springerseriesin series in...springerseriesin materialsscience editors: r.hull r.m.osgood,jr....

Springer Series in

materials scienceEditors: R. Hull R. M. Osgood, Jr. J. Parisi

The Springer Series in Materials Science covers the complete spectrum of materials physics,including fundamental principles, physical properties, materials theory and design. Recognizingthe increasing importance of materials science in future device technologies, the book titles in thisseries ref lect the state-of-the-art in understanding and controlling the structure and propertiesof all important classes of materials.

51 Point Defectsin Semiconductorsand InsulatorsDetermination of Atomicand Electronic Structurefrom Paramagnetic HyperfineInteractionsBy J.-M. Spaeth and H. Overhof

52 Polymer Filmswith Embedded Metal NanoparticlesBy A. Heilmann

53 Nanocrystalline CeramicsSynthesis and StructureBy M. Winterer

54 Electronic Structure and Magnetismof Complex MaterialsEditors: D.J. Singh andD. A. Papaconstantopoulos

55 QuasicrystalsAn Introduction to Structure,Physical Properties and ApplicationsEditors: J.-B. Suck, M. Schreiber,and P. Haussler

56 SiO2 in Si MicrodevicesBy M. Itsumi

57 Radiation Effectsin Advanced Semiconductor Materialsand DevicesBy C. Claeys and E. Simoen

58 Functional Thin Filmsand Functional MaterialsNew Concepts and TechnologiesEditor: D. Shi

59 Dielectric Properties of Porous MediaBy S.O. Gladkov

60 Organic PhotovoltaicsConcepts and RealizationEditors: C. Brabec, V. Dyakonov, J. Parisiand N. Sariciftci

Series homepage – http://www.springer.de/phys/books/ssms/

Volumes 1–50 are listed at the end of the book.

C.J. Brabec V. DyakonovJ. Parisi N.S. Sariciftci (Eds.)

Organic PhotovoltaicsConcepts and Realization

With 148 Figures

13

Dr. Christoph J. BrabecSiemens AGCT MM1 Innovative ElectronicsPaul-Gossen-Strasse 10091052 Erlangen, Germany

Dr. Vladimir DyakonovFaculty of PhysicsDept. of Energyand Semiconductor ResearchUniversity of Oldenburg26111 Oldenburg, Germany

Professor Jurgen ParisiFaculty of PhysicsDept. of Energy and Semiconductor ResearchUniversity of Oldenburg26111 Oldenburg, Germany

Professor Niyazi S. SariciftciInstitute of Physicsal Chemistryand Linz Institute of Organic Solar CellsUniversity of LinzAltenberger Strasse 694040 Linz, Austria

Series Editors:Professor R. M. Osgood, Jr.Microelectronics Science Laboratory, Department of Electrical EngineeringColumbia University, Seeley W. Mudd Building, New York, NY 10027, USA

Professor Robert HullUniversity of Virginia, Dept. of Materials Science and Engineering, Thornton HallCharlottesville, VA 22903-2442, USA

Professor Jürgen ParisiUniversitat Oldenburg, Fachbereich Physik, Abt. Energie- und HalbleiterforschungCarl-von-Ossietzky-Strasse 9-11, 26129 Oldenburg, Germany

ISSN 0933-033x

Library of Congress Cataloging-in-Publication Data

Organic photovoltaics : concepts and realization / C.J. Brabec ... [et al.].p. cm. – (Springer series in materials science ; 60)Includes bibliographical references and index.

1. Photovoltaic cells. 2. Organic semiconductors. I. Brabec, C.J. (Christoph J.), 1966-II. Series.TK8322.075 2003 621.3815’42–dc21 2002044659

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Preface

During and immediately after the oil crisis in the early 1970s, a tremendouseffort was devoted to the development of photovoltaic solar cells, in orderto utilize the cleanest of all possible renewable energy sources, i.e., sunshine.The well-established silicon device technology totally dominates the markettoday. Organic semiconducting materials represent a promising alternativeand a rather new approach, even though the basics of photovoltaic applica-tions were described some time ago. Compounds such as merocyanines1 andphthalocyanines2 that are readily deposited as thin films by vacuum evap-oration gave solar-to-electric power conversion efficiencies of about 1% forsmall-sized photovoltaic elements.

Achieving efficient solar energy conversion on a large scale and at lowcost is one of the most important technological challenges for the near fu-ture. It therefore appears highly intriguing to think of extensive organic solarcells based on transparent, flexible, cheap, and easy-to-process thin plasticfilms, cut from rolls and deployed on permanent structures and surfaces.Whereas conjugated polymers have found successful technological applica-tions as light-emitting diodes, the first attempt to prepare photovoltaic el-ements with these materials alone (e.g., polyacetylene) was rather discour-aging.3 Indeed, the photovoltaic effect involves the generation of electronsand holes in the semiconductor device under illumination and their sub-sequent collection at opposite electrodes. In organic semiconductors, bothcharge separation and charge mobility are limited to some extent. Followingthe encouraging breakthrough observation of reversible, metastable, and ul-trafast photo-induced electron transfer from donor-type conjugated polymersto acceptor-type fullerene molecules, a novel photovoltaic device concept –in a sense similar to the first steps of natural photosynthesis – based on thestructural ordering of an interpenetrating network (by mixing the donor–acceptor composite to a bulk heterojunction blend with increased effective1 G.A. Chamberlain: Solar Cells 8, 47 (1983).2 J. Simon, J.-J. Andre: Molecular Semiconductors (Springer, Berlin, 1985).3 J. Kanicki: in Handbook of Conducting Polymers, Vol. 1, ed. by T.A. Skotheim

(Marcel Dekker, New York, 1985) p. 543.

VI Preface

interface area) gives rise to power conversion efficiencies up to 2.5% and aquantum yield approaching unity.4,5,6

Besides the efficiency criterion, long-term stability is another crucial prob-lem common to all possible applications of semiconducting polymers. To date,light-emitting diodes based on conjugated polymer materials have generallybeen provided with industrial encapsulation techniques that allow for a shelflifetime of several years as well as an operational lifetime of some tens of thou-sands of hours. In the case of a photovoltaic device or even a single devicecomponent, the trade-off between operational lifetime and efficiency versuscost will determine the market penetration capability of these types of solarcells. The purpose of the present volume is to provide a snapshot of the stateof the art in fundamental organic/plastic solar cell research with particularemphasis on educational aspects.

The editors would like to express their gratitude to all authors for thelarge amount of time and effort that went into preparing the broad spectrumof contributions printed hereafter. Special thanks are due to Claus Ascheron,Angela Lahee, Petra Treiber, and Stephen Lyle from Springer-Verlag, Hei-delberg, for continuous commitment, efficient support, and skillful technicalassistance.

Erlangen, Oldenburg, Linz, Christoph J. BrabecJanuary 2003 Vladimir Dyakonov

Jurgen ParisiNiyazi Serdar Sariciftci

4 N.S. Sariciftci, L. Smilowitz, A.J. Heeger, and F. Wudl, Science 258, 1474 (1992).5 G. Yu, J. Gao, J.C. Hummelen, F. Wudl, A.J. Heeger: Science 270, 1789 (1995).6 N.S. Sariciftci, A.J. Heeger: in Handbook of Organic Conducting Molecules and

Polymers, Vol. 1, ed. by H.S. Nalwa (Wiley, New York, 1996) p. 414; S.E. Shaheen,C.J. Brabec, N.S. Sariciftci, F. Padinger, T. Fromherz, J.C. Hummelen: Appl.Phys. Lett. 78, 841 (2001); C.J. Brabec, N.S. Sariciftci, J.C. Hummelen: Adv.Funct. Mater. 11, 15 (2001).

Contents

1 Photoinduced Charge Transferin Bulk Heterojunction CompositesChristoph J. Brabec, Vladimir Dyakonov . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Conjugated Polymer–Fullerene Blend:A Highly Efficient Systemfor Photoinduced Charge Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Molecular Semiconductor Picture of Conjugated Polymers . . . . . . . . 41.2.1 Molecular Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Optical and Electronic Properties . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.3 Characterisation of Excited States . . . . . . . . . . . . . . . . . . . . . . . . 71.2.4 Photoinduced Electron Transfer

in Pure Conjugated Polymers and Molecules . . . . . . . . . . . . . . . 101.2.5 Photoinduced Electron Transfer in Donor–Acceptor Systems . 15

1.3 Detection of Charges in Conjugated Polymers . . . . . . . . . . . . . . . . . . . 161.3.1 Pump–Probe Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.3.2 Application of Pump–Probe Spectroscopy in the ms Range

to Conjugated Polymer/Fullerene Blends . . . . . . . . . . . . . . . . . . 191.4 Kinetics of Photoinduced Charge Generation

in Conjugated Polymer/Fullerene Blends . . . . . . . . . . . . . . . . . . . . . . . 211.5 Light-Induced Electron-Spin Resonance Detection

of the Charge Transfer Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261.6 Oligo-Phenylene Vinylene: A Model System

for Donor–Acceptor Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2 Optical and Spectroscopic Propertiesof Conjugated PolymersDavide Comoretto, Guglielmo Lanzani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.1 Material and Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.1.1 Optical Constants and Electronic Structure . . . . . . . . . . . . . . . . 612.1.2 Determination of n by Spectroscopic Methods . . . . . . . . . . . . . . 622.1.3 Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652.1.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

VIII Contents

2.2 Spectroscopic Properties of Excited States . . . . . . . . . . . . . . . . . . . . . . 712.2.1 Basic Notions of Pump–Probe Spectroscopy . . . . . . . . . . . . . . . . 722.2.2 Interpretation of Pump–Probe Experiments . . . . . . . . . . . . . . . . 732.2.3 Isolated Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752.2.4 Condensed Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802.4 Appendix: Derivation of (2.17) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802.5 Appendix: Overview of Decay Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . 82References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3 Transport Properties of Conjugated PolymersReghu Menon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.1 Disorder and Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923.2 Conduction in Conjugated Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.3 Metal–Insulator Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 993.4 Hopping Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053.5 Magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1083.6 Thermopower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1133.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4 Quantum Solar Energy Conversionand Application to Organic Solar CellsGottfried H. Bauer, Peter Wurfel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

4.1 Solar Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1184.2 Solar Cells and General Quantum Converters . . . . . . . . . . . . . . . . . . . 120

4.2.1 Two-Level Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1214.2.2 Fermi Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1224.2.3 Quasi-Fermi Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1224.2.4 Transition Rates and Optical Properties . . . . . . . . . . . . . . . . . . . 1234.2.5 Current–Voltage Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.3 Semiconductor Solar Cells as Two-Band Systems . . . . . . . . . . . . . . . . 1274.3.1 Fermi Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1284.3.2 Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1294.3.3 Quasi-Fermi Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1304.3.4 Interaction of Light with Matter . . . . . . . . . . . . . . . . . . . . . . . . . . 1314.3.5 Generation of Electron–Hole Pairs . . . . . . . . . . . . . . . . . . . . . . . . 1354.3.6 Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

4.4 Radiative Limit for Solar Cell Efficiencies . . . . . . . . . . . . . . . . . . . . . . . 1384.4.1 Current–Voltage Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

4.5 Charge Separation in Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1414.5.1 Charge Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1434.5.2 Transport Equations for Semiconductor Solar Cells . . . . . . . . . . 1474.5.3 Charge Transport in Low Mobility Materials . . . . . . . . . . . . . . . 148

Contents IX

4.5.4 Carrier Mobilities in Organic Semiconductors . . . . . . . . . . . . . . . 1504.5.5 Equivalent Circuits for Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . 151

4.6 Conclusions for Solar Cell Requirements . . . . . . . . . . . . . . . . . . . . . . . . 1534.6.1 Special Geometrical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1534.6.2 Particular Optical Design/Multispectral Conversion . . . . . . . . . 155

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

5 Semiconductor Aspectsof Organic Bulk Heterojunction Solar CellsChristoph J. Brabec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

5.1 Device Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1605.1.1 Single-Layer Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1605.1.2 Heterojunction Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1625.1.3 Bulk Heterojunction Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . 163

5.2 Device Aspects and Transport Properties . . . . . . . . . . . . . . . . . . . . . . . 1695.2.1 Transport Properties of Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 1695.2.2 Metal/Conjugated Polymer Contacts . . . . . . . . . . . . . . . . . . . . . . 1775.2.3 Simulation and Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

5.3 Performance Analysis of Bulk Heterojunction Solar Cells . . . . . . . . . 1855.3.1 Precise Calibration of Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . 1865.3.2 Production: Device Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1885.3.3 Short-Circuit Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1905.3.4 Open-Circuit Voltage Voc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2055.3.5 Fill Factor FF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2145.3.6 Spectral Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2215.3.7 Temperature Behavior of Bulk Heterojunction Solar Cells . . . . 2295.3.8 Stability of Polymeric Semiconductors and Devices:

A Molecular View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2365.3.9 Processing of Polymeric Semiconductors:

Blending with Conventional Polymers . . . . . . . . . . . . . . . . . . . . . 2405.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

6 Organic Photodiodes: From Diodes to BlendsOlle Inganas, Lucimara Stolz Roman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

6.1 Thin Film Organic Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2506.2 Optical Mode Structure in Thin Film Organic Structures.

Optimization of Bilayer Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2516.3 Internal and External Quantum Efficiencies

of Organic Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2636.4 Electrical Transport in Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 2646.5 Nanostructure in Polymer/Molecule and Polymer/Polymer Blends . 2656.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

X Contents

7 Dye-Sensitized Solar CellsJan Kroon, Andreas Hinsch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

7.1 Operating Principles and Cell Structure of the nc-DSC . . . . . . . . . . . 2757.2 Manufacture of a Standard Glass/Glass nc-DSC . . . . . . . . . . . . . . . . . 2777.3 Module Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

7.3.1 Series Connection of Glass/Glass Devices:Z- and W-Type Interconnection . . . . . . . . . . . . . . . . . . . . . . . . . . 279

7.3.2 Series Connection: Three-Layer or Monolithic Module . . . . . . . 2807.4 Sealing Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2807.5 Technological Development and the State of the Art . . . . . . . . . . . . . 2817.6 Large Scale Batch Processing of Mini-Modules . . . . . . . . . . . . . . . . . . 2837.7 Long Term Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

7.7.1 Stability Tests on Indoor Dye PV Modules . . . . . . . . . . . . . . . . . 2857.7.2 Long Term Stability Tests on High Power nc-DSC . . . . . . . . . . 286

7.8 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

List of Contributors

Gottfried H. BauerFaculty of Mathematicsand Natural SciencesInstitute of Physicsand Semiconductor PhysicsCarl von Ossietzky University26111 Oldenburg, [email protected]

Christoph J. BrabecSiemens AGCTMM1 Innovative PolymersPaul Gossenstrasse 10091052 Erlangen, [email protected]

Davide ComorettoINFM Dipartimento di Chimicae Chimica IndustrialeUniversita degli Studi de GenovaVia Dodecaneso 3116146 Genova, [email protected]

Vladimir DyakonovFaculty of PhysicsDepartment of Energyand Semiconductor ResearchUniversity of Oldenburg26111 Oldenburg, [email protected]

Andreas HinschFraunhofer Institutefor Solar Energy SystemsHeidenhofstrasse 279110 Freiburg, [email protected]

Olle InganasBiomolecular and OrganicElectronicsDepartment of PhysicsLinkoping University58183 Linkoping, [email protected]

Jan KroonEnergy Research Centreof the NetherlandsECNWesterduinweg 3P.O. Box 11755 ZG Petten, [email protected]

Guglielmo LanzaniINFM Dipartimento di FisicaPolitecnico di MilanoPiazza Leonardo da Vinci20133 Milano, [email protected]

Reghu MenonDepartment of PhysicsIndian Institute of ScienceBangalore 560 012, [email protected]

XII List of Contributors

Jurgen ParisiFaculty of PhysicsDepartment of Energyand Semiconductor ResearchUniversity of Oldenburg26111 Oldenburg, [email protected]

Lucimara Stolz RomanDepartment of PhysicsFederal University of ParanaCuritibaParana 81531-990, [email protected]

Niyazi Serdar SariciftciInsitute of Physical Chemistry &Linz Instituteof Organic Solar CellsUniversity of LinzAltenberger Strasse 694040 Linz, [email protected]

Peter WurfelInstitute of Applied PhysicsUniversity of KarlsruheKaiserstrasse 1276128 Karlsruhe, [email protected]

1 Photoinduced Charge Transferin Bulk Heterojunction Composites

Christoph J. Brabec and Vladimir Dyakonov

It is indeed intriguing and very attractive to think of photovoltaic elementsbased on thin plastic films with low cost but large areas, cut from rolls anddeployed on permanent structures and surfaces. In order to fulfil these re-quirements, cheap production technologies for large scale coating must beapplied to a low cost material class. Polymer photovoltaic cells hold the po-tential of such low cost cells. Flexible chemical tailoring of desired properties,combined with the cheap technology already well developed for all kinds ofplastic thin film applications, precisely fulfill the above-formulated demandsfor cheap photovoltaic device production. The mechanical flexibility of plasticmaterials is welcome for all photovoltaic applications onto curved surfaces inindoor as well as outdoor applications.

The study of organic semiconducting materials has emerged over the lastfew decades as a field rich in fundamental science concerning unique electronicphenomena and photophysics. The development of organic photovoltaic de-vices is just one application of this fundamental work. Other examples areorganic light-emitting diodes and transistors. ‘Plastic’ photovoltaic devicesoffer the possibility of low-cost fabrication of large-area solar cells for har-vesting energy from sunlight. Apart from possible economic advantages, or-ganic materials also possess low specific weight and are mechanically flexible,properties desirable for a solar cell.

Several approaches to organic photovoltaic active composites have beeninvestigated to date. These include strategies based on photoinduced chargetransfer between layers of low-molecular-weight organic molecules (LMWmolecules) [1,2], within halogen-doped organic single crystals [3], withinsingle-component molecular dyads [4], between layers of conjugated polymersand LMW molecules [5], within conjugated polymers and polymer blends[6,7], and within a single-layer blend of a conjugated polymer and an LMWmolecule [8–10]. The materials described in this article are of the latter type.

Compared with research efforts devoted to small-molecule organic mate-rials, the organic polymeric photovoltaic materials (and here especially thedonor/acceptor ‘bulk heterojunction composites’) represent a relatively re-cent approach to exploiting photoinduced charge transfer phenomena forsolar energy conversion. Due to progress in polymer synthesis, conjugatedpolymers are now available with a purity comparable to the small organicmolecules. The organic electronics community is beginning to regard boththe small molecules and the conjugated polymer as classical semiconductors

2 Christoph J. Brabec and Vladimir Dyakonov

and to apply standard semiconductor models to describe their electro-opticalbehaviour.

It is the purpose of this chapter to introduce photoinduced charge transferphenomena in bulk heterojunction composites, i.e., blends of conjugated poly-mers and fullerenes. Phenomena found in other organic solar cells such as pris-tine fullerene cells [11,12], dye sensitised liquid electrolyte [13] or solid statepolymer electrolyte cells [14], pure dye cells [15,16] or small molecule cells [17],mostly based on heterojunctions between phthalocyanines and perylenes [18]or other bilayer systems will not be discussed here, but in the correspondingchapters of this book.

1.1 Conjugated Polymer–Fullerene Blend:A Highly Efficient Systemfor Photoinduced Charge Generation

Several attempts to use organic polymeric semiconductors as the active com-ponent in photovoltaic devices have been reported over the last two decades.Interest in the photovoltaic properties of conjugated polymers like polyacety-lene, various derivatives of polythiophenes and poly(phenylenevinylenes)arose from the discovery of mobile photoinduced charged states in this classof organic semiconductors. The idea of using this property in conjunctionwith a molecular electron acceptor to achieve long-lived charge separationwas based on the stability of photoinduced nonlinear excitations (such asthe polaron) on the conjugated polymer backbone. Independently, the SantaBarbara group and Osaka group reported studies on the photophysics of mix-tures and bilayers of conjugated polymers with fullerenes [19–27]. The exper-iments clearly evidenced an ultrafast (subpicosecond), reversible, metastablephotoinduced electron transfer from conjugated polymers onto C60 in solidfilms (Fig. 1.1). Once the photoexcited electron is transferred to an acceptorunit, the resulting cation radical (positive polaron) species on the conjugatedpolymer backbone is known to be highly delocalized and stable, as shownin electrochemical and/or chemical oxidative doping studies. In particular,the long lifetime of the charge transferred state and the high quantum effi-ciency of this process (≈ 100%) in conjugated polymer/fullerene compositesas compared to pristine conjugated polymer films favoured the developmentof photocells.

The first photovoltaic devices based on this photoinduced electron transferwere diodes consisting of bilayers from conjugated polymers and fullerenes.Rectification ratios on the order of 104 were demonstrated, but photovoltaicpower conversion efficiencies of these devices were low due to the small chargegenerating interface. The superior solubility of functionalized fullerenes com-pared to C60 made it possible to produce highly fullerene-loaded compos-ite films. Significant improvement of the relatively low collection efficiencyof the D/A bilayer has been achieved through control of the morphology

1 Photoinduced Charge Transfer in Bulk Heterojunction Composites 3

e-

hν

O

O

O

O

O

O

O

OC

Fig. 1.1. Schematic drawing of photoinduced electron transfer between a conju-gated polymer and a fullerene

of the donor/acceptor components in a composite film to get an interpene-trating network. Power conversion efficiency of solar cells made from MEH–PPV/fullerene composites was subsequently increased by two orders of mag-nitude. The central photophysical results of this ultrafast photoinduced elec-tron transfer will be discussed by reviewing experiments from two well charac-terised conjugated polymers, an alkoxy PPV (MEH–PPV or MDMO–PPV)and P3OT. The chemical structures of these polymers as well as of the mostfrequently used fullerenes are given in Fig. 1.2.

The polymers depicted here are predominantly p-type semiconductors inthe sense that they can be easily oxidised (p-doped), while the correspondingreduction (n-doping) destabilises the semiconductor. Nevertheless, polymericn-type semiconductors are available [28–45]. Another class of n-type semicon-ductors is the fullerenes, small molecules with an interesting symmetric andalmost spherical cage structure. In detail, the structure is that of a truncatedicosahedron with one carbon atom at each point of intersection, bringing to-gether a total of sixty carbon atoms. As a matter of fact, it is identical withthe official FIFA1 football although it is smaller. Since the C60 structurewas fully understood and explained by Kroto, Smalley and co-workers [46] inthe 1980s, intensive research has been carried out in a wide variety of fields,related to many different properties of C60 and future applications.1 Federation internationale de Football Association.


trans-polyacetylene

** n

Polyparaphenylene

** n

polythiophene

S ** n

polyparaphenylene-vinylene

*

*n

polyisothianaphthene

S ** n

polycarbazole

N

**n

polyaniline

N N

H

N N **

Hn

PCBM C60

O

O

Fig. 1.2. Chemical structure of widely used conjugated polymers

Fullerene (and derivatives of fullerenes) have an alternating single anddouble bond structure along the equator, comparable to that of conjugatedpolymers. Here the sp2 structure is not planar but arched around the cen-tre of the sphere. If the molecular orbital levels of C60 are calculated usingHuckel theory, it is found that the LUMO (t1u) has triply degenerate conduc-tion band level and the HOMO (h1u) has fivefold degenerate valence bandlevel. C60 can accept as many as 6 electrons. This makes the molecule wellsuited to act as acceptor in a photoinduced electron transfer system. Chemicalmodifications of fullerenes change or improve chemical, electrical and opti-cal properties such as solubility, colour, absorption, stability, and acceptorstrength.

1.2 Molecular Semiconductor Pictureof Conjugated Polymers

1.2.1 Molecular Structure

The distinguishing feature of all conductive polymers is the unsaturatedcarbon-based alternating single and double bond structure of the polymer


backbone, the so-called conjugated carbon chain. To simplify, the conjugatedpolymer trans-polyacetylene2 will be taken as a model here, as it has the sim-plest chemical structure of this group of materials. Its quasi-one-dimensionalstructure is held together by trigonal planar σ-orbitals between the carbonatoms in the backbone. Only three of the four valence electrons of carbonparticipate in this σ-backbone. This leaves one remaining electron per car-bon atom, which is located perpendicular to the trigonal plane in a pz orbital.All these leftover pz orbital electrons from adjacent carbons overlap to formthe π-system. This can be described as a delocalised electron cloud with a pe-riodic alternating density, which tempts one to speak about single or doublebonds.

A phase B phase

E

Fig. 1.3. Structure of two equivalent trans-polyacetylene chains

Since trans-polyacetylene has two equivalent structures (A phase and Bphase) with identical ground state energy, as depicted in Fig. 1.3, it is calleda degenerate ground state conjugated polymer, which is a specific property ofthis structure. The system of π-electrons delocalises along the carbon chainand this, together with the weak inter-chain interaction, allows us to speakabout the quasi-one-dimensional nature of polyacetylene. Theoretical calcu-lations show that, if the single and double bonds were of equal length, theπ-electron band would be half-filled with electrons due to the Pauli princi-ple and the polymer would be a metal. Peierls predicted that this cannot bethe case, because of instability of this structure against kF phonons, and thebackbone dimerises into longer single bonds and shorter double bonds [47],as depicted in Fig. 1.4. This is a spontaneous reaction and decreases the crys-talline symmetry in a way which minimises the ground state energy of theoccupied band. During this minimisation, the potential ‘string energy’ of thedimerised polymer chain is increased and this leads to an equilibrium state,where the total energy of the polymer chain is lowered. The Brillouin zone re-2 The other isomer is called cis-polyacetylene. This has a slightly different structure

with non-degenerate ground state energy.


u0

u0

a

Fig. 1.4. Polyacetylene chain before dimerisation (top) and after dimerisation (bot-tom)

duces to half of the original length and occupies the range −π/2a < k < π/2a.This change in electron density during a π → π∗ allowed transition, depictedin Fig. 1.5, is an asymmetric change in the dipole moment and a reductionin the bond strength as the electron is transferred from a bonding to anantibonding orbital.

-π/a -π/a π/aπ/a

E E

k

Fig. 1.5. Transition from metallic behaviour with half-filled π-band to a bandgapsemiconductor due to Peierls distortion

1.2.2 Optical and Electronic Properties

Su, Schrieffer and Heeger have modelled infinite trans-polyacetylene chainstheoretically (SSH model) [48,49] and originally published this work in 1979.The model is applicable to one-dimensional carbon–hydrogen compoundswith degenerate ground state energies. Electron–phonon coupling is takeninto consideration, but the electron–electron interaction is neglected. Peierls’distortion predictions explain the development of two molecular bands,namely the π-band originating from the highest occupied molecular orbital(HOMO) and the π∗-band originating from the lowest unoccupied molecular


Fig. 1.6. π → π∗ transition in ethane

orbital LUMO, with an energy gap in-between. In the SSH model, the bandgap Eg of the organic semiconductor is given by the expression

Eg = 8αu0 , (1.1)

where α symbolises the electron–phonon coupling and u0 the dimerisationdistance (see Fig. 1.4). This means that, because of the dimerisation, a tran-sition from metal to semiconductor occurs.

1.2.3 Characterisation of Excited States

When two trans-polyacetylene chains with different phases are put together,an obvious disturbance occurs in the standard conjugation pattern. The bondalternation defect that appears is known as a neutral soliton (Fig. 1.7). Thiskind of quasi-particle has an unpaired electron but is electrically neutral andis isoenergetically mobile along the polymer chain in both directions. Thissoliton gives rise to a state in the middle of the otherwise empty energy gapthat can be occupied by zero, one or two electrons (Fig. 1.8).


Neutral soliton

Fig. 1.7. Neutral soliton in trans-polyacetylene

HOMO

LUMO

+q / 0Charge / Spin 0 / ½ -q / 0

Fig. 1.8. Three types of soliton. Note the reversed spin–charge relation

If one looks at the non-degenerate case instead of the degenerate groundstate case, a slightly different picture emerges. Most conjugated polymershave non-degenerate ground states since their possible structures are notenergetically equivalent. Examples of this are the aromatic and quinoid formsof polythiophene as shown in Fig. 1.9.

Quinoid

Aromatic

S

S*

S

S

S

S* n

S

S*

S

S

S

S* n

Aromatic Quinoid

E

Fig. 1.9. The lowest ground state energy is that of the aromatic form of polythio-phene

A number of different quasi-particles, called polarons, excitons and bipo-larons are possible in non-degenerate ground state conjugated polymers. Po-larons are charged quasi-particles which induce a lattice deformation (Fig.1.10). These quasi-particles give rise to new states within the forbiddenbandgap and are observable via optical transitions with well defined ener-gies. The extra energy required to change the bond alternation and increasethe less energetically preferable quinoid structure provides the confinement


Positive polaron

Spinconfiguration

Opticaltransitions

S S

S

S

S S

Negative polaron

Spinconfiguration

Opticaltransitions

S S

S

S

S S

Fig. 1.10. Structure, spin configuration and optical transitions for the positive andnegative polarons. Note that only two transitions are optically allowed

potential that prevents the equal charges of bipolarons from separation. Onthe other hand, Coulomb interaction between the charges hinders their re-combination and the state is in equilibrium.

Excitation of the polymer creates one electron and a hole on the chain.This effect is particularly important when the electron–hole interactions arestrong. Coulomb attraction keeps them together and we consider the twoopposite charges as a bound electron–hole pair. An exciton (Fig. 1.11) isnamed according to its delocalisation. If it is localised, it is called a Frenkelexciton and, if it is delocalised, i.e., it extends over many molecular units, itis a Mott–Wannier type of exciton.

Finally, the structure and the energy diagram of bipolarons is given inFig. 1.12. Bipolarons are double charged carriers where a strong interactionwith the lattice (electron–phonon interaction) can lead to a stabilization oftwo charges despite the Coulomb repulsion. A more detailed and completediscussion of quasiparticles, their generation, their occurrence and extendedconcepts can be found in the literature [50–52].


Singletexciton

Exciton

Tripletexciton

S S

S

S

S S

Fig. 1.11. Energy diagram of singlet and triplet excitons

Spinconfiguration

Opticaltransitions

Positive bipolaron

S S

S

S

S S

Negative bipolaron

Spinconfiguration

Opticaltransitions

S S

S

S

S S

Fig. 1.12. Structure, spin configuration and optical transitions for positive andnegative bipolarons

1.2.4 Photoinduced Electron Transferin Pure Conjugated Polymers and Molecules

The initial interest in conjugated polymers originated from their ability tosupport high electrical conductivity. The withdrawal or addition of electronsleads to p- or n-type doping. The doping mechanism differs from the oneknown for inorganic crystals, where a substitution of the lattice atom takesplace. In conjugated polymers, doping occurs via a charge transfer reactionfrom the intentionally (or unintentionally) introduced counterion. In any case,


S ing le t P air Trip le t Pa ir m S

+ 1

-1

0IS C

Fig. 1.13. Energy levels of a pair of polarons in singlet and triplet states in amagnetic field. If 2J = 0, the triplet sublevel mS = 0 will degenerate with thesinglet state and can be (de-)populated via intersystem crossing

a net electric charge is introduced onto the polymer chain. [Note that theblending of conjugated polymers with a strong electron acceptor, such as thefullerene C60, can be referred to as photodoping, since charge transfer takesplace only in the excited state, i.e., under photo-excitation (see below).]

According to experimental observations, the primary photo-excitation ofconjugated polymers generates intra-chain singlet excitons. These are pairsof electrons and holes with opposite spin, bound by the Coulomb attrac-tion (see Fig. 1.13). Exciton formation is connected with a modification inthe geometry. The distorted region is distinguished by a change of the aro-matic into the quinoid form. Exciton decay occurs through radiative andnon-radiative processes. Radiative decay of excitons results in photolumines-cence (PL). The conjugated polymers described here belong to the class ofso-called non-degenerate ground state polymers, where two possible bond al-ternation resonance forms, the aromatic geometry and the quinoid geometry,are energetically unequal. The stable charged excitations are polarons andbipolarons.

The charged quasiparticles can be probed by electrical dc conductiv-ity measurements (for polarons), magnetic susceptibility (for polarons andbipolarons), electron–spin resonance (ESR) (for polarons) and optical mea-surements (for polarons and bipolarons). As ESR is well suited for studyingspin-carrying polarons, optical modification of the ESR (optically detectedmagnetic resonance ODMR) can be applied to link the emissive or absorbingproperties of the polymer with its spin state.

One of the unresolved problems in the physics of conjugated polymers isthe magnitude of the exciton binding energy. There is some controversy inthe literature over the nature of primary excitations in polymers. A compre-hensive summary on the topic can be found in the book [53], where excitonbinding energy values between 1 eV and kT are reported. According to onepoint of view, the primary excitations are free charges (electrons and holes).They give rise to the peak of the photocurrent in the first few picoseconds[54]. These charges thermalize and form polaronic excitons which recombineand emit visible light. Another point of view, based on site-selective fluo-


rescence measurements [55,56], claims that the singlet exciton is primary,and the photocurrent observed in the polymer is due to the ionisation ofexcitons. Neither experimental finding seems to be able to rule out the alter-native model. The ultrafast photocurrent peak observed might be due to adisplacement current, i.e., due to polarisation of the excitons or polaron pairs,as discussed in [57]. A theoretical estimate of the exciton binding energy inPPV based on effective mass calculations leads to the value of 0.4 eV [58].Steady state photo-conduction experiments on PPV-derivative films give thevalue 0.4 eV [59]. In their CW-photoconductivity measurements, the authorssucceeded in separating intrinsic from extrinsic photoconductivity.

Reactions that include neutral excitations in conjugated polymers arehighly intriguing. By studying the dependence of the PL on the conjugationlength of the polymer (oligomers), it was found that the PL is red-shiftedas the length of the oligomers increases, which means that the singlet exci-ton is an intra-chain exciton and fills the whole conjugation segment, 6 to 7monomers in length [60]. Once formed, a singlet exciton can be transformedinto a triplet intra-chain exciton via intersystem crossing. As we shall see laterin this chapter, the intra-chain triplet exciton, in contrast to the singlet ex-citon, is much more localised, not larger than the benzene ring in conjugatedPPV, and is less sensitive to the oligomer size. This agrees with theoreticalinvestigations performed on oligo(phenyl-vinylene) [61].

Alternatively, the singlet exciton can decay via electron transfer to theneighbouring chain, or to the next conjugated segment of the same chain.This process forms a charge-transfer (CT) inter-chain or an inter-conjugatedsegment exciton, sometimes called a polaron pair [62]. From the next neigh-bouring chain site, the movable polaron can hop to a further chain still be-longing to the pair, at least at distances not exceeding the Onsager radius.This pair is called a geminate pair to emphasise the common origin of nega-tive and positive polarons, in contrast to a non-geminate polaron pair whichis formed by charges donated by different ‘parents’. As we shall see later,the formation of geminate pairs and/or non-geminate pairs is closely relatedto the issue of singlet excitons versus free polarons. A detailed analysis ofthe (positive) sign of the spin effects in PPV shows that the population ofpolaron pairs via free polarons with non-correlated spins is less favourable.

Polaron Pair State. There are a number of experimental observationswhich can be interpreted neither by invoking charged excitations injected orphoto-generated in the polymer, nor by excitons. However, it may happenthat the singlet exciton is broken, as described above, and a pair of charges,negative P− and positive P+ polarons, are separated onto adjacent chains,but still bound by the Coulomb attraction. These pairs will be referred toas polaron pairs. Polaron pairs are intermediate states between electronicmolecular excitations and free charge carriers. They are formed by excitationof the photo-conductivity in polymers and other molecular solids, as well as


by the combination of free charge carriers of opposite sign injected into thepolymer [62–66]. The polaron pair possesses the main property of a pair, thatis, it has a recombination rate within the pair competing with dissociation.Interplay between recombination and dissociation determines the lifetime ofthe pair. In a simple monomolecular model, which is valid under Coulombinteraction, the pair can be treated as a quasi-particle with lifetime τpairobeying τ−1

pair = krec + kdiss.Polaron pairs were introduced to account for the effect of magnetic fields

on photo-conductivity [67]. Later, they were invoked to explain long-livedstates observed in photoinduced absorption [65]. Polaron pairs may thus beconsidered as a common phenomenon in semiconducting polymers. It is worthnoting at this point, however, that the status of the polaron pair as a quasi-particle leads to some disagreement both in the literature and in discussions,especially if one attempts to assign certain bands in the optical spectra topolaron pairs. However, the situation is very much different in magnetic res-onance experiments. There, recombination in pairs of spins is responsible forthe effects observed. This process involves pairs of charges (short-lived orlong-lived) purely by definition [68].

Polaron pairs can be produced by dissociation of neutral excitations (i.e.,a single exciton dissociates due to the inter-chain interaction), or they canbe independently generated under optical excitation. The formation yield ofthe intra-chain polaron pairs via dissociation of singlet excitons is estimatedat 10% [69]. In the electroluminescence regime, they are inevitably formed ascharge carriers approach each other. Since both charge carriers, the electronand the hole, are carrying the spin, there are four possible relative spin ori-entations. Two of them are ‘pure’, with both spins up or down, whilst twoothers are linear combinations of the up–down and down–up configurations.One of the four possibilities is a singlet configuration, the three others aretriplet states. In the EL regime, all of them are equally probable. It is thespin statistics that governs the formation rate of one or other spin state.Bearing in mind that only a singlet configuration will produce fluorescence,one recognises the importance of spin transformations within the pair duringits lifetime.

In the PL regime, the situation is entirely different. The singlet exciton canbe a source of charge carriers. This pair of charges will be predominantly ina singlet state. The pair is geminate. If the pair is formed from the precursorof the free charges, the final product will be the same as in the EL regimedescribed above. These pairs are non-geminate. The four possible relative spinorientations within the pair of polarons, and hence their energies, will dependon the magnetic field applied. In the absence of a magnetic field (B0 = 0),four energy levels are degenerate. In the static magnetic field (B0 �= 0),the energies will depend on the relative spin orientations of the respectivepolarons. This is shown in Fig. 1.13. In the case of distant pairs, i.e., whenthe exchange interaction 2J is negligible, the magnetic sublevel T0 (mS = 0)


possesses the same energy as the singlet state S. A particle in the state Scan pass over into T0. The energy argument alone, however, is not enoughto transform a singlet pair into a triplet. One needs magnetic interaction toturn the spin over. Such an interaction can be a hyperfine interaction (HFI)due to the magnetic moments of protons. In other words, the mixed S–T0state can be (de-)populated via intersystem crossing.

Electron back transfer is the opposite process to exciton dissociation andcan positively influence the EL intensity, provided energy requirements arefulfilled. A detailed analysis of the transformation within polaron pairs iscarried out in [70].

The ODMR experiments mentioned above show that photo-generated sin-glet excitons in conjugated polymers dissociate due to the inter-chain inter-action with the formation of polaron pairs [70]. The latter process is crucialif one considers these materials as candidates for efficient light emitters. Inthe reverse application of the OLED as a photodetector, charge transfer willplay a constructive role. For an efficient photodetector, charge generation inundoped conjugated polymers is too low and must be significantly enhanced.Photo-generation of charges can be stimulated by adding a strong acceptorfor charge carriers to the polymer. This effect was discovered in conjugatedpolymer–fullerene composites [8,71]. The fullerene C60 is electronegative andits LUMO lies below the LUMO of PPV, as shown schematically in Fig. 1.14.

VB

CB

HOMO

LUMO

S

S

S

S

S* *n

Energy

Fig. 1.14. Schematic energy diagram for a photoinduced electron transfer betweena conjugated polymer and buckminsterfullerene C60


1.2.5 Photoinduced Electron Transferin Donor–Acceptor Systems

Interdisciplinary research on charge transfer processes has been going on fora long time. The general outline of an intra- or intermolecular photoinducedelectron transfer in a donor–acceptor composite can be divided into steps fora clearer understanding [72]. Here the letters D and A denote charge donorand acceptor, respectively, and 1 and 3 indicate whether the excited state isa singlet or triplet.

Initial step D + A −→ 1,3D∗ +A excitation on D

Second step 1,3D∗ + A −→ 1,3(D–A)∗ excitation delocalisationon D–A complex

Third step 1,3(D–A)∗ −→ 1,3(Dδ+–Aδ−)∗ initiation of chargetransfer

Fourth step 1,3(Dδ+–Aδ−)∗ −→ 1,3(D+•–A−•) formation of an ionradical pair

Final step 1,3(D+•–A−•) −→ D+• +A−• charge separation

At each intermediate step, the process can relax back to the ground state byreleasing energy in the form of emitted radiation or heat. In step 3, the symbolδ is introduced. It denotes the fraction of charge transferred, continuously inthe range between 0 < δ ≤ 1, where δ = 1 is the state where the wholeelectron has been transferred. For the formation of the ion radical pair instep 4, certain conditions must be fulfilled:

ID∗ − AA − UC < 0 . (1.2)

These conditions concern the ionisation potential ID∗ of the excited stateof the donor, the electron affinity AA of the acceptor, and the attractiveCoulomb force of the separated radicals UC, including polarisation effects.In the case of charge transfer from a polymer to a neighbouring acceptormolecule, a stabilisation of the photoinduced charge separation (final step) ispossible through carrier delocalisation on the cation radicals D+• (polarons)along the polymer chain and a structural relaxation of the anion radicalsA−•. The requirements from (1.2) are summarised in a schematic drawing ofthe energy levels of a conjugated polymer/fullerene couple (Fig. 1.14).

After a photon has excited the conjugated polymer to form an exciton,the C60 accepts one electron due to its high electron affinity and establishesthe anion C−

60. What is left on the polymer chain is a cation radical, i.e., apositive polaron, as depicted in Fig. 1.14, which is a mobile charge carrierthat can move along the polymer backbone. This transfer is an exothermalreaction, where energy from the system is released.

In many cases it will be seen, that the simple five-step scheme given aboveis not sufficient to describe more complex systems, i.e., donor–acceptor cou-ples in solution or covalently linked donor–acceptor couples. More sophisti-


cated and realistic models for electron transfer reactions will be discussedlater in this chapter.

Photoinduced electron transfer in organic molecules is an intensively in-vestigated topic in physics, chemistry and biology, through a fundamentalinterest in the photophysics of excited states and also in order to provide asynthetic approach to a deeper understanding of solar energy conversion ingreen plants. The discovery of a very efficient photoinduced electron transferfrom conjugated polymers to Buckminsterfullerene (C60) [8] opened up vari-ous new aspects with potential applications to photovoltaics, non-linear opticsand artificial photosynthesis. While in such composites the forward electrontransfer time is remarkably fast, back transfer is seriously hindered, result-ing in metastable charge separated states with lifetimes on the μs timescaleas already mentioned. Thus, in this system, the stabilisation of radical ionsis intrinsic in comparison to natural photosynthesis, where electron transfercascades cause the spatial separation and stabilisation of photoexcited rad-icals. The early stages of the photoinduced electron transfer process will bediscussed below [73–78].

