973 K The portion of thisspectrumbeyond about 700 nmcannot be seenbut represents infrared heat radiation [4]

11 Introduction j7

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

is in the visible corresponding toT 5973K (The sharp dips seen in Figure 11 attestto the wavelength resolution of themeasurement but are not central to our questionof the energy input to earth These dips are atomic absorption lines presumably fromsimple atoms and ions in the atmosphere surrounding the sun)

A related aspect of the radiation is the pressure it exerts which isU3frac14 (43 c) sSBT4 It is estimated that the temperature at the center of the sun is 15 107 K whichcorresponds to radiation pressure [4(3 3 108)] sm 567 108Wm2K4

(15 107 K)4frac14 0126Gbar where 1 barfrac14 101 kPa This is large but a small part ofthe total hydrostatic pressure of 340Gbar at the center of the sun

The area under this curve measured above the earths atmosphere represents1366Wm2 available at all times (and over billions of years) A fraction a (thealbedo about afrac14 03) of this is reflected back into space However if we take theradius of the earth as 6371 km then the power intercepted neglecting a is174 1017 Wfrac14 174 PW (petawatts) By comparison the worldwide power con-sumption for all purposes in 2008 was 147 TW and the average total electricpower usage in the United Sates in 2004 was 460GW [5] which is only 26 parts permillion (ppm) of the solar energy flux If there are 7 billion people on the earth thispower is 24900 kWper person On the basis of 460GWand 294million persons inthe United States (in 2004) the electrical power usage for 2004 was 156 kW perperson in the United States Worldwide total energy usage per person works out as147 TW7 billionfrac14 210 kW per person

There is thus a vast flow of energy coming from space even after we correct for thereflected light (albedo) and the absorption effects in the atmosphere The question ofwhether it can be harvested for human consumption is related to its dilute nature Atground level in the United States an average solar power density is about 205Wm2For example an auto at 200 HP corresponds to 200 746wattsfrac14 14 920W andwould require a collection area 73m2 much bigger than a solar panel that could beput on the roof of the car To supply the whole country at a conversion efficiencyof 20 a surface area of dimension about 65 miles would provide 460GW leavingopen questions of overnight storage of energy and distribution of the energy

The challenge is to turn the incoming solar flux (andor other secondary sources ofsun-based energy like the wind and hydroelectric power) into usable energy on thehuman level In advanced societies it represents energy for transportation presentlyindicated by the price per gallon of gasoline and the cost per kWh of electricity

Our second interest in a book that focuses on nanophysics or quantum physicsthat applies to objects and devices on a size scale below 100 nm or so is to learnsomething about how the sun releases its energy and to think ofwayswemight createa similar energy generation on earth

The spectrum in Figure 13 closely resembles the shape of the Planck black bodyradiation spectrum plotted versus wavelength for 5973K This spectrum wasmeasured in vacuum above the earths atmosphere and directly measures the hugeamount of energy perpetually falling on the earth from the sun quoted as 1366Wm2If we look at the plot with units milliwatts(m2 nm) the area under the curve is thepower density Wm2 To make a rough estimate the area is the average value about700mW(m2 nm) times the wavelength range about 2000 nm So this roughestimate gives 1400Wm2

8j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

This spectrum (Figure 13) wasmeasured by an automated spectrometer carried ina satellite well beyond the earths atmosphere The sharp dips in this spectrum areatomic absorption lines the sort of feature that can be understood only withinquantum mechanics The atoms in question are presumably in the sunsatmosphere

We are interested in the properties of the sun that is not only the source of allrenewable energy excluding the geothermal and tidal energies and includingbiofuels that are grown renewably by photosynthesis but also serves as a modelfor fusion reactions that might be implemented on earth The power density at thesurface of the sun can be calculated from this measured power density shownin Figure 13 If the radiation power density just above the earth is measured as1366Wm2 then the power density at the surface of the sun can be obtained as

P frac14 1366W=m2 ethDes=RsTHORN2 frac14 6312 107 W=m2 eth13THORN

using the values above for the distance to the sun and the suns radius Des and Rsrespectively Since we have a good estimate of the suns surface temperature T fromthe peak position in Figure 13 we can use this power density to estimate theemissivity e using the relation Pfrac14 esSBT