1.3 Detection of Charges in Conjugated Polymers

1.3.1 Pump–Probe Spectroscopy

A powerful method for monitoring the generation of charges is pump–probespectroscopy (photoinduced absorption spectroscopy). This type of spec-troscopy uses a pump beam to excite the semiconductor, while the probebeam monitors the excited state. Depending on the pump and probe sources(i.e., the pulse length of the laser and the photon density of the probe beam),this technique can work with time resolutions between 10 fs and > 10 s,thereby allowing one to observe processes with very different kinetics, suchas the generation and recombination of photoinduced charges. A general out-line of an experimental setup for the ms time range is sketched in Fig. 1.15.The ms time resolution is created by modulating the laser beam with a me-chanical chopper.

In order to obtain quantitative results, pump–probe spectra have to becorrected for the optical density of the sample following the Lambert–Beerlaw of absorption. The correction can be performed in the following way:

corr PIA =PIA

A(λexc), A(λexc) =

Iabs

I0= 1 − T (λexc) ,

T (λexc) = 10−OD(λexc) . (1.3)

The optical density OD at the excitation wavelength λexc is the product of theabsorption coefficient α and the film thickness z. Combining the above three


PC

UV/Vis - IR-

Vacuum pumps

Detector

Cryostat

lq N2

Chopper

Ar+ laser

Optical fibre

Fig. 1.15. Pump–probe setup for the ms regime

expressions yields the correction term for a pump–probe spectrum (photoin-duced spectrum PIA):

corr PIA =PIA

1 − 10−OD(λexc). (1.4)

Furthermore, it is important to know the relation between the fractionalchange in transmission −ΔT/T and the changes in probe absorption. It canbe approximated in the following way. Neglecting reflection and scattering bythe sample and assuming that both the incident probe light and the pumplight are radiated along the z axis, the light intensity I is given by

I(z) = I0e−αz . (1.5)

If the absorption depth L within the sample decreases exponentially accordingto the Lambert–Beer law, the density of populated excited states N(z) obeys

N(z) = N0e−L−1z . (1.6)

The fraction of absorbed probe photons in an infinitesimal thickness dz isestimated by

dI

I(z) =

[−αz − σN0e−L−1z

]dz , (1.7)

where σ is the absorption cross-section of the excited species for the probebeam. This gives the logarithm of the transmission of the probe beam throughthe sample after integration over the whole sample depth (0 → D):

lnT = lnID

I0= −

∫ D

0

[αz + σN0e−L−1z

]dz . (1.8)


The change in transmission of the probe due to the pump source, consideringonly the normalised fraction, is given by

T − T0

T=

ΔT

T= exp

[−σN0L

(1 − e−L−1D

)]− 1 . (1.9)

This expression can be analysed in two ways depending on the nature of thesample. In the case of a thin film [in comparison with the absorption depthof the pump light (D � L)], and small transmission changes (σN0D � 1),the following is valid:

−ΔT

T≈ (σN0)D (D � L) . (1.10)

In the case of a thick film [in comparison with the absorption depth of thepump source (D � L)], the change in transmission remains small and wefind

−ΔT

T≈ (σN0)L (D � L) . (1.11)

It is interesting to note that the quantum efficiency for a photoinduced processlike charge carrier generation can be estimated from (1.10) and (1.11) if theabsorption cross-section of the generated species is known.

Generally there are two different methods for measuring excited statespectra in the ms time regime. Typically, IR PIA spectra are not recordedwith the lock-in technique but by referencing several hundred accumulatedsingle beam spectra (by FTIR spectrometer) under illumination and in thedark, while UV/VIS PIA uses a lock-in detector to filter out signal changesdue to photoexcitation.

The IR PIA and the UV/VIS PIA are therefore usually recorded ondifferent time scales, which demands more discussion. The measurement ofphotoinduced absorption with the lock-in technique described above is verysensitive to photoexcitation lifetimes. Photoexcitations with lifetime τ con-siderably longer than the inverse of the chopping frequency 1/ω contributeto the PIA response with 1/τ , while photoexcitations with lifetime shorterthan 1/ω contribute with τ . For photoinduced absorption measurements inthe IR with the accumulation technique as described above, all photoexci-tations contribute in proportion to their lifetime. This results typically ina difference in the intensity of the spectra if recorded using different tech-niques. One has therefore to be very careful in the calculation of the numberof photoinduced charges (i.e., the quantum efficiency for photoinduced chargegeneration) from PIA techniques in the ms time regime, which is only correctfor conditions far from the steady state. The quantum efficiency for photo-generation of long-lived charge carriers can be derived from measurements atvery low light intensity or far from the steady state, so that ωτ � 2π [79].In these cases the number of photogenerated carriers will be proportional tothe photogeneration quantum yield. Basically one can conclude, that PIA


spectroscopy in the ms regime is only sensitive to long-lived carriers andconsequently dominated by trapped carriers.

Depending on the kinetics of the excited state, the changes in ΔT as afunction of the pump beam intensity I, when fitted to a power law equation−ΔT ∝ Ip, are indicative of the recombination mechanism of the species.For values of p close to unity, monomolecular decay of the excited species isassumed, whilst for p ≈ 0.5, a bimolecular decay mechanism is supposed. Ex-cited state lifetimes can be determined by fitting the changes in transmissionas a function of the modulation frequency ω to either the expression (1.12)for monomolecular decay or (1.13) for bimolecular decay [108]:

−ΔT ∝ Igτm√1 + ω2τ2

m

, (1.12)

−ΔT ∝√

Ig

β

α tanhα

α + tanhα. (1.13)

Here τm is the lifetime for monomolecular decay and g the efficiency of gen-eration of the photoinduced species. The bimolecular decay constant β de-termines the intensity of the PIA signal via (1.13), where α = π/ωτb andτb = (gIβ)−0.5, the bimolecular lifetime under steady-state conditions. It isimportant to note that the bimolecular lifetime τb depends on experimentalconditions such as concentration and pump beam intensity.

1.3.2 Application of Pump–Probe Spectroscopy in the ms Rangeto Conjugated Polymer/Fullerene Blends

The potential of the CW–PIA method is demonstrated by following thecharge generation in the prototype conjugate polymer MDMO–PPV uponmixing with a fullerene (Fig. 1.16). For pristine MDMO–PPV (as for mostconjugated polymers) the quantum efficiency for charge generation is ratherlow (below 1%). Luminescence is strong and can exceed 30% quantum effi-ciency in solution. The excited state spectrum of pristine MDMO–PPV showsa single broad absorption feature centred at 1.3 eV, which is typically inter-preted as triplet–triplet absorption. The lifetime of this triplet state is of theorder of 100 μs at 100 K.

Upon addition of methanofullerene the excited state absorption changesdramatically, resulting in two closely spaced bands at 1.23 and 1.35 eV fol-lowed by a plateau up to 2.1 eV. Additionally, the photoluminescence ofthe polymer is quenched by nearly three orders of magnitude. The occur-rence of luminescence quenching can be explained by various mechanisms.The excited singlet state can also relax to the ground state by non-radiativeprocesses (thermal heating), such as energy transfer by electron transfer pro-cesses. In the case of conjugated polymer/fullerene blends, electron transfer isso fast (as will be shown below) that the other mechanisms are not relevant.


1,2 1,4 1,6 1,8 2,0-2x10-4

0

2x10-4

4x10-4

6x10-4

8x10-4

(a)

-ΔT

/T

Photon Energy (eV)

1,2 1,4 1,6 1,8 2,0

0

2x10-4

4x10-4

6x10-4

(b)

-ΔT

/T

Photon energy (eV)

Fig. 1.16. PIA spectrum of MDMO–PPV (a) with and (b) without fullerenes.Spectra are taken at T = 100 K and with a time resolution of 8 ms

Consequently, the excited state absorption pattern of the polymer/fullereneblend mirrors the absorption of the photoinduced charge carriers, as outlinedin the introduction.

The peak between 1.2 and 1.4 eV is attributed to the higher energy po-laron transition. The bandgap of the semiconductor is identified by the changein sign of the measurement signal. The plateau close to the bandgap cannot beexplained in the classical polaron picture. It has been suggested that chargedcarriers delocalised over two or more polymeric chains might originate in thisabsorption feature [80,81].

Observation of the charged carrier is even more favourable in the IRregime (photoinduced IRAV studies). In semiconducting, conjugated poly-mers, the quasi-one-dimensional electronic structure has to be strongly cou-pled to the chemical (geometrical) structure. As a result, nonlinear excita-tions (solitons, polarons and polaron pairs) are dressed with local structural


distortions creating states at energies within the forbidden π–π∗ gap. ‘New’vibrational infrared absorption bands with large intensities (IRAV modes) areinduced by doping and/or photoexcitation. Solitons and polarons are charged‘defects’ which break the local symmetry and therefore make Raman modesinfrared active.

IRAV doping studies of P3OT [82,83] show significant differences in theIRAV bands depending on the doping mechanism (i.e., chemical, electro-chemical, photodoping). In the theoretical framework of the model presentedby Zerbi et al. [84], the IRAV bands correspond to totally symmetric Ramanactive vibrational Ag modes, which couple to the π-electron system alonga so-called effective conjugation coordinate. The charge distribution in theformed polaronic or bipolaronic state causes high dipole moment changes dur-ing vibration, thereby breaking the symmetry. In general, in the frequencyrange between 1600 and 800 cm−1, four Ag modes exist in polythiophene,for instance. In unsubstituted polythiophenes, these give rise to a patternof three strong bands in the photoinduced absorption spectrum [85] and inthe doping-induced absorption spectrum [86], as well as to three main Ra-man bands. A link [87] is established between the doping-induced electronicstate within the semiconducting π–π∗ energy gap and the IRAV bands of thedoping-induced infrared spectrum, based on a linear response theory [88].Figure 1.17 shows the pump–probe spectra for polythiophene in the energyrange representative of the IRAV absorption bands and the lower polaronabsorption band compared with the linear absorption spectra taken frompolythiophenes doped using various methods.

1.4 Kinetics of Photoinduced Charge Generationin Conjugated Polymer/Fullerene Blends

In order to learn about the true quantum efficiency of photogeneration onetherefore has to study the photoinduced charge generation mechanism atfaster time scales. Pump–probe spectroscopy utilising a few optical-cycle laserpulses (5–6 fs) in the visible spectral range with broadband frequency conver-sion techniques [89] now makes it possible to study extremely fast optically-initiated events with unprecedented time resolution. Such a setup was usedto time-resolve the kinetics of the charge transfer process from a polymerchain to a fullerene moiety in thin films of poly[2-methoxy, 5-(3′,7′-dimethyl-octyloxy)]-p-phenylene vinylene (MDMO–PPV) and [6,6]-phenyl C61 butyricacid methyl ester (PCBM). Solutions prepared from 1 wt% solutions oftoluene on thin quartz substrates were studied.

Experiments were performed using a visible optical parametric ampli-fier based on noncollinear phase-matching in β-barium borate, followed bya pulse compressor using chirped dielectric mirrors. This optical source pro-vides ultrabroadband pulses, with bandwidth extending from 500 to 720 nm,compressed to an almost transform-limited duration of 5–6 fs. The pump–


1000 2000 3000 4000 5000 6000

Chem (ultraweak) Chem (weak) Chem (strong) Photo ElectroChem (weak) ElectroChem (strong)

resc

aled

spe

ctra

[a. u

.]

energy [cm-1]

Fig. 1.17. Comparison of doping-induced absorption for P30T over an extendedenergy range. Doping was achieved (i) chemically via exposure to iodine vapour forthree different exposure times, (ii) by (pump–probe) photoexcitation, (iii) electro-chemically for two current exposure times

probe setup is based on a standard noncollinear configuration and differentialtransmission ΔT/T is measured using two different techniques:

• time-resolved measurements at a specific wavelength are obtained byspectrally filtering the probe pulse (after passing through the sample)and combining differential detection with lock-in amplification;

• ΔT/T measurements over the entire pulse bandwidth are performed usingan optical multichannel analyser. In all measurements, the maximumsignal is a few percent and linearity is verified to avoid saturation effects.

All experiments are carried out at room temperature.The excited state pattern of a conjugated polymer/fullerene composite

is shown in Fig. 1.16. First, the dynamics of pure MDMO–PPV excited bya sub-10-fs pulse is compared with the dynamics of MDMO–PPV/PCBM


500 550 600 650 700

(a)

Abs

orp

tion,

ΔT

/T

Wavelength (nm)

500 550 600 650 700

(b)

~

~~

~

0.5%

15

32

66

100

132

200

cw

dela

y (f

s)

ΔT/T

Wavelength (nm)

Fig. 1.18. Spectrally resolved pump–probe spectrum of pristine MDMO–PPV com-pared to highly fullerene-loaded MDMO–PPV/PCBM composites at various de-lay times. (a) Absorption spectrum of a pure MDMO–PPV film (solid line) andΔT/T spectrum at 200 fs pump–probe delay (dashed line). (b) ΔT/T spectra of theMDMO–PPV/PCBM blend (1:3 wt. ratio) at various time delays following reso-nant photoexcitation by a sub-10-fs optical pulse. The CW PA of the blend (�) wasmeasured at 80 K and 10−5 mbar. Excitation was provided by the 488 nm line ofan argon ion laser, chopped at 273 Hz

composites. Figure 1.18a shows the absorption spectrum of MDMO–PPV(solid line) and the ΔT/T spectrum at 200 fs pump–probe delay (dashed line).In agreement with previous results [90], the ΔT/T signal can be attributedto a superposition of photobleaching (PB) of the ground state absorptionand stimulated emission (SE) from the photoexcited state. SE dominates forprobe wavelengths longer than 600 nm, for which the ground state absorptionvanishes. The shape of the ΔT/T spectrum of pure MDMO–PPV does notshow any major evolution in the first few picoseconds from photoexcitation,apart from an overall decay.

By adding PCBM to the polymer matrix, the excited state evolution sce-nario changes dramatically. Figure 1.18b shows a sequence of ΔT/T spectrafor MDMO–PPV/PCBM composites excited by a sub-10-fs pulse. At earlytime delays (see the 15 fs and 33 fs data) the spectrum closely resemblesthat of pure MDMO–PPV, confirming the predominant excitation of thismolecule. The SE band from MDMO–PPV rapidly gives way to a photoin-duced absorption (PA) feature, the formation of which is completed within


about 100 fs. After this initial, fast evolution, the ΔT/T spectrum remainsstationary on the timescale of the experiment (40 ps). This PA feature isassigned to the PPV cation radical (positive polaron) by comparison to thenear-steady state ΔT/T spectrum of a MDMO–PPV/PCBM composite plot-ted as black squares. This band provides a direct signature for the chargetransfer process.

0 100 200 300 400 500 600

1200 1400 1600

457 nm

1064 nm

FT of ΔT/T

Intensity

[a.u.]

Energy [cm-1]

610 nm

ΔT

/T [

a. u

.]

Time [fs]

Fig. 1.19. Quenching of the coherent vibrational oscillations of MDMO–PPV uponphotoinduced charge transfer. The ΔT/T dynamics for pure MDMO–PPV (contin-uous line) and for MDMO–PPV/PCBM (1:3 wt. ratio) (dashed line), excited by asub-10-fs pulse, was recorded at the probe wavelength of 610 nm. The inset showsthe Fourier transform of the oscillatory component of the MDMO–PPV signal, thenonresonant Raman spectrum of MDMO–PPV (excitation 1064 nm) and the res-onant Raman spectrum of an MDMO–PPV/PCBM sample (excitation 457 nm).For the resonant Raman spectrum of MDMO–PPV, it was necessary to quench thestrong background luminescence by adding PCBM

In Fig. 1.19, the excited state dynamics of pure MDMO–PPV at a probewavelength of 610 nm is plotted as a continuous line. The features at negativeand near-zero delays at this and other wavelengths are due to coherent cou-pling and pump-perturbed free induction decay [91]. The rise time of the SEsignal was found to be independent of the probe wavelength in a broad wave-length range (560–680 nm) and is assigned to vibronic relaxation (Kasha’srule). The strong oscillations superimposed on the signal probe the motionof the vibrational wavepacket launched by the ultrashort pump pulse on the


multidimensional excited state potential energy surface [92]. Ultrashort pulsescoherently excite vibrational motion both in the ground and excited statesof a molecule: in our case, in the SE region, the excited state contribution isexpected to be dominant.

Additional experiments were performed using a chirped excitation pulse[93], which confirmed that the oscillatory component of the signal is composedof a ground state and an excited state contribution, whereas the weights ofthe two contributions depend on the probe wavelengths. The inset in Fig.1.19 shows the Fourier transform of the oscillatory component of the signalas compared to the resonant and non-resonant Raman spectrum of the poly-mer. The correspondence between the excited state frequencies measured inthe pump–probe experiment and the ground state frequencies measured byCW Raman scattering indicates that no major geometrical rearrangement istaking place following photoexcitation. This observation supports the nowwidely accepted assumption that primary photoexcitations in MDMO–PPVare spatially localised and of molecular (excitonic) character.

The dynamics of the charge transfer process can be determined more ac-curately by ΔT/T measurements at a fixed probe wavelength as a function ofpump–probe delay. Figures 1.19 and 1.20 show the dynamics of the blend atdifferent probe wavelengths compared to those of the pure polymer. A fastrise to positive values of ΔT/T , due to SE from the polymer, is immediatelyfollowed by a fast decay until the signal stabilises on negative ΔT/T , indi-cating the PA of the charge transferred state. Probing at around 700 nm,where the polymer shows negligible SE, the ΔT/T signal goes directly tonegative values. These data substantially confirm the results of the spectralmeasurements (Fig. 1.18b), proving the rapid formation of the MDMO–PPVcharged state, which is completed within about 100 fs after excitation. By anexponential fitting of the PA rise, a time constant for the electron transferprocess of 45 ± 3 fs can be calculated.

Experiments carried out on various blends with MDMO–PPV:PCBMweight ratios ranging from 1:3 to 1:0.5 all displayed the same ultrafast electrontransfer process, with a dynamics which was found to be almost independentof concentration. For much lower PCBM concentrations (weight ratios lowerthan 1:0.05), the formation time of the PA band increases to a few ps andthe formation rate becomes a linear function of PCBM concentration. Thisindicates that, as previously observed [94], at low acceptor concentrationswe enter a new regime in which the charge transfer process is mediated bydisorder-induced diffusion of the excitations, which migrate until they reacha site favourable for charge transfer.


0 200 400 600

580 nm

700 nm

τ = 39 fs

τ = 45 fs

ΔT/T

[a.

u.]

Time [fs]

Fig. 1.20. Time resolution of photoinduced charge transfer in MDMO–PPV/PCBM composites. ΔT/T dynamics for pure MDMO–PPV (continuous line)and MDMO–PPV/PCBM (�) at probe wavelengths of 580 nm and 700 nm. Dottedlines are single exponential fits to the PA of the composites

1.5 Light-Induced Electron-Spin Resonance Detectionof the Charge Transfer Process

ESR is a proven technique for detecting intrinsic or extrinsic paramagneticcentres in semiconductors and insulators. For a detailed description, see [95].In a conventional resonance experiment, the sample is placed inside a mi-crowave cavity and the magnetic component of the microwave field B1 isnormal to the external static magnetic field B0 provided by an electromag-net. ESR is concerned with magnetically induced splitting of electronic spinstates. When the microwave energy equals the separation between Zeemanlevels of the paramagnetic species (ions, radicals, electrons/holes, defects,etc.), resonant absorption of the microwave power occurs (if the transitionsatisfies the appropriate selection rules) and can be measured by a sensitivedetector. ESR transitions obey the following condition (for spin S = 1/2):

hνμω = gμBB0 ,

where νμω is the microwave frequency, B0 the static magnetic field strength,μB the Bohr magneton, h Planck’s constant, and g the spectroscopic splitting


factor. For a free electron, we have g = 2.0023. When hνμω matches thevalue of the Zeeman splitting between magnetic sublevels, the energy of themicrowave field will be absorbed by the paramagnetic defect in the sample.The presence of paramagnetic centres can be established in this way.

Light-induced ESR (LESR) can only detect those spins that are generatedby optical excitation of the sample investigated. The LESR experimentalprocedure consists of a comparison between two measurements:

• ESR in a non-illuminated sample (dark ESR),• ESR in an illuminated sample (light-on ESR).

In conjugated polymers, we also perform a third measurement:

• ESR after switching-off the excitation (light-off signal), for the case ofphoto-degradation or photo-oxidation of the sample.

The main deliverables of ESR (and LESR) are:

1. the g-factor of the paramagnetic centre,2. the spin state (doublet, triplet, or even higher multiplets),3. the symmetry of the magnetic environment,4. the number of spins,

and, by taking the above information into account, detailed information canbe obtained on intrinsic/extrinsic paramagnetic defects.

No ‘dark’ ESR signals have been found in films of pure MDMO–PPV or inPCBM. Instead, a strong light-induced ESR signal was observed, as shownin Fig. 1.21a. The main observation here is the formation of two indepen-dent paramagnetic species (both S = 1/2) with slightly different g-factorsg = hνμω/μBB0: g1 = 2.0025 and g2 = 1.9995. The deviation of the g-factorsof radicals in the conjugated π-electron systems from the free-electron valueof 2.0023 is due to a non-compensated orbital moment, which induces anadditional magnetic field. The latter is due to the transfer of the unpairedelectron from the σC–C orbital to the first excited state, i.e., the π∗-orbital,as discussed in [96]. Being a material constant, the g-factor allowed us toidentify the signals as a positive polaron on the polymer chain (g > 2) andan electron accepted by the fullerene (g < 2). The small g-factor differencefor both photo-generated species means that one cannot study them sepa-rately due to a strong overlap of the ESR signals. (The overlap does indeedinvolve some uncertainty in the interpretation of the signal as a superpo-sition of two signals.) Those LESR signals, however, were found to have adifferent microwave power saturation behaviour due to different spin-latticerelaxation times T1. At the highest available microwave power, one can al-most suppress the positive polaron signal. In contrast, the intensity of the‘electron on the fullerene’ signal goes to zero at very low power. We were thusable to determine the individual g-factors.

Another finding is the persistent character of both photo-generatedspecies. After switching off the exciting light, the number of spins decreases,


2,010 2,005 2,000 1,995 1,990

20mW

200mW

20μW

g -fac tor

LES

R in

tens

ity [a

.u.]

a )

Fig. 1.21. (a) Light-induced ESR intensity as a function of the g-factor in anMDMO–PPV/PCBM blend. νμω = 9.5 GHz, T = 100 K, λexc = 488 nm, Pμω =20 μW, 20 mW, and 200 mW. (b) A doubly integrated LESR signal of the promptcontribution as a function of the excitation power dependence. Squares correspondto the positive polaron signal and circles to C−

60

but does not vanish. The dependence of the LESR intensity on the excitationintensity dependence revealed the bimolecular recombination mechanisms forthe ‘prompt’ charges, as shown in Fig. 1.21b. (The value of the double integralis related to the number of spins in the sample.) The number of persistent(long-lived) carriers in the sample was found to be independent of the lightintensity to which the sample was exposed previously (not shown here). Theexistence of persistent charge carriers is an important issue from the stand-point of photovoltaic applications of these blends.

There is another way to separate the overlapping signals, i.e., to workat higher magnetic fields. This follows from the resonance condition hνμω =gμBB0 and implies, at the same time, the use of a higher microwave fre-


1,994 1,996 1,998 2,000 2,002 2,004 2,006

C60

.-

P+

gx = 2.0003

gz = 1.9982

g// = 2.00345

g| = 2.00245g

y = 2.00015

LE

SR

inte

nsity

[a

.u.]

g-factor

Fig. 1.22. High-field LESR in an MDMO–PPV/PCBM blend. νμω = 95 Hz, T =100 K, λexc = 448 nm, Pμω = 10 mW

quency. We carried out the experiments at approximately ten times highermagnetic fields and ten times higher microwave frequency, i.e., 95 GHz in-stead of 9.5 GHz. Figure 1.22 shows LESR spectra measured at a microwavefrequency of 95 GHz. Two groups of lines, one from positive polarons onthe polymer chain and the second group from an electron on the fullerenemolecule can be clearly seen. The highly improved resolution of the 95 GHzLESR allows one not only to separate the signals and precisely determine theirsplitting factors (g-factors), but also to reveal a previously hidden structurewithin each group of lines. From the analysis of the line shape, we obtainedinformation about the symmetry of the photo-generated species. The positivepolaron on the polymer chain has an axial symmetry with the values of theg-tensor g1 = 2.00345 and g2 = 2.00245. The C60 radical anion has a lower,rhombic symmetry with the values gx = 2.0003, gy = 2.00015, gz = 1.9982.

Figures 1.23a and b illustrate computer simulated ESR spectra of posi-tive polaron P+ and C−

60 signals in two frequency ranges, (a) 9.5 GHz and(b) 95 GHz with identical components of the g-tensors, line width and am-plitudes. The signals that overlap at 9.5 GHz can be clearly separated at95 GHz, and coincide with the experimental ones in one important aspect:the g-anisotropy can be clearly resolved.

1.6 Oligo-Phenylene Vinylene: A Model Systemfor Donor–Acceptor Interactions

In the previous section an attempt was made to explain the occurrence ofsuch efficient charge transfer by the outstandingly fast kinetics of this pro-cess. However, it is clear that intimate mixing and close contact of the p-


1,9965 1,9980 1,9995 2,0010 2,0025 2,0040

b)

95GHz

g|| =2.00345g_|_=2.00245

gX=2.0003gY=2.00015gZ=1.9982

ES

R in

ten

sity

g-factor

1,98 1,99 2,00 2,01 2,02

a)

9.5GHz

g|| =2.00345g_|_=2.00245

gX=2.0003gY=2.00015gZ=1.9982

ES

R in

ten

sity

g-factor

Fig. 1.23. ESR spectra simulation for (a) 9.5 GHz and (b) 95 GHz frequencyranges. Parameters of g-tensors and line width are identical

type (MDMO–PPV) semiconductor with the n-type semiconductor (PCBM)phase are prerequisites for the fast kinetics of the charge transfer. In the caseof demixing or phase separation, the charge transfer kinetics would be limitedby diffusion of the exciton to a proper charge transfer site.

In order to overcome the problems with morphology and the compatibil-ity between two phases, the concept of covalently linked p-type and n-typesemiconductors was taken into consideration. In this concept, an electronacceptor (n-type) is chemically attached close enough to an electron donor(p-type) to guarantee charge transfer reactions. The rapid advancement infunctional chemistry allows for instance the covalent functionalization of n-type fullerenes with p-type PPVs. A model class of such materials are con-jugated oligomers with a well defined size covalently linked to fullerenes [97].Such C60-based donor–acceptor dyads have mainly been synthesised and in-vestigated to gain insight into intramolecular photophysical processes, suchas energy and electron transfer reactions [98]. Further, these dyads can serveas model compounds for true ambipolar semiconductors and are thus inter-esting as materials for bulk heterojunction photovoltaic cells [99,103]. Apartfrom being well-defined model systems for photophysical characterisation,the covalent linkage between donor and acceptor in these molecular dyadsprovides a simple method for achieving dimensional control over the phasesegregation in D–A networks.

In this section the aim is to discuss the photophysical properties of a ho-mologous series of well-defined donor-C60 dyad molecules with a π-conjugatedoligo(p-phenylene vinylene) as the donor moiety (OPVn–C60, n = 1–4, wheren is the number of phenyl rings, Fig. 1.24)3 as model compounds for ambipo-lar semiconductors with a high yield for photoinduced charge generation.General concepts of charge transfer theories will then be outlined.3 It is instructive to point out that while OPV1–C60 is the smallest member of the

homologous series of OPVn–C60 dyads, it lacks a vinylene bond and is thereforeformally not an oligo(p-phenylene vinylene)–C60 derivative.


OPV1-C60: m = 0OPV2-C60: m = 1OPV3-C60: m = 2OPV4-C60: m = 3

OO

OO

N

m

MP-C60

m

OO

OO

N

OPV2: m = 1OPV3: m = 2OPV4: m = 3

Fig. 1.24. Structure of OPVn–C60 dyads and OPVn and MP–C60 model com-pounds

Interestingly, it will be demonstrated that both energy and electron trans-fer reactions occur in solution on short timescales depending on the conjuga-tion length of the oligomer and the polarity of the solvent. In apolar solvents,energy transfer is observed, while in more polar solvents a photoinduced elec-tron transfer occurs for n = 3 and 4, and to some extent for n = 2. Fromfluorescence spectroscopy it is inferred that the electron transfer in polarsolvents is likely to be preceded by energy transfer, and hence occurs in atwo-step process. The discrimination between energy and electron transfer issemi-quantitatively accounted for by the Weller equation for photoinducedcharge separation [104]. In thin solid films, photoinduced electron transfer isobserved for the two longest systems, i.e., OPV3–C60 and OPV4–C60. Usingthe latter as the single photoactive material, a working photovoltaic cell canbe demonstrated. An excellent introduction to the photoexcitation patternsof organic molecules can be found in [105].

Ground State Absorption Spectra. The linear absorption spectra ofOPVn–C60 dyads in dilute chloroform solution (Fig. 1.25) closely corre-spond to a superposition of the spectra of individual donor and acceptor.Very similar spectra were recorded in other solvents, such as toluene ando-dichlorobenzene (ODCB). Hence, the covalently-linked fullerene and OPVmoieties retain the electronic properties of the separate molecules, and chargetransfer in the ground state does not occur. For all dyads the spectra exhibitstrong absorptions between 200 and 350 nm and a weak absorption at about703 nm (Fig. 1.25 inset), characteristic for fulleropyrrolidines. For OPV2–C60,OPV3–C60, and OPV4–C60 distinct absorptions are observed at 360, 412 and438 nm, respectively. These positions are similar to the absorption maximafound in dilute chloroform solutions of OPV2 (357 nm), OPV3 (406 nm),and OPV4 (436 nm), respectively, and are ascribed to the π–π∗ transition ofthe OPVn moieties. The UV/VIS spectra demonstrate that it is possible toexcite the fullerene moiety selectively at 528 nm (one of the lines available


300 400 500 600 700 800

0.0

0.5

1.0

1.5

OPV1-C60 OPV2-C60 OPV3-C60 OPV4-C60

Abs

orba

nce

/ O.D

.

Wavelength / nm

600 700 800

0.00

0.01

0.02

Fig. 1.25. UV/VIS spectra of donor–acceptor OPVn–C60 dyads (1.8 × 10−5 M) inchloroform

from the Ar ion laser), since the OPVn moieties do not absorb at this wave-length. Due to the low absorption coefficient of the fulleropyrrolidine in the440–470 nm region, the OPV4 moiety, and to some extent the OPV3 moiety,can be excited selectively with light at 458 nm. It is not possible to selectivelyexcite either the OPV2 or OPV1 segments without concomitant excitationof the fullerene moiety.

Electrochemistry. The cyclic voltammograms of OPVn–C60 (n = 1 to4) exhibit one to three quasi-reversible one-electron oxidation waves fromthe OPVn moiety and one reduction wave from the pyrrolidine-bridged-C60moiety. While the first oxidation potential decreases with increasing n, thereduction potential remains constant at −0.70 V vs. SCE. The half-wave po-tentials for the first oxidation and reduction waves of the OPVn–C60 dyads,OPVns and MP–C60 are collected in Table 1.1. The oxidation potentials ofthe OPVn–C60 dyads are shifted to slightly higher potentials in comparisonwith the dimethyl-substituted OPVn oligomers. This shift is tentatively as-cribed to the different influence of an electron-withdrawing fullerene moietycompared to that of an electron-donating methyl group.Before describing the photoexcitations of the OPVn–C60 dyads and theOPVn/MP–C60 mixtures in solution, the photophysical properties of theindividual reference compounds (OPVn and MP–C60) are briefly discussed.

Photoexcitation of OPVn in Solution. The photoexcitations of oligo(p-phenylene vinylene)s (OPVns, n = 2–7) [106] can be summarised as follows.The singlet excited state OPVn(S1) decays radiatively or non-radiatively tothe ground state and via intersystem crossing to the OPVn(T1) triplet state.The singlet excited state lifetimes τ have been determined for OPV3 (τ =


Table 1.1. Redox potentials of OPVn–C60, OPVn and MP–C60 V vs. SCE, asdetermined in dichloromethane

Compound E0red [V] E0

ox1 [V]

OPV1–C60 −0.70 1.19OPV2–C60 −0.70 0.97OPV3–C60 −0.70 0.85OPV4–C60 −0.70 0.77OPV2 0.90OPV3 0.80OPV4 0.75MP–C60 −0.70

1.70 ns) and OPV4 (τ = 1.32 ns) in toluene solution at room temperatureand there is no significant dependence of τ on the nature of the solvent [106].The CW-modulated photoinduced absorption (PIA) spectra of OPV3 andOPV4 under matrix-isolated conditions in 2-methyltetrahydrofuran at 100 Kexhibit a Tn ← T1 transition at 2.00 and 2.27 eV for OPV3 and at 1.80 eVfor OPV4 with triplet excited state lifetimes of 7.9 and 3.6 ms, respectively[106]. The intensity of the Tn ← T1 absorption increases linearly with thepump intensity, consistent with a monomolecular decay mechanism [106].

Photoexcitation of MP–C60 in Solution. The photoexcitation of MP–C60 in toluene or ODCB results in weak fluorescence at 1.74 eV and a long-lived triplet excited state. The fluorescence quantum yield in toluene is knownto be 6 × 10−4 [107]. Singlet excited state lifetimes of 1.45 ns [103] and1.28 ns [107] have been reported for toluene solutions. The quantum yieldfor intersystem crossing from MP–C60(S1) to MP–C60(T1) is near unity [107]and the lifetime of this triplet state is about 200 μs [103]. The triplet statePIA spectrum of MP–C60 exhibits a Tn ← T1 absorption at 1.78 eV with acharacteristic shoulder at 1.54 eV [103]. The energy level of the MP–C60(T1)triplet state has been determined from phosphorescence to be at 1.50 eVabove the ground state level [107].

Intramolecular Singlet-Energy Transfer in OPVn–C60 Dyads inToluene. The fluorescence spectra of the OPVn–C60 (n = 1, 2, 3, and 4)dyads dissolved in toluene are shown in Fig. 1.26. The spectra were correctedfor the Raman scattering of toluene.4 Although fluorescence from the OPVn

4 Fluorescence spectra were corrected for the Raman scattering of ODCB or tolueneby subtracting the spectrum of the pure solvents from the spectra of the OPVn–C60 solutions, after correcting for the absorbed light intensity by measuring thesecond-order diffraction of the excitation light from the grating of the monochro-mator.


400 500 600 700 800 9000

2

4

60

2

4

0

2

4

0

1

Wavelength / nm

No

rma

lize

d I

nte

nsi

tya

b

d

c

Fig. 1.26. Fluorescence spectra of OPVn–C60 dyads in toluene and ODCB recordedat 295 K. (a) n = 1, λexc = 330 nm, (b) n = 2, λexc = 366 nm, (c) n = 3,λexc = 415 nm, and (d) n = 4, λexc = 443 nm. The fluorescence spectra in toluene(continuous lines) were normalised to the fullerene emission at 715 nm. The residualOPVn emission for n = 2–4 can be seen in the 400–600 nm range. The emissionof the OPVn–C60 dyads in ODCB (dash-dotted lines) is normalised with the sameconstant as used for the emission in toluene. A near complete quenching of thefullerene emission is observed for n = 2–4, while the OPVn emission decreases onlyslightly

moieties of the dyads can be observed for n > 1, it is quenched by more thanthree orders of magnitude compared to that of the pristine OPVn oligomers(Table 1.2). Apart from the strongly quenched OPVn emission, the spectrashow a weak fullerene fluorescence of MP–C60(S1) at 715 nm (Fig. 1.26).The excitation spectra of the fullerene fluorescence coincide with the absorp-tion spectra of the OPVn–C60 dyads (Fig. 1.27). Surprisingly, the fullerenefluorescence quantum yield in toluene is equal for all four dyads, nearly iden-tical to that of MP–C60, and does not alter with the excitation wavelength.Hence, the fluorescence spectra of OPVn–C60 provide clear evidence for an


300 400 500 6000

1

0

1

0

1

0

1

Wavelength / nm

No

rma

lize

d I

nte

nsi

tya

b

d

c

Fig. 1.27. Normalised UV/VIS absorption (solid lines) and fluorescence excitationspectra of the fullerene emission at 715 nm (dashed lines) of the OPVn–C60 dyadsin toluene at 295 K. (a) n = 1, (b) n = 2, (c) n = 3, and (d) n = 4. In each casethe fluorescence excitation spectrum shows a close correspondence to the absorptionspectrum

efficient intramolecular singlet energy transfer from the OPVn(S1) state tothe fullerene moiety for n > 1.5

An estimate for the rate constants of the intramolecular singlet energytransfer kET can be obtained from the extent of quenching of the OPVnfluorescence in the dyads and the singlet excited state lifetime of the OPVnoligomers [103] by

kET =QOPVn − 1

τOPVn, (1.14)

where τOPVn is the lifetime of the singlet excited state of the pristine OPVnmolecules and QOPVn is the quenching ratio of the OPVn fluorescence of theOPVn–C60 dyad in comparison with the OPVn molecule. The rate constants5 For n = 1 the question of an energy transfer is less relevant because the

OPV1 moiety cannot be excited without a simultaneous strong absorption ofthe fullerene moiety.


Table 1.2. Quenching factors Q of the OPVn and MP–C60 fluorescence of theOPVn–C60 dyads in toluene and ODCB. Singlet excited state lifetime τ of theOPVns in toluene solution. Rate constants kET for energy and ki

CS, kdCS for charge

separation

QOPVn τ kET QOPVn QMP–C60 kiCS kd

CS

toluene [ns] [s−1] ODCB ODCB [s−1] [s−1]

OPV2–C60 5200 8100 5OPV3–C60 3500 1.70 2.1×1012 3500 26 1.7×1010 6.3×1013

OPV4–C60 1500 1.32 1.1×1012 1900 > 50 >3.4×1010 >7.2×1013

are collected in Table 1.2 and indicate that an extremely fast (about 1 ps)singlet energy transfer occurs in OPV3–C60 and OPV4–C60.

The MP–C60(S1) state formed via the intramolecular singlet-energy trans-fer in the OPVn–C60 dyads is expected to decay predominantly via intersys-tem crossing to the MP–C60(T1) state, apart from some radiative decay. Con-sistent with this expectation, the PIA spectrum recorded for all four dyadsin toluene solution shows the characteristic MP–C60 T1 ← Tn absorption at1.78 eV with a shoulder at 1.54 eV (Fig. 1.28a). The PIA bands increase in anear-linear fashion with the excitation intensity (−ΔT ∝ Ip, p = 0.80–1.00)consistent with a monomolecular decay mechanism. The lifetime of the tripletstate lies in the range 140–280 μs.

Observations from fluorescence and PIA spectra provide strong evidencethat in toluene the OPVn moieties of the OPVn–C60 dyads with n > 1 serveas an antenna system to funnel the excitation energy to the fullerene moiety.6

Intermolecular Triplet-Energy Transfer in OPVn/MP–C60 Mix-tures in Toluene. The photophysical processes change dramatically whenmixtures of MP–C60 and OPVn in toluene are excited instead of the co-valently bound OPVn–C60 dyads. Although intermolecular energy transferfrom singlet excited oligo(p-phenylene vinylene)s to MP–C60 is energeticallypossible in OPVn/MP–C60 mixtures, it is less likely to occur because suchtransfer is limited by diffusion and the singlet excited state has a nanosec-ond lifetime. Hence the OPVn(S1) state in these mixtures will decay viafluorescence and intersystem crossing to the OPVn(T1) state.

The PIA spectrum of MP–C60 and OPV4 (1:1 molar ratio) in toluene,recorded upon selective excitation of OPV4 at 458 nm, exhibits a band at1.80 eV with a weak shoulder at 1.52 eV (Fig. 1.29). The PIA signal in thehigh-energy region is obscured by the extremely intense OPV4 fluorescence inthe region 1.85–2.5 eV, which could only be partially corrected. The negative6 For n = 1 the question of an energy transfer is less relevant because the

OPV1 moiety cannot be excited without a simultaneous strong absorption ofthe fullerene moiety.


n = 3

n = 2

n = 4

n = 1

n = 2

n = 3

n = 4

a-Δ

T/T

1 .0×10-3

1.0 1.5 2.0

b

Energy / eV

-Δ

T/T

1 .0×10-4

Fig. 1.28. (a) PIA spectra of OPVn–C60 dyads (4 × 10−4 M) in tolueneat 295 K, recorded with excitation at351.3 and 363.8 nm for n = 1 and 2and at 457.9 nm for n = 3 and 4. (b)PIA spectra of OPVn (4×10−4 M) co-dissolved with MP–C60 (4 × 10−4 M)in toluene at 295 K with excitation at528 nm

−ΔT/T above 2 eV is an artefact caused by this correction. A monomoleculardecay mechanism is inferred from the intensity dependence of the 1.80 eV PIAband (−ΔT ∝ Ip, p = 0.89–0.92). A lifetime of around 200 μs was determinedby varying the modulation frequency between 30 and 3800 Hz.

1.0 1.5 2.0-0.1

0.0

0.1

0.2

0.3

-ΔT

/T x

103

Energy / eV

Fig. 1.29. PIA spectra of OPV4 (4 ×10−4 M) co-dissolved with MP–C60

(4 × 10−4 M) in toluene at 295 K,recorded with excitation at 457.9 nm


The spectral features and lifetime are characteristic for the MP–C60(T1)state. They do not coincide with the PIA spectrum recorded for OPV4, whichshows a maximum at 1.80 eV, without any shoulder to lower energy [106].Observation of the MP–C60(T1) spectrum and hence the quenching of theOPV4(T1) state indicates that, after intersystem crossing, an efficient inter-molecular triplet energy transfer occurs from the OPV4(T1) state to MP–C60,generating the MP–C60(T1) state. Because the photogenerated OPV4(T1)state is quenched by the presence of MP–C60, we conclude that the tripletstate energy of OPV4 is higher than 1.50 eV, the triplet state energy ofMP–C60. Since shorter oligo(p-phenylene vinylene)s are expected to have aneven higher triplet level, we can conclude that the fullerene triplet level cor-responds to the lowest excited state in toluene for all dyads studied here.

Consistently, the PIA spectra of toluene solutions containing MP–C60and OPVn (n = 2, 3 or 4) in a 1:1 molar ratio, recorded using selectivephotoexcitation of MP–C60 at 528 nm (Fig. 1.28b), invariably exhibit an ab-sorption at 1.78 eV with an associated shoulder at 1.54 eV, characteristicof MP–C60(T1) [103]. The monomolecular decay (−ΔT ∝ Ip, p = 0.89–0.96)with lifetime 150–260 μs associated with these PIA bands supports this as-signment. Furthermore, weak fullerene fluorescence at 1.73 eV (715 nm) isobserved under these conditions for all three mixtures. No characteristic PIAbands of OPVn+• radical cations or MP–C−•

60 radical anions are discernibleunder these conditions. From these observations we conclude that electrontransfer from the ground state of the OPVn molecules to the singlet or tripletexcited state of MP–C60 does not occur in toluene solution.

Intermolecular Electron Transfer in OPVn/MP–C60 Mixturesin o-Dichlorobenzene. The dielectric constant (permittivity) of ODCB(ε = 9.93) is significantly higher than that of toluene (ε = 2.38). Photoin-duced electron transfer will be favoured in this more polar solvent, because theCoulombic attraction between the resulting opposite charges is more screenedand the charged ions are better solvated than in toluene. Indeed, the PIAspectra of 1:1 molar mixtures of MP–C60 and OPV4 or OPV3 in ODCB givedirect spectral evidence for intermolecular photoinduced electron transfer.For both mixtures an intense PIA spectrum of the charge-separated statewas observed after selective excitation of MP–C60 at 528 nm (Fig. 1.30b andc). Strong absorption was observed for the OPV4+• (0.66, 1.52, and 1.73 eV)and OPV3+• (0.77, 1.70 and 1.97 eV) radical cations, together with the char-acteristic absorption band of the MP–C−•

60 radical anion at 1.24 eV.For each PIA band, the change in transmission as a function of the mod-

ulation frequency was recorded and fitted to the expression for bimoleculardecay, resulting in estimates for the charge-separated state lifetime of 2.5–3.1 ms for OPV4+•/MP–C−•

60 and 4.1–4.7 ms for OPV3+•/MP–C−•60 , respec-

tively. Increasing the pump beam intensity resulted in a non-linear increasein the absorption intensities (−ΔT ∝ Ip, p = 0.62–0.71). Although for bi-


molecular decay a square root intensity dependence of the PIA signal is oftenobserved, it is noticeable that the pump intensity dependence of the PIAsignal becomes linear when the modulation frequency is much larger thanthe inverse bimolecular lifetime [108]. In the present case with ω = 275 Hzand τ ≈ 2–5 ms, both are of the same magnitude and an intermediate valuecan be expected. Therefore, we conclude that the results are consistent withbimolecular decay, and hence with a recombination of positive and negativecharges. Since MP–C60 is initially excited, we attribute the formation of rad-ical ions to an intermolecular electron transfer between ground state OPV3or OPV4 as a donor and the triplet state of MP–C60 as an acceptor.7

For the mixture of OPV2 and MP–C60 in ODCB, the PIA spectrumrecorded with selective excitation of MP–C60 at 528 nm (Fig. 1.30a) exhibitsthe transitions of the MP–C60(T1) state at 1.78 and 1.54 eV, which increaselinearly with the excitation intensity (−ΔT ∝ Ip, p = 0.99–1.00) and cor-respond to a lifetime of 170–290 μs. Together with the concurrent absenceof polaron absorption, we infer that intermolecular charge transfer betweenOPV2 and MP–C60 does not occur in ODCB.

Intramolecular Electron Transfer in OPVn–C60 Dyads ino-Dichlorobenzene. Figure 1.26 shows the Raman-corrected emission spec-tra of the OPVn–C60 dyads in ODCB obtained upon (near) selective pho-toexcitation of the OPV moiety. Similarly to solutions in toluene, the fluo-rescence of the OPVn moiety of the dyads is strongly quenched compared tothe fluorescence of pristine OPVn in ODCB. The quenching ratios QOPVn

collected in Table 1.2, are somewhat larger than those in toluene. However,the most dramatic difference between the fluorescence spectra of the OPVn–C60 dyads recorded in the two different solvents is the strong quenching offullerene emission at 715 nm for solutions of OPV2–C60, OPV3–C60, andOPV4–C60 in ODCB, but not for OPV1–C60. The fullerene quenching ratioQC60 , calculated with respect to the fluorescence of MP–C60 in ODCB, in-creases with the conjugation length of the OPVn moiety, from approximately5 for OPV2–C60, via 26 for OPV3–C60, to more than 50 for OPV4–C60 (Table1.2). The quenching of the fullerene emission in the dyads may result eitherfrom an ultra-fast process that quenches the initially formed OPVn(S1) stateor from a rapid relaxation of the MP–C60(S1) state, once this is formed viaenergy transfer. The experimental observation that the residual OPVn fluo-rescence of the OPVn–C60 dyads in ODCB is comparable to that in toluenegives support to the latter explanation.

Intramolecular charge separation is energetically favoured over inter-molecular charge separation because the spatial separation of charges, andhence the Coulomb term, is limited by the fixed distance between donor7 Formally, such an electron transfer could be considered as a hole transfer in

which a positive charge is transferred from the fullerene to the oligo(p-phenylenevinylene).


0.5 1.0 1.5 2.0

0.00

1.00

2.00

Energy / eV

0.00

0.50

1.00

-Δ T

/T x

103

0.00

0.05

0.10

b

a

c

Fig. 1.30. PIA spectra of OPVn (4 × 10−4 M) co-dissolved with MP–C60

(4 × 10−4 M) in ODCB at 295 K, recorded with excitation at 528 nm. (a)OPV2/MP–C60, (b) OPV3/MP–C60, (c) OPV4/MP–C60

and acceptor within the covalent donor–acceptor dyad. Since intermolecu-lar photoinduced electron transfer occurs in mixtures of MP–C60 and OPV4or OPV3 in ODCB, we may expect intramolecular photoinduced electrontransfer to occur in the corresponding OPV3–C60 and OPV4–C60 dyads inODCB as well. However, the lifetime of an intramolecularly charge-separatedstate in molecular donor–fullerene dyads does not usually extend into themicrosecond regime, but is limited to the low nanosecond time domain [98],although some exceptions exist [109–113]. In general, excited states with alifetime τ � 10 μs cannot be detected with the CW-modulated PIA techniquebecause the steady state concentration achieved in the modulated experimentwill be below the detection limit (ΔT/T ∼ 10−6). It is therefore surprising tosee that the PIA spectra of OPV3–C60 and OPV4–C60 dissolved in ODCB


0.5 1.0 1.5 2.0 2.5

0.00

0.10

Energy / eV

0.00

0.05

-ΔT

/T x

103

0.00

0.10

0.00

0.10

0.20

0.30

d

c

b

a

Fig. 1.31. PIA spectra of OPVn–C60 dyads in ODCB at 295 K for (a) n = 1, (b)n = 2, (c) n = 3 and (d) n = 4. The spectra were recorded with excitation at 351.1and 363.8 nm for n = 1 and 2 and at 457.9 nm for n = 3 and 4

exhibit the characteristic absorption of a charge-separated state (Fig. 1.31cand d).

Although the intensities of the OPVn+• radical cation and MP–C−•60 rad-

ical anion absorption are significantly lower in comparison with the PIA sig-nals observed for mixtures of OPVn and MP–C60 in ODCB, the characteristicfeatures are evident. Remarkably, lifetimes up to 20 ms can be observed forthese charge-separated states. In view of the expected (sub)nanosecond life-time [98], we consider this extremely long lifetime to be incompatible with anintramolecular charge-separated state, and attribute the signals to an inter-molecular charge-separated state. This intermolecular charge-separated stateis formed either by direct charge transfer between singlet excited OPVn–C60(S1) and a second dyad in the ground state or by charge transfer from theshort-lived intramolecular charge-separated OPVn+•–C−•

60 state to a neutralOPVn–C60 dyad resulting in separate OPVn+•–C60 and OPVn–C−•

60 radical


ions. The longer lifetime as compared to OPVn/MP–C60 (n = 3, 4) mixturesis due to the lower concentration of the OPVn+•–C60 and OPVn–C−•

60 radicalions and hence the reduced bimolecular decay rate.

Photoexcitation of OPV2–C60 in ODCB leads to seemingly contradictoryobservations. While fullerene emission is partly quenched (Fig. 1.26, Table1.2), consistent with electron transfer, the MP–C60(T1) state is observed inthe PIA spectrum (Fig. 1.31b), indicating a combination of energy transferand intersystem crossing. The result can be rationalised as follows. If theenergy level of the lowest-lying neutral excited state OPV2–C60(T1) is closeto the energy level of the intramolecular charge-separated state, energy andelectron transfer will occur simultaneously. The likelihood of this degeneracywill be demonstrated in the section on energetics of charge transfer.

The PIA spectrum of OPV1–C60 in ODCB shows the absorption of thefullerene triplet state (Fig. 1.31a) and no significant quenching of the fullereneemission is observed (Fig. 1.26a). Both observations are consistent with theabsence of an intramolecular photoinduced electron transfer in OPV1–C60,which can be rationalised by the high oxidation potential of the OPV1 moiety.

Photoinduced Electron Transfer of OPVn–C60 in Thin Films. Thinfilms of OPVn–C60 (n = 1 to 4) were prepared by casting from solutiononto quartz substrates. For OPV1–C60 and OPV2–C60 the PIA spectra ofthe thin films recorded at 80 K with excitation at 351 and 363 nm are sim-ilar (Fig. 1.32a and b). In both spectra a broad, low intensity absorptionis discernible between 1.0 and 2.2 eV, with a maximum at about 1.72 eV.The exact origin of the broad band is unknown at the present time. Thespectrum shows some similarity to that of the MP–C60(T1) state in solution,while the two characteristic absorption bands of oligo(p-phenylene vinylene)radical ions are absent. Therefore, we tentatively assign the spectra (at leastin part) to triplet–triplet absorption of the fullerene moiety. The lifetime ofthe MP–C60(T1) state, as derived from modulation frequency dependencymeasurements, is about 230 μs for OPV1–C60 and 275 μs for OPV2–C60.These spectral characteristics suggest that photoinduced electron transferdoes not occur (or occurs only to a small extent) in thin films of OPV1–C60and OPV2–C60.

The PIA spectra of thin films of OPV3–C60 and OPV4–C60 recordedwith excitation at 458 nm differ dramatically from those of OPV1–C60 andOPV2–C60 (Fig. 1.32c and d). For OPV3–C60 and OPV4–C60 the character-istic absorption band of the MP–C−•

60 radical anion is observed at 1.25 eV.Furthermore, the spectra show absorption for the OPV3+• and OPV4+•

radical cations at 0.82 and 1.66 eV (OPV3+•) and at 0.64, 1.44 and 1.70 eV(OPV4+•). These observations give direct spectral evidence for photoinducedelectron transfer.

The intensity of the PIA bands increases approximately with the squareroot of the pump intensity (−ΔT ∝ Ip, p = 0.46–0.57 for OPV3–C60 and


0.5 1.0 1.5 2.0 2.5

0.00

1.00

Energy / eV

0.00

0.25

0.00

0.10

-ΔT

/T x

103

0.00

0.10

c

b

d

a

Fig. 1.32. PIA spectra of OPVn–C60 thin films on quartz for (a) n = 1, (b) n = 2,(c) n = 3 and (d) n = 4. The spectra were recorded at 80 K with excitation at351.1 and 363.8 nm for n = 1 and 2 and at 457.9 nm for n = 3 and 4, with 25 mWand a modulation frequency of 275 Hz

p = 0.36–0.50 for OPV4–C60). This square-root intensity dependency indi-cates a bimolecular decay mechanism, consistent with the recombination ofpositive and negative charges. Varying the modulation frequency from 30 to3800 Hz results in a continuous decrease of the intensity of the PIA bandsof OPV3–C60 and OPV4–C60, indicating a distribution of lifetimes. The av-erage lifetime of the charge-separated states in thin films of OPV3–C60 andOPV4–C60 is of the order of 0.5–1.5 ms. This long lifetime in the films is instrong contrast with the short lifetime of the intramolecular charge-separatedstate as inferred from the experiments in ODCB. Typically, the lifetime of anintramolecular charge-separated state in fullerene-containing dyads and tri-ads is on the (sub)nanosecond timescale, although a few examples are knownwith a lifetime in the microsecond domain [109–113]. We therefore suggest


that the long lifetimes in the film are due to migration of the hole and/or theelectron to other molecules in the film, subsequent to the photoinduced elec-tron transfer [114]. The resulting intermolecular charge-separated state canno longer decay via the fast geminate intramolecular back electron transferand will therefore have an increased lifetime.

Photovoltaic Devices with OPV4–C60. The increased lifetime of thecharge-separated state, which extends into the millisecond time domain,opens the possibility of using the OPVn–C60 dyads as the active materialin a photovoltaic device. As an important difference with previous bulk het-erojunction cells, the covalent linkage between donor and acceptor in thesemolecular dyads restricts the dimensions of the phase separation between theoligomer and the fullerene that could freely occur in blends of the individualcomponents. This can be considered as a primitive attempt to obtain moreordered and better-defined phase-separated D–A networks.

-3 -2 -1 0 1 2 310-3

10-2

10-1

100

101

102

Cur

rent

/ m

A c

m-2

Voltage / V

Fig. 1.33. Semi-logarithmic plot of the current/voltage curves of aPET/ITO/PEDOT-PSS/OPV4–C60/Al photovoltaic cell in which OPV4–C60 is the active material. Open squares represent dark curve and solid squareswere recorded under about 65 mW cm−2 white light illumination

To test the applicability of the molecular dyads for light energy conversion,we have prepared photovoltaic devices in which OPV4–C60 is sandwiched be-tween aluminium and polyethylenedioxythiophene polystyrenesulfonate (PE-DOT/PSS) covered ITO electrodes. Figure 1.33 shows the semi-logarithmicplot of the I/V curves of a typical device in the dark and under white lightillumination of a halogen lamp at about 65 mWcm−2. The I/V curves arecompletely reversible and the device shows diode behaviour with a rectifica-tion ratio between −2 and +2 V of approximately 100, which shows that the


device has few or no shunts. In the dark a small kink is discernible in the semi-logarithmic plot of the I/V curve between 0 and 1 V, representing the smallohmic contribution from the shunt resistance. Under about 65 mWcm−2

white light illumination, a short-circuit current (Isc) of 235 μAcm−2 and anopen-circuit voltage (Voc) of 650 mV are observed for this device.

The fill factor (FF), defined as ImaxVmax/IscVoc, is 0.25. The relatively lowFF may be explained by recombination of charges at the ITO electrode. Thepresent values of Isc and Voc are significantly enhanced in comparison with thedevice characteristics of a related C60-oligophenylenevinylene dyad [102] andquite similar to those previously reported for π-conjugated polymer/fullerenesolar cells [115], although there has been considerable progress in energyconversion efficiencies of these devices recently [116].

Results indicate that a bicontinuous network of the donor and accep-tor moieties is indeed formed in a film of OPV4–C60. Two factors limit theintrinsic efficiency of the OPV4–C60 based device compared to that of thecorresponding poly(p-phenylene vinylene)/fullerene blends. First, the absorp-tion spectrum of OPV4 oligomer does not cover the wavelength range of thecorresponding polymer due to the reduced conjugation length. Second, the in-trinsic fullerene/OPV weight ratio of 0.71 in OPV4–C60 is significantly lowerthan the optimised polymer/fullerene weight ratio of 4, currently used in themost efficient polymer solar cells.

Energetic Considerations for Energy and Electron Transfer. To ra-tionalise the observed differentiation between energy and electron transferby photoexcited OPVn–C60 dyads in apolar and polar solvents, we calcu-lated the change in free energy for charge separation (ΔGcs) using the Wellerequation [104]:

ΔGcs = e [Eox(D) − Ered(A)] − E00 (1.15)

− e2

4πε0εsRcc− e2

8πε0

(1r+ +

1r−

)(1

εref− 1

εs

).

In this equation Eox(D) and Ered(A) are the oxidation and reduction poten-tials of the donor and acceptor molecules or moieties measured in a solventwith relative permittivity εref , whilst E00 is the energy of the excited statefrom which the electron transfer occurs and Rcc is the centre-to-centre dis-tance of the positive and negative charges in the charge-separated state. Theradii of the positive and negative ions are given by r+ and r−, εs is therelative permittivity of the solvent, −e is the electron charge and ε0 is thevacuum permittivity.

For OPVn–C60 and mixtures of OPVn and MP–C60 in solution, Eox andEred were determined via cyclic voltammetry in dichloromethane (ε = 8.93)(Table 1.1). The distances Rcc in the dyads (Table 1.3) were determined bymolecular modelling, assuming that the charges are located at the centres ofthe OPV and fullerene moieties. For intermolecular charge transfer, the value


Table 1.3. Centre-to-centre distance Rcc of donor and acceptor in OPVn–C60

dyads, radius r+ of OPVn radical cation, energy of OPVn(S1) state, and calculatedfree energies of intramolecular Gcs and intermolecular G∞

cs charge-separated statesin OPVn–C60 dyads and OPVn/MP–C60 mixtures

Rcc r+ EOPVn(S1) Solvent Gcs G∞cs

[A] [A] [eV] [eV] [eV]

OPV1–C60 7.0 3.3 4.77 Toluene 2.10ODCB 1.64

OPV2–C60 9.5 4.0 3.03 Toluene 1.99 2.56ODCB 1.48 1.56



of Rcc was set to infinity. The radius of the negative ion of C60 was set to r− =5.6 A, based on the density of C60 [109]. To estimate the radii for the positiveions (a radius being a gross simplification for the one-dimensionally extendedconjugated OPV moieties!), the Van der Waals volume of OPV molecules wasused, ignoring the 2-methylbutoxy side chains because the positive charge willbe confined to the conjugated segment. For stilbene, an experimental valueof r+ = 3.96 A can be obtained from the density (ρ = 1.159 g cm−3), derivedfrom X-ray crystallographic data [117] via r+ = (3M/4πρNA)1/3.

For the other oligomers no crystallographic data are available and we cal-culated the van der Waals volumes of benzene, stilbene, 1,4-distyrylbenzene,and 4,4′-distyrylstilbene using Macromodel and an MM2 force field. Aftercorrection for a 26% free-volume in a closed-packing of spheres, the values inTable 1.3 were obtained. The experimental and theoretical values for stilbeneare in close agreement. With these approximations, the free energies of theintramolecular (Gcs) and intermolecular (G∞

cs ) charge-separated states havebeen calculated (Table 1.3) and the relative ordering of the states is depictedin Fig. 1.34.

From Fig. 1.34b and Table 1.3 it is clear that the intramolecular charge-separated state is energetically located below the OPVn(S1) state in bothsolvents and for each n. However, in toluene all charge-separated states arehigher in energy than the MP–C60(S1) and MP–C60(T1) states. In ODCBthe situation changes dramatically: the energy of the intramolecular charge-separated state drops below that of the MP–C60(S1) state for each n, andeven below that of the corresponding MP–C60(T1) state except for n = 1,indicating that electron transfer will result in a gain of free energy for n > 1.In fact the predictions based on the Weller equation (Table 1.3) are in ex-cellent agreement with the quenching of the MP–C60(S1) fluorescence, asshown in Fig. 1.26, which occurs for n > 1. For the intermolecular charge-


1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

intermolecular intramolecular

OPV3(S1)

a

MP-C60(T1)

MP-C60(S1)

Ene

rgy

/ eV

OPV1(S1)

OPV4(S1)

OPV2(S1)

b

OPV4(S1)

OPV3(S1)

OPV2(S1)

MP-C60(T1)

MP-C60(S1)

Fig. 1.34. Excited state energy levels. The singlet (S1) energy levels of OPVn andMP–C60 (solid bars) were determined from fluorescence data. The MP–C60(T1) level(solid bar and dashed line) was taken from phosphorescence data in the literature[107]. The levels of the charge-separated states for (a) intermolecular charge transferin OPVn/MP–C60 mixtures and (b) intramolecular charge transfer in OPVn–C60

dyads were determined using (1.2) (see text and Table 1.3). Open squares are fortoluene and solid squares for ODCB

separated states, the only relevant state for comparison is the MP–C60(T1)state, since these charge-separated states are formed via the triplet manifold.Table 1.3 and Fig. 1.34a show that intermolecular electron transfer is energet-ically favoured in ODCB for OPV3 and OPV4 but not for OPV2,8 again infull agreement with the experimental results inferred from PIA spectroscopy(Fig. 1.30).

The close correspondence of experimental results with the relative order-ing of the various excited states as derived from the Weller equation showsthe strength of this approach in explaining the discrimination between pho-toinduced energy and charge transfer in conjugated oligomer–fullerene dyads.

Kinetics of Energy and Electron Transfer. A semi-quantitative esti-mate for the rate constants of the various photophysical processes can beobtained from fluorescence quenching. Based on the quenching ratios of theOPV fluorescence and the OPVn singlet excited state lifetimes, the rate con-stants for energy transfer reactions in toluene solutions were estimated to liebetween 1.1× 1012 and 2.1× 1012 s−1 for OPV3–C60 and OPV4–C60 (Table

8 From similar calculations for the mixture of OPV1 and MP–C60, free energiesfor the charge-separated state of 2.87 and 1.76 eV are estimated in toluene andODCB, respectively. Since these energies are much higher than the MP–C60

triplet energy, no photoinduced electron transfer is to be expected.


kr

kisc

kńr

kísc

k´r

knr

kET

kCSd

kCSi

kTT/k´TT

S0

T1

S1

Tn

S0

T1

S1

Tn

CS

OPVn MP-C60

kr

kisc

kńr

kísc

k´r

knr

kET

kCSdkCS

i

kTT/k´TT

S0

T1

S1

Tn

S0

T1

S1

Tn

CS

kr

kisc

kńr

kísc

k´r

knr

kET

kCSd

kCSi

kTT/k´TT

S0

T1

S1

Tn

S0

T1

S1

Tn

CS

OPVn MP-C60

kr

kisc

kńr

kísc

k´r

knr

kET

kCSd

kCSi

kTT/k´TT

S0

T1

S1

Tn

S0

T1

S1

Tn

CS

Fig. 1.35. Schematic diagram describing energy levels of singlet (S0, S1), triplet(T1, Tn), and charge-separated (CS) states of OPVn–C60 dyads. The energy transfer(kET) and indirect (ki

cs) and direct (kdcs) charge separation reactions are indicated

with curved dotted arrows. The solid arrow describes the initial excitation of theOPVn moiety. Other symbols are: kr and k′

r for the radiative rate constants, knr andk′nr for the non-radiative decay constants, kics and k′

ics for the intersystem crossingrate constants, and kT and k′

TT for the rate constants for triplet-energy transfer,in each case for OPVn and MP–C60, respectively

1.2). We assume that similar rate constants for energy transfer will apply toODCB solutions since the energy level and lifetime of the singlet excited statesare not strongly affected by the polarity of the solvent [106]. For OPV2–C60,OPV3–C60, and OPV4–C60 intramolecular photoinduced electron transfer isobserved in ODCB, as evidenced from the quenching of the MP–C60(S1) fluo-rescence. In principle, electron transfer can either take place directly from theinitially formed OPVn(S1) state or indirectly, in a two-step process, via theMP–C60(S1) state (Fig. 1.35). For indirect photoinduced electron transfer,i.e., subsequent to singlet energy transfer to the MP–C60, the rate constant(ki

cs) is given by

kics =

QC60 − 1τC60

, (1.16)

where QC60 is the quenching ratio of the fullerene emission of the OPVn–C60dyads in ODCB in comparison with MP–C60 and τC60 is the lifetime of the


singlet excited state of MP–C60 (1.45 ns) [103]. The values for kics in Table

1.2 show that the electron transfer from the MP–C60(S1) state occurs on atimescale of about 60 ps for OPV3 and about 30 ps for OPV4. If a directelectron transfer from the OPVn(S1) state were to occur, the decrease infullerene emission would necessarily result from a quenching of the OPVn(S1)state since it would be faster than the energy transfer reaction. In this casethe rate constant kd

cs for electron transfer can be derived from

kdcs =

(QOPVn − 1)(QC60 − 1)τOPVn

. (1.17)

The calculated values of kdcs (Table 1.2) indicate that direct intramolecular

electron transfer would have to be extremely fast (14–16 fs). Moreover, if di-rect electron transfer were to occur, an additional quenching of the residualOPVn emission must be expected. However, Fig. 1.26 shows that there is nosignificant additional quenching of the OPVn emission in ODCB in compari-son with the quenching already achieved by energy transfer in toluene. Hence,the fluorescence quenching experiments strongly suggest that photoinducedelectron transfer in the OPVn–C60 dyads in ODCB solution is a two-stepprocess, involving singlet-energy transfer prior to charge separation.9

Activation Barrier for Charge Separation. Further insight into thekinetics of charge separation can be obtained from the activation barrier forcharge separation. The Marcus equation provides an estimate for the barrierfor photoinduced electron transfer from the change in free energy for chargeseparation ΔGcs and the reorganisation energy λ [118]:

ΔG‡cs =

(ΔGcs + λ)2

4λ. (1.18)

The reorganisation energy consists of internal λi and solvent λs contributions.The former can be calculated in the Born–Hush approach via [107,109,119]

λs =e2

4πε0

[12

(1r+ +

1r−

)− 1

Rcc

](1n2 − 1

εs

), (1.19)

where n is the refractive index of the solvent. For the internal reorganisationenergy we estimate λi = 0.3 eV [98,107,109]. The values for λ = λi + λsobtained in this way are compiled in Table 1.4 for n > 1, together withthe free energy change (ΔGcs) and barrier (ΔG‡

cs) for intramolecular electrontransfer in the OPVn–C60 dyads relative to the OPVn(S1) and MP–C60(S1)excited states. Table 1.4 shows that forward photoinduced charge separationin OPVn–C60 dyads in ODCB originating from the MP–C60(S1) state is in

9 Formally, such an electron transfer could be considered as a hole transfer inwhich a positive charge is transferred from the fullerene to the oligo(p-phenylenevinylene).


the ‘normal’ Marcus region (λ > −ΔGcs), resulting in a barrier for electrontransfer in OPVn–C60 of less than about 0.1 eV for n > 1. Forward photoin-duced charge separation originating from the OPVn(S1) state would occurin the Marcus ‘inverted’ region (λ > −ΔGcs), irrespective of the solvent orconjugation length of the OPVn donor (Table 1.4). The latter is a conse-quence of the higher energy of the singlet-excited state. The estimates forΔG‡

cs change only slightly when different values are used for λi. When λi isvaried from 0.2 to 0.4 eV, ΔG‡

cs remains less than 0.1 eV for both OPV3–C60and OPV4–C60 in ODCB.

Table 1.4. Reorganisation energy λ, free energy change ΔGcs and barrier ΔG‡cs for

intramolecular electron transfer in OPVn–C60 dyads in different solvents relativeto the energies of the OPVn(S1) and MP–C60(S1) states

Compound Solvent λ OPVn(S1) MP–C60(S1)[eV] ΔGcs ΔG‡

cs ΔGcs ΔG‡cs

[eV] [eV] [eV] [eV]

OPV2–C60 Toluene 0.34 −1.04 0.36 0.23 0.24ODCB 0.80 −1.55 0.18 −0.28 0.09



The non-adiabatic charge separation rate constant is a function of theenergy barrier ΔG‡

cs, the reorganisation energy, and the electronic couplingV between donor and acceptor in the excited state [120]:

kcs =(

4π3

h2λkBT

)1/2

V 2 exp(

−ΔG‡cs

kBT

). (1.20)

Using the values for λ and for kcs and ΔG‡cs for the direct and indirect charge

transfer mechanisms as listed in Table 1.3 and Table 1.4, it is possible toestimate the electronic coupling. For the indirect mechanism, i.e., chargeseparation subsequent to singlet energy transfer, the values calculated for Vusing (1.20) and ki

cs are V i = 30 ± 3 cm−1 for OPV3–C60 and OPV4–C60in ODCB. For the direct mechanism, (1.20) indicates that V should be ofthe order of V d = 1300–2600 cm−1 to explain the very high rate constantskdcs. Clearly such a strong coupling would cause significant differences in the

absorption spectrum of the OPVn–C60 dyads in comparison with the linearsuperposition of the spectra of OPVns and MP–C60, which is not observedexperimentally. Moreover, such strong coupling is much larger than the in-teraction expected between two chromophores separated by a bridge of threesigma bonds [109,121].


Kinetic analysis supports the conclusion inferred from the residual OPVnfluorescence of the OPVn–C60 dyads in ODCB that charge separation inthese systems is preceded by energy transfer.

1.7 Conclusion

In organic semiconductors and blends of organic semiconductors with differ-ent electron affinity, photophysics in general and photoinduced charge trans-fer phenomena in particular can be qualitatively understood and described byclassical models for charge transfer reactions. The occurrence of photoinducedcharge (or energy) transfer can be predicted from relative HOMO–LUMO en-ergy considerations. The outstandingly fast kinetics of these reactions is stillnot understood and opens to question the currently discussed models forcharge transfer reactions. A forward transfer time below 40 fs cannot be ex-plained by classical charge transfer models without making unreasonable as-sumptions for material parameters (i.e., the overlap integral). Further effortsare needed to fully understand photoinduced charge transfer in conjugatedpolymer/fullerene composites.

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2 Optical and Spectroscopic Propertiesof Conjugated Polymers

Davide Comoretto and Guglielmo Lanzani

The use of plastics to replace other more traditional structural materials likewood, metals and alloys has generated important changes in our everydaylives. The reduction in weight and costs has made plastics one of the mostwidely used structural materials in our society. Plastic materials are formedby very long chains (polymers or macromolecules) in which one or morerepetitive units are covalently linked together several times. These units aremainly composed of carbon, hydrogen, oxygen, nitrogen and sulphur. All thepolymeric chains are then packed together by secondary bonds giving riseto the bulk material. During the polymerization process, defects may occurin the regular connection, branching and cross-linking, thereby modifyingthe properties of the material. An additional source of disorder in polymericmaterials is due to the fact that each macromolecule can be composed ofdifferent numbers of repeating units, thus giving rise to a distribution ofmolecular weights. The study of these properties is a traditional topic inmacromolecular science [1].

From the electronic point of view, common experience suggests that plas-tics are good electrical insulators. Poly(tetrafluoroethylene) (CF2CF2, PTFE,see Fig. 2.1) or polyethylene (CH2CH2, PE, see Fig. 2.1) for instance possess avery low electrical conductivity (10−19–10−20 ohm−1cm−1, for PTFE). How-ever, in the late 1970s a new class of polymers with semiconducting propertieswas developed in several research laboratories. These polymers are charac-terized by the presence of conjugated carbon bonds in their backbone, givingrise to the alternation of single and double (or triple) carbon–carbon bonds.In this way, the π-electrons are delocalized along the backbone, generating ahighly mobile electron cloud. The optical gap of conjugated polymers (CP) islowered to the visible energy range (1.5–3 eV) with respect to non-conjugatedpolymers (7–8 eV for PE [2]), conferring semiconducting properties uponthem. Chemical doping of CPs increases the conductivity by several ordersof magnitude, almost as efficiently as in copper [3]. The discovery of theseproperties and subsequent developments were recognized worldwide by theyear 2000 Nobel Prize for chemistry [4]. Further progress in the study of thetransport properties of this class of materials has revealed that small hydro-carbon conjugated molecules may even exhibit superconducting properties[5].

Even though the conductivity achieved by doped CPs can be very high,they have poor stability in ambient conditions, thus preventing wide use in

58 Davide Comoretto and Guglielmo Lanzani

real devices. However, other interesting characteristics related to the semicon-ducting properties of CPs have been exploited in optoelectronic devices, suchas high luminescence quantum yield, photoinduced charge transfer processes,carrier transport and nonlinear optical properties. These facts combined withtheir processability, low cost and mechanical properties, unmatched by con-ventional inorganic semiconductors, make CPs promising materials for plasticelectronics in the third millennium [6].

In order to understand the fundamental electronic properties that providethe basis for working devices, it is important to study spectroscopic proper-ties of the ground and excited electronic states of the CP. There have beencontinued improvements in the quality of materials and techniques used toinvestigate them, allowing a deep insight into the photophysics of CPs andorganic solids in general. The result has been an exponential growth in thenumber of published papers in the field.

The aim of this chapter is to discuss the basic spectroscopic and opticalproperties of CPs. In Sect. 2.1 we will review the techniques adopted tocarry out an optical characterization of CP samples. It will be shown thatin high quality CP films (controlled surface, thickness, homogeneity, etc.) adetailed characterization of their optical constants (complex refractive index,n = n+ik) can now be achieved, providing deep insights into their electronicstructure. This is important for solar cells because a detailed knowledge of nmakes it possible to account for their reflectivity losses. It would be interestingto extend the study of n to excited electronic states, but at present thisis a very difficult task. We limit our discussion to the photophysics of CPexcited states, which are fundamental to describing the properties exploited inorganic optoelectronic devices (Sect. 2.2). In fact, charge and energy transferprocesses, the mechanism of generation and decay of singlet or triplet excitonsand polarons, and the role of intra- and intermolecular excitations can be wellunderstood by femtosecond pump-and-probe spectroscopy.

2.1 Material and Optical Properties

Optical properties are usually related to the interaction of a material withelectromagnetic radiation in the frequency range from IR to UV. As far as thelinear optical response is concerned, the electronic and vibrational structureis included in the real and imaginary parts of the dielectric function ε(ω) orrefractive index n(ω). However, these only provide information about statesthat can be reached from the ground state via one-photon transitions. Two-photon states, dark and spin forbidden states (e.g., triplet) do not contributeto n(ω). In addition little knowledge is obtained about relaxation processesin the material. A full characterization requires us to go beyond the linear ap-proximation, considering higher terms in the expansion of n(ω) as a functionof the electric field, since these terms contain the excited state contribution.

2 Optical and Spectroscopic Properties of Conjugated Polymers 59

n

FF

FF

n

HH

HH

n Teflon Polyethylene Trans-polyacetylene

R'

n

R

R

R'

X

n Polydiacetylene derivatives Poly(p-phenylene-vinylene) derivatives

nS

R'R

R'

R'

R

R

Y

Y

Polythiophene derivative Ladder-type poly(p-phenylene)

Fig. 2.1. Chemical structure of polymers discussed in the present chapter


The experimental techniques adopted to measure linear and nonlinear op-tical properties are quite different and must be discussed separately. In broadterms, linear properties can be measured using low intensity probes and highspectral resolution. They are usually understood in the frequency domain.Nonlinear responses on the contrary need very large intensities, typicallyachieved in short pulses, and are discussed in the time domain. In additionto these physical considerations, we have to remember that time-resolvedspectroscopy and optical characterization usually require good optical qual-ity samples, so our understanding of the physics of these materials is closelylinked to their quality.

The first CPs to be synthesized were polyacetylene (CH)x, polythiophenes(PT), and polydiacetylenes (PDAs) (see Fig. 2.1 for their chemical structure).Most of these polymers are infusible and insoluble. This makes it difficult tocarry out spectroscopic studies on them, and such studies are often lim-ited to the case of samples dispersed in pressed KBr pellets. These pelletsstrongly scatter the light and transmittance and/or reflectance spectra mustbe recorded using an integrating sphere which allows collection of the diffusedlight. In spite of the low optical quality of the pellets, interesting informa-tion can be obtained, such as the energy position of electronic transitions aswell as a rough estimate of the degree of electron–phonon interactions [7,8],which play (jointly with the electron correlation) an important role in CPspectroscopy. In fact, the vibronic structure of the absorption spectrum, dueto the vibrational modes of molecules in excited electronic states, is oftenobserved. When the fine structure of the line shape can be resolved and it ispossible to assign the vibrational modes (usually more than one), informa-tion is obtained about the square of the nuclear displacement with respectto the ground state configuration [9]. Further theoretical modelling, whichis in fact seldom accomplished [10], is needed to determine the displacementsign. In principle, the overall relaxation time of the excited states could bederived from the absorption line width. However, the low optical quality ofthe pellets, inhomogeneous broadening due to the distribution of conjuga-tion lengths, and all the defects typical of polymers combine to prevent suchdetermination. This suggests the use of transient spectroscopic techniques,described in Sect. 2.2.

A fundamental improvement in the optical quality of CP samples wasachieved by increasing their processability and making them soluble in com-mon organic solvents. Different synthetic strategies have been employed toreach this goal, such as the insertion of flexible side chains increasing the con-formational entropy of the main chain [7,11] (substituted PPV, PT or PDAs),the use of non-conjugated polymeric precursors that are thermally convertedto the conjugated polymer after film processing [12–14] [PPV, Durham–Graz(CH)x] or block copolymers with a non-conjugated group joined to a conju-gated segment (both as pendant chain or in the main backbone) [15]. Thesolubility of the polymer or of its precursor is extremely important because


it allows one to spin- or drop-cast films of good optical quality in very simpleand cheap ways. The availability of films cast from solutions makes it pos-sible to produce various optoelectronic devices with multilayered structureand also to obtain a more detailed optical and spectroscopic characterizationof the material [16,17].

2.1.1 Optical Constants and Electronic Structure

It is well known that the electronic structure of molecules or solids can bedirectly connected to optical properties, our physical observables, through thecomplex dielectric constant at optical frequencies. A detailed analysis of thissubject is discussed in several textbooks [18]. Here we shall only highlight themain results. From the solid state point of view, direct optical transitions, i.e.,transitions in which the energy �ω is conserved and the photon momentum isnegligible, are related to the imaginary part of the complex dielectric constantε = ε1 + iε2 by

ε2(ω) =e2

m2ω2π2

∫d3k |u · pij |2 δ(Eij − �ω) , (2.1)

pij = − i�Δ

∫cell

w∗c∇wvd3r , (2.2)

where u is the unit polarization vector of the magnetic field, m the electronmass, �ω the photon energy, Eij the transition energy, pij the matrix elementof the momentum operator between the i and j states, Δ the volume ofthe unit cell, and w the periodic part of the Bloch wavefunction. From themolecular point of view, the quantum theory of time dependent perturbationsimplies the following formula for ε [18]:

ε1 + iε2 = 1 + 4πNα = 1 + ω2p

∑m

|fm0|2ω2

m0 − ω2 − iΓω, (2.3)

fm0 =2m�ωm0

�2 |xm0|2 , (2.4)

where α is the molecular polarizability, ω2p = 4πNe2/m the squared plasma

frequency, N the dipole density, and Γ the damping term. fm0 is the oscilla-tor strength and �ωm0 the transition energy, both between the ground state0 and excited state m. From the previous relations it is clear that the elec-tronic structure derived from the theory can be directly compared with theε spectra, thus providing a deeper physical insight than indirect comparisonswith rough absorbance spectra.

In addition to the important connection with the electronic structure ofthe material described previously, n (n2 = ε) plays a major role in the perfor-mance of optoelectronic devices. Its value is very important in characterizing


the propagation and losses of lasing modes in waveguides, rings and micro-cavities [19]. In multilayer LED devices, the real part of the refractive indexof the polymer film defines the amount of light reflected back into the device,thus preventing its escape. It is therefore a critical parameter governing theexternal quantum efficiency in LEDs [16,17]. In photovoltaic devices, n is re-sponsible for reflectivity losses, which reduce the number of photons reachingthe heart of the device and hence diminish its efficiency. This problem canbe overcome by anti-reflecting (lower n) coatings or by engineering suitablesurfaces [20].

2.1.2 Determination of n by Spectroscopic Methods

In this section we focus on spectroscopic methods used to determine the realand imaginary parts of n(ω). It is not our aim to discuss all the methods usedin semiconductor physics, but only those commonly applied to CP, based onreflectance/transmittance and ellipsometric measurements. At the end, wereport briefly on other methods that are seldom used or work only in reducedspectral ranges.

Reflectance and Transmittance. It is well known that when light crossesthe interface between two media it is both reflected and transmitted. Thequantitative amount of the two phenomena at the interface (supposed to beflat) is described by the Fresnel equations that relate the intensity of the elec-tromagnetic reflected (r) and transmitted (t) fields with those of the incidentlight [21–23]. These equations depend on the complex dielectric constants ofthe media and on their geometry, namely, the incidence angle φ0, related tothe refraction angle φ1 by Snell’s law (n0 sinφ0 = n1 sinφ1), and the thick-ness of the film. (Here the lower indices indicate the different media in whichpropagation takes place.) Moreover, they depend on the polarization of theincident light.

The simplest case is that of a semi-infinite medium, i.e., a strongly absorb-ing medium (1, n1 = n + ik) preventing the incident light from reaching theback of the sample. Only the reflected light can be collected and, in typicalexperimental conditions of near-normal incidence (φ0 ≤ 10◦) with the lightcoming from the air (0, n0 = 1), the s and p components are identical andthe absolute reflectance assumes the well known form

R =(

n1 − n0

n1 + n0

)2

=(n − 1)2 + k2

(n + 1)2 + k2 . (2.5)

It is clear that (2.5) contains two unknowns, namely n and k. We need anadditional independent measurement in order to determine them.

This problem is solved using the Kramers–Kronig (KK) integral equa-tions, which connect the dispersive (real part) and dissipative (imaginarypart) reaction processes, by using the fundamental principle of causality and


linearity between stimulus and reaction [24]. The KK relations are widelyused not only in optics but also to study the mechanical [25] and piezoelectric[2] relaxation properties of polymers. Absolute reflectivity at nearly normalincidence is an optical function often used in the study of thick organic films,both in their semiconducting [13,26–32] and metallic [33,34] states. For thesereasons, we report here the corresponding KK relation between the phaseθ(ω) and the modulus R of r, viz.,

θ(ω) = −ω

πP∫ ∞

0

lnR(ω′)ω′2 − ω2 dω′ , (2.6)

where P denotes the principal value of the integral. θ(ω) could then be cal-culated at any frequency if the full spectrum of R(ω) were known. Since thisis not possible, empirical extrapolations beyond the available experimentalrange are necessary. At high energies, above the upper limit R2(ω2) of theexperimental data, the function

R = R2

(ω2

ω

)p

(2.7)

is adopted, where the exponent p is chosen in such a way as to reproducethe experimental values of some separately measured optical properties atdifferent frequencies. ω2 is usually around 5–6 eV, but spectral characteri-zation in vacuum UV is sometimes available [29]. In the low energy limit,the extrapolation is different if the material is semiconducting (an eventuallyflat spectral dependence, thus neglecting phonon contributions) [13,26,32] ormetallic (Hagen–Rubens tail) [18,33]. Knowing R(ω) and θ(ω), the problemof determining the real and imaginary parts of an optical function for a semi-infinite medium is solved.

The natural extension of this model is to consider a free-standing film,i.e., a thin transmitting sample not deposited on a substrate. In this casewe have two interfaces (assumed to be flat) and transmission and reflectionFresnel coefficients at both interfaces (air/material and material/air). Eventhough it is not easy to produce such films, some examples are reported inthe CP literature [13,14,26,27,32]. Assuming that the medium is in vacuum(n0 = n2 = 1) with thickness d, it is easy to calculate the total reflectance Rand transmittance T of the sample as [21–23]

R =R

[1 + e−2αd + 2e−αd cos

4πnd

λ

][1 + e−2αd + 2e−αd cos

(4πnd

λ+ 2δ

)] , (2.8)

T =e−αd

[(1 − R)2 + 4R sin2 δ

][1 + e−2αd + 2e−αd cos

(4πnd

λ+ 2δ

)] , (2.9)

tan δ =2k

n2 + k2 − 1. (2.10)


Equations (2.8) and (2.9) describe the total reflectance and transmittanceconsidering the coherent sum of all the contributions coming from the twointerfaces. In the ideal case this gives rise to a progression of interferencefringes in the spectral region where absorption is negligible [13,26,27,32,35].The effect is smeared out by any imperfection in the surface or by inhomo-geneity in the thickness. When these effects are not too pronounced, weakfringes can be observed and partial coherence of the reflected and transmittedcontributions at the interfaces has to be taken into account. In this context,several examples are reported both for inorganic [36,37] and organic [32]semiconductors. If defects fully destroy coherence, (2.8) and (2.9) become

R = R +(1 − R)2Re−2αd

1 − R2e−2αd, (2.11)

T =(1 − R)2Re−αd

1 − R2e−2αd. (2.12)

At this point, both in the case of coherent [(2.8) and (2.9)] and incoherent[(2.11) and (2.12)] R and T spectra, numerical inversion of the correspondingequations delivers n if the thickness is known. The model is easily extendedto several flat and parallel interfaces, as in the case of a multilayer depositedon a substrate [21,22]. In this case, as the thickness of the layers and n forthe substrate are known, numerical inversion of the corresponding equationsyields n for the unknown layer [38–41]. The critical feature of this procedure isthe accurate determination of the thickness (tens to hundreds of nanometres)of the different layers. This is what limits uncertainty in the determinationof n.