4 This gives emissivity efrac14 0998 whichseems reasonable

Before we turn to an introductory discussion of how the sun stays hot let usconsider thermal radiation from the earth raising the question of the energy balancefor the earth itself The earths surface is 70 ocean and it seems the averagetemperature TE must be at least 273K Assuming this the power radiated from theearth is

P frac14 4pR2EsSBethTETHORN4 eth14THORN

Initially we suppose that this power goes directly out into space (A more accurateestimate of the earths temperature is 288K see Ref [3] p 11

Using REfrac14 6173 km and taking emissivity efrac14 1 this is Pfrac14 1606 PW Let uscompare this with an estimate of the absorbed power from the sun being morerealistic by taking the Albedo (fraction reflected) as 03 So power absorbed is 174 PW(1 03)frac14 1218 PW Since the earth maintains an approximately constant temper-ature this comparison indicates that a net loss discrepancy of 388 PW if we neglectany heat energy comingup from the core of the earth (It is estimated that heatflowupfrom the earths center is Qfrac14 443 1013Wfrac14 00443 PW which is relatively smallOf this 80 is from continuing radioactive heating and 20 from secular coolingof the initial heat 443 TW is a large number (a bit larger than shown in Table 11) buton the scale of the solar influx it is not important in our approximate estimate So wewill neglect this for the moment) [6]

Thus a straightforward estimate of power radiated from earth exceeds the well-known inflow To resolve the discrepancy it seems most plausible that the radiatedenergy does not all actually leave earth but a portion is reflected back A greenhouseeffect reduces the black body radiation 1606 PW down close to the 1218 PW netradiation input from the sun (Figure 14)We can treat this as return radiation from a

11 Introduction j9

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

greenhouse of temperature TG So the modified energy balance is

P frac14 4pR2EsSBfrac12ethTETHORN4ethTGTHORN4 frac14 1218 PW eth15THORN

where we have taken the greenhouse temperature TG as 1913 K in a simpleanalysis According to Richter (op cit p 13) the most important greenhouse gasesare CO2 and water vapor [3]

1112 An Introduction to Fusion Reactions on the SunIn the simplest terms the power densityPfrac14 63MWm2 leaving the surface of the suncomes fromnuclear fusion of protons to create 4He in the core of the sun Let usfindthe total power radiated by the sun This is 4pR2

s 6312MW frac14 382 1026 Wmaking use of Rsfrac14 0696 106 km This 382 1026W is such a large value do weneed fear the sun will soon be depleted Fortunately we can be reassured that thelifetime of the sun is still going to be long by estimating its loss of mass from the

Figure 14 Earth as seen from space NASAThe cloud cover is evident and is a factor both inthe Albedo 03 (the fraction of sunlight ontothe earth that is reflected) and in the trapping ofreradiated heat energy from the earth at 290K(greenhouse effect) The accurate sphericalshape comes from maximizing attractivegravitational energy which caused thecondensation of primordial dust into thecompact initially molten earth The

condensation energy is estimated (see text) asU frac14 06GM2

E=RE frac14 224 1032 J which isequal to (1) times the present rate of globalpower usage times 5 1011 years The power inthe oceans wave motions is estimated as56 TW see text The radiation powerintercepting the earth from the sun is 174 PWwhich is 249MW per person on a 24 h 7 daybasis counting 7 billion people

10j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

radiated energy Using the energyndashmass equivalence of Einstein

DMc2 frac14 DE eth16THORN

ona yearly basiswehaveDEfrac14 382 1026W 315 107 syearfrac14 120 1034 JyearThis is equivalent to DMfrac14 (120 1034 Jyear)c2frac14 1337 1017 kgyear AlthoughDM is large it is tiny in comparison to the much larger mass of the sun Mfrac14 199 1030 kg Thus wefind that the fractional loss ofmass per yearDMM for the sun is1337 1017 kgyear 199 1030 kgfrac14 672 1014year This is tiny indeed so theradiation is not seriously depleting the suns mass On a scale of 54 billion years theaccepted age of the earth the fractional loss of mass of the sun during the wholelifetime of earth taking the simplest approach has been only 0036