Ellipsometry. Determination of n(ω) by KK analysis and coupled measure-ments of R and T are affected, respectively, by the problem of the tails addedto the experimental R(ω) spectra and by the need to perform R and T mea-surements separately. These problems, which introduce some uncertainty, canbe solved by spectroscopic ellipsometry. The technique involves analyzing thepolarization of a light beam reflected by a surface. The incident beam mustbe linearly polarized and its polarization should be allowed to rotate. A sec-ond linear polarizer then analyzes the reflected beam. The roles of polarizerand analyzer can be exchanged. The amplitudes of the s and p componentsof the reflected radiation are affected in a different way by reflection at thesurface. The important function describing the process is the ellipsometricratio ρ, which is defined as the polarization of the reflected wave with respectto the incident wave, expressed as the ratio between the Fresnel coefficientsfor p and s polarizations:

ρ =rp

rs= eiΔ tanΨ , (2.13)

where Ψ is related to the variation in the intensity of the signal while Δ isthe relative phase. A single ellipsometric measurement allows us to determine


independently the two parameters tanΨ and cosΔ. These do not have aphysical meaning, but they can be related through appropriate modeling tothe complex refractive index of the system [42]. In fact, in the simple case ofa semi-infinite medium in vacuum, the dielectric constant takes the form [22]

ε = sin2 φ0 +(1 − ρ

1 + ρ

)2

sin2 φ0 tan2 φ0 . (2.14)

The technique can also be used for multilayered structures. The correspond-ing equations are then more complicated and are usually applied to inorganicsemiconductors [36–38] due to their better defined interfaces and geometrycompared with organic semiconductors. In the case of transparent media(k = 0), the ellipsometric equations can be used to determine both n and thethickness of the film with sensitivity below 1 A. This is much better than canbe achieved by methods based on R and T , thus reducing the uncertaintyin the n determination. Several examples of ellipsometry applied to CPs arereported in the literature [32,43,44].

Other Methods. The methods for determining n described in the previoussections have essentially two advantages: they are quite simple and they pro-vide the spectral dependence of the optical properties. For these reasons theyare widely used in the CP scientific community. However, other methods havebeen successfully applied, such as waveguide spectroscopy [35,45–50], surfaceplasmon resonance [49,51], and photothermal deflection spectroscopy (PTDS)[45,52,53]. The first two are limited to selected wavelengths (the laser lines),but can provide, in addition to n, its anisotropy (in-plane and out-of-planecomponents), as well as its nonlinear optical components if used with high il-lumination power. PTDS is particularly useful for determining small losses inthe transparent spectral region with very high accuracy (usually better thenthat achieved by spectroscopic methods). Further techniques are describedin the literature [23,54].

2.1.3 Anisotropy

Up to now we have considered the CP film as an amorphous, homogeneousand isotropic medium. However, CPs are intrinsically anisotropic since the π-electrons are delocalized along the macromolecule backbone. An anisotropicoptical response, typical of oriented samples, is extremely important both forfundamental science (e.g., comparison with theoretical predictions) and fortechnological reasons (polarized emission is recommended in displays [55,56]).The orientation process for conjugated polymers is very difficult and severalapproaches have been used to remove the typical random-coil conformationof CP and to induce the extended aligned conformation. It is not the aim ofthis article to review all orientational techniques used with CPs. However, itshould be mentioned that very high degrees of orientation have been achieved


for several families of CPs merely using the tensile drawing technique. Thiscan be applied either to a non-conjugated precursor which is then converted toa CP [13–15,32,57] or to conjugated polymers blended in ultrahigh molecularweight (UHMW) polyethylene (PE) [58,59]. In all other cases the orienta-tion obtained is poor or, even if excellent, is due to a particular choice andengineering of the polymer and substrate, thus preventing its more generalapplication. Examples of these techniques are the growth of single crystals[60,61] and the deposition of epitaxial [62] or rubbed films [55,63].

We shall now discuss ways in which anisotropic optical constants of ori-ented CP films can be studied. First of all, we have to set out the motivationfor this task. If we are interested in determining the anisotropic optical con-stants of the film in order to reveal details in the electronic structure of thematerial, only highly oriented films should be considered. Otherwise mis-alignments of the polymeric chains mask their intrinsic anisotropies [26]. Onthe other hand, it is also interesting to characterize samples that could pos-sess some unintentionally induced anisotropy due to the deposition processand/or morphology. These anisotropies, even if small, can significantly af-fect the properties of the films (light propagation [45–50] and light emission[17,64]).

Assuming the sample highly oriented with cylindrical symmetry (a goodapproximation for orientation by mechanical stretching), it possesses uniaxialsymmetry and the dielectric tensor is diagonal. In this case its componentalong the stretching direction (parallel component) and two identical compo-nents in the perpendicular direction (perpendicular components) are easilydetected by simply orienting the optical axis (stretching direction) parallel orperpendicular to the plane of incidence of the light. In this case, the expres-sions for R and T for parallel and perpendicular components are found from(2.8) and (2.9) by inserting the corresponding component of n (n‖ and n⊥)[21,22]. In the case of ellipsometry, we have to write four Fresnel coefficientsfor p and s polarizations and for orientation of the optical axis parallel andperpendicular to the incidence plane [30,32,65,66]:

r‖s =

cosφ −√

n2⊥ − sin2 φ

cosφ +√

n2⊥ − sin2 φ

, r‖p =

n‖n⊥ cosφ −√

n2⊥ − sin2 φ

n‖n⊥ cosφ +√

n2⊥ − sin2 φ

, (2.15)

r⊥s =

cosφ −√

n2‖ − sin2 φ

cosφ +√

n2‖ − sin2 φ

, r⊥p =

n2⊥ cosφ −

√n2

⊥ − sin2 φ

n2⊥ cosφ +

√n2

⊥ − sin2 φ, (2.16)

where r‖,⊥p and r

‖,⊥s are the Fresnel reflection coefficients for p and s po-

larized light with the optical axis of the sample parallel or perpendicular tothe incidence plane. The incidence angle is φ and the detector is fixed at theangle −φ in the incidence plane. On the basis of a couple of ellipsometric mea-surements performed for the two orientations of the sample at fixed incidence


angle φ, we can invert equations (2.15) and (2.16) numerically and extract n‖and n⊥. Since these nonlinear equations provide multiple solutions, we haveto select the correct values by comparing the ellipsometric results obtainedat different incidence angles and/or compare with those found using differentmethods (if available).

When optical anisotropies form spontaneously in the polymeric film dur-ing deposition, the situation is more complicated. Significant effects are ob-served in optical and spectroscopic properties, such as LED emission [17]and waveguide propagation [45–50,52,64]. For these films, accurate evalua-tion of the optical constants is more difficult and must be based on vari-able incidence angle measurements, as in the case of surface plasmon res-onance [45–47], waveguide propagation [48–50,52], ellipsometry [64,67], andreflectance/transmittance [68].

2.1.4 Examples

As a relevant example of the procedures described previously for determiningnω and investigating the electronic structure of CPs, we refer to the case ofhighly stretch-oriented PPV [32,69]. Figure 2.2 shows the polarized transmit-tance and near-normal-incidence reflectance spectra of highly stretch-orientedPPV. In the near infrared, a progression of well resolved interference fringesis observed for both kinds of measurement. The different paths of the fringesdetected for the two polarizations reveal the anisotropy of the refractive in-dex. Above 2 eV, several electronic transitions are detected in the reflectancespectra. For the parallel component, a strong signal associated with the 0–0 vibronic transition of the lowest absorption band is observed at 2.48 eV(peak I) and is followed by a well-resolved vibronic progression with peaksat 2.70 and 2.95 eV, and by a shoulder at 3.10 eV. (For a detailed discussionof the vibronic progression, see [32].) The change in slope of the spectrumaround 3.76 eV indicates the presence of additional transitions (peak II). Onthe high energy side of the spectrum, a low intensity peak is observed at4.71 eV, accompanied by a shoulder at 4.56 eV (peak III). The lowest opticaltransition and its vibronic satellites cannot be detected in the perpendicu-lar component of the reflectance spectrum. For this spectrum a transition isonly revealed in the UV spectral region at 4.47 eV. A fourth transition (peakIV), whose polarization is at present not fully characterized, has also beenidentified [32,69].

From the data reported in Fig. 2.2 and from spectroscopic ellipsometrymeasurements, the anisotropic complex optical constants of oriented PPVhave been determined [32,69]. Several different data analyses, described pre-viously, were carried out on the R and T spectra in order to extract n, bothbelow and above the HOMO–LUMO transition (transparent free-standingfilm and bulk material, respectively). In order to evaluate n below 1.6 eV,where the sum of R and T is equal to 1 within experimental error, a nu-merical inversion of the R and T spectra was performed by assuming k = 0


2.0 2.3 2.7 3.0 3.3 3.7 4.0 4.3 4.7 5.00.0

0.2

0.4

0.6

0.8

1.0

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Energy (eV)

Fig. 2.2. Polarized transmittance (dashed line) and near-normal-incidence re-flectance (continuous line) spectra of highly stretch-oriented PPV

and modeling its reflectance and transmittance as described by (2.8) and(2.9). The values of n used as input for the numerical inversion were ob-tained from the pronounced interference fringes observed in transmittanceand/or reflectance spectra. In this spectral region, the model provides the ndispersion spectra (for the parallel and perpendicular components) as well asthe sample thickness d in very good agreement with values obtained usinga comparator (17–18 μm). The same model was also used without imposingthe condition k = 0. In this way, n can be determined in the full spectralrange where T is available, thus affording a description of the increase in theabsorption coefficient at the absorption edge where the approximation k = 0is no longer valid. The values of n and k obtained by means of this simulationmodel account very well for the interference fringes and provide k = 0 below1.6 eV, according to the first procedure used.

With an appropriate extrapolation of the data beyond the highest andlowest measured energies, we also calculated n by Kramers–Kronig (KK)analysis [32]. The agreement between the optical constants determined bythe R and T inversion procedures and those obtained from KK analysis isvery good (see Fig. 2.3).

Finally, n was determined by spectroscopic ellipsometry. The main draw-back with this technique when applied to anisotropic samples is that themeasured ellipsometric functions tanΨ and cosΔ are related both to theincidence angle and the anisotropic reflectance coefficient for polarizationsparallel and perpendicular to the incidence plane. The parameters thus haveto be deconvolved from a set of measurements performed with different ori-entations of the sample [see (2.15) and (2.16)]. The complex refractive indexdetermined by ellipsometry is reliable only in the spectral region where thesample can be considered as a bulk material. In fact, below the absorption


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 1 2 3 4 5

k

Energy (eV)

(b)

0

1

2

3

4

5

6

(a)

Fig. 2.3. (a) Real and (b) imaginary parts of the refractive index of highly orientedPPV for the parallel and perpendicular components. Continuous line: KK analysis.Dot-dashed line: ellipsometry with φ = 65◦. Dotted line: ellipsometry with φ = 70◦.Squares: inversion of R and T using (2.8) and (2.9) with k = 0. Circles: inversionof R and T with (2.8) and (2.9)

edge, a spurious depolarized light component due to reflection on the backsurface of the sample is superimposed on the ellipsometric component, thusaffecting tanΨ and the n spectra. In fact, in Fig. 2.3, below 2.3 eV, the nspectra obtained by ellipsometry are very noisy and are significantly differentfrom those obtained by the other methods. Above the HOMO–LUMO tran-sition, the agreement between the KK and ellipsometric results is very goodfor the parallel component (Fig. 2.3). Comparison of results obtained withdifferent techniques is less successful for the perpendicular polarization sincethe weakness of the signals makes all the ellipsometric measurements more


sensitive to any small experimental or sample imperfections. However, theymay still be considered satisfactory.

From these data and in particular from the study of the polarization ofthe optical transition, an assignment of the spectra has been provided on thebasis of quantum chemical calculations, extended to include the electroniccorrelation [32,69,70]. We summarize here the main results.

Peak I (parallel polarized) originates from π–π∗ transitions between delo-calized (d) levels. Its transition energy is blueshifted with respect to the ex-perimental data due to solid state effects and geometric relaxation, neglectedin the theoretical calculations discussed here [32,69]. Peak III originates froml → d∗/d → l∗ (l localized) transitions and has a dominant polarization per-pendicular to the chain axis, while peak IV results from l → l∗ excitationsand is polarized parallel to the chain axis.

Concerning peak II, quantum chemical calculations suggest that theshoulder observed in the parallel reflectance spectrum at about 3.7 eV (seeFig. 2.2) corresponds to an optical transition between delocalized levels (d →d∗), induced by finite-size effects (borders of the conjugated segment) andis polarized along the chain axis, in full agreement with experimental data.Since the intensity of this peak is expected to decrease when the chain lengthis increased [32,70], its small signal suggests a reduced contribution of the(conjugated) chain ends and hence the presence of relatively long conjugatedsegments (which should not be confused with the chain length).

It is interesting to compare the properties of PPV with those of its alkoxy-substituted derivative. They have a very similar polarized absorption spec-trum [59] but a different assignment, in particular as far as peak II is con-cerned. These PPV derivatives are characterized by the appearance around3.7 eV of new absorption peaks, mostly described by l → d∗/d → l∗ excita-tions, due to the breaking of charge conjugation symmetry upon attachmentof electroactive substituents on the backbone [70]. The main effect of thealkoxy groups is to decrease the separation between the energies of the low-est l → d∗/d → l∗ and d → d∗ excitations and thus to enhance the strengthof the interaction between the two types of excitation. This allows efficientintensity borrowing from the lowest absorption band which contributes to theintensity of peak II. The latter is also expected to decrease for growing chainlength [70]. Quantum chemical calculations show that the transition dipolemoment of these new peaks is governed by their weak d → d∗ character(i.e., the contributions of the l → d∗/d → l∗ excitations tend to cancel eachother), thus yielding a polarization along the chain axis [70] in full agreementwith experimental data [59]. The polarized optical spectra of PPV and itssubstituted derivatives have also been interpreted on the basis of electronicband structure calculations implemented with excitonic effects [59,71]. Eventhough this theoretical method, widely used in solid state physics, seems tobe very different from the quantum chemical approach, they are both hoped


to merge into a unified picture describing experimental polarized optical datawhich have only become available in the last couple of years [32,59,69].

From the optical standpoint, oriented PPV derivative samples blendedin UHMW PE, very important for fundamental physics, invite an additionalcomment. If in addition to ascertaining their spectroscopic properties wewished to perform a full optical characterization, we would encounter prob-lems. In fact, by applying (2.8) and (2.9) [or (2.15) and (2.16)], we can onlydetermine an effective n, which is not intrinsic but depends on the amounts ofthe different materials (PPVs and UHMW PE) mixed together to obtain theblends. To our knowledge, the effective medium theories [72] usually adoptedfor inorganic semiconductors and based on the molar fractions of the compo-nents have never been used for CPs blended into a matrix. A study of thisproblem could be very useful for organic solar cells where photoinduced donorand acceptor molecules are mixed together. The problem is further compli-cated by the fact that n for CPs, fullerenes and other typical molecules usedin these devices is not known in detail, so that the basic ingredients for effec-tive medium models are lacking. In addition, the core of these devices is theinterpenetrating bicontinuous donor/acceptor molecular network [73]. Thecomplex refractive index of this blend retains a strong contribution due tomolecular interaction which is difficult to relate to any optical constants thatmay be derived from the study of pure bulk films, thus making the problemnon-trivial.

2.2 Spectroscopic Properties of Excited States

Organic solar cells are based on the photoinduced charge transfer process,i.e., the transfer of an electron from the excited states of the donor molecule(usually a conjugated polymer) to a molecular acceptor. In this way the cre-ation of stable polarons allows collection of mobile charges at the electrodes.If the charge generation process is to be successful, competing photophysicalmechanisms have to be reduced. These include radiative and non-radiativerecombination of the geminate pair, polaron recombination or triplet excitonformation. A great deal of fundamental research is therefore dedicated tostudying these excitations, using a number of experimental and theoreticaltools, in order to understand the basic photophysical processes involved andthereby improve device efficiency.

The elementary excitations of a conjugated polymer chain can be de-scribed within the mono-electronic approach as electron and hole quasipar-ticles [74] in a one-dimensional band structure, possibly weakly bound intoextended Wannier-type excitons [71,75]. Within this framework, electron–phonon interactions lead to a peculiar family of exotic excitations includingsolitons, polarons, polaron pairs and bipolarons. In many cases, however,disorder is so significant that the polymer films are better described as anensemble of relatively short conjugated segments [76], essentially behaving


as molecules. Their elementary excitations can then be described as singlet,triplet and charge transfer states [77], possibly modified by intermolecularinteractions into dimers, polaron pairs and excitons (Frenkel-type). This ap-proach is particularly suitable when dealing with conjugated oligomers oflimited size because they are a good reference system without the disordertypical of polymers.

Since all these excitations possess clear spectroscopic fingerprints, a verypowerful tool for studying their photophysics is the so-called pump-and-probetechnique, which can be related to the optical nonlinearities of the material.As far as optical properties are concerned, the change in refractive index uponexcitation (Δn or Δk), either optical or otherwise, is the ‘nonlinear’ part ofthe optical response. Traditionally two approaches have been developed tomeasure nonlinearities, based on different techniques:

• Measuring Δn in a spectral region were Δk is much smaller. Such nonlin-earities are referred to as non-resonant (associated with virtual states),being excited by photon energies far away from any electronic transition.These nonlinearities can be exploited in photonic devices for full opticalsignal processing, in which optical losses due to ‘real’ absorption are keptlow [31,45–52,78].

• Measuring Δk in order to investigate photo-excited state properties asso-ciated with the CP physics. The latter nonlinearities, measured by trans-mission techniques, are called resonant, being associated with absorptionby real states (via single- or multi-photon transitions). The correspond-ing Δn which is also present and causes a reflectivity change is neglectedbecause it affects transmission only weakly [79].

A clear-cut distinction between the two processes is the time response, whichis ultrafast in the former (essentially instantaneous), and finite (associatedwith the lifetime of real excitations) in the latter. Here we limit our discussionto resonant nonlinearities, which are crucial for describing the fundamentalworking mechanisms of organic photovoltaic cells. Examples will be reportedconcerning isolated molecules and the condensed phase.

2.2.1 Basic Notions of Pump–Probe Spectroscopy

In the basic experiment, a first optical pulse (pump) is absorbed by thesample. A second, time-delayed pulse of weaker intensity is used to probe thechange in optical response. Commonly, the test pulse probes the change intransmission, given in the small signal limit as

ΔT (ω, τD)T

= Kσ(ω)∫

A(τD − t)G(t) dt . (2.17)

In this expression K groups together a number of constant factors, σ(ω) isthe cross-section of the photoinduced transition, and A(t) is the response


function containing the photoinduced population ΔN(t). Finally, G(t) is theexperimental pump–probe cross-correlation and represents the time resolu-tion. In Sect. 2.4, we describe in some detail how (2.17) is obtained and whichapproximations are involved.

A few other observations are relevant here. Around t = 0, i.e., whenpump and probe overlap in time and space, nonlinear interference-like effectsmay take place, giving rise to the so-called coherent artifact [80]. This isa scattering of pump amplitude in the probe direction due to the transientgrating formed by coherent superposition of the two beams. This effect createsa large spike in the transient transmission signal, lasting a time comparable tothe coherence time of the pulses. This occurs only in degenerate experiments,when pump and probe are coherent. If the pulse duration is comparable to orshorter than a characteristic dephasing time in the sample, coherence may beinduced in the sample. The latter usually appears in the pump–probe timetrace [81] as a periodic modulation. Vibrational coherence, for instance, givesrise to periodic modulation of the transmitted signal at frequencies typicalof nuclear motion. The latter may provide useful information on the vibronicdynamics [82], but due to its complexity, we will not discuss these effectshere. The interested reader is referred to more specific publications [83].

The outcomes of a pump–probe experiment are the cross-sections σji (ω)

for each excited state population i and transition j and the kinetics ΔNi(t) ofthe excited state population. The investigated temporal and spectral rangeand also the excitation density used in the experiment depend on the lasersource. Essentially two approaches are followed, either a high pulse repetitionrate (MHz) and small pulse energy (0.1 nJ) or vice versa (Hz–kHz, mJ–μJ). Spectral tunability in the former is achieved by parametric generation(optical parametric oscillators OPO). In the latter it is achieved by whitelight supercontinuum generation and parametric amplification (OPA). Thespectral range easily covers the visible, and in some cases may reach the nearinfrared [84]. Recently, experiments have also been carried out in the mediuminfrared region [85]. The time resolution is typically of the order of 100 fs andthe time domain extends to hundreds of ps or a few ns. For longer time delays,completely different techniques are used, based on electronic time resolution.

2.2.2 Interpretation of Pump–Probe Experiments

The transmission difference spectrum ΔT/T , i.e., the normalized differencebetween T for the excited state and T for the ground state contains onlythree types of signal, as sketched in Fig. 2.4:

• photobleaching (PB),• stimulated emission (SE),• photoinduced absorption (PA).

PB is the reduction of optical density in the region of ground state absorp-tion and corresponds to positive ΔT (increased transmission). It stems from


the depletion of the ground state population number due to the missingmolecules now in the excited state. The PB spectral shape resembles that ofground state absorption. What is generally regarded as SE is an increasedtransmission in the fluorescence (PL) spectral region, i.e., a process of lightamplification due to transitions such as 2 → 1′. Its spectral shape resemblesthat of the PL, with some exceptions:

• the 0–0 transition cannot generally be distinguished from PB, and actu-ally contributes to it,

• SE may originate from a hot excited state and appear blueshifted withrespect to PL,

• there is an ω4 correction factor, accounted for by the Einstein theory ofspontaneous and stimulated transitions [86].

Finally, PA is associated with negative ΔT and is due to optical transitionsfrom newly occupied states (following photoexcitation) to higher-lying levels,such as 2 → 3 or 4 → 5. PA bands are very often asymmetric towards highenergy due to underlying vibrational structure which is seldom resolved [87].

SE

PA

PB PA

1

2

3

5

4

1’ 1

2

3

5

4 Pump

a) EXCITATION b) PROBING

2’’’

Fig. 2.4. (a) The excitation process. The pump radiation (solid line) populates ahigh-lying vibronic level. Relaxation (dashed line) populates lower-lying states. Thepopulation is redistributed: black circles correspond to occupied states and whitecircles to empty states. (b) Probing. Photobleaching (dotted lines), photoinducedabsorption (PA) and stimulated emission (SE) (solid lines). Only one vibrationalreplica is shown (tilted arrow)

In conjugated polymers and oligomers, the behavior of photoexcited statesobeys general rules of molecular photophysics, such as the Kasha [88] andVavilov [77] rules. These are empirical observations, rather than exact state-ments or laws. However, they provide a useful basis for discussion. The Kasharule states that fluorescence occurs from the lower-lying excited state, inde-pendently of the excitation energy. The Vavilov rule states that the fluo-


rescence quantum yield is independent of the excitation energy. Both followfrom the observation that intramolecular vibrational relaxation (IVR) andinternal conversion (IC) are extremely fast with respect to radiative decay ofthe lowest singlet state S1. IVR is the process of excess vibrational energy re-distribution, which proceeds from optically coupled modes to other molecularmodes and ultimately to the environment. (The latter is called vibrationalcooling.) IC is the radiationless transition between two electronic states ofthe same multiplicity. Linear conjugated chains display important deviationsfrom such rules. In particular the Vavilov rule may not be fulfilled due toalternative relaxation paths, such as charge separation and singlet fission,which are usually present in the solid state.

2.2.3 Isolated Molecules

We begin with the excited states of ‘isolated’ linear π-conjugated moleculesstudied in solutions, dilute blends or particular crystals. The notion that dis-solved molecules are isolated is only partially true, due to their interactionwith the environment (usually the solvent) and to its polarization. For in-stance, in the case of solvents inducing hydrogen bonding (like methanol), theisolated molecule approximation fails. Moreover, highly polar solvents mayintroduce phenomena not observed in isolated molecules dissolved in nonpo-lar solvents. New energy deactivation channels or enhancements of certainreaction paths can occur, such as charge transfer reactions. The high dielec-tric constant of the solvent screens ion interactions and lowers their energy[89], thereby increasing the CT rate. The effect becomes dramatic if the con-jugated oligomers possess a permanent dipole moment [90] which acts as adoorway for energy dissipation to the polar solvent.

There are several ways of isolating molecules, in addition to dilution inappropriate solvents. For instance, extremely long PDA chains can be dilutedin their monomer single crystal by exploiting the peculiar polymerizationmechanism [91] of this class of polymers. In the case of CPs blended with non-conjugated macromolecules (polyethylene, polymethylmethacrylate, etc.) orinclusion crystalline compounds [92], the interaction between molecule andenvironment is usually strongly suppressed, but at the expense of the sampleoptical density, in a way that may easily challenge the common sensitivity oftime-resolved techniques.

Assuming that an isolated conjugated molecule can be obtained, its pho-tophysics can be summarized as follows. The ΔT/T spectrum immediatelyfollowing photoexcitation shows the spectral features of the pump-inducedexcited state. This is usually a vibronic state with a very short lifetime andits spectrum can only be detected using ultrashort pulses with time durationaround 50 fs or less [93]. The lowest singlet state S1 is populated after ultrafast(< 100 fs) IVR, with efficiency close to one. The ΔT/T spectrum shows PB ofthe ground state absorption, SE (for emitting CPs) and PA due to S1 → Sn

transitions. Deactivation of the singlet state occurs radiatively, by photon


emission, or is radiationless, by IC and ISC to the triplet manifold. IC is dueto non-adiabatic coupling between electronic states. In ring-containing con-jugated systems it depends on the conformational mobility, being enhancedin more mobile systems [94]. ISC is due to spin–orbit coupling, which mixesthe spin character of the molecular wavefunction, yielding a non-negligibleprobability of radiationless energy transfer from the singlet to the tripletmanifold [95]. The build-up of the triplet state population follows in this casethe decay kinetics of the singlet state [96]. The limiting rate is indeed thetotal singlet lifetime.

0 p s

4 0 p s

1 0 0 p s

450 500 550 600 650 700

w a v e len g th (n m )

-0 .08

-0 .06

-0 .04

-0 .02

0.00

0.02

0.04

0.06

ΔT

/T

200 ps

600 ps

Fig. 2.5. Transmission difference spectra ΔT/T of quaterthiophene in solution.Photobleaching (PB) is seen as a rise towards the low wavelength edge and de-velops outside the experimentally accessible spectral range. Stimulated emission(SE) and photoinduced absorption (PA) from S1 are seen at 500 nm and 675 nm,respectively. They decay in about 600 ps and a new PA band appears, at 560 nm,assigned to triplet–triplet transitions. A clear isosbestic point occurs at 600 nm.The data are an example of intersystem crossing in photoexcited molecules inducedby spin–orbit wavefunction mixing


As an example, Fig. 2.5 shows ΔT/T spectra measured at different pump–probe delays for a thiophene oligomer in solution. The initial spectrum showsSE (at 500 nm) and PA (at 675 nm) due to transitions from S1. Thesefeatures decay and a new PA band grows at 560 nm, assigned to triplet–triplettransitions. The isosbestic point at about 600 nm clearly indicates the simplemother–daughter kinetics and the presence of a single rate characterizingboth singlet decay and triplet formation. This behavior is typical of ISC.The thus-populated triplet state is long-lived (μs–ms) due to the reducedprobability of T1–S0 transitions. Charged states are seldom observed on theultrafast time scale when in solution, i.e., they do not play a major role inthe primary excitation and relaxation processes of isolated molecules.

2.2.4 Condensed Phase

Photophysics in the condensed phase is much more involved than in solutions.In fact, there is much debate on the subject and the nature of the primaryexcitations are not easily assigned. Due to new mechanisms not yet elucidatedor identified, singlet, triplet and charged states are all possible candidates forobservation at short times, and there are experimental claims and evidence foreach of them [97–103]. Defects and impurities may mask the identification ofmolecular states, which can also be substantially modified by intermolecularinteractions [61,104,105].

First, we discuss thermalization of the optically excited state. There areessentially two processes in the condensed phase. One is an intramolecularprocess, the very same IVR we discussed earlier. Very little data exists onsuch phenomena [100], but there is no reason to think that it should differfrom data for isolated molecules. It is very likely completed within 100 fs.The second mechanism is intermolecular, either inter-conjugated-segment orinter-chain. This is an energy relaxation process within the disorder-induceddistribution of states. It may occur on the 1–10 ps time scale [106]. Its opti-cal signature on short time scales is redshift of spectral features and loss ofdichroism induced by linearly polarized exciting radiation. The redshift stemsfrom the longer conjugation length of molecules at the bottom of the distri-bution. Polarization loss is consequent to energy migration within randomlyoriented molecules. As an example, Fig. 2.6 shows data obtained in films ofmethyl-substituted ladder-type poly(p-phenylene) (mLPPP, Fig. 2.1), fromwhich an estimate of the time scale of the process can be extracted.

Intermolecular deactivation paths may substantially affect IC in the con-densed phase. In general it is not true that the whole excited state popula-tion reaches S1. Charge separation is one of the possible channels for energyto follow, giving rise to a branching with neutral states. The process seemsmore favorable from higher-lying states [107,108]. In this case, charge-transferstates can be intermediate before complete dissociation. The physical mech-anisms responsible for the charge photogeneration processes (direct polaron


2.2 2.3 2.4 2.5 2.60.0

0.4

0.8

1.2

1.6

ΔT (

arb.

un.)

Energy (eV)

0 3 6 9 12

498

496

494

492

SE p

eak

(nm

)

Time (ps)

-10 0 10 20 30 40 50

0.0

0.4

0.8

1.2

1.6

λpr@780 nm

ΔT (

arb

.un

.)

Time (ps)

0 1 2 3 4 50.0

0.1

0.2

0.3

0.4

0.5

Pho

toin

duce

d A

nis

otr

opy

Time (ps)

Fig. 2.6. Top panel : spectral migration of SE measured in photoexcited films ofmLPPP. The two spectra are SE just following excitation and after 10 ps. Theinset shows the shift of the SE peak with time on a wavelength axis. Bottom panel :photoinduced dichroism decay in mLPPP films following excitation with linearlypolarized 390 nm pulses after 150 fs. The inset shows the pump–probe traces forparallel (higher) and perpendicular (lower) pump–probe polarization. Both datasets are assigned to the same phenomena, namely, energy migration within theconjugated segments or chains


generation, charge transfer states, polaron pairs, etc.) in conducting polymersare widely discussed in [103].

Singlet fission into a spin-correlated triplet pair may also take place. Thisprocess essentially circumvents the spin selection rule and allows generationof triplets on an ultrashort time scale. The observations discussed for spin–orbit coupling ISC no longer hold. In particular, singlet and triplet featuresappear on the same time scale because fission takes place during IVR. Suchtriplets are correlated in pairs and may decay faster then conventional onesdue to mutual ‘geminate’ recombination. The phenomenon is not necessarilyrestricted to the three-dimensional case [109], but may also take place inlong conjugated chains. It has been discussed in some detail for solid state,isolated polydiacetylene chains [91,110].

500 600 700 800 900

0.4 ps

400 ps

2 %

x 5

Wavelength (nm)

Δ T/T

Fig. 2.7. Transmission difference spectra ΔT/T of mLPPP films following photoex-citation at 390 nm and after 150 fs. The spectrum for 0.4 ps pump–probe delayshows features of S1: PA at 840 nm, SE at about 500 nm and the edge of PB below450 nm. For 400 ps pump–probe delay, the spectrum (enhanced by a factor of 5)shows very weak signatures of S1 and contains new features: PA at 680 nm is as-signed to charged states and PA at 950 nm to the triplet state. Here the generationmechanism has not yet been elucidated for either species

Finally, the presence of molecular aggregates in samples with complexmorphology can play an important role in emission [111] because they canhave large radiative rates and behave as energy sinks in the excited material[112]. As an example, Fig. 2.7 shows the ΔT/T spectra of an mLPPP film.The spectrum at short time delays (0.4 ps) exhibits singlet S1 features: PBat 450 nm, SE at 500 nm and PA at 840 nm. These decay on the 100 ps timescale. The spectrum at 400 ps shows absorption bands assigned to charged


and triplet states at 650 nm and 950 nm, respectively, which are longer-lived.The quantum yield for charge generation is very low, below 10%, as estimatedassuming equal cross-section for neutral and charged states. Its mechanism,investigated in some detail in [113], is not yet fully understood as the exactbalance between radiative and non-radiative states remains unclear. It seemsthat the larger efficiency for charge photogeneration can be obtained only inmixed, donor–acceptor-type systems. Particularly relevant for photovoltaicapplications are the CP–fullerene derivative composites. Recent pump–probeexperiments with sub-10-fs time resolution have shown that charge separation(electron transfer from the polymer to the fullerene molecule) occurs within100 fs [114]. Being so fast, the forward process is extremely efficient. Backtransfer is, however, extremely slow, making this system very appealing forphotovoltaic applications [73].

2.3 Conclusion

In this chapter we have reviewed a number of techniques used for opticalcharacterization of organic samples, in particular those concerning the de-termination of complex optical constants and the dynamics of elementaryphotoexcitations. It has been stressed that very good optical quality samplesare needed in order to obtain reliable estimates of the refractive index. Ingeneral, samples with controlled morphology, low defect and impurity con-centration, and good optical quality allow more reliable photophysical studiesand hence better determination of the intrinsic properties of the material.

A number of fundamental issues in the field of organic photoactive ma-terials are still open and much work is required. As a matter of fact, inspite of the exceptionally fast improvement in organic photovoltaic cells, ourunderstanding of the microscopic mechanisms controlling charge photogen-eration and transport, in particular with respect to the local environmentand morphology on the nano- and mesoscopic scales, have yet to be thor-oughly investigated. New techniques derived from those discussed here mayturn out to be useful in this context, e.g., micro-optical spectroscopy or near-field spectroscopy, perhaps applied to devices operating under real workingconditions.

2.4 Appendix: Derivation of (2.17)

For the pump and probe experiments, the transmission T of a sample isdefined in a very simple way, neglecting the reflectivity losses described inSect. 2.1:

T =It

I0= e−αd = e−2.303A , (2.18)

where A = log(1/T ) is the absorbance or optical density and d the sam-ple thickness. The absorption coefficient is related to the population of the


starting level by means of the cross-section σ(ω), which contains the wave-functions of the system and the transition operator: α(ω) = σ(ω)N . Thefrequency dependence describes the line shape of the absorption spectrum.Given a pulse of intensity I(t) impinging upon the sample surface, a slowdetector usually measures the time-integral of the transmitted pulse, i.e., thetransmitted energy

Et =∫

I(t)e−αddt = E0e−αd . (2.19)

When the sample is excited, a photoinduced non-equilibrium distribution ofthe population induces a change in T and thus also in A :

2.303ΔA = Δα d = − lnT ∗

T,

where T ∗ is the transmission of the excited sample.The change in the population distribution Ni(t) of the i th level due to

the pump excitation is ΔNi(t). Let us assume for simplicity that a singleΔN(t) population is induced. There is a new absorption associated with thispopulation, given by Δα(ω) = σ(ω)ΔN(t). [Usually many excited states iare involved, and more than one transition starts from each state with ratesproportional to σij(ω)ΔNi, so that the real equation is a sum over i and j.]ΔN(t) depends on the material and is represented by the impulsive responsefunction A(t) (i.e., the response to a delta-like pulse). Given the finite du-ration of the pulse, shorter but not negligible compared with A(t), the realchange in α is described by a convolution:

Δα(ω, t) = σ(ω)ΔN(t) = σ(ω)∫

A(t − t′)IP(t′) dt′ , (2.20)

where the subscript P reminds us that the pulse is the pump. As an example,the response function A(t) may be the single exponential

A(t) =αP

�ωPe−t/τ ,

where τ is the lifetime of the excited state and �ωP is the pump photon energy.Omitting the frequency dependence for simplicity, the energy transmitted bythe excited sample is then

E∗t =

∫It(t − τD)e−[α+Δα(t)]d dt . (2.21)

The normalized transmission change, or transmission difference, is

ΔEt(τD)Et

=E∗

t − Et

Et=

∫It(t − τD)e−[α+Δα(t)]d dt

e−αd

∫It(t) dt

− 1 , (2.22)


which becomes simpler in the small signal limit, i.e., when

e−Δα d ≈ 1 − Δα d .

We now find

ΔEt(τD)Et

=

∫It(t − τD)Δα(t)d dt∫

It(t) dt

. (2.23)

Finally, from the expression for Δα, we obtain

ΔEt(τD)Et

= K

∫dtIt(t − τD)

∫dt′A(t − t′)IP(t′) . (2.24)

This quantity is often referred to as ΔT/T , the normalized transmission dif-ference, and it is the observable in the basic pump–probe experiment. Withsimple mathematical treatment [115], equation (2.24) can be written in themore appealing form

ΔT (ω, τD)T

= Kσ(ω)∫

A(τD − t)G(t) dt , (2.25)

describing the ΔT/T transient spectrum. In this expression

G(t) =∫

dt′It(t − t′)IP(t′)

is the experimental cross-section, representing the experimental time resolu-tion. It is a characteristic of the laser system and is generally measured bythe second harmonic generation (SHG) technique.

2.5 Appendix: Overview of Decay Kinetics

Single exponential kinetics occurs in the basic situation when the decay rateat time t is proportional to the population N(t) via a constant coefficient k,viz.,

dN

dt= kN .

k represents the overall molecular decay rate, comprising radiative (R) andnon-radiative (NR) contributions: k = kR+kNR. This kinetics is the basis forany qualitative discussion concerning time scale and process probability, butit is actually rarely encountered in real experiments, especially when studyingsolid state samples. There is a rich literature on mathematical models thatcan reproduce virtually any non-exponential kinetics, but it can be extremelydifficult to assess which one is physically relevant.


It seems to the authors that the simplest and most reliable explanation fornon-exponential decay is a distribution of decay rates, the latter being causedby disorder with various sources: site energy due to a distribution of conjuga-tion lengths or local environment (diagonal disorder), inter-site energy (off-diagonal disorder), dispersive transport, density fluctuations, and so on. Byintroducing a time-dependent rate K(t) in the rate equation, non-exponentialpopulation decay is obtained. Typical functions are the stretched exponen-tial exp(−t/τ)α and the power law t−α, which can fit most non-exponentialdecays measured in polymer films (see for instance [91], [110] and the refer-ences therein). A good rule for discussing transient properties is then to lookat time scales (i.e., the time for completing a process) rather than at rates,searching for correspondences which corroborate the interpretative model inother observables: wavelength, temperature, excitation density, electric field,magnetic dependence, and so on.

Several observables in time-resolved kinetics carry important informationand are quite easily measured: the excitation density dependence, the polar-ization dependence, and sometimes a periodicity in the time structure. Thefirst one allows us to distinguish between mono-molecular and bi-molecular(or many-body) reactions. If the dynamics changes when the excitation den-sity changes, this is a clear indication of excited state interactions or highlynonlinear (double excitation) processes, without the ambiguities inherent inkinetic analysis of measurements made at only one excitation density. Thesecond observable mentioned above is a very interesting tool for studying bothrelaxation and energy migration. Provided that sufficient structural data areavailable, much information can be extracted on the nature of the excitationand its propagation. In short, a linearly polarized pump induces a dichro-ism in the sample (notably in isotropic samples) and a loss of polarizationmemory. The randomization of the initial preferred orientation is caused byonly a few processes that can thus be identified. One is energy migrationto molecules with different orientations, and another is a redistribution ofthe wavefunction amplitude, caused by a relaxation process. A third, usuallyunimportant on the ps time scale, is molecular rotation.

Finally periodic structures in the time traces provide information on thecoherence of the excited state. Low modulation frequencies are due to coher-ent acoustic phonons and bring information on the energy relaxation process(conversion of electronic energy to phonons), sound propagation and energycooling in the systems (from their dynamics) [116]. As recently observed [82],high frequency modes indicate coherent nuclear motion along optically cou-pled coordinates (usually active in Raman modes as well). This opens up awealth of new possibilities for time-resolved spectroscopy.

Acknowledgements. A number of people contribute daily to the realizationof exciting new ultrafast experiments, and without their work we could nothave written this chapter. In particular we would like to thank Giulio Cerullo,


Mauro Nisoli, Salvatore Stagira and Margherita Zavelani-Rossi. Thanks goalso to Sandro De Silvestri for his continued support of our activity. We aregrateful to Dr. Maddalena Patrini and Prof. Franco Marabelli for severalstimulating discussions on the study of semiconductor optical constants inthe friendly environment of the Optical Spectroscopy Laboratory at the A.Volta Department of Physics, University of Pavia.

Finally, very special thanks are due to Prof. Giovanna Dellepiane, towhom both authors owe a great deal. She introduced us to this excitingresearch field, and was teacher and leader for several years, giving us theencouragement and motivation to forge ahead.

Financial support from the Ministry of University, Scientific and Techno-logical Research is also gratefully acknowledged.

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93. G. Lanzani, G. Cerullo, M. Zavelani-Rossi, S. De Silvestri: Synth. Met. 116, 1(2001)

94. G. Lanzani, M. Nisoli, S. De Silvestri, G. Barbarella, M. Zambianchi, R. Tubino:Phys. Rev. B 53, 4453 (1996)

95. J.B. Birks: in Photophysics of Aromatic Molecules (Wiley, London, 1970)96. B. Kraabel, D. Moses, A.J. Heeger: J. Chem. Phys. 103, 5102 (1995)97. J.M. Leng, S. Jeglinski, X. Wei, R.E. Benner, Z.V. Vardeny: Phys. Rev. Lett.

72, 156 (1994)98. G.J. Denton, N. Tessler, N.T. Harrison, R.H. Friend: Phys. Rev. Lett. 78, 733

(1997)99. B. Kraabel, V.I. Klimov, R. Kohlman, S. Xu, H-L. Wang, D. McBranch: Phys.

Rev. B 61, 8501 (2000)100. S.V. Frolov, Z. Bao, M. Wohlgenannt, Z.V. Vardeny: Phys. Rev. Lett. 85,

2196 (2000)101. J.W. Blatchford, S.W. Jessen, L.B. Lin, J.J. Lih, T.L. Gustafson, A.J. Epstein,

D.K. Fu, M.J. Marsella, T.M. Swager, A.G. MacDiarmid, S. Yamaguchi, H.Hamaguchi: Phys. Rev. Lett. 76, 1513 (1996)

102. M. Yan et al.: Phys. Rev. Lett. 72, 1104 (1994)103. N.S. Sariciftci (Ed.): Primary Photoexcitations in Conjugated Polymers:

Molecular Exciton Versus Semiconductor Band Model (World Scientific, Sin-gapore, 1997)

104. G. Klein: Chem. Phys. Lett. 320, 65 (2000)105. S.V. Frolov et al.: Chem. Phys. Lett., in press106. R. Kersting, U. Lemmer, R.F. Mahrt, K. Leo, H. Kurz, H. Bassler, E.O. Gobel:

Phys. Rev. Lett. 70, 3820 (1993)107. C. Zenz, G. Lanzani, G. Cerullo, W. Graupner, G. Leising, S. De Silvestri:

Chem. Phys. Lett. 341, 63 (2001)108. M. Wohlgenannt, W. Graupner, G. Leising, Z.V. Vardeny: Phys. Rev. Lett.

82, 3344 (1999)109. M. Wohlgenannt, W. Graupner, G. Leising, Z.V. Vardeny: Phys. Rev. Lett.

82, 3344 (1999)110. G. Lanzani, S. Stagira, G. Cerullo, S. De Silvestri, D. Comoretto, I. Moggio,

G. Dellepiane: Chem. Phys. Lett. 313, 525 (1999)111. M. Muccini, E. Lunedei, D. Beljonne, J. Cornil, J.L. Bredas, C. Taliani: J.

Chem. Phys. 109, 23 (1998)112. R.F. Mahrt, T. Pauck, U. Lemmer, U. Siegner, M. Hopmeier, R. Henning, H.

Bassler, E.O. Gobel, P. Haring Bolivar, G. Wegmann, H. Kurz, U. Scherf, K.Mullen: Phys. Rev. B 54, 1759 (1996)

113. W. Graupner, G. Cerullo, G. Lanzani, M. Nisoli, E.J.W. List, G. Leising, S.De Silvestri: Phys. Rev. Lett. 81, 3259 (1998)

114. C.J. Brabec, G. Zerza, N.S. Sariciftci, G. Cerullo, G. Lanzani, S. De Silvestri,J.C. Hummelen: in Ultrafast Phenomena XI, ed. by T. Elsaesser, S. Mukamel,M.M. Murnane, N.F. Scerer (Springer Series in Chemical Physics, Berlin, 2001)p. 589

115. Starting with ΔT/T = kIt ∗ (A × IP), where ∗ and × are the correlation andconvolution operators, respectively, we apply the Fourier transform, keeping inmind the fundamental identities:

F [kIt ∗ (A× IP)] = F ∗(It)F (A× IP) = F ∗(It)F (A)F (IP)


= F (A)[F ∗(It)F (IP)

]= F (A)F (It ∗ IP)

= A× (It ∗ IP)

116. G.S. Kanner, S. Frolov, Z.V. Vardeny: Phys. Rev. Lett. 74, 1685 (1995)

3 Transport Propertiesof Conjugated Polymers

Reghu Menon

In the last decade, investigations into the physical properties of organic semi-conductors have shown that these materials have several interesting featuresas regards applications in electrical and optical devices. The semiconductingand metallic properties of π-electron-rich systems, both small molecules andpolymers, have shown exciting properties compared with conventional sys-tems [1–3]. This is mainly due to the presence of delocalized π-electrons,which play a crucial role in the electrical and optical properties of con-jugated systems. A wide range of materials, from simple donor–acceptormolecules, oligomers, and complex supramolecular assemblies to large sizemacromolecules, are available as organic semiconductors. Moreover, the phys-ical and chemical properties of these materials can be tailored by molecularlevel engineering. Since organic semiconductors have a wide range of chemicalstructures (size, shape, etc.), functionality, crystallinity, morphology, disor-der, impurities, etc., the physical properties show a wide variety of behavior,and often not as simple as in the case of inorganic semiconductors. Hence,in terms of both materials and physical properties, these systems are quitecomplex and several parameters govern physical phenomena and device per-formances.

The electrical transport properties of metallic/semiconducting/insulatingorganic systems are of considerable importance, especially when trying tounderstand the operating mechanism of organic material devices. In general,intrinsic molecular level properties (e.g., HOMO and LOMO levels, ioniza-tion potentials, electron affinity, Coulomb correlations, etc.) and extrinsicproperties (e.g., crystallinity, morphology, disorder, intermolecular interac-tions, impurities, etc.) contribute to electrical transport properties. It is notusually that easy to sort out and identify these individual contributions.In high quality single crystals of small organic molecules (e.g., pentacene)the main features of electrical transport are dominated by intrinsic proper-ties. Batlogg and coworkers have observed the fractional quantum Hall effect,gate-induced superconductivity, Shubnikov–de Hass oscillations, low carrierscattering rates, low density of impurity trap levels, low density of surfacestates, and coherent band transport in high quality crystals of organic semi-conductors [4]. Moreover, the mobility of carriers in high quality crystals ofpentacene and other small organic molecules can be as high as 105 cm2/V sat low temperatures. These results show that intrinsic transport propertiesin organic semiconductors are almost identical to those observed in inorganic

92 Reghu Menon

semiconductors. However, these intrinsic features are highly susceptible tovariations through the influence of extrinsic parameters like morphology, dis-order, intermolecular interactions, etc. This is mainly due to the fact thatvan der Waals interactions among the molecules are rather weak, and theintermolecular order is easily perturbed by extrinsic factors.

Generally, the disorder in intermolecular interactions increases as the or-ganic molecule gets larger and more complex, and this plays a crucial rolein electrical and optical properties. For example, as the size of the moleculeincreases from pentacene through oligothiophenes to polythiophenes, the de-gree of disorder in solid state molecular packing increases. As a result thecarrier mobility in long-chain polymer devices is lower than in small molec-ular devices [3,5].

The ease with which materials can be processed, especially in high quality,large area thin films (e.g., by spin or drop casting), improves as the molecularweight of the material increases. In contrast, conventional techniques (evap-oration, sputtering, etc.) for obtaining thin films from low molecular weightmaterials are more cumbersome and expensive. It is therefore essential tocompromise between optimal physical properties and ease of fabrication whenconsidering the commercial viability of molecular/polymeric electronic andphotonic devices. Thin film photovoltaic diodes made from pentacene [4], withan external energy conversion efficiency as high as 2.4% for a standard solarspectrum, constitute quite a promising candidate for plastic solar cells. How-ever, compared with conjugated polymers like poly(para-phenylenevinylene)derivatives, they are not so amenable to large scale manufacturing. From thisstandpoint, the conjugated polymers are expected to play a major role infuture plastic solar cells [6]. It is therefore of great importance to understandthe charge transfer properties in conjugated polymers. Taking these factsinto account, this chapter mainly focuses on the electrical transport proper-ties of conjugated polymers, and little will be said about small molecules andoligomers.

3.1 Disorder and Localization

It is well known from Bloch’s theorem that wavefunctions of electrons in aperiodic potential do not undergo significant attenuation because of the co-herent constructive interference of the scattered waves. Nevertheless, thermalvibrations of ions, imperfections in the periodic lattice, etc., offer the usuallyobserved resistance to the flow of electric current even in the most perfectcrystals of metals. Moreover, Bloch’s model explains why crystalline metalshave large conductivity, with a mean free path (the distance in which thephase memory of the scattered waves almost vanishes) of the order of a fewmicrons at very low temperatures. If all lattice sites have nearly the sameenergy, then the wavefunctions of the Bloch states extend over a large lengthscale and the charge transport is ballistic. The Bloch levels, energy bands

3 Transport Properties of Conjugated Polymers 93

due to the overlap of the discrete energy levels in atoms, etc., lead to thedevelopment of band structure in solids. In crystalline solids, band structureand band filling play an important role in charge transport properties [7].

Even in the case of the most perfect crystalline solids, there exists somedisorder due to dislocations, impurities, defects, nonuniform distribution ofdopants in doped semiconductors, and so on. This ‘intrinsic’ disorder affectsthe electronic structure and physical properties of solids. If the randomnessof the disorder potential is substantial with respect to the bandwidth of thesystem, then the delocalized electron sea undergoes fragmentation to formlakes and rivers, due to the localization of electronic wavefunctions. Apartfrom the bandwidth, the degree of localization of wavefunctions depends onthe electronic dimensionality of the system. In 3D systems, even if the wave-function is locally perturbed near the fluctuating random disorder potential,it usually extends well beyond the interatomic distance in the case of weakdisorder. In 1D systems, on the other hand, the presence of any infinitesimaldisorder can easily induce exponential localization of all electronic states dueto repeated back-scattering. This means that the eigenstates have almost zeroamplitude on all the sites in a 1D lattice. Moreover, 1D systems are inher-ently susceptible to Peierls instability, which induces a gap in the Fermi leveland drives the system into an insulating state [1,2]. Even in 3D systems, thepresence of strong disorder exponentially decreases the overlap of the wave-function: |Ψ(r)| ∼ exp(|r − r0|/Lc), where Lc is the localization length of thelocalized state]. In addition, the phase of the wavefunction varies randomlyfrom site to site. Disorder thus engulfs both the overlap and the phase of thewavefunctions, and the formation of a coherent state that remains delocalizedover several lattice sites becomes difficult.

In the presence of strong disorder, the spreading of wavefunctions is sup-pressed. Consequently the tails of wavefunctions overlap with exponentiallysmall amplitude and this makes coherent charge transport rather difficult,especially at low temperatures. In the cases of weak and strong scattering ofcharge carriers, the Boltzmann and Kubo–Greenwood formalisms are usedto model charge transport, respectively [7]. In strong scattering, the phase ofthe wavefunction varies randomly from site to site, and the minimum valueof the mean free path (� = vτ , where v is the group velocity of the electronat the Fermi surface and τ is the relaxation time) approaches the interatomicdistance at which the Boltzmann method is no longer applicable. This lowerlimit for the mean free path is based upon the Ioffe–Regel criterion (that �cannot be less than the de Broglie wavelength). However, in recent studies ofmetallic fullerenes, high-temperature superconducting oxides, etc., in whichelectrons/holes can be scattered by intramolecular vibrations, the resistivityat high temperatures implies that � can be much lower than the interatomicdistance. This demonstrates that the fundamental principle requiring that �has to be larger than the interatomic distance is not always valid [8].

94 Reghu Menon

In 1958, Anderson [9] showed that localization of electronic wavefunctionsoccurs if the random component of the disorder potential is large with respectto the bandwidth of the system, as shown in the schematic diagram in Fig. 3.1.The mean free path (�) in a system with bandwidth B, random potential V0,and interatomic distance a is given by

1�= 0.7

1a

(V0

B

)2

.

The ratio V0/B determines the transition from coherent diffusive propagationof wavefunctions (delocalized states) to the trapping of wavefunctions in ran-dom potential fluctuations (localized states). If B > V0, then the electronicstates are extended with large mean free path. By tuning the ratio V0/B, itis possible to have a continuous transition from extended to localized statesin 3D systems, with a critical value for V0/B. Above this critical value, wave-functions fall off exponentially from site to site and the delocalized statescannot exist any more in the system. The states in band tails are the first toget localized, since these rapidly lose the ability for resonant tunnel transportas the randomness of the disorder potential increases. If V0/B is just belowthe critical value, then delocalized states at the band center and localizedstates in the band tails could coexist.

Fig. 3.1. Random potentials vs. bandwidth, wavefunctions and density of states

The critical energy that separates localized from extended states is calledthe mobility edge (Ec). Mott pointed out that, as the extent of disorder


increases, the Fermi energy EF crosses Ec, and the Anderson metal–insulator(M–I) transition occurs. The scaling theory of localization [9] showed that theM–I transition is a continuous, second order phase transition in 3D systems,and this suggests that the conductivity of a metal goes smoothly to zero asEF → Ec. Recently, similar results have also been observed in 2D systems[10].

Further to the non-interacting disorder-induced localization model, byturning on electron–electron (e–e) interactions in the interactive picture, thediffusive motion of charge carriers decreases as the extent of disorder in-creases. This enhanced Coulomb interaction also contributes to the localiza-tion process. Moreover, the interchain transfer integral t and onsite Coulombcorrelations (Hubbard U) play a major role in the localization process, es-pecially in 1D systems. The wavefunctions get localized when t < U , andthe system moves to the insulating side. The converse is also valid. Thisinteraction-driven M–I transition is usually called the Mott–Hubbard tran-sition. Generally, reduced electronic dimensionality amplifies the effects ofdisorder and interaction in the localization–delocalization transition. For ex-ample, in 1D, even in the absence of disorder, the interchain transfer integralshould be larger than the onsite electronic correlation energy to attain themetallic state [11]. Hence, in quasi-1D systems like conducting polymers, tis expected to play a major role (as important as the charge carrier density)in the M–I transition. In disordered quasi-1D systems like doped conjugatedpolymers, t, U , B, V0 and carrier density n play significant roles in the M–Itransition and charge transport. In general, to attain the metallic state inconducting polymers t > U , B > V0 and n ∼ 1020 cm−3.

3.2 Conduction in Conjugated Systems

The onset of the optical absorption edge (band gap) in several conjugatedpolymers ranges from 1.0 to 4.0 eV [1–3]. Hence, undoped conjugated poly-mers have a wide range of properties from semiconducting to insulating. In3D inorganic semiconductors, the primary excitations are usually electronsand holes (also excitons at very low temperatures). In conjugated polymers,due to the intrinsic low dimensionality of the system, charge carriers tendto have a strong coupling to the lattice. This factor together with e–e cor-relation effects and other molecular structural details can lead to the for-mation of various types of excitation in conjugated polymers. For example,solitons (in degenerate ground state structures like polyacetylene), polaronsand bipolarons (in nondegenerate ground state structures like polypyrrole,etc.), bound excitons (in strongly correlated systems like polydiacetylene,etc.), electrons and holes (injected carriers in semiconducting polymer de-vices) and free carriers (in fully doped metallic conjugated polymers). Exci-tations like solitons, polarons, bipolarons and excitons are spread over severalangstroms along the conjugated segment. Furthermore, morphological factors

96 Reghu Menon

(e.g., crystallinity, amorphous nature, intermolecular interactions, etc.) andthe degree of disorder (both intra- and interchain) combine with the widerange of charge carrier species, making the charge transport mechanism inconducting polymers quite complex compared with conventional systems. Ingeneral, the conjugation length (extent of the delocalized π-electrons in thepolymer backbone), interchain interactions, carrier density and degree of dis-order are the most significant parameters, playing major roles in the chargetransport mechanism in conducting polymers.

In conjugated polymers, charge carriers can be created by light-inducedphotocarrier generation, chemical doping and injection of carriers from elec-trodes in an electric field. The photogenerated and field-induced carriers aretransient with short lifetimes, whereas the carriers in chemically doped sys-tems are stabilized by the presence of counterions. In pristine semiconductingconjugated polymers, the mobility (drift velocity developed by the carrier inan electric field per unit electric field) can be considered as a measure of therelative ease with which the carrier moves in the system in the presence ofan electric field. The mobility μ is related to the conductivity σ by σ = neμ,where n is the number of carriers per unit volume and e is the charge of thecarrier. The mobility is also related to the diffusion coefficient D by the Ein-stein relation μ = eD/kBT , where kB is Boltzmann’s constant and T is thetemperature in kelvins. In organic semiconductors, the mobility of electronsand holes can be quite different due to various factors like traps, lifetimes,effective mass, etc.

In general, the carrier transport mechanism depends on the width of theband in which it moves. Typical bandwidths parallel and perpendicular to thechain axis in conjugated polymers are 0.5–5 and 0.01–0.1 eV, respectively [1–3]. The bandwidth B is mainly determined by the overlap of the carrier wave-functions in its initial and final state. In well ordered systems, when B � kBT(or kBT > B), band transport (or hopping transport) usually dominates thecharge transport mechanism. In organic semiconductors at room tempera-ture, hopping mobilities are much lower than 1 cm2V−1s−1 and band mobili-ties are greater than 1 cm2V−1s−1. These values depend on the experimentaltechnique used for the mobility measurement (e.g., time-of-flight, transientphotoconductivity, field effect transistor, space-charge-limited current, chargeextraction in linearly increasing voltage, or magnetic resonance techniques).The broad distribution of energy traps caused by defects/impurities/grainboundaries, the relative orientation of the conjugated segments in the sam-ple with respect to the measuring probe, etc., are some of the reasons forthe wide variation in mobility values obtained by different types of mea-surements. However, Batlogg and coworkers [4] have recently shown that, byimproving the perfection of organic semiconductor crystals, the mobility canbe substantially increased, and coherent band transport can also be achieved.Furthermore, by enhancing the conjugation length and interchain/molecularinteractions, it is possible to increase the mobility.


In various types of disordered system, a universal behavior in the field de-pendence of mobility (lnμ ∝ E0.5) has been observed [5]. Recently, Martens etal. [11] found that long-range energy correlations can give rise to this type ofbehavior in conjugated polymers. In this correlated Gaussian disorder model,the field dependence of μ is due to energetic disorder and intersite spacing forhopping transport, which provides a measure of the length scale involved inthe charge transport process. On the other hand, in devices fabricated fromcrystalline conjugated oligomers, several regimes of transport have been ob-served in the current–voltage characteristics, from Ohmic at low voltages totrap-free space-charge-limited current types of behavior at high voltages. Itseems that this wide range of behavior is due to the presence of acceptor-liketrap levels at the grain boundaries in these polycrystalline materials. Schon etal. [12] observed that even a small variation in trap density and its energieshas dramatic effects on the mobility, and its temperature and field depen-dence. Hence, even in the case of high quality crystalline conjugated systems,the intrinsic (conjugation length, etc.) and extrinsic (traps, etc.) contribu-tions to charge transport properties are mixed up, and it is quite difficult toidentify the individual contributions from various factors.

Fig. 3.2. Schematic diagram for conductivity (300 K) in various systems

The situation in doped conjugated systems is rather different [13]. Theconductivity of doped conjugated systems, and comparison with other typesof system, is shown schematically in Fig. 3.2. This indicates that the conduc-tivity can be varied by nearly 15 orders of magnitude in doped conjugated

98 Reghu Menon

systems. Conductivity is usually expressed in terms of carrier density n, meanfree path �, effective mass m, and so on, and it is given by

σ = ne2τ/m ∼ ne2�/�kF ∼ neμ ∼ e2DN(EF) ,

where e is the electronic charge, τ is the relaxation time, � ∼ ντ (ν is theFermi velocity), kF is the Fermi wave vector, μ ∼ eτ/m is the carrier mo-bility, D is the diffusion coefficient, and N(EF) is the density of states atthe Fermi level. This expression does not work in a straightforward fashionin conducting polymers. This is mainly due to the fact that disorder is aninherent feature of polymers, which often exhibit complex morphology, hav-ing partially crystalline and partially amorphous regions in the system. Theintrinsic quasi-one-dimensionality, intra- versus interchain transport, disor-der, various types of charge carriers (e.g., polarons, bipolarons, electrons,holes, excitons, etc.), inhomogenous distribution of dopants, traps and im-purity levels, structural and morphological features, etc., make the chargetransport process in conducting polymers quite complicated compared withconventional systems. In spite of all these adverse factors, it is possible toattain 105 S/cm in high quality iodine-doped polyacetylene, which is nearlythe same as in metals like aluminum.

The doping process in conjugated systems is rather different from thatin inorganic semiconductors [13]. For example, in doped silicon, dopants likephosphorous, boron, etc., are substituted into the host atomic sites, and theresulting free electrons/holes are highly mobile in the crystalline 3D lattice.On the other hand, in conjugated systems, dopants are not substitutionalbut interstitial. X-ray studies show that dopants are situated adjacent to theconjugated chains (within 2–3 A). In this intercalary doping process (as ingraphite intercalation compounds), electrons are either removed via oxida-tion (p-type doping) or introduced via reduction (n-type doping). These extracharge carriers, created by doping, move along the polymer chains, makingthem conducting and metallic. The conductivity of conjugated polymers in-creases by several orders of magnitude at doping levels as low as 1%. This ismainly due to the fact that the localized states in a strongly energy dependentdensity of states are filled up quickly, even at very low doping levels, and thisexponentially increases the charge transport process and conductivity [11].The maximum doping level can be as high as 30–50%, which correspondsto one dopant for every two or three monomer units. In high quality dopedsystems, wavefunctions of extended states are fairly delocalized and overlapto form the electron sea (at least, well-networked lakes and rivers). In fullydoped, metallic conducting polymers, n is of the order of 1021 cm−3, � isapproximately 10 A, τ is around 10−14 s and m is nearly the electron mass.

As far as charge transport in conjugated polymer photovoltaic devicesis concerned, efficient photogeneration of excitons and their dissociation toelectrons and holes, and further, the rapid trap-free migration of these chargesto the electrodes are required to build up a reasonably good open-circuitvoltage. Hence, for efficient charge collection, the mobility of both electrons


and holes should be high, and trapping–detrapping processes should be quitelow.

3.3 Metal–Insulator Transition

In crystalline inorganic semiconductors the M–I transition is mainly driven bythe critical carrier density, and it occurs at 1018–1019 cm−3. Further, the con-ductivity near the M–I transition is around 100 S/cm, and the role played bydisorder is less severe. In conducting polymers, however, disorder, interchaininteractions, carrier density, etc., play crucial roles in the M–I transition [13].In conducting polymers, in order to turn on adequate interchain transport,and to make the transport more three-dimensional and metallic, the requiredcritical carrier density is of the order of 1020 cm−3. Moreover, the strengthof the interchain transfer integral mimics the role of carrier density, in thesense that more interchain transport means more carriers participating inthe delocalized metallic (three-dimensional) transport. However, both intra-and interchain disorder play a vital role, since in a quasi-one-dimensionalconductor, the carriers are highly susceptible to localization in the presenceof any disorder. This influences the carrier density in localized and extendedstates, hence tuning the relative position of the mobility edge with respect tothe Fermi level. Martins et al. [11] recently pointed out that, even in the ab-sence of disorder, the interchain transfer energy must overcome the Coulombcorrelations U in order to achieve the metallic state.

Fig. 3.3. Conductivity σ‖ and σ⊥ vs. T for I-(CH)x at various stretching ratios l/l0

100 Reghu Menon

The presence of a metallic state in high quality conducting polymers iswell known from several measurements [13]. For example, the presence of atemperature-independent Pauli spin susceptibility down to low temperatures,a linear term in specific heat, a quasi-linear temperature dependence of ther-mopower, a large finite conductivity at T → 0 (indicating the presence of acontinuous density of states with a well-defined Fermi energy), large metallicreflectance in the infrared (indicating the presence of free carriers), etc., haveprovided adequate evidence for the metallic state in conducting polymers. Al-though a positive temperature coefficient of resistivity (TCR) is a desirablequality for a good metal, this is not the case for several amorphous metals.In particular, in disordered metallic conducting polymers it is quite hard toachieve a positive TCR, since kF� (order parameter in the disorder-inducedM–I transition) is not much larger than the Ioffe–Regel limit (kF� ∼ 1). Thismeans that the best metallic conducting polymers are just on the metallicside of the M–I transition. This is largely due to the fact that, althoughconductivity along the chain direction can be as high as 105 S/cm, conduc-tivity across the chain direction is of the order of 102 S/cm, and this playsa crucial limiting role in three-dimensional charge transport. This is quitewell illustrated in the case of oriented iodine-doped polyacetylene I-(CH)x,σ‖ ∼ 50 000 S/cm, σ‖/σ⊥ ∼ 100, resistivity ratio ρr = ρ(1.4 K)/ρ(300 K) < 2,crystalline fraction roughly 80%, crystalline coherence length roughly 100 A,as shown in Fig. 3.3.

Fig. 3.4. Resistivity vs. T for a PPV-H2SO4 sample dedoped from C to L


The temperature dependence of conductivity σ(T ) for unoriented (CH)xis typical of an insulator. By increasing the orientation of chains/fibrils, σ(T )becomes weaker both parallel and perpendicular to the chain axis [14]. Al-though σ‖/σ⊥ ∼ 100, the behavior of σ(T ), and consequently the mechanismfor charge transport, is nearly identical in both cases (σ‖ and σ⊥). Moreover,this indicates that weak interchain transport plays the limiting role in bulkcharge transport properties.

Fig. 3.5. W (d lnσ/d lnT ) vs. T for data in Fig. 3.4. (a) A–E on the metallic side.(b) H–L on the insulating side and F, G in the critical regime

The role of the carrier density in M–I transitions is shown for an orientedsulfuric acid–polyparaphenylenevinylene (PPV-H2SO4) sample. The opticalanisotropy of this oriented PPV sample, from dichroic ratio measurementsat 1520 cm−1, is nearly 50 [15]. The value of ρr continuously increases uponreducing the carrier density by systematically dedoping the sample, as shownin Fig. 3.4. However, it is difficult to locate the M–I transition from the σvs. T plot alone. Instead, the W = d(lnσ)/d(lnT ) vs. T plot for the samedata is shown in Fig. 3.5. If the system is in the metallic regime with a weaknegative TCR, then W shows a positive temperature coefficient at low tem-peratures. Moreover, this ensures that there is a finite conductivity as T → 0.As ρr increases, W (T ) gradually moves from positive (metallic) to negative

102 Reghu Menon

(insulating) temperature coefficient, via the temperature independent W ofthe critical regime (samples F and G), as shown in Fig. 3.5.

Fig. 3.6. Conductivity [σ‖ (left) and σ⊥ (right)] vs. T for a PPV-H2SO4 sample

The metallic state in PPV-H2SO4 (σ‖ ∼ 10 000 S/cm, σ‖/σ⊥ ∼ 100,ρr < 2, crystalline fraction roughly 70%, crystalline coherence length roughly80 A) can be described [13,15] by the localization–interaction model:

σ(τ) = σ0 + mT 1/2 + bT p/2 ,

where the second term due to e–e interactions and the third term due tolocalization are corrections to σ0, m depends on the diffusion coefficient andinteraction parameter, b is a constant and p is determined by the scatteringmechanism. The fit to this model, for both parallel (having positive andnegative TCR below 20 K) and perpendicular directions to the chain axis, isshown in Fig. 3.6.

In oriented metallic conducting polymers, with large anisotropy in con-ductivity, the anisotropic diffusion coefficient factor should be taken intoaccount in the above model. The robustness of this metallic state can beverified from the field dependence of conductivity at low temperatures. Forexample, in the case of sample E with σ‖ ∼ 2 200 S/cm (see Fig. 3.4), whichis just on the metallic side of the M–I transition, a field of 8 T can induce atransition to the insulating state, as shown in Fig. 3.7. The corresponding Wvs. T plot (Fig. 3.7a) is consistent with the fact that the system has movedfrom the metallic to the critical/insulating side. This is a typical example


to show that, although σ‖ can be large very near the M–I transition, σ⊥and interchain transport is below the critical threshold, so that a field caneasily suppress the crucial interchain transport, inducing large σ‖ → 0 asT → 0 (at 8 T field). This highlights the significance of interchain transportin conducting polymers near the M–I transition.

. .

Fig. 3.7. Field-induced transition from metallic to insulating regime. (a) W vs. Tfor a metallic PPV-H2SO4 sample (E from Fig. 3.4) at 0, 5 and 8 T fields. (b)Conductivity vs. T 0.1 fit for the same data

In unoriented, metallic, conducting polymers like polypyrrole (PPy) [16],polyaniline (PANI) [17], and polythiophenes (PT, PEDOT) [18,19], the ex-tent of disorder can be categorized by the size and volume fraction of thelong-range ordered domains in the system [σ(300 K) ∼ 300 S/cm, ρr < 3,crystalline fraction roughly 50%, crystalline coherence length roughly 30 A].In fully doped samples, the extent of disorder determines the density of delo-calized carriers and the M–I transition, by tuning the mobility edge with re-

104 Reghu Menon

spect to the Fermi level. As a typical example, the disorder in electropolymer-ized PPy-PF6 samples can be controlled by varying the sample preparationtemperature from −40◦C (crystalline, metallic, ρr < 3) to room temperature(amorphous, insulating, ρr > 100). The W vs. T plot for a series of suchPPy-PF6 samples near the M–I transition is shown in Fig. 3.8. Although thetotal carrier densities in all these PPy-PF6 samples are nearly identical, thecontinuous evolution from the metallic to insulating side is due to increasingdisorder for samples prepared at higher temperatures. This illustrates thedisorder-induced M–I transition in conducting polymers.

Fig. 3.8. W vs. T for PPy-PF6 samples in metallic, critical and insulating regimes

A PPy-PF6 sample in the critical regime of M–I transition [σ(T ) ∝ T β

at low temperatures, where β lies between 0.3 and 1, and W = β in theW vs. T plot] can be made metallic by enhancing interchain transport athigh pressures. It can also be made insulating by shrinking the overlap of thewavefunctions at high fields [20], as shown in Fig. 3.9. This highlights therole of the intrinsic quasi-one-dimensional nature of conducting polymers incharge transport. In particular, it brings out the fact that interchain trans-port is quite sensitive to extrinsic perturbations. These studies near the M–Itransition indicate that it is possible to achieve coherent free-carrier trans-port in conducting polymers if the wavefunctions of extended states overlapsignificantly.


Fig. 3.9. W vs. T for a PPy-PF6 sample in the critical regime. The pressure-induced transition to the metallic regime and the field-induced transition to theinsulating regime

3.4 Hopping Transport

As the randomness in disorder potential increases, the overlap of the wave-functions of localized states decreases exponentially. As a result, carriersundergo thermally-assisted hopping transport [7]. This change in the tem-perature dependence of conductivity is easily detected from the W vs. Tplots, since the temperature coefficient of W (T ) varies markedly for metallic(positive), critical (T -independent) and insulating (negative) regimes, at lowtemperatures. In conducting polymers, as ρr increases above 10, W (T ) usu-ally shows a negative temperature coefficient. Mott has shown that, on theinsulating side of the M–I transition, with a nonvanishing density of states inbands near the Fermi level, the low temperature dependence of resistivity be-comes exponential, i.e., ρ(T ) = ρ0 exp[(T0/T )γ ], where γ = 1/(d+1), d is thedimensionality of the system, T0 = q/[kBN(EF)L3

c ], q is a numerical coeffi-cient, N(EF) is the density of states at the Fermi level, and Lc is the localiza-tion radius of states (rate of fall-off of the envelope of the wave function) nearthe Fermi level. As the temperature decreases, the average hopping length[r ∼ Lc(T0/T )γ ] increases as T−1/4. Hence this type of transport is usuallyreferred to as variable range hopping (VRH). In VRH, a carrier just belowthe Fermi level jumps to a state just above it, and the farther it jumps, thegreater is the choice of states available. It usually jumps to a state for whichthe energy required [E ∼ 4.2r3N(EF)] is as small as possible. In contrast,

106 Reghu Menon

in nearest-neighbor hopping [ρ = ρ0 exp(A/kBT )] with constant activationenergy A, the average hopping length is of the order of the mean separationbetween localized states, and it does not vary with temperature. The valueof T0 in VRH gives an estimate of how far the system has moved to the in-sulating side. Moreover, the localization length can be determined from T0,which gives some idea about the length scale of the localized wavefunctions.

In conducting polymers, as the system moves deeper into the insulatingside, the resistivity follows a T−1/2 dependence, which can be observed viathe change in slope of the W vs. T plots. This T−1/2 dependence may be dueto contributions from VRH in one dimension, Coulomb gap in the densityof localized states (due to Coulomb interactions between carriers, the den-sity of states in the immediate vicinity of the Fermi level is diminished) andcharging effects in granular metallic systems. In the latter, the range of tem-peratures in which the T−1/2 dependence has been observed usually extendsto higher temperatures (e.g., up to 100 K). On the other hand, in Coulombgap systems and VRH in one-dimensional systems, the T−1/2 dependence isusually observed at temperatures below 20 K. Furthermore, in highly insulat-ing conducting polymers a T−1 dependence has also been observed, typicalof nearest-neighbor activated transport.

Fig. 3.10. ln ρ vs. T−1/4 fit for PANI-CSA samples at various values of ρr

The ln ρ vs. T−1/4 plot for a series of PANI-CSA samples [21] with in-creasing ρr is shown in Fig. 3.10. The samples with ρr ∼ 1.66 and 2.94 arein the metallic and critical regimes, respectively. Hence the deviation from astraight line fit is noticeable for these samples in Fig. 3.10. For samples withvalues of ρr < 103, the T−1/4 fit yields a straight line, and when ρr > 103,


the T−1/2 fit is more appropriate. This is consistent with the results obtainedfrom W vs. T plots [21]. The ln ρ vs. T−1/4 plot for a series of iodine-dopedpolyalkylthiophene samples [21] is shown in Fig. 3.11. In these samples, asthe value of ρr increases, the T−1/4 fit deviates at low temperatures, and inthese cases the T−1/2 fit gives a better straight line fit. The value of T0 isquite sensitive to the type of fit, whether T−1/4 or T−1/2. The crossover fromT−1/4 to T−1/2 can be used to identify how far the system has moved intothe strongly disordered regime. Moreover, if it occurs below 10 K, then itgives some evidence for the opening up of a Coulomb gap in the density ofstates, and that in turn gives an estimate for e–e interactions in the system[16].

Fig. 3.11. ln ρ vs. T−1/4 fit for iodine-doped polyalkylthiophene samples

In strongly disordered conducting polymers, the conducting regions canbecome segregated by insulating barriers or they can be weakly connectedby resistive pathways. In such a scenario, the charge transport mechanism iseither due to charging effects in granular metals or else it is of a percolativetype. The T−1/2 fit for a wide temperature range (e.g., 4–100 K) is an in-dication of the granular metallic nature of the system. Percolative transportcan be observed in blends in which the conducting polymer is dispersed inan insulating matrix. The formation of self-assembled networks in conductingpolymer blends (e.g., PANI-CSA in PMMA) provides a new class of percolat-ing systems in which the aspect ratio (the ratio of the length to the diameter)of conducting objects is much larger than one. This makes the percolation

108 Reghu Menon

Fig. 3.12. Transmission electron micrograph for PANI-CSA (0.1%)/PMMA blendnear the percolation threshold

threshold much lower than the 16% volume fraction observed in classicalpercolation systems [22]. The multiply-connected, phase-separated morphol-ogy of the conducting network has a fractal geometry near the percolationthreshold, as shown in Fig. 3.12. The percolation threshold in such systemscan be as low as 0.1% volume fraction of conducting polymer. The typical sce-nario imagined for a percolating medium with links (PANI-CSA fibrils), nodes(crossing points of the links) and blobs (dense, multiply-connected regions)can be observed in the transmission electron micrograph (see Fig. 3.12). Thetemperature dependence of resistivity [22] of a series of PANI-CSA/PMMAblends is shown in Fig. 3.13. The temperature dependence of resistivity isrelatively weak, especially at T > 20 K, compared with other types of perco-lating system. This type of conducting polymer network has very interestingfeatures in its charge transport properties. Conducting polymer networkshave been demonstrated to be useful as carrier injection electrodes in semi-conducting polymer light-emitting diodes and as the grid in polymer gridtriodes [2].

3.5 Magnetoresistance

The classical transverse magnetoresistance (MR) is mainly due to the bendingof the charge carrier trajectory by the Lorentz force. It is proportional to thesquare of the field, with the proportionality constant expressed as a functionof charge transport scattering time [23]. In crystalline 3D metals the dominant


Fig. 3.13. Resistivity vs. T for PANI-CSA/PMMA blends at various volume frac-tions f of PANI

contribution to the weak positive MR (usually less than 5% increase) is dueto classical orbital motion. Moreover, the MR gives information about thesecond derivative of the density of states at the Fermi energy with respect toenergy. Nevertheless, in an ideal 1D conductor the transverse orbital motion isrestricted, so that the carriers cannot follow a circular motion in the magneticfield. For this reason, there is hardly any MR in an ideal 1D conductor.

However, this scenario is not appropriate when the interchain transfer in-tegral is turned on in a 1D system, and this is the case in several quasi-1Dsystems. Since, MR probes the local charge carrier dynamics in conductingsystems, MR data can be used to determine microscopic transport propertyparameters, e.g., the elastic and inelastic scattering length, scattering time,etc. Furthermore, MR results supplement conductivity data and it is essentialto check the internal consistency of the models used in understanding chargetransport properties. Although the complementary Hall effect is another im-portant transport property, the Hall voltage is quite low in conducting poly-mers (a few μV). This means that it is difficult to measure accurately andalso that the interpretation of data in disordered quasi-1D conductors is notparticularly straightforward [23].

110 Reghu Menon

Even in typical disordered metals, the classical model for MR breaks downdue to quantum corrections to conductivity, especially at low temperatures[13]. In the presence of weak disorder, carriers get localized by repeated back-scattering due to constructive quantum interference, and this is called weaklocalization (WL). A weak magnetic field can destroy this interference processand delocalize the carrier. As a result, a negative MR (resistivity decreaseswith field, usually less than 3%) can be observed at temperatures around 4 K.Another quantum correction to low temperature conductivity is due to e–einteraction contributions. This is mainly due to the fact that carriers inter-act more often when they diffuse slowly in random disorder potentials. Theresistivity increases (usually less than 3%) with field due to e–e interactioncontributions. Hence, the total low-field magnetoconductance (MC, Δσ) dueto additive contributions from WL and e–e interactions is given by

Δσ(H, T ) =1

12π2

( e

�

)2G0l

3inH2 − 0.041

(gμB

kB

)2

αγFσT−3/2H2 ,

where the first (positive MC) and second (negative MC) terms on the rightside are due to WL and e–e interaction contributions, respectively, G0 = e2/�,lin is the inelastic scattering length, g is the g-value of the electron, μB is theBohr magneton, and αγFσ depends on m, the diffusion coefficient and otherinteraction parameters. From Δσ vs. H2 plots at low fields, lin, the diffusioncoefficient, etc., can be estimated [13].

Fig. 3.14. Magnetoconductance vs. field for I-(CH)x at 4.2 K (circles), 2 K(squares) and 1.2 K (triangles): (a) transverse and (b) longitudinal


The transverse and longitudinal MC in iodine-doped oriented(CH)x (σ‖ ∼ 10 000 S/cm, σ‖/σ⊥ ∼ 100, ρr ∼ 3) is shown in Fig. 3.14. Whenthe field is transverse (or longitudinal) relative to both chain axis and currentdirections, the sign of the MC is positive (or negative) due to the dominantcontribution from WL (or e–e interactions) [14]. The maximum in MC, as inFig. 3.14a, is due to competing contributions from WL and e–e interactions.At fields below 2 T, the slope of the positive MC does not vary significantly asa function of the field. However, at fields above 2 T, the positive contributionto MC decreases by lowering the temperature to 1.2 K. This suggests thatwhen the field is transverse to the chain axis, the WL contribution (positiveMC) dominates at lower fields and higher temperatures. In contrast, the e-einteraction contribution (negative MC) dominates at higher fields and lowertemperatures. When the field is longitudinal relative to both chain axis andcurrent directions, the negative MC becomes stronger at higher fields andlower temperatures, as shown in Fig. 3.14b. This indicates that in longitu-dinal MC the WL contribution is negligible at all fields and temperatures.Hence the negative MC is mainly due to e–e interaction contributions. Simi-lar anisotropic MC has been observed in other oriented metallic conductingpolymers like PPV-H2SO4 [15].

The e–e interaction contribution shows a universal scaling behavior in theMC [15]. The scaling behavior is given by

Δσ(H, T ) = σ(H, T ) − σ(0, T ) ∝ T 1/2f(H/T ) ,

where f(H/T ) is the scaling function. A [Δσ(H, T )/T 1/2] vs. (H/T ) plot foran oriented metallic PPV-H2SO4 sample is shown in Fig. 3.15. Contributionsfrom WL and e–e interactions to MC are easily distinguished. In transverseMC (Fig. 3.15a), the deviation from the scaling behavior at H/T < 3 indi-cates the importance of the WL contribution whereas, in longitudinal MC(Fig. 3.15b), all the data points collapse to a line, due to the scaling behaviorof the e–e interaction.

This scaling behavior in oriented metallic conducting polymers clearlyshows that anisotropic MC is due to anisotropy in WL, which is maximizedwhen the field is transverse to the chain axis. The orbital character of thescattering and the flux enclosed by the back-scattering paths of the carriersleads to the anisotropic contribution of WL to MC. The flux is determinedby the normal cross-section of the charge carrier back-scattering paths withrespect to the field direction. The inelastic scattering length along the chainaxis is much larger than that across the chain axis, and this leads to theansiotropy in the cross-section of the flux. This in turn reduces the WL con-tribution to longitudinal MC. Since these microscopic geometric parametersare involved in MC, it is a quite useful probe for understanding the role ofmorphology in charge transport parameters [15].

In unoriented metallic conducting polymers like PANI-CSA, PPy-PF6,PEDOT-PF6, etc. [σ(300 K) ∼ 300 S/cm, ρr < 3], the sign of MR is positiveat all fields and temperatures. In these systems, the conductivity is not large

112 Reghu Menon

Fig. 3.15. Universal scaling plot of magnetoconductance for a metallic PPV-H2SO4

sample: (a) transverse and (b) longitudinal

enough to have any significant contribution from WL. Moreover, the extent ofdisorder is quite high so that the e–e interaction contribution is substantial.The MR shows H2 and H1/2 dependence at low and high fields, respectively[13]. In metallic samples, the positive MR is nearly 5–10% (at 1.4 K and 8 T).As the extent of disorder ρr increases, the positive MR increases considerably[16]. This is shown in the case of PPy-PF6 samples near the M–I transition, asin Fig. 3.16. The e–e interaction contribution to the positive MR is usually lessthan 5% (at 1.4 K and 8 T). Hence any additional contribution to the positiveMR arises from hopping transport in disordered regions of the system, whichcan be quite substantial as the extent of disorder increases. This indicatesthat MR, at very low temperatures and high fields, can be used to probe theextent of disorder in metallic conducting polymers.


Fig. 3.16. Magnetoresistance vs. resistivity ratio ρr for various PPy-PF6 samplesfrom metallic (ρr < 3) to insulating

3.6 Thermopower

The standard Mott equation for diffusion thermopower Sd in metallic systemsis a function of the first derivative of the density of states at the Fermi level,and it is expressed as

Sd(T ) =π2

3kB

ekBT

[d lnσ(E)

dE

]EF

,

where the energy dependence of σ(E) arises from the details of the bandstructure and scattering mechanisms [13,24]. In typical metals, the lineartemperature dependence of S(T ) is complicated by phonon drag contribu-tions, the Umklapp process, scattering and interaction processes, etc. Thesign of the thermopower is usually consistent with the positive or negativecharge of the carrier. However, several exceptions have been observed in var-ious systems including conducting polymers [13]. A detailed understandingof S(T ) requires the electronic and band structure of the system to be wellknown, and this is not the case in conducting polymers.