Where does all this energy come from It originates in the strong force ofnucleons which is large but of short range a few femtometers Chemical reactionsdeal with the covalent bonding force nuclear reactions originate in the strong forceabout a million times larger The energy is from burning hydrogen to make heliumin principle similar to burning hydrogen to make water but the energy scale is amillion times larger

In more detail the composition of the sun is stated as 735 H and 249 He bymass so the obvious candidate fusion reaction is the conversion of H into He Thebasic protonndashproton fusion cycle leading to helium in the core of the sun (out to about025 of its radius) has several steps that can be summarized as

4p 4He thorn 2ethorn thorn 2ue eth17THORN

This says that four protons lead finally to an alpha particle (two protons and twoneutrons which forms the nucleus of the Helium atom) two positive electrons andtwo neutrino particles

This is a fusion reaction of some of the elementary particles of nature whichinclude besides protons and neutrons positive electrons (positrons) and neutrinosue Positrons and neutrinosmay be unfamiliar but a danger is to become intimidatedby unnecessary details rather than in an interdisciplinary field to learn and makeuse of essential aspects The important aspect here is that energy is released whenparticles combine to formproducts the sumofwhosemasses are less than themassesof the constituents Furthermore as we will learn this reaction can proceed onlywhen the source particles have high kinetic energy to overcome Coulomb repulsionwhen the charged particles coalesce In addition the essential process of quantummechanical tunneling an aspect of the wave nature of matter allows the reaction toproceed when the interparticle energies are in the kiloelectron volt (keV) rangeavailable at temperatures above 15million K From elementary physics we recall thatthe average kinetic energy per degree of freedom in equilibrium at temperature T is

Eav frac141=2kBT eth18THORNwhere Boltzmanns constant kBfrac14 138 1023 JK The energy units for atomicprocesses are conveniently expressed as electron volts such that 1 eVfrac14 16 1019

11 Introduction j11

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources

Jfrac14 16 1019Ws Chemical reactions release energy on the order of 1 eV per atomwhile nuclear reactions release energies on the order of 1MeV per atom seeFigure 15 A broad distribution of particle speed v is allowed in the normalizedMaxwellndashBoltzmann speed distribution

DethvTHORN frac14 ethm=2pkBTTHORN3=24pv2expethmv2=2 kBTTHORN eth19THORN

While one may have learned of this in connection with the speeds of oxygenmolecules in air it usefully applies to the motions of protons at 15 million K in thecore of the sun

The most probable speed is (2 kTm)12 that corresponds to a kinetic energy Ekfrac1412mv2 of kT In connection with the probability of tunneling through the Coulombbarrier which rises rapidly with rising interparticle energy (particle speed) one seesthat the high-speed tail of the MaxwellndashBoltzmann speed distribution is importantThe overlap of the speed distribution falling with energy and the tunnelingprobability rising with energy typically as exp[(EGEk)

12] as we will learn laterleads to what is known as the Gamow peak for fusion reactions in the sun (Thesuns neutrino output has been measured on earth and is now regarded as insatisfactory agreement with the pndashp reaction rate in the core of the sun [9])

The energy release of this reaction can be calculated from the change in the mic2

terms Using atomic mass units u we go from 4 10078 to 40026 thorn 2 (11836)frac14951 103 u and using 9351MeVas uc2 we find 889MeV per 4He neglecting theneutrino energy The atomicmass unit u is nearly the protonmass but defined in factas 112 the mass of the carbon 12 nucleus

We should point out the large scale of the fusion energy release here nearly 9MeVon a single atom basis This is about a million times larger than a typical chemicalreaction on a single molecule basis The nuclear force that binds the protons andneutrons in the nuclei is indeed about a million times stronger than the typical

Figure 15 The suns radiating power comes largely from nuclear fusion of protons p into 4He at15million KMass (nucleon) numberAfrac14Z thorn N pD and T are equivalent respectively to 1H 2Hand 3H (reproduced from Ref [8] Figure 1)

12j 1 A Survey of Long-Term Energy Resources