In undoped conducting polymers [σ(300 ∼ K) < 10−6 S/cm], S(300 K) ∼1 mVK−1. This value decreases upon doping, and in fully doped systemsS(300 K) ∼ 10 μVK−1. Although conducting polymers are intrinsicallyquasi-1D and highly disordered, a remarkable linear S(T ) has been observedin high quality metallic samples down to 10 K [16,21]. This indicates thatthe thermal current carried by phonons is less impeded by insulating barriers

114 Reghu Menon

Fig. 3.17. Thermopower vs. T for various PPy-PF6 samples: from the metallic side(circles) to the insulating side (squares)

present in the system, unlike the scattering and mean free path of carriersinvolved in conductivity. The typical behavior of S(T ) for PPy-PF6 samplesnear the M–I transition is shown in Fig. 3.17. The data for all four samples,both metallic and insulating, show a linear S(T ) down to 10 K, althoughthe ρr of these samples varies by more than three orders of magnitude. Therelatively large value of S(300 K) ∼ 10 μVK−1 indicates the possibility thatthe partially filled π-band is somewhat narrow (of the order of 1 eV). Thedensity of states at the Fermi level estimated from the equation for Sd(T ) isnearly 1 state per eV per four rings of pyrrole [16].

The thermopower in VRH hopping transport is given by the expression,

Shop(T ) =12

kB

e

Δ2hop

kBT

[d lnN(E)

dE

]EF

,

where Δhop is the mean hopping energy, and Shop(T ) ∝ T 1/2 for Mott’s VRH[13]. As ρr increases, S(T ) has contributions from both Sd(T ) and Shop(T ).Then empirically, the total sum of S(T ) can be expressed as

S(T ) = AT + BT 1/2 + C ,

where A is the linear slope of S(T ), and B and C are fitting parameters.The hopping contribution to S(T ) has been systematically investigated byYoon et al. [21] in doped PANI samples. The gradual variation in S(T ), frompositive linear temperature dependence to negative temperature dependence,


as shown in Fig. 3.18, is indicative of the dominant negative hopping contri-butions in addition to metallic diffusion thermopower. It is well known thatthe morphology of HCl- and H2SO4-doped PANI is more granular in nature,with ρr ≥ 106, so that the contribution from Shop can be substantial. Thisscenario is consistent with σ(T ) and the morphology of the system. ThusS(T ) is another probe for investigating the correlation between the struc-ture/morphology and charge transport in conducting polymers.

Fig. 3.18. Hopping contribution S − AT to thermopower vs. T for various dopedPANI samples

3.7 Conclusion

Transport properties in conducting polymers are governed to a large extentby structural and morphological features. In general, the effective conjugationlength, interchain interactions, carrier density and extent of disorder deter-mine electrical and optical properties. Interchain charge transport plays assignificant a role as the carrier density in the M–I transition. W vs. T plotshave shown that the M–I transition can be continuously tuned by varyingthe carrier density, disorder, interchain transport, magnetic field, etc. In themetallic state for highly conducting oriented systems, both the weak local-ization and e–e interaction play significant roles in charge transport. Evenin oriented metallic samples of (CH)x and PPV-H2SO4 (σ‖ > 10 000 S/cm,σ‖/σ⊥ ∼ 100), the behavior of σ(T ) and magnetoresistance are nearly identi-cal, both along and across the chain axis, indicating that interchain transportis the limiting factor in transport properties like mobility, mean free path, etc.

116 Reghu Menon

The anisotropic MR in oriented metallic samples can be used to probe themicroscopic level correlation between the orientation of chains and transportproperties.

The extent of disorder, interchain transport and carrier density deter-mines the contributions from coherent and hopping transport. As the ex-tent of disorder increases, hopping transport dominates, as shown by theT−1/4 dependence of the conductivity. Hopping transport significantly en-hances positive magnetoresistance. In conducting polymer blends like PANI-CSA/PMMA, a percolative-type transport has been observed at low volumefractions of conducting polymer. The metallic linear temperature dependenceof thermopower persists to systems just on the insulating side. However, thehopping contribution dominates in highly disordered insulating systems.

These results indicate that improving interchain/molecular transport andreducing the extent of disorder holds the key for enhancing charge trans-port properties like mobility, mean free path, etc., in organic semiconduc-tors. To this end, a comprehensive understanding of the correlation betweenstructural/morphological features and charge transport properties is essen-tial. Hence, more detailed investigations into microscopic charge transportparameters are required to improve the performance of organic semiconduc-tor devices.

Acknowledgements. The author would like to thank Mr. A.K. Mukherjeefor his help with the preparation of figures.

References

1. H.S. Nalwa (Ed.): Handbook of Organic Conductive Molecules and Polymers,Vols. 1–4 (Wiley, New York, 1997)

2. T.A. Skotheim, R.L. Elsenbaumer, J.R. Reynolds (Eds.): Handbook of Con-ducting Polymers (Dekker, New York, 1998)

3. G. Hadziioannou, P.F. van Hutten (Eds.): Semiconducting Polymers (Wiley-VCH, Weinheim, 2000)

4. J.H. Schon et al.: Science 288, 2338 (2000); Science 287, 1022 (2000); Science289, 599 (2000); Science 290, 963 (2000); Nature 406, 702 (2000); Nature 403,408 (2000)

5. E.M. Conwell: in Handbook of Organic Conductive Molecules and Polymers, ed.by H.S. Nalwa, Vol. 4 (Wiley, New York, 1997) p. 1

6. C.J. Brabec, N.S. Sariciftci: in Semiconducting Polymers, ed. by G. Hadziioan-nou, P.F. van Hutten (Wiley-VCH, Weinheim, 2000) p. 515

7. N.F. Mott: Metal–Insulator Transition, 2nd edn. (Taylor & Francis, London,1990)

8. O. Gunnarsson, J.E. Han: Nature 405, 1027 (2000)9. P.W. Anderson: Phys. Rev. 109, 1492 (1958); P.A. Lee, T.V. Rama-krishnan:

Rev. Mod. Phys. 57, 287 (1985)10. S.V. Kravchenko, D. Simonian, M.P. Sarachik, W. Mason, J.E. Furneaux: Phys.

Rev. Lett. 77, 4938 (1996)


11. H.C.F. Martens, H.B. Brom, R. Menon: Phys. Rev. B 64, 201102 (2001); H.C.F.Martens, J.A. Reedijk, H.B. Brom, D.M. de Leeuw, Reghu Menon: Phys. Rev. B63, 073203 (2001); H.C.F. Martens: Charge Transport in Conjugated Polymersand Polymer Devices, Ph.D thesis (Leiden University, 2000)

12. J.H. Schon, B. Batlogg: Appl. Phys. Lett. 74, 260 (1999); J.H. Schon, Ch. Kloc,R.A. Laudise, B. Batlogg: Phys. Rev. B 58, 12952 (1998)

13. R. Menon, C.O. Yoon, D. Moses, A.J. Heeger: in Handbook of ConductingPolymers, 2nd edn., ed. by T.A. Skotheim, R.L. Elsenbaumer, J.R. Reynolds(Dekker, New York, 1998) p. 27; R. Menon: in Handbook of Organic ConductiveMolecules and Polymers, Vol.4, ed. by H.S. Nalwa (Wiley, New York, 1997) p. 47

14. C.O. Yoon, R. Menon, A.J. Heeger, E.B. Park, Y.W. Park, K. Akagi, H. Shi-rakawa: Synth. Met. 69, 79 (1995); R. Menon, K. Vakiparta, Y. Cao, D. Moses:Phys. Rev. B 49, 16162 (1994)

15. M. Ahlskog, R. Menon, A.J. Heeger, T. Noguchi, T. Ohnishi: Phys. Rev B 53,15529 (1996); M. Ahlskog, R. Menon, A.J. Heeger, T. Noguchi, T. Ohnishi:Phys. Rev. B 55, 6777 (1997); M. Ahlskog, R. Menon: J. Phys. Cond. Matt.10, 7171 (1998)

16. C.O. Yoon, R. Menon, D. Moses, A.J. Heeger: Phys. Rev. B 49, 10851 (1994)17. R. Menon, Y. Cao, D. Moses, A.J. Heeger: Phys. Rev. B 47, 1758 (1993); R.

Menon, C.O. Yoon, D. Moses, A.J. Heeger, Y. Cao: Phys. Rev. B 48, 17685(1993)

18. A. Aleshin, R. Kiebooms, R. Menon, F. Wudl, A.J. Heeger: Phys. Rev. B 56,3659 (1997); A. Aleshin, R. Kiebooms, R. Menon, A.J. Heeger: Synth. Met. 90,61 (1997)

19. S. Masubuchi, Fukuhara, S. Kazama: Synth. Met. 84, 601 (1997); T. Fukuhara,S. Masubuchi, S. Kazama: Synth. Met. 92, 229 (1998)

20. R. Menon, C.O. Yoon, D. Moses, Y. Cao, A.J. Heeger: Synth. Met. 69, 329(1995)

21. C.O. Yoon, R. Menon, D. Moses, A.J. Heeger, Y. Cao, T.A. Chen, X. Wu,R.D. Reike: Synth. Met. 75, 229 (1995); C.O. Yoon, R. Menon, D. Moses, A.J.Heeger, Y. Cao: Phys. Rev. B 48, 14080 (1993)

22. R. Menon, C.O. Yoon, C.Y. Yang, D. Moses, P. Smith, A.J. Heeger: Phys. Rev.B 50, 13931 (1994); R. Menon, C.O. Yoon, C.Y. Yang, D. Moses, A.J. Heeger,Y. Cao: Macromolecules 26, 7245 (1993)

23. A.B. Pippard: Magnetoresistance in Metals (Cambridge University Press, NewYork, 1989)

24. A.B. Kaiser: Phys. Rev. B 40, 2806 (1989); Synth. Met. 45, 183 (1991)

4 Quantum Solar Energy Conversionand Application to Organic Solar Cells

Gottfried H. Bauer and Peter Wurfel

4.1 Solar Radiation

When studying the limits of solar energy conversion, either by thermal orquantum processes, the sun has traditionally been treated as a blackbody(thermal equilibrium) radiator with surface temperature 5 800 K and dis-tance 1.5 × 1011 m from Earth. A blackbody absorbs all incident radiationirrespective of its wavelength and direction of incidence and is representedclassically by a hole in a cavity.

Its fundamental importance derives from the fact that the energy densityof radiation in the cavity does not depend on the properties of the cavity, i.e.,properties of the walls or the cavity size, provided it is large compared to thewavelength of the radiation. In the following we will discuss radiation not asa function of wavelength but as a function of photon energy, because it is thephotons (light quanta) that are absorbed and excite electrons in matter.

According to Planck, blackbody radiation implies a universal dependenceof the energy density per photon energy interval d(�ω). This results in anenergy current density djE,bb per photon energy interval d(�ω) given by

djE,bb

d(�ω)=

2Ωh3c2

(�ω)3

exp(

�ω

kT

)− 1

, (4.1)

emitted from a hole in the cavity into the solid angle Ω, perpendicularly tothe area of the hole. The cavity temperature T is the only variable, by whichthe energy current density (intensity) of the radiation is controlled. Radiationdescribed by (4.1) is thus called thermal radiation.

Any other body which has absorptivity a(�ω) = 1 for photons with energy�ω will emit radiation according to (4.1). Although the sun consists mainlyof protons, alpha particles and electrons, its absorptivity is a(�ω) = 1 forall photon energies �ω, by virtue of its enormous size. Its temperature is nothomogeneous, but emitted photons originate from a relatively thin surfacelayer a few hundred kilometres thick, in which the temperature is constantand in which all incident photons are absorbed. Conversely, only photonsemitted within this surface layer may reach the surface of the sun. The solarspectrum observed just outside the Earth atmosphere agrees well with (4.1)

4 Quantum Solar Energy Conversion in Organic Solar Cells 119

for a temperature TS = 5800 K, taking the solid angle subtended by the sunas ΩS = 6.8 × 10−5.

The spectrum of solar radiation observed at the surface of the Earth ismodified by scattering and absorption in the atmosphere. In particular, it isattenuated in the ultraviolet and infrared regions. The degree of attenuationdepends on the composition of the atmosphere and the photon path throughit. The latter is longer than the radial thickness of the atmosphere whenphotons arrive obliquely. As a standard spectrum for which solar cell effi-ciencies are rated, a distance of 1.5 times the thickness of the atmosphere ischosen and the spectrum is designated AM1.5 (air mass 1.5). The solar spec-trum outside the atmosphere is accordingly AM0. Both spectra are shown inFig. 4.1. The total energy current density obtained by integrating over thespectrum amounts to 1.35 kW/m2 for the AM0 spectrum and 1.0 kW/m2

for the AM1.5 spectrum.

Fig. 4.1. Energy current densities per photon energy of AM 0 (dotted line) andAM 1.5 (solid line, [1]) solar radiation. The thin solid line is the spectrum of a5 800 K blackbody emitted into the solid angle 6.8 × 10−5

Even more important for quantum energy converters, e.g., solar cells,than the energy current density is the photon current density, because it de-termines the rate at which electrons are excited. Neglecting impact ionisationeffects, the excitation of one electron requires at least one absorbed photon.

120 Gottfried H. Bauer and Peter Wurfel

The photon current density is derived from (4.1) by dividing by the photonenergy �ω. Hence,

djγ,bb

d(�ω)=

2Ωh3c2

(�ω)2

exp(

�ω

kT

)− 1

. (4.2)

Figure 4.2 shows the spectra of the photon currents for AM0 and AM1.5conditions.

Fig. 4.2. Photon current densities per photon energy of AM 0 (dotted line) andAM 1.5 (solid line) solar radiation, calculated from data in Fig. 4.1

For the more general case of a body which reflects and transmits part ofthe incident radiation, so that it has absorptivity a(�ω) < 1, Kirchoff found(even before Planck) that the intensity of thermal radiation is proportionalto the absorptivity of the body, i.e.,

djEd(�ω)

= a(�ω)2Ωh3c2

(�ω)3

exp(

�ω

kT

)− 1

. (4.3)

4.2 Solar Cells and General Quantum Converters

The main characteristic of solar quantum converters or solar cells in gen-eral is that states for electrons exist only for certain energy levels. For solid


materials, these levels are degenerate and broadened into bands. In semicon-ductor terminology, the highest and, at room temperature, almost completelyoccupied energy range is called the valence band. The next higher, largelyunoccupied energy range is called the conduction band. In organic materials,by analogy with molecules, the broadening can be small and the highest oc-cupied states are called HOMO states (highest occupied molecular orbital).In the next highest energy range, states are called LUMO states (lowest un-occupied molecular orbital). These two energy ranges are separated by theenergy gap EG.

Photons are absorbed in matter by electron transitions across the energygap, from the lower to the higher energy range. After an electron is excited,there is an additional electron in the upper range and there is an additionalempty state called a hole in the lower range. Holes have the properties ofpositively charged particles with a positive mass. Consequently, the excitationof an electron can be described equivalently as the generation of an electronand a hole in different bands. This has the advantage that, by their differentnames, they are already recognised as different particles. Although this is alsotrue for electrons in the valence band and electrons in the conduction band,it is easily overlooked.

Solar cells are made from materials in which electron–hole pairs are gener-ated when photons are absorbed. This effect produces chemical energy withinthe absorber and this chemical energy has to be transformed into electricalenergy. In order to generate an electrical current, holes have to move in thedirection of the electric current, whereas electrons must move in the oppo-site direction. This movement requires a geometrical structure: the solar cell.Here, the criteria for the structure of a solar cell will be developed in themost general sense to include recent developments, such as dye solar cells ororganic solar cells, and even to be open to future solar cell concepts.

4.2.1 Two-Level Systems

A 2-level system is the most general electronic model of a solar cell. It allowsa simple but nevertheless rigorous treatment of optical transitions and for-mulation of the excited state. For organic materials, a 2-level system mighteven be more appropriate than a band system.

For our formal treatment of the fermionic 2-level system we assume thatwe may describe the behaviour of electrons in the one-electron approximation.Then each electron is represented by a wave function that is independent ofthe wave functions of other electrons, and the individual wave functions maybe linearly superimposed. This picture often proves useful in the context ofinorganic semiconductors [2,3]. However, it may be highly questionable inorganic and molecular matter, where excitonic [4] and polaronic effects areoften predominant [5].


The system we now consider has a lower energy level at ε1 and an upperlevel at ε2. The occupation of the states at these levels in equilibrium with theblackbody radiation from the surroundings (300 K) obeys Fermi statistics.

4.2.2 Fermi Distribution

According to Fermi statistics, the probability of finding an electron in a statein which it has energy ε2 is

f(ε2) =1

exp(

ε2 − εF

kT

)+ 1

. (4.4)

The probability of finding a state at ε1 which is not occupied by an electron,i.e., the probability of finding a hole, is

1 − f(ε1) =1

exp(

−ε1 − εF

kT

)+ 1

. (4.5)

The total concentrations ne and nh of electrons and holes, respectively, followfrom these relations by multiplying by the appropriate densities of states D1and D2 at energies ε1 and ε2:

ne(ε2) = D2f(ε2) , nh(ε1) = D1[1 − f(ε1)] . (4.6)

If the numbers of electrons and holes are much smaller than the correspond-ing densities of states, the Fermi functions in (4.4) and (4.5) may be approxi-mated by Boltzmann distributions by neglecting the +1 in the denominator.

An interesting consequence of the Boltzmann approximation is that theproduct of the electron and hole densities, viz.,

nenh = D1D2 exp(

−ε2 − ε1

kT

)= n2

i , (4.7)

is a constant of the system. If we increased the number of electrons over theintrinsic density ni (by donating them from a different system), the numberof holes would decrease, and vice versa.

The value of the Fermi energy EF, that is, its position on the energyscale between ε1 and ε2 follows from the condition that the distribution ofelectrons over all the states must obey charge conservation.

4.2.3 Quasi-Fermi Distribution

Any additional excitation over the excitations present in equilibrium withbackground radiation of temperature T leads to an increase in the electron


and hole densities. These deviations from equilibrium require different Fermienergies for the states ε1 and ε2:

ne(ε2) =D2

exp(

ε2 − εF,2

kT

)+ 1

, nh(ε1) =D1

exp(

−ε1 − εF,1

kT

)+ 1

.

(4.8)

In the Boltzmann approximation, the product of the electron and hole con-centrations is

nenh = D1D2 exp(

−ε2 − ε1

kT

)exp

(εF,2 − εF,1

kT

)

= n2i exp

(εF,2 − εF,1

kT

). (4.9)

4.2.4 Transition Rates and Optical Properties

We analyse the absorption and emission of photons for radiative transitionsbetween states at energies ε1 and ε2, involving photons with energy in therange from �ω to �ω + d(�ω). The rate of upward transitions from states atε1 to states at ε2 is

drup(�ω) = |M |2D12f(ε1)[1 − f(ε2)]djγ(�ω)d(�ω)

d(�ω) , (4.10)

where M contains the matrix element for the transition, D12 is the combineddensity of states between which the transition occurs, f(ε1) represents theprobability of finding an occupied state at energy ε1 and [1 − f(ε2)] is theprobability for an empty state at energy ε2.

Likewise, the rate of stimulated emission of photons is

drstim(�ω) = |M |2D12[1 − f(ε1)]f(ε2)djγ(�ω)d(�ω)

d(�ω) . (4.11)

Finally, the rate of spontaneous emission is

drspont(�ω) = |M |2 c0

nDγ(�ω)D12[1 − f(ε1)]f(ε2)d(�ω) , (4.12)

where the density of states for photons in the solid angle Ω in a medium withrefractive index n is

Dγ(�ω) =2Ωn3

h3c30(�ω)2 , (4.13)

and c0 is the velocity of light in vacuum.Stimulated emission is a process in which a photon is duplicated, produc-

ing one additional photon in exactly the same state as the incident photoninitiating the transition. It follows that these photons cannot be distinguished


from non-absorbed photons. The absorption rate at which photons disappear,which defines the absorption coefficient α(�ω), is then

drabs(�ω) = drup(�ω) − drstim(�ω) (4.14)

= |M |2D12[f(ε1) − f(ε2)]djγ(�ω)d(�ω)

= α(�ω)djγ(�ω)d(�ω)

,

where

α(�ω) = |M |2D12[f(ε1) − f(ε2)] . (4.15)

This important relation allows us to replace the matrix element and thecombined density of states in the spontaneous emission rate by the absorptioncoefficient α(�ω) and makes this treatment applicable to real materials oncethe absorption coefficient is known:

drspont(�ω) = α(�ω)c0

nDγ(�ω)

[1 − f(ε1)]f(ε2)f(ε1) − f(ε2)

d(�ω) . (4.16)

Inserting f(ε1) and f(ε2) from (4.8) and remembering that the energy differ-ence ε2 − ε1 over which the transitions occur equals the photon energy �ω,equation (4.16) becomes

drspont(�ω) = α(�ω)c0

nDγ(�ω)

d(�ω)

exp[

�ω − (εF2 − εF1)kT

]− 1

. (4.17)

Equation (4.17) is a generalisation of Kirchhoff’s and Planck’s laws and isvalid for materials that are neither black nor have a single Fermi distributionover all states.

The difference between the Fermi energies μeh = εF2 − εF1 is the freeenergy per electron–hole pair of the ensemble, also called the chemical poten-tial of electron–hole pairs. It is free of entropy and we may therefore hope totransfer it into electrical energy without losses. If electron–hole pairs are notallowed to leave the 2-level system, i.e., under open-circuit conditions, theyhave to recombine and emit one photon per pair annihilation. These photonscarry the free energy of the electron–hole pairs, and μγ = μeh = εF2 − εF1 isrecognised as their chemical potential.

The above treatment is valid quite generally, even if εF2 − εF1 > �ω,when the denominator in (4.17) is negative. Under the same conditions, theabsorption coefficient in (4.15) is also negative, and the spontaneous emissionrate in (4.17) remains positive. When the absorption coefficient is negative,stimulated emission overcompensates the rate of upward transitions and the2-level system amplifies the incident light exactly as in a laser. The conditionεF2 − εF1 > �ω is also known as the lasing condition and is called inversion.

If εF2 − εF1 < �ω by several kT , a condition fulfilled for low intensityexcitations such as those occurring in solar energy conversion, the −1 in the


denominator of (4.17) may be neglected allowing us to express the rate ofspontaneous emission under solar excitation in terms of the rate of sponta-neous emission dr0

spont(�ω) in the dark, i.e., in equilibrium with the back-ground radiation of temperature T , where εF2 − εF1 = 0 in (4.17):

drspont(�ω) = dr0spont(�ω) exp

(εF2 − εF1

kT

). (4.18)

In equilibrium with the background radiation, the absorption rate is, ofcourse,

dr0abs(�ω) = dr0

spont(�ω) . (4.19)

In our 2-level system, one electron–hole pair is generated per absorbed pho-ton. The absorption rate of photons in (4.14) is therefore equal to the gener-ation rate dg of electron–hole pairs,

dg = dg0 + d(Δg) = α(�ω)dj0

γ(�ω) + dΔjγ(�ω)d(�ω)

d(�ω) , (4.20)

which is due to the absorption of photons dj0γ from the 300 K radiation and

from additional radiation dΔjγ from the sun. In the same way, the rate ofphoton emission in (4.17) or (4.18) yields the rate drrad at which electron–holepairs are annihilated by radiative recombination:

drrad = dr0spont(�ω) exp

(εF2 − εF1

kT

). (4.21)

4.2.5 Current–Voltage Characteristic

For an electrical current to flow through the 2-level system, the holes have tomove in the direction of current flow and the electrons, due to their negativecharge, in the opposite direction. We consider some sort of valve or semi-permeable membrane which allows the electrons to enter or leave the 2-levelsystem at an energy of ε2 only on one side and the holes at an energy of

Fig. 4.3. Separation of electrons and holesgenerated by photon absorption in the ab-sorber is achieved by membranes allowing elec-trons to flow towards the n-contact and holesto flow towards the p-contact


ε1 only on the other side (see Fig. 4.3) [6]. From the continuity equation forelectrons or holes, we obtain

divjQ = e(dg − drrad) . (4.22)

Integrating over the thickness l of the 2-level system, we find the total currentjQ, since the hole current is zero at the membrane for the electrons (x = 0)and equals the full current at the hole membrane (x = l), where the electroncurrent is zero:

jQ = −e

∫ (dg0 + dΔg − drrec

)dx (4.23)

= e

∫dr0

spont

[exp

(εF2 − εF1

kT

)− 1

]dx − e

∫Δdg dx .

By virtue of the membranes, the Fermi energy of the upper level translatesinto the Fermi energy at the electron membrane, whilst the Fermi energyof the lower level becomes the Fermi energy at the hole membrane. Thedifference between the Fermi energies of the two membranes is related to thevoltage V between the contacts to the membranes by

eV = εF2 − εF1 . (4.24)

Equation (4.23) is the familiar current–voltage characteristic of a diode. Forlarge negative voltages and in the dark, the small reverse current is given by

jrev = e

∫dr0

spontdl , (4.25)

and under additional illumination, there is a current under short-circuit con-ditions:

jsc = −e

∫Δdg dl = −edΔjγ,abs . (4.26)

With these expressions, the current–voltage characteristic becomes

jQ = jrev

[exp

(eV

kT

)− 1

]+ jsc . (4.27)

Figure 4.4 shows how this current–voltage characteristic results from a bal-ance between the emitted and absorbed photon currents. Under open-circuitconditions, where absorbed and emitted photon currents are equal, the chem-ical potential of electron–hole pairs is μeh,oc = eVoc. At this splitting of theFermi energies, all electron–hole pairs recombine in the absorber at a ratewhich balances the generation rate. In order to be able to feed an exter-nal current, the recombination rate must be lowered by reducing the split-ting of the Fermi energies. The maximum current the system can provide isjsc = −edΔjγ,abs under short-circuit conditions, where the Fermi energies are


Fig. 4.4. The photon current djγ,emit emitted by the 2-level system as a function ofthe chemical potential μeh of its electron–hole pairs. The useful current of electron–hole pairs is given by the difference between the absorbed and emitted photoncurrents, viz., jQ/e = dΔjγabs − djγ,emit

not separated and none of the electron–hole pairs generated by illuminationexceeding the 300 K radiation are able to recombine.

The electrical energy supplied by the system is given by the product of thecurrent and voltage. It is represented by the solid rectangle in Fig. 4.4, whichis the largest rectangle between the emitted and the absorbed photon currentsand defines the point of maximum power. Due to the steep exponential rise ofthe emitted photon current with the chemical potential μeh, a small reductionby about 3kT from the open-circuit value μeh,oc is sufficient to allow a supplyof electrons and holes to the external circuit which differs little from itsmaximum value under short-circuit conditions.

The efficiency is found by dividing the electrical energy current by theincident energy current, given by the product of the incident (and absorbed)photon current and the photon energy �ω, shown as the dashed rectanglein Fig. 4.4. The conversion efficiency for monochromatic solar radiation isshown in Fig. 4.5 as a function of the energy gap εG = �ω.

It must be emphasised that the diode characteristic is the result of thedependence of the recombination rate on the difference of the Fermi energiesand of the ability of the membranes to transmit one type of carrier and blockthe other. In other words, the reverse current (eV < 0) is limited becauseelectrons and holes cannot flow out of the system at a greater rate than theyare generated. The forward current (eV > 0) is limited because electrons andholes flow into the system and replenish electron–hole pairs at the rate atwhich they recombine, and this rate increases exponentially with voltage.

4.3 Semiconductor Solar Cells as Two-Band Systems

If the electrons in a material are distributed in broad ranges over energy,the pure 2-level system is no longer an appropriate model. It is, however,


Fig. 4.5. Conversion efficiency η of a 2-level system for monochromatic solar radi-ation of photon energy �ω from the non-concentrated AM 0 spectrum (solid line)and for maximum concentration (dashed line)

easily extended to describe the distribution of electrons over energy bandsby summing over all states and the corresponding transitions given in the2-level system. For a 2-band system we will use semiconductor terminology.We call the lower band the valence band with an upper energy bound at εV,and the upper band the conduction band with a lower energy bound at εC.

4.3.1 Fermi Distribution

Analogously to the formulations in (4.8), the total number of electrons perunit volume in the conduction band is found by integrating the density ofstates per energy interval multiplied by the Fermi distribution in (4.4) overthe energy range of the conduction band:

ne =∫

εC

f(εe)D(εe) dεe , (4.28)

where εC designates the bottom of the conduction band. Since the Fermifunction decreases exponentially with increasing energy, if εC exceeds theFermi energy by a few kT , only states in the lower part of the conductionband contribute to the integral in (4.28). As a result, the total number ofelectrons is, to a good approximation,

ne = NC exp(

−εC − εF

kT

), (4.29)

where NC is the effective density of states. For ideal semiconductors, in whichthe electrons in the conduction band behave like free electrons, but with aneffective mass m∗

e , the effective density of states becomes

NC = 2(2πm∗

ekT

h2

)3/2

. (4.30)


However, (4.29) is valid more generally, for different energy distributions ofthe states, for which the value of NC differs from (4.30).

The total concentration nh of holes in the valence band is found in thesame way, by applying the occupation function (4.5) multiplied by the densityof states in the valence band. The result of integrating over all states in thevalence band yields

nh = NV exp(

εV − εF

kT

), (4.31)

where NV is the effective density of states in the valence band.The Fermi energy εF, lying between the conduction and valence bands,

follows from the condition of charge conservation.

4.3.2 Doping

In semiconductors and insulators, the position of the Fermi level εF and withit the number of electrons in the conduction band and holes in the valenceband can be altered by incorporating foreign atoms. Two kinds of atom canbe distinguished. Donors are electrically neutral if occupied and are positivelycharged if empty, whilst acceptors are negatively charged if occupied and neu-tral if empty. Donors and acceptors can have states with energies anywhereon the energy scale. However, only donor states with energies within a fewkT below the conduction band and acceptor states within a few kT abovethe valence band are effective for doping. The incorporation of donors thenleads to an increase in the electron density in the conduction band, whilstthe Fermi energy is located in the upper half of the band gap, leaving thedonors mainly unoccupied. The incorporation of acceptors with energy closeto the valence band increases the density of holes, shifts the Fermi energyinto the lower half of the band gap and leaves the acceptors mainly occupiedand negatively charged.

Which atoms behave as donors or acceptors can be predicted in simplecases. If a silicon lattice atom engaged with its 4 outer electrons in chemicalbonds is replaced by arsenic which has 5 outer electrons, only 4 of them areneeded for chemical bonding. The fifth is then easily ionised and free to moveas a conduction electron, leaving a positively charged donor behind. In thesame manner boron, which has 3 outer electrons, will accept a fourth electronfrom the valence band for chemical bonding, if replacing a silicon atom, thusgenerating a hole in the valence band and becoming negatively charged.

If both donors and acceptors are present in the same material, they com-pensate each other. The electron donated by the donor is found to be acceptedby the acceptor with no effect on the number of free electrons or holes.

Without illumination, i.e., in equilibrium with the 300 K radiation fromthe surroundings, all materials having states in 2 different energy ranges havethe interesting property, following directly from (4.29) and(4.31), that theproduct nenh of electron density in the upper energy range and hole density


in the lower energy range is independent of doping. It has the same value forno doping, when the electron and hole densities are equal and are called theintrinsic density ni:

nenh = NCNV exp(

−εC − εV

kT

)= n2

i . (4.32)

By doping, the density of one type of carrier is increased at the expense ofthe other type. In fact n-type materials are made by incorporating donors.If the electrons are mobile, they are good electron conductors and poor holeconductors. On the other hand, p-type materials are made by incorporat-ing acceptors. If the holes are mobile, they are good hole conductors andpoor electron conductors. We shall see that these properties are extremelyimportant for the functioning of a solar cell.

Moreover, we shall keep in mind that the incorporation of dopants createsadditional states for electrons and holes within the energy gap (often calledimpurity states). As a consequence, it unavoidably allows transitions to andfrom these states. This introduces additional recombination processes, whichreduce the minority carrier lifetimes compared with lifetimes in the undopedmaterial.

4.3.3 Quasi-Fermi Distributions

Even without illumination or current flow, electrons and holes are in a dy-namic equilibrium. They are constantly generated and then disappear by re-combination, and the concentrations in (4.29) and (4.31) given by the Fermidistribution are expectation values or time averages. In equilibrium with theblackbody background radiation, any generation process is in detailed bal-ance with its inverse, a recombination process. Deviations from this detailedbalance result in a perturbation.

For a deviation from the equilibrium with the background radiation, pre-dictions for the distribution of electrons and holes are possible under certainassumptions which are justified in most realistic cases. A typical assumptionis, for example, that the electrons in the conduction band scatter frequentlywith vibrating atoms in such a way that the times for momentum relaxationand energy relaxation are short compared to their lifetime in the conductionband, after which they are annihilated in a recombination reaction with ahole. Under these conditions, the distribution of the electrons over the statesin the conduction band results in a larger entropy than in any other distri-bution for the same number of electrons and the same temperature.

As a result, we are allowed to use Fermi statistics for the distributionof electrons and holes as in (4.29) and (4.31). In this case, detailed balancefor the distribution within each band is maintained to a very good approxi-mation. Due to the additional generation, however, the electrons in the con-duction band are not in detailed balance equilibrium with the holes in thevalence band. As a result, the occupation probability (1− fV) of the valence


band with holes and the occupation probability fC of the conduction bandwith electrons, refer to the same temperature, the temperature of the lattice,but have different Fermi energies. We have

ne = NC exp(

−εC − εF,C

kT

), (4.33)

where, in contrast to (4.29), the Fermi energy is now denoted εF,C to indicatethat it belongs to a Fermi distribution which is only valid in the energy rangeof the conduction band. If for the holes in the energy range of the valenceband the relaxation times are also small compared to the lifetime of the holes,they are distributed according to a Fermi distribution and their total densityis given by

nh = NV exp(

εV − εF,V

kT

), (4.34)

where εF,V is the Fermi energy, indicating that the hole distribution followsfrom a Fermi distribution that is only valid in the energy range of the valenceband.

The product of electron and hole densities is now

nenh = NCNV exp(

−εC − εV

kT

)exp

(εF,C − εF,V

kT

)

= n2i exp

(εF,C − εF,V

kT

). (4.35)

Since the Fermi energy εF,C is the electrochemical potential of the electronsin the conduction band and −εF,V is the electrochemical potential of theholes, the difference εF,C − εF,V turns out to be the chemical energy perelectron–hole pair.

4.3.4 Interaction of Light with Matter

Insofar as the geometrical size of a body is large compared to the wavelengthof electromagnetic radiation, we formulate their interaction in terms of spa-tially continuous dielectric and magnetic properties, such as the dielectricand magnetic susceptibilities ε = ε(ω) and μ = μ(ω). Furthermore, for suf-ficiently small frequencies ω, or photon energies ε = �ω below the cohesionenergy (insufficient to decompose the material or destroy its structure, i.e.,a few eV or less), we describe the effects of light–matter interaction in thewave picture represented by Maxwell’s equations:

∇ × E = −μμ0∂H

∂t, ∇ × H = j + εε0

∂E

∂t, (4.36)

with ∇ · H = 0 (no magnetic monopoles), local charge neutrality

∇ · E = −ρ/εε0 ≈ 0 ,


and

j = |σ(ω, E,B)|E ≈ σE ,

where E and H designate the electric and magnetic field strengths, j is theelectric current density, ρ is the net space charge density, and |σ(ω, E, B)| rep-resents the second rank conductivity tensor containing the effects of electricand magnetic fields, commonly approximated with a polynomial representa-tion of |B| up to second order. σ is the electric conductivity tensor appropriatefor non-ferromagnetic materials (μ ≈ 1) and negligible Hall effects.

A further spatial derivative of the first Maxwell equation and the appro-priate substitution yields

∇ ×(

μμ0∂H

∂t

)= μμ0

∂(∇ × H)∂t

=∂

(j + εε0

∂E

∂t

)∂t

,

∇ ×(

μμ0∂H

∂t

)= σμμ0

∂E

∂t+ μμ0εε0

∂2E

∂t2= −∇ × (∇ × E) . (4.37)

In terms of just one of the fields, e.g., the electric field, we have

σμμ0∂E

∂t+ μμ0εε0

∂2E

∂t2= −∇(∇ · E) + ΔE = ΔE . (4.38)

With μ, ε and σ independent of E, the solution of this second order partialdifferential equation is composed of transverse harmonic waves

Ei0 exp(iωit) exp(−iki·x) . (4.39)

Due to the conservation of the components of the propagating waves ori-ented parallel [E(ω), H(ω)], and perpendicular [D(ω) = εε0E(ω),B(ω) =μμ0H(ω)] to the plane separating different media, particular field terms E,D, H, and B occur for forward and backward propagation, demonstratingthat only a fraction of the electric and magnetic field amplitudes propagateacross interfaces of different phases. Correspondingly, only a fraction of theenergy of the electromagnetic wave, which we know as the Poynting vectorS = E × H, is coupled from one medium into the next.

The complete description of the individual components of the propagatingfield amplitudes with their appropriate projection onto the interface of thetwo media is given by the Fresnel equations.

The attenuation of the amplitudes along the propagation path in ourwave description enters through the imaginary part −iε2 of the complex di-electric function ε = ε1 − iε2. The latter translates into a complex refractiveindex n = n − ik. Both result from the electrical conductivity term σ. Thecorresponding attenuation of the Poynting vector in our system, which weassume to respond in a linear way to field perturbations, accordingly shows


an exponential attenuation with the path length travelled in the dampingmedium,

|S(x)| = |S(x0)| exp[−α(|x − x0|)] , (4.40)

and the argument α = α(ω) in the exponent emerges as the optical absorptioncoefficient.

In the following sections, we will apply these features of propagating elec-tromagnetic wave packages, in particular the initiation of a backward propa-gation and the attenuation on simple geometrical configurations. In this waywe shall quantify the coupling of light with matter and the correspondingabsorption of light in matter.

Absorption of Radiation. The probability for an incident photon of en-ergy �ω to be absorbed per unit length in matter is given by the absorptioncoefficient α(�ω). The rate drabs at which photons with energy between �ωand �ω + d(�ω) are absorbed (number of photons per unit volume and unittime) at a given location x is proportional to the photon current densitydjγ(�ω, x) at this location:

drabs(�ω, x) = α(�ω)djγ(�ω, x) . (4.41)

Equation (4.41) contains all selection rules for optical transitions and it con-tains all transitions between pairs of states involving the same photon energy�ω. It thereby models a system with broad bands as being made up of amultitude of 2-level systems. The absorption coefficient can in principle becalculated from theoretical models. Here we will use it as an experimentallydetermined quantity.

Due to absorption, the current density of photons with energy �ω de-creases exponentially with distance x from the surface after some of the pho-tons have been reflected there:

djγ(�ω, x) = djγ(�ω, 0)[1 − r(�ω)] exp[−α(�ω)x] . (4.42)

Reflection. The reflectivity r(�ω) for vertical incidence on a plane interfacebetween two media is given by

r(�ω) =∣∣∣∣ n1(�ω) − n2(�ω)n1(�ω) + n2(�ω)

∣∣∣∣2

. (4.43)

The complex index of refraction n = n− ik has a real part n, called the indexof refraction, and an imaginary part k, called the index of absorption, relatedto the absorption coefficient α by k = αλ/2π. For the important case wheremedium 1 is air with n1 = 1, the reflectivity from the surface of medium 2 is

r(�ω) =[n2(�ω) − 1]2 + k2

2(�ω)[n2(�ω) + 1]2 + k2

2(�ω). (4.44)


Most semiconducting materials have a rather large index of refraction n2 anda small index of absorption k2. A typical value of n2 in the near infrared is3.5, as found for silicon or gallium arsenide. The resulting large reflectivity ofabout 30% must be reduced by an anti-reflection coating. This is an interme-diate, non-absorbing layer at the interface between medium 1 and medium2 with refractive index n =

√n1n2 =

√n2 and thickness λ/4n, where λ

is the vacuum wavelength, somewhere in the red of the solar spectrum, forwhich the reduction of the reflectivity leads to the largest improvement inthe absorbed photon current.

Disregarding multiple reflection, the absorptivity, defined as the photoncurrent absorbed in a body of thickness d divided by the incident photoncurrent is

a(�ω) = [1 − r(�ω)] {1 − exp[−α(�ω)d]} . (4.45)

Ideally, the absorptivity is a(�ω) = 1 for photons with energies �ω ≥ εGexceeding the band gap of the absorber, and a(�ω) = 0 for photons with�ω < εG.

Light Trapping. If the absorption coefficient α and/or the thickness d ofa material are small, insufficient absorption can be improved by a geometri-cal structure that traps the light. This structure ensures, for example, thatweakly absorbed light after being reflected from the rear surface strikes thefront surface from the inside at an angle θ which is larger than the limitingangle for total internal reflection, i.e., sin θ > 1/n2. Assuming that multipletotal reflection of weakly absorbed photons leads to their isotropic and ho-mogeneous distribution within the absorber, its absorptivity a is increasedby a factor of 4n2

2, which is typically around 50.

Incident light

so lar ce ll

substra te

Fig. 4.6. Incident light is deflected in a corru-gated thin film solar cell, leading to total in-ternal reflection at the interface with the sub-strate and at the front surface

Figure 4.6 shows a light-trapping structure for a thin film, where reflectionfrom the rear surface is also caused by total internal reflection.


4.3.5 Generation of Electron–Hole Pairs

Photons of energy �ω from the sun and the 300 K surroundings are regularlyabsorbed in band-to-band transitions, and (4.41) is the generation rate forelectrons (in the conduction band) and holes (in the valence band).

Since some of the photons may be absorbed in transitions which do notgenerate electron–hole pairs, a quantum efficiency β is defined such that thegeneration rate of electron–hole pairs (number per unit volume and unit time)is

dg(�ω, x) = β(�ω)α(�ω)djγ(�ω, x) . (4.46)

The generation dG per unit area is obtained by integrating over the thicknessof a body. According to (4.45),

dG(�ω) = a(�ω)djγ(�ω, 0) . (4.47)

The total generation by photons incident on an area A is found by integrat-ing over the contributions from all photon energies and equals the absorbedphoton current

G = A

∫a(�ω)djγ(�ω, 0) = jγ,abs . (4.48)

Thermalisation. As we have already seen, any generation of electron–holepairs in addition to generation in (thermal and chemical) equilibrium withthe 300 K surroundings perturbs the energy and momentum distributionof the electrons and holes. It relaxes due to frequent scattering with otherelectrons or holes and with vibrating atoms into a distribution with an averageequilibrium kinetic energy of 3/2kT for each electron and each hole. If theenergy of the absorbed photon �ω is larger than the band gap εG + 3kT ,the excess energy is dissipated into lattice vibrations within a picosecond(10−12 s). This thermalisation loss in conjunction with the non-absorption ofthe photons with �ω < εG is responsible for the loss of almost 60% of theincident energy from an AM0 solar spectrum even for the most favourableband gap of around 1.3 eV.

As a consequence of the very fast momentum and energy relaxation of hotcarriers resulting from absorption of photons with �ω > εG, photon excessenergy can hardly be exploited even if it is much larger than the band gap andwould be sufficient to generate one or more additional electron–hole pairs. Itis only if the photon energy is more than about 3 times the band gap thatthe kinetic energy of the electron and the hole may be sufficient to generatean additional electron–hole pair by impact ionisation. However, this processhas a small probability and, since high energy photons are rare in the solarspectrum, quantum efficiencies β > 1 are not found in solar cells.


4.3.6 Recombination

Electrons and holes which have been generated and do not flow out of theabsorber to contribute to an electrical current must eventually recombine.Recombination [7] is a chemical reaction of an electron with a hole, in whichthe electron and the hole are annihilated. Conservation of momentum andenergy requires other particles to be involved. In a radiative recombinationprocess, a photon is emitted to carry the momentum and the energy. Innon-radiative recombination, one or more phonons or atomic vibrations arecreated or absorbed, often mediated by states in the band gap caused byimpurities. In Auger recombination, which is also non-radiative, energy andmomentum are given to another electron or another hole, which subsequentlyloses this energy by thermalisation via scattering. In each case the primarystep consists of the reaction of an electron with a hole, and the rate at whichelectrons (and holes) are annihilated by recombination is

re = Cnenh =ne

τe, (4.49)

which defines the lifetime τe of the electrons in their energy range. In general,τe may depend on the concentration of holes and electrons and will thus de-pend on the generation rate of electron–hole pairs. The recombination rate ofholes always equals the recombination rate of electrons, since they disappearpairwise. The recombination partners are not necessarily free holes in the va-lence band and free electrons in the conduction band, and the concentrationand lifetime of free holes may differ from that of free electrons.

In some simple cases τe is independent of the generation rate, becausethe density of holes with which the electrons recombine is so large that itis little affected by the additional photogeneration of electron–hole pairs.One example is the recombination of electrons with holes in impurity states,if the material is not sufficiently pure, so that the concentration of holes inimpurities is large. Another example is electron recombination with free holesin the valence band, if the density of free holes is large due to p-type doping.

Non-Radiative Recombination. In non-radiative recombination, the en-ergy of a recombining electron–hole pair ends up in vibrations of atoms. Thesevibrations, called phonons, are quantised and have energies of the order of10 meV. This is much smaller than the energies of electron–hole pairs, whichare typically in the range 1–3 eV. Many phonons must, therefore, be gener-ated simultaneously to take up the energy of the electron–hole pair. Sincethis process has a comparably small probability, non-radiative recombinationis only predominant if mediated by states in the energy gap, which allow therecombination process to proceed stepwise with a smaller number of phononssimultaneously generated. This argument shows the importance of avoidingany imperfections, such as impurities and lattice defects, which give rise tostates in the gap.


At the metal contacts of a solar cell, however, states within the energygap cannot be avoided. Metals have a continuum of states below and abovethe Fermi energy, which aligns with the Fermi energy of the adjacent semi-conductor. It thus lies within the energy gap and recombination probabilitiesat the interface with the contacts are very large as a consequence. A strategyfor avoiding excessive interface recombination at the contacts would requirethe contact area to be as small as possible. A more elegant and more effec-tive elimination of interface recombination would be achieved if one type ofphotogenerated carrier, either electrons or holes, could be kept at a distancefrom the contact interface.

Recombination destroys electrons and holes which one would like to seeflowing out of the solar cell to produce a charge current. It should thereforebe prevented. In real materials, non-radiative recombination is often predom-inant, but it can, in principle, be avoided by proper purification and doping.Radiative recombination, however, cannot be avoided without losing the abil-ity to absorb light. For a solar cell, this is the process which ultimately limitsits performance.

Radiative Recombination. The rate of radiative recombination followsfrom the relations (4.17) and (4.11) for a 2-level system. Since we have ex-pressed the spontaneous emission rate in terms of the absorption coefficient,integration over all transitions involving identical photon energies is alreadytaken into account by using the absorption coefficient for the 2-band system.Integration over all photon energies occurring in transitions between the con-duction band and the valence band yields the rate of radiative recombination:

rrad =∫

α(�ω)2Ωn2

h3c2

(�ω)2d(�ω)

exp[

�ω − (εFC − εFV)kT

]− 1

. (4.50)

If the difference between the Fermi energies is smaller than the photon energyby several kT , well justified for solar cells which are far from lasing, the −1in the denominator can be neglected and a very simple relation results:

rrad = r0rad exp

(εFC − εFV

kT

), (4.51)

where r0rad is the spontaneous emission rate in (thermal and chemical) equi-

librium with the 300 K surroundings, resulting from (4.50). In doing so, theabsorption coefficient α(�ω) is assumed to have the same value under so-lar irradiation as in the dark, an assumption also well justified at least fornon-concentrated solar irradiation.

The total rate at which photons are emitted by radiative recombinationinto one hemisphere Ω = π through a surface of area A into the surrounding


air (n = 1) follows by integrating (4.50) over the thickness l to give

jγ,emit = Rrad =∫ ∫

α(�ω)2π

h3c2

(�ω)2d(�ω)

exp[

�ω − [εFC(x) − εFV(x)]kT

]− 1

dx .

(4.52)

Again, as for the 2-level system, (4.52) can be well approximated in homoge-neous solar cells by

jγ,emit = R0rad exp

(εFC − εFV

kT

), (4.53)

where the total recombination rate R0rad in equilibrium with the background

radiation at T = 300 K results from (4.52) for εFC − εFV = 0.In order to calculate the total rate of radiative recombination in a body,

as for any other recombination process, the spatial dependence of the Fermienergies must be known. According to (4.33) and (4.34), this is equivalentto knowing the spatial variation of the electron and hole densities. To beprecise, for radiative recombination, we only need to know the variation ofthe difference between the Fermi energies, equivalent to the product of theelectron and hole densities. It is interesting to note that in the dark, nenh =n2

i everywhere, independently of the separate spatial variations of the electronand hole densities. This shows that, in the dark, the photon generation rateis homogeneous. Since it equals the absorption rate, the photon density ishomogeneous, too, even in locations which cannot be reached by photonsincident from the outside.

4.4 Radiative Limit for Solar Cell Efficiencies

Since radiative recombination is tied on one side to the absorption coefficient,which should be as large as possible to facilitate the absorption of solarradiation, and on the other side to the difference between the Fermi energiesεFC − εFV, which is the free energy per electron–hole pair and should alsobe as large as possible, radiative recombination is quite unavoidable. Onthe contrary, in a solar cell, which does not emit photons under open-circuitconditions, non-radiative recombination is dominant and causes the differencebetween the Fermi energies εFC − εFV to be too small for a sizeable emissionaccording to (4.52). In an optimal situation, all recombination is radiative.The efficiency for this situation is the maximum efficiency a 2-band solar cellcan have [6,8–10].

For optimal absorption, we assume that the absorptivity in (4.45) is

a(�ω ≥ εG) = 1 , a(�ω < εG) = 0 . (4.54)


This eliminates all spurious absorption that does not lead to electron–holepairs. It also excludes emission of low energy photons, that is, those with�ω < εG, the energy gap of the material.

To keep the calculation simple, we also assume that the electrons andholes, although generated at a rate which decreases with distance from thesurface, are distributed homogeneously in the material due to their goodmobility.

4.4.1 Current–Voltage Characteristic

As for the 2-level system, we require that electrical contact be made to the2-band system in such a way that, at one contact, which will be the nega-tive contact of the solar cell, only electrons are exchanged with an externalcircuit, whereas holes are exclusively exchanged through the second contact,the positive contact of the solar cell under energy conversion conditions. Asbefore, the charge current is

jQ = −e(G − Rrad) , (4.55)

which can also be expressed as

jQ = e(jγ,emit − jγ,abs) . (4.56)

With (4.52), this transforms as for the 2-level system into

jQ = jrev

[exp

(eV

kT

)− 1

]− eΔG , (4.57)

where jrev = eR0rad is the reverse saturation current resulting from the radia-

tive generation rate in the dark, which follows from (4.52) for εFC − εFV = 0,and ΔG is the generation rate in excess of the generation rate in the dark.

Figure 4.7 shows the charge current jQ as a function of the voltage V =(εFC − εFV)/e. The current at short circuit is jsc = −eΔG = −ejγ,abs andthe voltage at open circuit is

Voc =kT

eln(1 +

ΔG

R0rad

)or Voc =

kT

eln(1 − jsc

jrev

). (4.58)

The generation rate ΔG is calculated from (4.2) for a blackbody spectrum of5 800 K incident from a solid angle 6.8 × 10−5, as subtended by the sun. Ascan be seen from Fig. 4.1, this blackbody spectrum is very close to the AM0spectrum and gives a total energy current density of 1.39 kW/m2, comparedwith 1.35 kW/m2 for AM0. The temperature of the solar cell and its sur-roundings is 300 K, which determines a reverse current of only 3×10−16 A/m2

due to the absorption of blackbody radiation from the surroundings.The point on the j/V characteristic where the product of voltage Vmpp

and current jQ,mpp has a maximum value is called the maximum power point


0.0 0.5 1.0-500

-400

-300

-200

-100

0

100

200

mppjQ,mp

Vmp

j Q /

A/m

2

voltage / V

Fig. 4.7. Current–voltage characteristic of a solar cell with only radiative recom-bination and a band gap of εG = 1.30 eV in blackbody radiation at 5 800 K and anincident energy current of 1.39 kW/m2

(mpp). It is found numerically. The maximum power is represented in Fig. 4.7by the largest rectangle within the current–voltage characteristic.

Figure 4.7 gives the current–voltage characteristic for a 2-band systemwith a band gap of 1.30 eV. The efficiency η is shown in Fig. 4.8. Withincreasing band gap εG, the short-circuit current decreases and the open-circuit voltage increases. The efficiency η, taken as the maximum power foreach band gap divided by the incident energy current density of 1.39 kW/m2,has a maximum value of 29.9% for a band gap of 1.30 eV.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.2

0.4

0.6

0.8

1.0

η

jSC / 1000 A/m 2

VOC / V

εG / eV

Fig. 4.8. Efficiency η, open-circuit voltage Voc, and short-circuit current densityjsc as a function of the band gap εG of a 2-band system illuminated by blackbodyradiation at 5 800 K with an incident energy current density of 1.39 kW/m2


4.5 Charge Separation in Solar Cells

As already stated, for a charge current to flow through the solar cell, electronsand holes must move in different directions. By convention, for the forwardcurrent, holes and electrons must move from the external circuit through thecontacts into the solar cell, where they disappear by recombination. For thereverse current, electrons and holes must move out of the solar cell, where theywere generated. In order to achieve this, the contacts themselves or the ma-terial in front of the contacts should have the properties of a semi-permeablemembrane. The active volume of the solar cell, in which generation and re-combination determine the electrical current, is between the membranes. Themembranes must be close enough to the place where the electron–hole pairsare generated, so that they can be reached within the lifetime of the carriers.

The n-membrane should transmit the electrons and block the holes, whilethe p-membrane should transmit the holes and block the electrons. Clearly,the n-membrane must have a large conductivity for electrons and a smallconductivity for holes, while the p-membrane must be a good hole and poorelectron conductor. These properties are easily achieved by doping. n-typedoping with donors increases the electron density and lowers the hole density.This results in a large electron and small hole conductivity. p-type doping byacceptors increases the hole conductivity and lowers the electron conductivity.Care must be taken to avoid excessive recombination in the membranes dueto impurity recombination or Auger recombination, which may result fromlarge doping densities. Figure 4.9 shows a good example of a solar cell con-sisting of an absorber and n- and p-membranes. An additional advantage ofthe membrane structure is the very effective isolation of the photogeneratedelectron–hole pairs from the metal n- and p-contacts on the outer side of themembranes. Interface recombination at the metal contacts is thus prevented.

This structure is ideal, but complicated. It requires 3 different materials,an absorber and 2 membranes, which should have a large band gap butdifferent electron affinities χe, in order to give rise to the barriers. We see thatthis structure transforms the difference between the quasi-Fermi energies ofthe absorber into a difference between the Fermi energies εF,left and εF,rightin the n- and p-contacts, which is the voltage V multiplied by the elementarycharge e.

As will be derived in Sect. 4.5.1, non-vanishing gradients of the Fermienergies are required to drive electron and hole currents. However, the largerthe conductivities, the smaller the gradients to drive the electron and holecurrents. In Fig. 4.9, where the photogenerated electrons move towards then-membrane on the left, the electron conductivity of the n-membrane is as-sumed to be so large that the gradient of εFC which drives the electron currentis negligibly small. The same holds for the gradient of εFV which drives thehole current through the p-membrane on the right. Since the quasi-Fermienergies coincide at the metal n- and p-contacts due the large recombinationprobability at interfaces with metals, a large gradient of εFV exists in the n-


Fig. 4.9. Energy diagram of the ideal solar cell structure in Fig. 4.5: absorberbetween an n- and a p-membrane [6]. Electrons can be exchanged through the n-membrane, while holes are blocked by a barrier in the valence band. Holes can onlybe exchanged through the p-membrane, while electrons are blocked by a barrier inthe conduction band

membrane and of εFC in the p-membrane. These gradients cause currents ofminority carriers, holes in the n-membrane and electrons in the p-membrane,going in the wrong direction. However, due to the very small concentration ofholes in the n-membrane, which can be seen from the large distance betweenεFV and εV in Fig. 4.9, the hole current in the n-membrane is negligibly small.By the same argument, the electron current in the p-membrane is negligible.

If the conductivity for the electrons on their path to the n-contact, and/orfor the holes towards the p-contact, is not large, non-vanishing gradients ofthe quasi-Fermi energies result. The voltage, which is the difference betweenthe Fermi energies in the n- and p-contacts is then smaller than the splittingof the Fermi energies inside the absorber. This is a voltage loss, identified asa voltage drop due to a series resistance in the solar cell.

The structure in Fig. 4.9 has the disadvantage that it introduces two in-terfaces between different materials. In real life, interfaces between differentmaterials give rise to a large number of interface states within the band gapwhich facilitate recombination. In a somewhat less ideal structure, one couldmake the absorber a p-type conductor itself, so that it serves simultaneouslyas the p-membrane and the absorber. One could also make the absorbern-type, making it act as the n-membrane. Finally, with the same base ma-terial, one part could be p-type and another part could be n-type, in whichcase both membranes are incorporated into the absorber, thus avoiding theinterfaces and interface states. The blocking of the carriers from reaching thewrong port and suffering recombination, however, may be less ideal in thispn-homostructure than in the heterostructure in Fig. 4.9. Silicon solar cells


are made this way. The point is that the p-type and n-type parts of the solarcell are the important ingredients, rather than the junction between them.

If the membrane properties of a solar cell structure are ideal, the current–voltage characteristic is as derived in Sect. 4.2.5. In the dark, the small currentin reverse direction is due to the small generation rate by photons from the300 K surrounding radiation. The current is small because electrons and holescannot flow out of the absorber at a rate which is larger than their generationrate. In the forward direction, electrons and holes are injected through themembranes into the absorber, where they recombine. If the recombinationrate increases in proportion to the product of the carrier densities as for ra-diative recombination, it increases exponentially with the difference betweenthe Fermi energies, equal to the voltage at the contacts with the membranes.

The current–voltage characteristic results from the balance between gen-eration and recombination rates. It is not, as is often thought, due to a barrierthat has to be surmounted by the charge carriers. Barriers are present in themembranes, but they should be insurmountable for one type of carrier andtransparent for the other.

4.5.1 Charge Transport

The macroscopic transport of particles requires a departure δf(u) from thehomogeneous and isotropic thermal equilibrium distribution in the velocityspace f0(r, u, t). The net motion of species in the entire velocity space nolonger vanishes:

∞∫−∞

u [f(x, u, t)] du =

∞∫−∞

u [f0(x, u, t) + δf(x, u, t)] du �= 0 . (4.59)

The deviation of the velocity distribution function from that in thermal equi-librium f0(r, u, t) is commonly formulated through terms which deviate fromthermal equilibrium and terms returning to it:

df(x,u, t)dt

=df↑(x, u, t)

dt− df↓(x, u, t)

dt. (4.60)

In particular, we write the above equation, composed of the sum of the rele-vant derivatives, and assume that the departure term is just balanced by thecollision term:

df(u)dt

=∂f(u)

∂t+ u· [∇xf(u)] +

(F

m∗

)· [∇kf(u)] −

[∂f(u)

∂t

]coll

= 0 .

(4.61)

For the stationary state we obtain

u· [∇xf(u)] +(

F

m∗

)· [∇kf(u)] −

[∂f(u)

∂t

]coll

= 0 . (4.62)


The collision term can be linearised:[∂f(u)

∂t

]coll

= − [f(u) − f0(u)]τcoll

. (4.63)

As a consequence of the wave behaviour of electrons in matter, we replace thevariable u by the wave vector k = m∗u/�, where m∗ designates the effectivemass of the carrier in the crystal, and we translate u into the group velocity

ugr = ∇k[ω(k)] =1�∇k[ε(k)] .

Accordingly, we rewrite (4.62) in the form

f(k) = f0(k) − τcoll

[u·∇xf(k) +

F

�·∇kf(k)

](4.64)

= f0(k) − τcoll

�

[[∇kε(k)]·[∇xf(k)] + F ·∇kf(k)

].

The particle flux density multiplied by the elementary charge yields the elec-tric current density

jQ,e = − e

4π3

∞∫−∞

u(k)f(k) dk = − e

4π3

∞∫−∞

1�[∇kε(k)]f(k) dk . (4.65)

Inserting f(k) from (4.64), we obtain the approximations

∇xf(k) = ∇xf0(k) , ∇kf(k) = ∇kf0(k) , (4.66)

jQ = − e

4π3

{ ∞∫−∞

1�[∇kε(k)]f0(k) dk (4.67)

−∞∫

−∞

τcoll

�2 [∇kε(k)][[∇kε(k)]·[∇xf0(k)] + F ·[∇kf0(k)]

]dk

}.

The first integral vanishes for reasons of symmetry, so we only need considerthe second term

jQ =e

4π3�2

∞∫−∞

τcoll[∇kε(k)][[∇kε(k)]·[∇xf0(k)] + F ·[∇kf0(k)]

]dk .

(4.68)

We now apply the quasi-free electron and hole relations for the energies inthe conduction and valence bands, with

εe,h = εC,V +�

2k2e,h

2m∗e,h

, ∇xεe,h = ∇xεC,V .


Approximating the Fermi distribution function so that for electrons, for ex-ample,

f0(ε) =1

exp

[εe(k(x)

)− εF(x)

kT

]+ 1

≈ exp

[−

εe(k(x)

)− εF(x)

kT

],

(4.69)

we can write, again as an example,

∇xf0(k) =∂f0

∂εe∇xεe +

∂f0

∂εF∇xεF = − f0

kT(∇xεe − ∇xεF) , (4.70)

and

∇kf0(ε(k)

)=

∂f0

∂εe∇kεe = − f0

kT∇kεe . (4.71)

The contribution of the electrons to the electric current density finally be-comes

jQ,e = − e

4π3�2kT[∇x(εC − εF) + F ]

∞∫−∞

τcollf0[∇kε(k)

]2dk . (4.72)

For small departures from thermal equilibrium, we assume isotropy in space,i.e.,

�2k2

x

2m∗e=

�2k2

y

2m∗e=

�2k2

z

2m∗e=

13

�2k2

2m∗e=

13εe,kin =

13(εe − εC) ,

(∇kεe)2 =23

�2

m∗e

�2k2

2m∗e

, (4.73)

and

dk = 4πk2dk = 4π

√2m∗3

e

�3

√εkindεkin = 4π

√2m∗3

e

�3

√εe − εCd(εe − εC) .

(4.74)

Introducing the quasi-free electron density of states

DCB = D(εe − εC) =(2m∗

e)3/2

4π2�3

√εe − εC ,

we arrive at

jQ,e = − 2e3kTm∗

e[∇x(εC − εF) + F ]

∞∫0

τcoll(εkin)f0(εkin)εkinD(εkin) dεkin .

(4.75)


Using the integral∞∫0

f0(εe − εC)D(εe − εC)[εe − εC] d(εe − εC) =3kTne

2,

we finally obtain

jQ,e = −ene

m∗e[∇x(εC − εF) + F ]

∫∞0 τcoll(εkin)f0(εkin)εkinD(εkin) dεkin∫∞

0 f0(εkin)εkinD(εkin) dεkin,

(4.76)

in which the ratio of the two integrals represents the mean relaxation time

〈τcoll〉 = 〈τcoll(εkin)〉 ,

given by

〈τcoll〉 =∫∞0 τcoll(εkin)f0(εkin)εkinD(εkin) dεkin∫∞

0 f0(εkin)εkinD(εkin) dεkin. (4.77)

Furthermore,

〈τcoll〉em∗

e= μe ,

where μe is the electron mobility. Equation (4.76) now reads

jQ,e = −ene〈τcoll〉m∗

e[∇x(εC − εF) + F ]

= eneμe

[1e[−∇x(εC − εF) − F ]

]. (4.78)

We introduce the force F as an electric field force by the gradient of theelectrostatic potential φ(x),

F = −e[−∇xφ(x)] .

Furthermore, we substitute −eφ(x) = εC + χe, and replace

∇x[−eφ(x)] = ∇x[εC + χe] = ∇xεC ,

where χe designates the electron affinity, assumed constant.The current density of electrons in the conduction band, for example,

turns out to be represented by the generalised force, the gradient of theFermi level. In the case of a departure from thermal equilibrium, it must ofcourse be replaced by the gradient of the corresponding quasi-Fermi level:

jQ,e = eneμe

[1e[∇xεFC(x)]

], (4.79)

jQ,h = enhμh

[1e[∇xεFV(x)]

]. (4.80)


It is worth remembering that we are still working with the one-electron pic-ture, and that we have applied the Boltzmann relation in order to approxi-mate Fermi and quasi-Fermi distribution functions, assuming the quasi-freeelectron and hole densities of states in the bands.

The above result from the Boltzmann equation must be interpreted inthe following way. There are two forces acting on all electrons at a givenlocation. One force is ∇x(εFC−εC), also known as the gradient of the chemicalpotential of the electrons, and the other is −eE, resulting from the electricfield. Since both forces act simultaneously, they must be combined into theresultant force ∇xεFC(x), before considering any motion of the electronscaused by forces.

4.5.2 Transport Equations for Semiconductor Solar Cells

In the most general situation, the current density in semiconductors and insolar cells is composed of electron and hole contributions: jQ = jh + je. Therelevant carrier concentrations ne(x) and nh(x) are subject to generation andrecombination and have to obey continuity equations

∂ne(x)∂t

+ ∇[ne(x)ue(x)] = ge(x) − re(x) , (4.81)

∂nh(x)∂t

+ ∇[nh(x)uh(x)] = gh(x) − rh(x) . (4.82)

Furthermore, electron and hole densities ne(x) and nh(x) are coupled byPoisson’s equation with the electrostatic potential φ(x):

∇2φ(x) = Δφ(x) = −ρ(x)εε0

=e[nh(x) − ne(x)]

εε0. (4.83)

Because of this coupling of the carrier concentrations with the electrostaticpotential, it is customary to decompose the current into two components, oneof which is due to the gradient of the electrostatic potential.

We expand the current density equations for electrons and holes and, forexample, for electrons, we replace

∇xεFC = ∇x[εC(x)] +kT

NC

[exp

(−εC − εFC

kT (x)

)]−1

∇x[ne(x)] . (4.84)

We then reintroduce −grad[εC(x)] = eE(x) as the electric field strength,convert the reciprocal electron concentration

1ne

=kT

NC

[exp

(−εC − εFC

kT

)]−1

, (4.85)

apply the Einstein relation to combine the mobility and diffusion coefficients,i.e., μekT = eDe, and arrive at the current density expressed in terms of adrift and a diffusion term:

jQ,e = eneμeE + eDe∇x[ne(x)] . (4.86)


The equivalent description holds for holes:

jQ,h = enhμhE − eDh∇x[nh(x)] . (4.87)

It must be emphasised that the drift and diffusion currents are fictitious. Theyresult from applying each of the two forces mentioned in the last sectionseparately to all electrons, rather than combining them into the resultantforce ∇xεFC(x).

An example shows that this leads to the wrong picture. If the two forcesare opposite and equal in magnitude, the resultant force acting on the elec-trons is zero and there is no current flow of electrons in the correct picture,besides their Brownian motion. If we took field and diffusion currents seri-ously, we would arrive at the astounding and incorrect picture that all elec-trons contribute at the same time to both the field current and the opposingdiffusion current. The sum of the drift and diffusion currents is zero as in thecorrect picture, but it is often overlooked that the components are fictitiousand are introduced only for computational reasons.

In an exact calculation of the distribution of the electrostatic potential,the carrier densities and their currents, (4.81)–(4.87) are solved simultane-ously, bearing in mind that only the sum of the diffusion and drift currentshas physical significance. Due to the complexity of the above relations and inparticular due to the coupling of electron and hole concentrations by Poisson’sequation, analytical solutions exist only for a few, very specific conditions.Generally, the determination of local carrier concentrations, current densi-ties, recombination rates, etc., requires extensive numerical procedures. Thisis especially true if they vary with time, but even in the steady state context.

In many cases, local details are not important and an overall balance ofgeneration and recombination, of extraction and injection of charge carriersgives the correct results for electrical and energy currents originating from asolar cell, as we know from extensive experience.

4.5.3 Charge Transport in Low Mobility Materials

Most of the novel semiconductors, primarily thin films, considered for photo-voltaic energy conversion do not show structural long range order, but consistof micro- or polycrystalline lattices or are even built up of amorphous, or lowconnectivity networks. The lack of translational symmetry, including grainboundaries, affects the propagation of particle wave functions and thus in-troduces a substantial increase in elastic and inelastic scattering of carriers.This in turn causes a substantial reduction in mobilities μ and lifetimes τ ,leading to reduced diffusion coefficients D and diffusion lengths L.

The collection of photogenerated charge carriers in a solar cell preparedfrom those materials has either to be achieved

• across the thickness di, which is determined by the absorption coefficientdi ≥ 1/α with the disadvantage L < di (e.g., amorphous hydrogenated


silicon pin-diodes, as well as some approaches with organic semiconduc-tors),

• or in a granular-type absorber with high porosity in which transport isimpeded by percolation (dye-sensitised TiO2 cells, and organic materialstructures).

For reasonable functioning of these low cost, low mobility semiconductorsolar cells, a considerable amount of the photogenerated chemical potentialεFC − εFV of the electron–hole ensemble must be used for carrier transport.An acceptable charge collection may be achieved if the extraction times forelectrons and/or holes are smaller than their recombination lifetimes, i.e.,

τextr,e ≤ τrec,e , τextr,h ≤ τrec,h . (4.88)

We introduce carrier mobilities μe and μh and multiply by the correspondinggradients of the quasi-Fermi levels to write the velocities in the form

ue = μe1e(−∇xεFC) , uh = μh

1e(−∇xεFV) .

We then translate them into times for extraction across the distances ξdi tothe n-membrane for the electrons and (1 − ξ)di to the p-membrane for theholes. With (4.88), the conditions for the recombination lifetime are

τrec,e ≥ diξ

ue=

e(diξ)2

ΔεFCμe, τrec,h ≥ di(1 − ξ)

uh=

e[di(1 − ξ)]2

ΔεFVμh, (4.89)

where we have replaced ∇xεFC by the voltage drop over the extraction lengthΔεFC/ξdi and correspondingly for the holes. The entire voltage drop or dropin quasi-Fermi levels then reads

ΔεF,transp = ΔεFC + ΔεFV ≥ ed2i

[ξ2

μeτrec,e+

(1 − ξ)2

μhτrec,h

]. (4.90)

Finally, after introducing the Einstein relation μe,hkT = eDe,h, we find

ΔεF,transp ≥ d2i kT

[ξ2

Deτrec,e+

(1 − ξ)2

Dhτrec,h

]= d2

i kT

[ξ2

L2e+

(1 − ξ)2

L2h

].

(4.91)

If the thickness di of the absorber, nominally equal to the reciprocal absorp-tion coefficient α−1, at optimised fractions diξ and di(1 − ξ) of the paths forelectrons and holes to travel to the contacts, exceeds the combined diffusionlength, a reasonable carrier collection can be achieved by spending the abovedrop in quasi-Fermi levels.

With identical recombination lifetimes τrec,e = τrec,h = τrec, the optimumratio of electron and hole travel lengths becomes

ξ

1 − ξ=

μe

μh,


and we derive

ΔεF,transp = ΔεFC + ΔεFV ≥ kT

1 + μh/μe

(di

Le

)2

. (4.92)

The first term in the best case is 0.5 kT, whereas the square of the ratio ofthe length across which charge carriers have to be collected and the specificdiffusion length [(di/Le)2 � 1] enters into the voltage drop necessary fortransport via the second term.

4.5.4 Carrier Mobilities in Organic Semiconductors

In most organic semiconductors the presence of charges modifies the localstructure of the network by deformation of the particular site. This so-calledpolaron formation thus creates scattering centres for other charges. Moreoverthese locally ‘trapped’ carriers commonly alter the energy conditions becauseof their Coulomb interaction. In combination with the polaron energy, thelatter may be attractive or repulsive. These effects, as they involve more thanone electron, force us to give up the one-electron picture and hence to usethe correlated-electron description.

As a consequence, carrier mobilities in these types of matter depend sig-nificantly on macroscopic quantities:

• higher temperatures tend to remove polarons,• electric fields also remove polarons, or reduce the space charge and thusdecrease the concentration of trapped charges,

• band/level bending at surfaces and interfaces reduces/increases the re-spective density of trapped charges.

Since the structure – including their dimensionality, such as wire-type ar-rangements, and bulky or 3-dimensional materials – and the electronic prop-erties of organic semiconductors presently considered for quantum solar en-ergy conversion are comparatively diverse, it is impossible to generalise theirimpacts and drawbacks on electron and hole mobility. However, we can givesome data concerning room temperature mobilities in ordered and disorderedmaterials. In comparison with conventional semiconductors like crystalline Si,Ge, or III-V semiconductors, in which electron or hole mobilities amount tosome 102–103 cm2/V s, even highly ordered organic semiconductors, mostlyprepared by vacuum deposition, exhibit values that are lower by at least 2orders of magnitude. Disordered structures exhibit even lower mobility valuesin the range 10−3–10−5 cm2/V s.

Tables 4.1 and 4.2 show room temperature mobilities of electrons andholes in various organic semiconductors (ordered single crystals as well asdisordered structures) from field-effect analyses.


Table 4.1. Highest electron mobilities from analyses of n-type organic field-effecttransistors [23]

Material Mobility [cm2/V s] Reference

Pc2Lu 2 × 10−4 [11]Pc2Tm 1.4 × 10−3 [11]C60(0.9)/C70(0.1) 10−4 [12]TCNQ 3 × 10−5 [13]C60 8 × 10−2–3 × 10−1 [14]PTCDI-Ph 1.5 × 10−5 [15]TCNNQ 3 × 10−3 [16]NTCDI 10−4 [16]NTCDA 3 × 10−3 [16]PTCDA 10−4–10−5 [17]F16CuPc 3 × 10−2 [18]NTCDI-C8F 6 × 10−2–10−1 [19]DHF-6T 2 × 10−2 [20]MePTCDI (crystalline) 5 × 10−4–6 × 10−5 [22]Cl4MePTCDI (amorphous) 2 × 10−6–7 × 10−6 [22]

Table 4.2. Highest hole mobilities from analyses of p-type organic field-effect tran-sistors [23]

Material Mobility [cm2/V s] Reference

Merocyanine 1.5 × 10−5 [24]Polythiophene 10−5 [25]Polyacetylene 10−4 [26]Phtalocyanine 2 × 10−2 [27]Poly(3-hexylthiophene) 10−1 [28]Poly(3-alkylthiophene) 10−3 [29]α-sexithiophene 3 × 10−2 [30]Pentacene 1.5 [21]α-ω-dihexyl-sexithiophene 1.3 × 10−1 [31]Bis(dithienothiophene) 5 × 10−2 [32]α-ω-dihexyl-quaterthiophene 2.3 × 10−1 [33]Dihexyl-anthradithiophene 1.5 × 10−1 [34]BTQBT 2 × 10−1 [35]

4.5.5 Equivalent Circuits for Solar Cells

The current–voltage characteristic of an ideal solar cell in (4.57) can be seenas the sum of the currents from a diode in the dark jQ = jrev[exp(eV/kT )−1]and from a current source contributing jQ = jsc. This leads to the equivalentcircuit of an ideal solar cell sketched in Fig. 4.10, consisting of an ideal diodeand a current source in parallel.


The simplest extension to real device operation in a stationary state con-sists in introducing losses via a series resistance Rs, which represents contactresistances, Ohmic losses in the front contact grid and in the rear contact, anda parallel resistance Rp, which includes any current bypassing the membranes(junction), and even shunt currents through short-cuts.

V

j-jsc

jD

V

j-jsc

jD

VD

jp

Rs

Rp

Fig. 4.10. Equivalent circuits for solar cells. Left : ideal solar cell consisting of acurrent source −jsc shunted by a diode. Right : real solar cell with additional shuntresistor Rp and series resistor Rs

The total current density for the real diode is now composed of threecontributions, the photoinduced short-circuit current, the diode current andthe shunt current through Rp:

j = jsc + jrev

[exp

(eVD

kT

)− 1

]+ jp

= jsc + jrev

[exp

(eVD

kT

)− 1

]+

VD

Rp. (4.93)

Replacing VD = V − jRs, the last relation becomes

j = jsc + jrev

[exp

(e(V − jRs)

kT

)− 1

]+ jp

= jsc + jrev

[exp

(e(V − jRs)

kT

)− 1

]+

V − jRs

Rp. (4.94)

The j/V curve is substantially modified by these two resistors, since theseries resistor consumes the voltage V (Rs) = jRs, whereas the shunt addsthe current density jp = (V − jRs)/Rp to the output current density.

For only small deviations from the ideal values Rs = 0, and Rp → ∞,the influence of both losses on the j/V curve can be derived analyticallyby differentiating (4.94) with respect to V . In particular modes of operationsuch as V (j = 0) = Voc (open circuit) and V (j = jsc) = 0 (short circuit), andprovided that Rs � Rp [a reasonable assumption since Rs and Rp designatethe departure from Rs,ideal = 0, and Rp,ideal → ∞, respectively], we find

∂V

∂j

∣∣∣∣j=0

= Rs +Rp

1 +jrevRp

VTexp

Voc

VT

≈ Rs (4.95)


and∂V

∂j

∣∣∣∣V =0

= Rs +Rp

1 +jrevRp

VTexp

(−jscRs

VT

) ≈ Rs + Rp ≈ Rp . (4.96)

The reciprocal derivatives of the j/V curve under illumination at open circuitand short circuit represent the series and parallel resistances Rs and Rp,respectively, of the diode device. Of course, for non-linear effects in the diode,these quantities are not constant but depend on voltage V , current density j(illumination level), reverse saturation current density jrev, and temperatureT .

4.6 Conclusions for Solar Cell Requirements

For good absorption, the thickness of the absorber in the planar configurationof Fig. 4.3 with normally incident light should be l � 1/α. Thin absorbersrequire large absorption coefficients. This gives an advantage to materialswith direct optical transitions over materials like silicon with indirect opticaltransitions, which must have a much greater thickness.

A driving force is needed to transport electrons and holes towards theirrespective membranes. This driving force is the gradient −gradεFC of theFermi energy for the electrons in the conduction band and similarly gradεFVfor the holes in the valence band. As we have seen, the time to reach themembranes must be short compared with the recombination lifetime. In ordernot to lose output voltage, the diffusion lengths Le,h of the carriers should bemuch larger than the distance to their membranes. For low mobility materials,a sizeable voltage drop occurs in the cell at the point of maximum power.For the planar configuration of Fig. 4.3, the condition for optimal operationis therefore Le,h � l � 1/α.

4.6.1 Special Geometrical Design

Improved Absorption by Light Trapping. If light trapping is employed,as shown in Fig.4.6, the thickness l of the absorber may be reduced even below1/α. However, this only works well in materials with a large index of refrac-tion. To a certain extent, this allows us to use even weakly absorbing materialsin thin film solar cells. A further advantage is the confinement of electron–holepair generation to a smaller volume than in a planar structure. For the samematerial, this leads to a larger concentration of electron–hole pairs, largerseparation of the Fermi energies and a larger voltage of the light-trappingstructure. Alternatively, for the same efficiency, a light-trapping structurewould tolerate a larger concentration of imperfections than a planar struc-ture. The larger surface area of light-trapping structures is a disadvantageand good passivation against surface recombination is even more importantthan in planar structures.


Improved Carrier Extraction by Intercalating Membranes. Withlight trapping, the condition for good extraction of electrons and holes re-quiring Le,h � l, is also relaxed, since a smaller thickness of the solar cellis possible. For low mobility organic materials, this condition is still a prob-lem. It ensures that electrons and holes generated in the absorber reach themembrane within their recombination lifetime. They can then pass into theexternal circuit. The distance of the membranes, however, is not limited bythe thickness l of the absorber, as can be seen in Fig. 4.11, and can be madearbitrarily short.

Fig. 4.11. Intercalating membranes in the absorber reduces the distance that elec-trons and holes have to travel from the place where they are generated in theabsorber to the membranes

The Dye Solar Cell. This structure is particularly well established in thedye solar cell, where the absorber is a dye interfaced between n-type TiO2as n-membrane and a redox system in an electrolyte as p-membrane [36].This cell is often called a dye-sensitised solar cell, which fails to recognise thedye as the main component, not only absorbing the light, but also acting asthe source of the separated Fermi energies and hence enabling gradients ofthe Fermi energies to drive electrons and holes into the external circuit. Wetherefore prefer to call the cell a dye cell.

Electrons and holes are not mobile at all in the dye. Electrons and holescan nevertheless tunnel into their membranes, since the dye layer is only amono-molecular coverage of the TiO2 particles immersed in the electrolyte.Sufficient absorption is achieved by forming a network of dye-covered TiO2particles, which is about 1 000 particles thick. Close contact between the p-membrane and the dye is achieved by a liquid electrolyte, containing a redoxcouple for charge transport, which penetrates the network of particles. Thisstructure has a disadvantage, originating from the bad transport propertiesof the dye: an interface is formed between n- and p-membranes with an area


about 1 000 times as large as the aperture area of the cell. It is extremelyfortuitous that this large area is not accompanied by large interface recom-bination. Another fundamental disadvantage is the prolonged path of theelectrons in the TiO2 network and of the holes in the electrolyte within thepores of the TiO2 network, which may lead to a voltage drop across a seriesresistance.

The Organic Solar Cell. The organic solar cell suffers from similar prob-lems. The absorber is the polymer. It is a p-type conductor and serves si-multaneously as the p-membrane. The diffusion length of the electrons inthe polymer is so small that the n-membrane, made up of C60 molecules,has to be very close to the location of light absorption, which also requiresthe polymer to be very thin. An interpenetrating network of polymer andC60 may solve this problem. Since this network is formed by mixing theC60 molecules with the polymer, a conducting connection among the C60molecules towards the n-contact and among the polymer chains towards thep-contact is not guaranteed. This is the problem of percolation. As with thedye solar cell, compensating for the small diffusion length of the electronsleads to a large interface area, resulting in increased interface recombinationand a prolonged path for the charge carriers, in the organic cell even moreso than in the dye cell. This may cause series resistance problems.

As a result of light trapping and intercalation, thin film solar cells can bemade of a thickness l, which apparently violate the condition Le,h � l � 1/α.Even with light trapping, the thickness l must be of the order of the pene-tration depth 1/α of the light. The diffusion length, on the other hand, canbe arbitrarily small, if caused by a small diffusion coefficient. The recombi-nation lifetime should always be as large as possible and should approach theradiative lifetime.

4.6.2 Particular Optical Design/Multispectral Conversion

One of the most serious problems of entropy generation in quantum solarenergy conversion is the loss of the excess photon energy �ω − (εG + 3kT )that is transferred to the lattice during thermalisation of electron–hole pairswithin 10−13–10−12 s to generate phonons. In the multispectral approachto quantum solar energy conversion, this excess photon energy is reducedby splitting the solar spectrum into ranges with particular photon energies�ωi, . . . , �ωi+δ and feeding these photons to individual absorber systems withappropriate optical threshold energies εG,i = �ωi. Spectrum splitting canbe performed in a spatially parallel configuration by wavelength dependentdiffraction from the original direction of light propagation with the help ofprisms, dichroitic mirrors, holographic structures, and so on. Alternatively,it can be achieved in an optical series connection by a sequence of absorberswith decreasing band gap energies, each absorbing only those photons withenergy �ωi ≥ εG,i and transparent to photons with �ωi < εG,i.


Fig. 4.12. AM 0 efficiencies of an ideal tandem system at 300 K versus band gapsof top (εG1) and bottom (εG2) cells [40]

From the solutions for the photon flux balances in the particular photonenergy ranges and the corresponding absorbers, including the appropriatedivergence terms for the respective currents, the optimized individual effi-ciencies and hence the total device efficiency can be calculated as a functionof the number ni of absorbers and, of course, the light concentration factor[37–39]. Naturally, each of the individual, optimized band gaps depends onthe number of ranges into which the spectrum has been subdivided, the con-centration factor, and the absorber temperature. In Fig. 4.12, the theoreticalefficiencies are illustrated for a tandem system under AM0 illumination interms of the band gaps of the bottom and top cells [40].

So far, due to the boundary conditions introduced by the technology forpreparing these devices, only ni = 2 (tandem cells) and ni = 3 (triple cells)seem to be of relevance [41,42].

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5 Semiconductor Aspectsof Organic Bulk Heterojunction Solar Cells

Christoph J. Brabec

During the last few years organic solar cells have been discussed as a promis-ing alternative to inorganic semiconductors for renewable energy production.These organic photovoltaic devices offer the possibility of low-cost fabricationof large-area solar cells for harvesting energy from sunlight. Organic solar cellsnaturally provide many desirable properties such as low price, low weight,flexibility and semi-transparency. These features have fuelled the interest ofboth academia and industry. Aside from possible economic advantages, or-ganic materials also possess low specific weight and are mechanically flexible– properties that are desirable for a solar cell to guarantee easy integrationof the modules on any surface, from glass windows to textiles and clothes.Several geometries for organic photovoltaic devices have been investigated todate. All in all, it appears fully worthwhile to follow up such a vision by re-search and development. The question is: what is the current status of thesesolar cells, and what further developments are needed to create a productfor the market? In the present chapter, various developments and aspectsof efficiency, stability, thin film physics and production technologies will bediscussed for one type of organic solar cell: the bulk heterojunction device.

Research into organic semiconducting materials has emerged over the lastfew decades as a field rich in the fundamental science of unique electronic phe-nomena and photophysics. The development of organic photovoltaic devicesis just one application of this fundamental work. These include devices basedon photoinduced charge transfer between layers of low-molecular-weight or-ganic molecules (LMW molecules) [1,2], within halogen-doped organic singlecrystals [3], within single component molecular dyads [4], between layers ofconjugated polymers and LMW molecules [5], within conjugated polymerblends [6], and within a single-layer blend of a conjugated polymer and anLMW molecule [8,9]. The devices described in this chapter are of the lattertype.

Efficiencies of the first polymeric solar cells based on hole-conductingconjugated polymers (mainly polyacetylene) were rather discouraging [7].However, an encouraging breakthrough to higher efficiencies was achievedby switching to different classes of electron-donor-type conjugated polymerssuch as polythiophenes (PT), and polyphenylenevinylenes (PPV) and theirderivatives, and by mixing them with suitable electron acceptors [8]. Proto-types of photovoltaic devices based on a polymeric donor/acceptor networkshowed solar energy conversion efficiencies of around 1% [9]. In particular,

160 Christoph J. Brabec

the photovoltaic properties and photophysics of conjugated polymer/fullerenesolid composites have been well investigated over the last few years [10].

Compared with research efforts devoted to small-molecule organic solarcells, polymeric organic solar cells (and especially the internal donor/acceptor‘plastic solar cells’) represent a relatively new approach to the exploitation ofsolar energy by organic materials. Thanks to progress in polymer synthesis,conjugated polymers are now available with similar purities to small organicmolecules. The organic electronics community is gradually coming to seeboth small molecules and conjugated polymers as classical semiconductorsand to apply standard semiconductor models to describe their electro-opticalbehavior. It is also the intention of this chapter to discuss the photovoltaicproperties of bulk heterojunction devices in terms of inorganic semiconductordevice physics. Concepts and models successfully describing observations ininorganic semiconductors and solar cells will be discussed with respect totheir relevance for organic devices and, if necessary, adapted to the specificrequirements of organic semiconductors.

As mentioned earlier, mixing electron-donor-type polymers with suitableelectron acceptors is a promising approach. In particular, the photophysicsof conjugated polymer/fullerene solid composites has been thoroughly inves-tigated over the last decade. A detailed understanding of the relevant pho-tophysics has made it possible to create prototype photovoltaic devices withsolar power conversion efficiencies of around 3%. This once again triggeredan upsurge in activity from several groups worldwide, pursuing this researchwith increasing support from industry as well as public finance.

Nevertheless, there remains a common problem for all applications of con-jugated polymers, namely, stability. Even though expectations with regardto the lifetimes of electronic devices are shrinking due to the very short lifecycles that are now fashionable for such applications, and even though theindustry may be more interested in the cost of an item than in having some-thing long-lasting, a shelf lifetime of several years and an operational lifetimeof tens of thousands of hours are required for all durable applications. Con-jugated polymers have to be protected from air and humidity to achieve suchlifetimes. These protection methods are being developed for organic light-emitting diodes (OLED) and organic photovoltaic (OPV) elements. Recentdevelopments in OLED research indicate that this technical development hasalready been achieved and that the stability problem has been overcome. Thismeans that large scale applications are now within reach and this in turn isthe essential basis for plastic solar cells.

5.1 Device Architectures

5.1.1 Single-Layer Diodes

Initial efforts to develop photovoltaic devices with polymeric semiconduc-tors (predominantly p-type conjugated polymers) used polyacetylene [7] and

5 Semiconductor Aspects of Organic Bulk Heterojunction Solar Cells 161

some polythiophenes [11,12]. From the first generation of conjugated poly-mers, poly(para-phenylenevinylene) (PPV) was the most successful candi-date for single-layer polymer photovoltaic devices [13]. Unsubstituted PPVis generally produced from a soluble precursor polymer with subsequent heatconversion. The radiative recombination channels of the injected electronsand holes within PPV and its derivatives, which resulted in light-emittingdiodes (LED) [14–17], opened up this class of easily processable materialswith high electroluminescence quantum efficiencies for photovoltaic devices.Interestingly, it is found that the same devices, under reverse bias, exhibitexcellent sensitivity as photodiodes [18]. In forward bias, tunnelling injectiondiodes exhibit relatively high efficiency electroluminescence, which is promis-ing for flat panel and/or flexible, large area display applications. In reversebias, on the other hand, the devices exhibit a strong photoresponse with aquantum yield > 20% (el/ph at −10 V reverse bias) [18]. Devices based onderivatives of polythiophene exhibit an even better photoresponse (80% el/phat −15 V), competing with UV sensitised Si photodiodes [18]. A photovoltaicresponse was observed under zero bias conditions. The integration of threefunctions, electroluminescence, photodetection and photovoltaic response, inthe same device offers special opportunities. This triple function capabilityoffers particular promise for novel, input–output displays powered by organicphotovoltaics.

+ -

vacuum level

φM1

φM2CB

VB

Eg

conjugated polymer(intrinsic SC)

low workfunctionmetal

high workfunctionmetal

P+

P-

hν

hν

Fig. 5.1. Charge generation process in a single-layer conjugated polymer deviceunder short-circuit conditions in the MIM model. VB valence band, CB conductionband, Eg bandgap, P+, P− positive and negative polarons


The simplest and most widely used organic semiconductor device is ametal–insulator–metal (MIM) tunnel diode with metal electrodes of asym-metrical work function (Fig. 5.1). In forward bias, holes from the high workfunction metal and electrons from the low work function metal are injectedinto a thin film of a single-component organic semiconductor. Due to theasymmetry between cathode and anode work functions, forward bias cur-rents for a single-carrier-type material are orders of magnitude larger thanreverse bias currents at low voltages. The rectifying diode characteristics canbe accompanied by radiative recombination channels of the injected electronsand holes within the molecular solid. The result is a light-emitting diode [15–17,19,20]. If photoinduced free charge carrier generation is allowed at the sametime, the device exhibits light emission under forward bias and a significantphotocurrent under a reverse bias field (dual function) [21]. Using the devicesfor photodetection under reverse bias, the potential difference between theelectrodes has to be high enough to overcome the Coulomb attraction forthe photogenerated excitons. Otherwise the absorbed photons will mainlycreate excitons, which decay geminately (either radiatively with photolumi-nescence or non-radiatively). The photocurrent efficiency of such devices willthus be limited. In the photovoltaic mode, where no external voltage is ap-plied and short-circuit conditions exist, the potential difference available inthe MIM device is caused by the difference between the work functions ofthe metal electrodes. In most cases (e.g., ITO and Al) the potential differ-ence due to this work function difference is not high enough to give efficientphotoinduced charge generation, limiting the operation of the photovoltaiccells. Some improvement was reported for photodiodes using a Schottky-typejunction formed between the conjugated polymer and one of the metal elec-trodes (Fig. 5.2). However, the problem of inefficient charge generation inconjugated polymers was not overcome by this approach [22–24].

To overcome this limitation to photoinduced charge carrier generation,a donor/acceptor (dual molecule) approach has been suggested [8,9,25,26].In general, in such devices, photocarrier generation is enhanced by usinga second, charge generation sensitizing component. For example, for a de-vice consisting of a composite thin film with a conjugated polymer/fullerenemixture, charge photogeneration efficiency is close to 100%. In such a single-composite photoactive film, a ‘bulk heterojunction’ is formed between theelectron donor and acceptor (Fig. 5.3). An extensive discussion of this con-cept is given below.

5.1.2 Heterojunction Diodes

Considering the energy band diagram of a bilayer in Fig. 5.4, the heterojunc-tion formed between (for example) a conjugated polymer and C60 should haverectifying current–voltage characteristics, even using the same metal contacton both sides (analogous to a p–n junction). One bias direction of such a


+++

---

vacuum level

φM1

φM2Ip

χSCB

VB

Eg

W

conjugated polymer(n-type SC)

metal 2

metal 1

Fig. 5.2. Energy diagram of a metal/semiconductor/metal Schottky barrier underopen-circuit conditions, when the metals have different work functions. φ workfunction, χs electron affinity, IP ionization potential, Eg energy gap, W depletionwidth

device (electron injection on the semiconducting polymer side or hole injec-tion on the C60 side) is energetically unfavorable. This polarity of the deviceresults in very low current densities. On the other hand, electron injectiononto C60 or hole injection into the semiconducting polymer is energeticallyfavorable. This polarity of the device results in relatively high current den-sities. Thus, organic semiconductor devices using two layers with differentelectronic band structures, as illustrated in Fig. 5.4, have rectifying diodecharacteristics. A photophysical interaction between the two molecular units(photoinduced electron transfer) occurs at the interface and gives rise to aphotocurrent as well as a photovoltaic effect. In that sense the essential dif-ference between the linear heterojunction of two organic thin films displayedin Fig. 5.4 and the bulk heterojunction displayed in Fig. 5.3 is the effec-tive interaction area between the donor and acceptor components: in thelinear heterojunction device, it is the geometrical interface, in the bulk het-erojunction, it is the entire volume of the composite layer. This results in anenhancement of short-circuit photocurrent by several orders of magnitude,making the bulk heterojunction approach quite attractive [9,25].

5.1.3 Bulk Heterojunction Solar Cells

For photovoltaic cells made with pure conjugated polymers, energy conversionefficiencies are typically 10−3–10−1%, too low to be used in practical appli-cations [18,59]. Photoinduced charge transfer across a donor/acceptor (D/A)


Fig. 5.3. Formation of a bulk heterojunction and subsequent photoinduced electrontransfer inside such a composite formed from the interpenetrating donor/acceptornetwork, plotted with the device structure for such a junction (a). The diagramsshowing energy levels of an MDMO–PPV/PCBM system for flat band conditions(b) and under short-circuit conditions (c) do not take into account possible inter-facial layers at the metal/semiconductor interface

(a)


Fig. 5.4. Schematic diagram of a bilayer and subsequent photoinduced electrontransfer at the interface of the two layers, with the device structure for such ajunction (a). The diagrams showing energy levels of an MDMO–PPV/C60 systemfor flat band conditions (b) and under short-circuit conditions (c) do not take intoaccount possible interfacial layers at the metal/semiconductor interface

(a)


interface thus provides an effective method for overcoming early carrier re-combination in organic systems and hence for enhancing their optoelectronicresponse. For photovoltaic cells made from a bilayer of a conjugated polymerand the electron-withdrawing fullerene C60, monochromatic energy efficien-cies as high as 1% and IPCE efficiencies as high as 15% have been measured[25]. Although the quantum efficiency for photoinduced charge separation isnear unity for donor–acceptor pairs, conversion efficiency is limited due tothe small charge-generating regions around the interface.

Consequently, interpenetrating phase-separated p-type/n-type (D/A)network composites, i.e., bulk heterojunctions, appear to be ideal photo-voltaic composites [9]. By controlling the morphology of the phase separationso that an interpenetrating network is formed, one can achieve a high interfa-cial area within a bulk material. Since any point in the composite is within afew nanometers of a D/A interface, such a composite is effectively a bulk D/Aheterojunction material. If the network in a device is bicontinuous, the collec-tion efficiency can be equally efficient. Creating the bulk D/A heterojunctionis obviously an important step towards creating efficient nanostructured p–njunctions in organic materials [18,27–32,37].

0,1 1 10 1000,0

0,3

0,5

0,8

1,0 Lum

inescence In

tensity [a. u.]

Short Circuit Current Isc

I sc [

a. u

.]

Concentration of PCBM [mol%]

0,0

0,3

0,5

0,8

1,0 Luminescence

Fig. 5.5. Luminescence quenching (bullets, right hand axis) and short-circuit cur-rent Isc (black squares, left hand axis) vs. molar fullerene concentration in a bulkheterojunction composite. The different onsets for percolation for the two phenom-ena (exciton diffusion versus ambipolar carrier transport) can be clearly seen

A bulk heterojunction is by definition a blend of p-type and n-type semi-conductors (donor/acceptor). As a prototype bulk heterojunction, we shalldiscuss the properties of polymer/fullerene blends. Apart from the poly-


mer/fullerene bulk heterojunction, the polymer/polymer bulk heterojunc-tion also looks promising. The use of polymers as both p-type and n-typesemiconductors is interesting from the point of view of blending and process-ing. Since there is almost no entropy of mixing for macromolecules, phaseseparation is expected in polymer blends, leading to a microstructured bulkheterojunction. Moreover, by using polymeric p-type and n-type semiconduc-tors, the full variability of the bandgap in polymeric semiconductors becomesavailable. Various successful attempts to form a purely polymeric bulk hetero-junction have been reported [26,33,34]. Of great importance is the formationof a bicontinuous network of the two polymers. Polymeric bulk heterojunc-tions are clearly distinguished from polymer/fullerene bulk heterojunctionsby one specific feature, namely, the percolation threshold. Conduction bythermally assisted hopping transitions between spatially separate sites in aninterpenetrating network [35] can be modelled by percolation theory. Ac-cording to percolation theory, the formation of interconnected paths of smallspherical molecules embedded in a three-dimensional matrix occurs at a vol-ume fraction of 17% [36]. This is experimentally verified by photocurrentmeasurements in conjugated polymer–fullerene devices [37]. Additionally, itis found that higher concentrations of the fullerene (methanofullerene, butalso pristine C60) relative to the conjugated polymer (typically 3:1) increasethe power efficiency by increasing the short-circuit currents. This is again inaccordance with percolation theory, where the average conductivity σ of onecomponent may be expressed as

σ =1lZ−1

c . (5.1)

In this equation, l is a characteristic length depending on the concentrationsof the sites, while Zc is the resistance of the path with the lowest averageresistance. Obviously, high fullerene concentrations enhance the conductivityby two mechanisms. Firstly, the higher concentration of sites decreases l, andsecondly, new paths with a lower overall resistance Zc may be formed. At highmixing ratios (3:1), excellent solubility of the fullerene and good compatibilitybetween the conjugated polymer and the fullerene are both necessary. Figure5.5 shows the onset of percolation in a polymer/fullerene bulk heterojunctionvia photocurrent measurements. The quenching of photoluminescence via thefullerene-loading of the network is plotted in the same graph. As expected,photoluminescence is already significantly quenched at fullerene concentra-tions around 1%, while the onset of photocurrent is observed around 17%. Forpolymer blends, the onset is reported at significantly lower concentrations.Best results for photovoltaic devices were obtained with about 5 wt.% of then-type semiconductor blended into the p-type semiconductor [34].

Finally, the working principle of a bulk heterojunction is summarizedschematically in Fig. 5.6. In contrast to a classical bilayer or a planar p-type/n-type junction (analogue to a p–n junction for inorganic semiconduc-tors), the photocarriers in a bulk heterojunction are generated throughout


C 3- C 3- C - C - C - O OMe

C 4- C 3-

C 3-

C 2- C -

C 2-

C 2-

O OMe

O OMe

O OMe

O OMe

O OMe O

OMe

O OMe

C - O 4+

C -

+ O 4+

O OMe

O OMe

C 3-

C 2- C - C -

O OMe

O OMe

Anode (ITO)

Cathode (Al, Ca)

O O

Fig. 5.6. Schematic drawing of a bulk heterojunction device. Charge generationoccurs throughout the bulk, but the quality of the two transport networks (p-and n-type channels) is essential for the functionality of the blend as an intrin-sic, ambipolar semiconductor. Light emission occurs at the semi-transparent ITOelectrode. Electron transport on the fullerenes is marked by full arrows and holetransport along the polymer by dotted arrows

the entire volume of the device. A further difference between bilayer andbulk heterojunction geometry is the origin of the rectification. In a bilayerdevice, the p–n junction is the origin of the rectification, while for a bulkheterojunction, rectification has to be introduced via selective contacts andthe subsequent built-in field (for a homogenous distribution of the p-type andn-type semiconductors, guaranteeing a homogeneous carrier distribution andthe absence of carrier diffusion gradients). Transport in a bulk heterojunctionwill depend on transport properties of individual components, but recombi-nation and trapping between the two components can drastically influencethe lifetime as well as the transport properties. Additionally, the morphologyof the blends is decisive: the demise and phase separation of the two compo-nents, together with transport paths leading to dead ends, will diminish thefunctionality of the blend as an intrinsic, ambipolar semiconductor.

Besides the different percolation threshold, polymer/fullerene and poly-mer/polymer bulk heterojunctions obey similar physical principles, whichwill be discussed in the following.


5.2 Device Aspects and Transport Properties

5.2.1 Transport Properties of Diodes

Before investigating the photovoltaic properties of diodes with single-polymerlayers, it is important to have a model that accurately describes the transportphenomena of the polymeric semiconductor, leading to a proper descriptionof the device operation in the dark. The key to describing single-layer poly-mer devices is the correct treatment of the temperature and field dependentmobility. The set of equations presented here allow us to model the current–voltage behaviour of single-layer polymeric p-type semiconductor (MDMO–PPV) diodes (MIM geometry) [38–40]:

ε0εr

e

∂E(x)∂x

= p(x) − n(x) − nt(x) ,

J = Jp + Jn = eμp[E(x)]p(x)E(x) + eμn[E(x)]n(x)E(x) ,

nt(x) =Nt

kTtexp

ε − Ec

kTt,

1e

∂Jn

∂x= −1

e

∂Jp

∂x= Bp(x)n(x) ,

μp(E) = μ0 exp(

− Δ

Kt

)exp

(γ√

E)

. (5.2)

The model suggests that at higher voltages the electron and hole currents inPPV-based devices with low contact barriers (as expected for selective Ohmiccontacts) are determined by the bulk conduction properties of the polymerand not by the injection properties of the contacts. The conduction of holes isgoverned by space-charge effects and field dependent mobility, while electrontransport is limited by traps.

Here Jp and Jn are the hole and electron current densities, respectively,μp and μe the hole and electron mobilities, and p(x) and n(x) the density ofmobile holes and electrons. The density of trapped electrons is denoted bynt(x). The bimolecular recombination constant B is the only fit parameterin this model. The field dependent mobility was originally derived by Pai etal. [41] to describe the mobility of photoinduced holes in PVK. Δ denotes anactivation energy and γ is a coefficient comparable to the field dependencein the Poole– Frenkel effect [42]. The model for electron traps assumes quasi-equilibrium between trapped and free electrons [43], with nt(ε) as the trapdensity of states at energy ε, Ec the energy of the conduction band, N thetotal density of traps, and kTt an energy characterising the trap distribution.The photovoltaic response of these devices is most significant between zerovoltage and the open-circuit voltage. The expansion of this model to lowvoltages for hole-dominated or electron-dominated devices again shows goodagreement with experiment.

One has to be aware that the I/V response of a diode is always a superpo-sition of its transport properties and metal/semiconductor properties. How-ever, in many cases it is possible to separate these two responses due to their


different voltage dependence. As a rule of thumb, the low voltage/low cur-rent behaviour of a diode is dominated by the metal/semiconductor interface,while the high voltage/high current regime reveals the transport propertiesof the semiconductor.

First the diode regime is discussed. The simplest and most widely usedmodel to explain the response of organic photovoltaic devices under illumi-nation is the metal–insulator–metal (MIM) tunnel diode with asymmetricalwork function metal electrodes [44–46]. The device operation of a MIM diodein the dark can be summarised as follows. In forward bias, holes from thehigh work function metal and electrons from the low work function metal areinjected into the organic semiconductor thin film. Because of the asymmetryof the work functions for the two different metals, forward bias currents areorders of magnitude larger than reverse bias currents at low voltage. Depend-ing on the difference in work function of the two metal electrodes, a MIMdevice has an inherent built-in electrical field. For carrier transport, a suffi-ciently high voltage must first be applied to reach the flat band condition. Byfurther voltage increase, an electrical field gradient then supports transport ofthe injected majority carriers. The current transport model described abovehas only recently been extended to a carrier generation term. Under light,the forward (high voltage) regime will not change qualitatively (if photore-sistivity and the creation of a photojunction can be neglected). The majorchange in the device occurs for the low voltage regime, where photocarriergeneration dominates the I/V characteristics. The three different regions inthe I/V curve of a solar cell are clearly observable in Fig. 5.7 together witha schematic drawing of the energy levels, assuming a rigid band model.

For the high voltage regime it is reasonable to suppose that a semicon-ductor of thickness L is contacted with two electrodes which, by virtue of alow energy barrier at the interface, are able to support the transport of aninfinite number of one type of mobile carrier. The current will then becomelimited by its own space charge, and this can in the extreme case reducethe electric field at the injecting contact to zero. This is realized when thenumber of carriers per unit area inside the sample approaches the capacitorcharge of the diode, i.e., εε0/e. This number of carriers can be transportedper unit transit time ttr = L/μ.

Trap-Free Case. Neglecting traps and intrinsic carriers in the semiconduc-tor, and once again neglecting the contribution from diffusion, the currentdensity is given by j = neμE, where n is the injected carrier concentration.Assuming that both electrodes form equally good contacts and that the fieldE is constant within the bulk of the semiconductor, double integration of thePoisson equation dE/dx = ne/εε0 (with dU/dx = E) yields the trap-freespace-charge-limited current (Child’s law):

jSCLC =98εε0μ

V 2

L3 . (5.3)


1E-09

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

I [A

]

Bias [V]

AlAlITOITOITOITO

ITOITOITOITO Al

AlAl

ITOITOITOITOITOITOITOITOITOITOITOITOITOITOITOITOITOITOITOITOITOITOITOITO

Al

ITOITOITOITOITOITOITOITOITOITOITOITOITOITOITOITO

Flat−Band

Zero Volt

forward Bias

Reverse Bias

Fig. 5.7. Typical I/V characteristics of a bulk heterojunction diode. The schematicband diagrams for the three different diode regimes are depicted in the figure ac-cording to the applied voltage

The charge carrier density decreases with increasing distance from the injec-tion contact according to

n(x) =34

εε0

e

V

L2

(L

x

)0.5

, (5.4)

while the local electrical field increases according to

E(x) =32

V

L

( x

L

)0.5. (5.5)

The average space charge density (per unit volume) becomes

π =32

εε0

e

V

L2 . (5.6)

The increase in the electric field with increasing distance from the injectingelectrode has an important consequence: current pulses are accelerated in thebulk of the sample, leading to a faster transit time than under space-charge-free conditions.

Taking into account thermally generated carriers (Ohmic behaviour atlow voltages), the following equation describes the transition from Ohm’slaw to Child’s law:

en0μU

L=

98εε0μ

V 2

L3 . (5.7)

The transition bias UT is given by

UT =89en0

L2

εε0. (5.8)


Shallow Traps. In the presence of traps, the nm mobile and nt trappedcarriers contribute to the space charge. Shallow traps mean that the delaytime in the trap is considerably shorter than the transit time of the injectedcarriers. Under these conditions, Child’s law (5.3) remains valid, if an effectivemobility μeff = θμ is used instead, weighted by the percentage of mobilecarriers θ = nm/(nm + nt).

Deep Traps. Deep traps can capture a carrier for a longer period than itstransit time, so that the carrier no longer contributes to the transport. In thecase of energetically discrete trapping levels, the functional dependence ofj(V, L) remains unaltered, but the current becomes activated. The activationenergy is equal to the trap depth. However, in cases of practical interest,traps are usually energetically distributed. In that case traps will fill fromthe bottom towards the top of the distribution as the applied electric fieldincreases. This is equivalent to an upward shift in the quasi-Fermi level withelectric field. As a consequence, θ increases with the electric field and thej(V ) characteristic becomes steeper, finally merging into Child’s law if thetotal number of traps is less than the number of charges the sample canaccommodate on the basis of Poisson’s law. An analytical solution for thisproblem can only be given in the case of an exponential/Gaussian distributionof traps. In both cases, the space-charge current is proportional to

jSCLC ∝ V l+1

L2l+1 , (5.9)

where l is a measure for the steepness of the distribution. Large l means aconstant trap density with energy within the bandgap. Figure 5.8 summarizesthe I/V characteristic for the various cases of space-charge limitation.

Valuable insight into the transport properties of semiconductors can begained from their temperature dependent I/V behaviour. Figure 5.9 showsthe I/V behaviour of an MDMO–PPV (p-type semiconductor) diode in theforward direction for various temperatures, ranging from 15 K through to294 K. The electrodes of this device (ITO/PEDOT on one side, Au on theother) have been chosen in such a way that it is a ‘hole-only’ device, i.e., neg-ative carriers will not be injected at either electrode. Analysis of the currentcharacteristic leads to the following conclusions. At higher temperatures, thehigh field current scales with an exponent of α ≈ 2.7, where α = l+1 and l isdefined in (5.9). Upon cooling, the exponent is lowered and at temperaturesbelow 200 K, the exponent becomes α ≈ 2. The low temperature behaviourcan thus be interpreted as SCLC behaviour in the trap-free limit, while thehigh temperature behaviour is most likely affected by traps (α > 2) that canbe frozen. In the low field regime, the current scales linearly with the voltage,as expected for Ohmic contacts. From the transition bias Vat (transition fromlinear scaling to quadratic SCLC scaling), the overall thermally activatedcarrier concentration inside the device is calculated as n ≈ 4 × 1015 cm−3.


Fig. 5.8. Different scaling regimes for space-charge-controlled devices

The transition to trap-free SCLC behaviour at lower temperatures allowsus to estimate the mobility of MDMO–PPV. At 190 K it is estimated atμ > 0.9 × 10−8 cm2/V s.

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

0.1 1

I [A

]

Bias [V]

15K 167K 210K 250K 294K

V ∝ I

V ∝ I2

V ∝ I2.8

Fig. 5.9. Temperature dependent I/V characteristics of a p-type diode(ITO/PEDOT/MDMO–PPV/Au), in which the two high work function electrodesguarantee hole-only conditions


By exchanging one of the electrodes, such a diode can be altered froma unipolar hole device into an ambipolar device. Figure 5.10 shows the I/Vcharacteristics of an ITO/PEDOT/MDMO–PPV/LiF-Al device. Here, theLiF-Al electrode should guarantee electron injection under forward bias.

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

0.1 1

I [A

]

Bias [V]

15K50K

167K210K250K280K294K

V ∝ I2

V ∝ I

Fig. 5.10. Temperature dependent I/V characteristics of a p-type diode (ITO/PEDOT/MDMO–PPV/LiF-Al), in which the different work functions of the elec-trodes guarantee ambipolar charge injection (electrons at the LiF-Al electrode, holesat the ITO/PEDOT electrode)

At lower voltages the current still scales linearly with the voltage. How-ever, at higher voltages (> 1.5 V), the shape of the I/V curve at roomtemperature is clearly altered compared to the hole-only device. An expo-nential upturn in the current is observed around 2 V, indicating the injectionof electrons and the opening of the diode. Lowering the temperature, thisdiode characteristic is rather quickly frozen out and, below 200 K, SCLCbehavior is once again observed (α ≈ 2). The mobility is calculated asμ ≈ 1.2 × 10−8 cm2/Vs. Considering the SCLC behavior with a mobilitycomparable to the hole-only device, it can be concluded that, at these lowtemperatures, the device once again becomes unipolar and hole-controlled.

Figure 5.11 summarizes the temperature dependent transport behaviorof unipolar and ambipolar diodes based on MDMO–PPV. Below 190 K, thehole-controlled device (ITO/PEDOT and Au contact) and the ambipolardevice (ITO/PEDOT and LiF-Al contact) behave identically. Trap-free SCLCtransport is observed and the mobility at this temperature is estimated tobe around 10−8 cm2/Vs. For the ambipolar device, a diode-like turn-on is


1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

0 1 2 3 4 5 6

I [A

]

Bias [V]

Au contact 294KAu contact 150KAl contact 294KAl contact 150KAu contact 15KAl contact 15K

Fig. 5.11. Comparison of the unipolar and ambipolar transport characteristics ofa p-type semiconductor (MDMO–PPV) based diode at different temperatures

observed under flat band conditions (≈ 1.5 V), determined by the injection ofelectrons. At lower temperatures, the contribution of electrons to the overallcurrent is frozen out.

Bulk heterojunction solar cells are true ambipolar devices. Due to chargeneutrality, the short-circuit current is a superposition of equal amounts ofpositive and negative carriers. Figures 5.12a and b show the temperaturedependence of the current characteristics of the standard bulk heterojunctiondevice (ITO/PEDOT/MDMO–PPV:PCBM/LiF-Al). At low bias, the darkcurrent scales linearly with the applied voltage. The diode turn-on (transitionto the flat band regime) occurs at around 1 V. The turn-on voltage of thedark device is related to the open-circuit voltage of the illuminated device.The same temperature trend is observed for both voltages. Upon cooling, theturn-on voltage and open-circuit voltage both start to increase (from 0.85to 1.16 V). The temperature dependence of the open-circuit voltage will bediscussed separately.

At high voltages, the injection current (for both the dark and illuminateddiodes) is several orders of magnitude higher than for pristine MDMO–PPVdevices. Trap-free SCLC transport is observed at room temperature and thecurrent scales quadratically with the voltage, in contrast to the trap-limitedtransport of the single-layer MDMO–PPV diodes. The mobility is calculatedfrom the SCLC regime with μ ≈ 10−3 cm2/V s, at least two orders of mag-nitude higher than the hole mobility of MDMO–PPV at room temperature.Together, these observations lead to the conclusion that the injection current


1E-11

1E-10

1E-09

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

1E-02

0.1 1

I [A

]

Bias [V]

15K35K50K75K

100k125K150K167K210K250K294K

V ∝ I1.17

V ∝ I2

1E-09

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

1E-02

0.1 1

I [A

]

Bias [V]

15K35K50K75K

100k125K150K167K210K250K294K

V ∝ I2

Fig. 5.12. Temperature dependent I/V characteristics of a bulk heterojunctiondevice (ITO/PEDOT/MDMO–PPV:PCBM/LiF-Al) in the dark (top) and underillumination (bottom)


in bulk heterojunction solar cells is controlled by injection of electrons fromthe negative electrode into the fullerene. Consequently, electron transport offullerenes (n-type semiconductor) is trap-free at room temperature and moreefficient than hole transport on the polymer (p-type semiconductor), as con-cluded from the different mobilities. Upon cooling, the scaling exponent α isincreased, and even at the lowest temperatures (15 K), no SCLC transportbehavior is observed.

Generally, SCLC scaling with α = 2 is not expected for ambipolar de-vices, since the presence of positive and negative carriers will shield the ap-plied electric field, thus shifting the onset for space charge to higher voltages[43]. For ambipolar devices with significantly different mobilities for holesand for electrons, the transport behavior of the more mobile carrier will beobserved. In the case of the bulk heterojunction solar cell, this is the n-typesemiconductor PCBM. Upon cooling, the scaling exponent α = 2 is lost andeven at the lowest temperatures α is always significantly larger than 2. Sincethe p-type polymer is expected to show trap-free transport below 200 K, itcan be concluded that low temperature transport properties of the bulk het-erojunction solar cell are chracterized by more balanced charge transport ofthe two carriers. It is interesting to note that the α = 2 relationship is al-ready lost at around 250 K, indicating that the n-type fullerene has a strongtemperature-activated mobility.

5.2.2 Metal/Conjugated Polymer Contacts

Understanding and describing the influence of electrodes with different workfunctions on the performance of polymeric semiconductor devices is still achallenging exercise. Despite the qualitative understanding discussed in theprevious section, the metal/organic semiconductor interface is worth closer in-vestigation due to its interesting physical features. The semiconductor/metalinterface is decisive in establishing the working principle of a device, and itseffect can be directly observed in the open-circuit voltage.

The diode properties of single-polymer p-type semiconductors (MEH–PPV) sandwiched between various low and high work function materials aregenerally quite well described by a MIM (metal–intrinsic–metal) model [47–49]. The existence of rigid bands is proposed in these diodes, but one hasto note that a rigid band model is only appropriate for truly intrinsic semi-conductor conditions in the device. Even if the semiconductor is intrinsic,application of the metal contacts could dope the semiconductor, which wouldagain increase the carrier concentration. Capacitance–voltage measurementsindicate an upper limit for the dark carrier concentration of 1014 cm−3 inorder to allow flat band conditions. Electro-absorption measurements [50,51]and XPS/UPS measurements [52,53] support the MIM picture for single-layerpolymeric semiconductor diodes.

Schottky-type contacts have also been reported. The occurrence of Schot-tky junctions is discussed in terms of the choice of semiconductor, the work


function and in particular the mobile carrier concentration of the semicon-ductor (mainly due to ionic impurities) [13,54–61].

According to quantum mechanics, carriers can tunnel through a barrierunder high electric fields. If the influence of an electrical field supports tun-nelling of carriers from the Fermi level of the metal into the semiconduc-tor, this phenomenon is referred to as field emission [62–67]. Field emissiongenerally becomes relevant at low temperatures. In the case of thermallyactivated tunnelling, the phenomenon is called thermionic field emission, incontrast to thermionic emission via a Schottky barrier. Both models sufferfrom simplifications. The field emission model ignores image charge effectsand invokes tunnelling of electrons from the metal through a triangular bar-rier into unbound continuum states. The model predicts the following currentcharacteristics:

I(E) = BE2 exp

(−4

√2meffΔ3/2

3�eE

). (5.10)

Field emission is characterized by its temperature independence. Here meffis the effective mass of the carrier in the dielectric. The essential assumptionof the Schottky model is that a carrier can gain sufficient thermal energyto cross the barrier that results from superposition of the external field andimage charge potential. Neither tunnelling nor inelastic carrier scattering istaken into account. The following current characteristic is predicted for theSchottky junction:

I(E) = AT 2 exp

⎡⎢⎢⎢⎣

−Δ −(

eE

4πεε0

)1/2

kT

⎤⎥⎥⎥⎦ . (5.11)

Both models have been applied to carrier injection into polymeric semicon-ductors and, despite their deficiencies, several properties such as the tem-perature independent current characteristics at higher field are adequatelydescribed [68,69,91].

Besides the classical Schottky contact, various surface mechanisms areknown to influence polymer–metal contacts. Band bending in metal/PPVinterfaces is also discussed in terms of surface states or chemical reactionsbetween the semiconductor and the metal [70–74]. An excellent review onconjugated polymer surfaces and interfaces is given by [129].

However, it is important to note that, since the seminal publication ofAviram and Rattner [75], there have been attempts to demonstrate thatsuitably designed organic semiconductors deposited in a layer between twoelectrodes would give current–voltage behavior analogous to the behaviorof a p–n junction, even when Schottky barrier or tunnelling effects due tothe metal electrodes are not important. There is a class of small molecular


semiconductors which have been reported to exhibit intrinsic electrical rec-tifying properties [76–78]. As the observation of asymmetric conduction isnot sufficient proof that rectification is a purely molecular process [79], onlythe introduction of passive organic layers between the active molecule andthe symmetrical electrodes provided conclusive evidence that the rectifier-likecharacteristics are attributable to molecular processes [80]. Recently, molec-ular rectification in polymer films has also been achieved by orientation ofpolar push–pull molecules contained in a polymer matrix [81,82].

In bulk heterojunction solar cells, the metal/semiconductor interface iseven more complex. Now the metal comes into contact with two semicon-ductors, one p-type (typically the polymer) and one n-type (typically thefullerene) semiconductor. A classical electrical characterization technique forstudying the occurrence of charged states in the bulk or at the interface of asolar cell is admittance spectroscopy. If a solar cell is considered as a capacitorwith capacitance C, the complex admittance Y is given by

Y = G + iωC , (5.12)

where G is the conductance, i the square root of −1 and ω the angularfrequency, so that ω = 2πf , where f is the frequency. For a semiconductor ora solar cell, the various contributions to the complex admittance are discussedfirst. If a space-charge region is apparent, thermally activated charge carrierscontribute to the device admittance. If an AC voltage is applied, these chargesrespond to the frequency and hence contribute to the complex admittance,until a critical frequency ω0 is reached. This value corresponds to the situationin which the device behaves like a dielectric medium. Furthermore, trap statesin the bulk or located at the interfaces may give rise to the device capacitanceby the capture or emission of free charge carriers. The characteristic featuresof these defect states can be derived from the C(ω) spectrum at certain criticalfrequencies ω0, where an instantaneous decrease in capacitance is observed. Ifa defect state with the emission rate τ = 1/ω0 is considered, the dependenceof the capacitance on the frequency ω is given by [83]

C ∝ ω20

ω2 + ω20

. (5.13)

This is a step function, where the critical frequency ω0 is the temperaturedependent parameter. The expression

ω0 =1τ= Nvvthσh exp

(− EA

kBT

)(5.14)

reveals the activation energy EA of the defect state and the dependence ofthe emission rate on temperature. Nv is the effective density of states inthe valence band, vth the thermal velocity of the charge carriers, and σh the


Fig. 5.13. Top: capacitance vs. frequency (ν = ω/2π) at different temperaturesT = 300–20 K (the spectra are not normalized with respect to the effective area ofthe device). Bottom: differentiated capacitance vs. frequency. The arrow indicatesincreasing measurement temperature

capture cross-section for holes. Since vth ∝ T 1/2 and Nv ∝ T 3/2, one mayexpress (5.14) in the form

ω0 =1τ= ξ0T

2σh exp(

− EA

kBT

), (5.15)

where ξ0 is the pre-exponential factor.Plotting ω0 as a function of the reciprocal temperature T−1 (Arrhenius

representation), one can derive the activation energy from the slope. Thetemperature dependent pre-exponential factor ν0 = ξ0T

2σh is then obtainedfrom the axis cutoff T−1 → 0 K−1.

Figure 5.13 (top) displays the frequency spectra of the measured ca-pacitance for temperatures ranging from 20 K to 300 K for a standardcell (ITO/PEDOT/MDMO–PPV:PCBM/Al). The arrow indicates increas-ing temperatures. One clearly observes a step which is shifted to higher fre-quencies as the temperature increases. In order to evaluate the position ofthe steps, it is better to plot ωdC/dω versus ω, rather than C(ω) versusω. Figure 5.13 (bottom) shows the normalised deviated frequency spectrumof the capacitance. The steps now appear as maxima within the individualcurves, and the corresponding critical frequency ω0 can be derived more ac-


Fig. 5.14. Capacitance (upper graph) and differentiated capacitance (lower graph)vs. temperature at different frequencies (indicated)

curately. A more detailed evaluation is given by the representation of thecapacitance as a function of temperature [Fig. 5.14 (top)] or the deviation−ωdC/dω [Fig. 5.14 (bottom)], respectively. In Fig. 5.14 (top) two stepscan be clearly distinguished. These shift towards higher temperatures withincreasing frequency. They correspond to different defect states with charac-teristic activation energies.

From the data plotted in Figs. 5.13 and 5.14, an Arrhenius evaluationcan be carried out. This is presented in Fig. 5.15. For both defect states, theactivation energies and the pre-exponential factors are calculated from thecurves obtained. For the first trap state, a relatively small activation energyof EA1 = 9 meV and a pre-exponential factor of ξ01 = 1.7 × 103 s−1K−2 arefound. This state is attributed to a very shallow defect, which may contributeto the observed thermally activated conductivity. A further defect is foundat EA2 = 177 meV and ξ02 = 2.2 × 104 s−1K−2. It can be shown that thisstep is independent of the DC bias [84], showing that bulk defects cannot beresponsible for it. For bulk defects, one would expect a weak bias sensitivitydue to the hopping nature of charge transport. At high electric fields, theCoulomb barriers which separate adjacent hopping centres should be loweredor raised when a DC voltage is applied (Poole–Frenkel mechanism). Further,C–V spectroscopy (Fig. 5.16) reveals that the capacitance of the solar celldoes not change (or only negligibly so) upon applying reverse bias, confirmingthe absence of a locally extended space-charge region in the device. Together


Fig. 5.15. Arrhenius representation. Data are derived from Fig. 5.13. The activa-tion energy and pre-exponential factors are defined in the text

Fig. 5.16. C–V dependence at 100 Hz for four different temperatures


with the temperature behavior of this defect, it is reasonable to suggest thatit originates from trapping centres at the composite–metal interface, probablyoriginated by a Fermi level pinning due to surface states (as discussed later).

5.2.3 Simulation and Modelling

n++ (LiF-Al)

p++ ( ITO/PEDOT)

Intrinsic SC

Eg ~ 2.2 eV

Anode

Cathode

Shunt

Fig. 5.17. One-dimensional devicescheme for simulating bulk heterojunc-tion solar cells

From the previous results it is reasonable to propose the following devicemodel for a bulk heterojunction solar cell (Fig. 5.17):

positive electrode/p++/i/n++/negative electrode .

The positive electrode is typically a transparent conducting oxide (TCO) likeITO, while the negative electrode is typically an Al, Ca, Ba, Mg, Al-LiF metallayer. The p++ and n++ layers are highly p- or n-doped thin semiconductorlayers and should establish selective quasi-Ohmic contacts at the individualelectrodes, thus introducing the selection principle to the solar cell. Whilethe p++ layer resembles the PEDOT layer in bulk heterojunction solar cells,the n++ layer is representative of all interface effects (such as doping ofthe semiconductor, filling of surface states, Fermi level pinning, dipole layeralignment, and so on) that may occur during electrode evaporation. Thephotoactive layer is regarded as an intrinsic layer i with a high quantumefficiency for charge generation.

This model is simulated by self-consistently solving the transport equa-tions in one dimension [85]. Figures 5.18a and b show the results from this


-3 -2 -1 0 1 210

-5

10-4

10-3

10-2

10-1

100

101

102

103

Measurement Simulation

Cur

rent

[mA

/cm

2 ]

Voltage [V]-2 -1 0 1 2

10-1

100

101

102 Measurement Simulation AM1.5

Pho

tocu

rre

nt

[mA

/cm

2 ]

Voltage [V]

(a) (b)

0.0 2.0x10-8 4.0x10-8 6.0x10-8 8.0x10-8 1.0x10-7 1.2x10-71E10

1E11

1E12

1E13

1E14

1E15

1E16

1E17

1E18

1E19

μe = μh electron density hole density

Car

rier

Den

sity

[cm

-3 ]

Distance from Front [m]

0.0 2.0x10-8 4.0x10-8 6.0x10-8 8.0x10-8 1.0x10-7 1.2x10-71E11

1E12

1E13

1E14

1E15

1E16

1E17

1E18

1E19

μe > μh electron density hole density

Ca

rrie

r D

en

sity

[cm-3 ]

Distance from Front [m]

0.0 2.0x10-8 4.0x10-8 6.0x10-8 8.0x10-8 1.0x10-7 1.2x10-7

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5 μe > μh Conduction Band Fullerene Valence Band MDMO-PPV Electron Quasi Fermi Level Hole Quasi Fermi Level

En

erg

y Le

vels

[eV

]

Distance from Front Electrode [m]0.0 2.0x10-8 4.0x10-8 6.0x10-8 8.0x10-8 1.0x10-7 1.2x10-7

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

μe = μh Conduction Band Fullerene Valence Band MDMO-PPV Electron Quasi Fermi Level Hole Quasi Fermi Level

Ene

rgy

Lev

els

[eV

]

Distance from Front Electrode [m]

(c) (d)

Fig. 5.18. Measurement and simulation of a bulk heterojunction solar cell in thedark (a) and under illumination (b). The dark I/V characteristics are plotted semi-logarithmically, whilst the illuminated characteristics are plotted on a linear scale.The bulk heterojunction was simulated as a diode with the following structure:positive electrode/p++/i/n++/negative electrode. (c) Local variation of the energylevels (top) and of the carrier densities for a bulk heterojunction solar cell withbalanced mobilities. (d) Local variation of the energy levels (top) and of the carrierdensities for a bulk heterojunction solar cell with higher electron mobility

simulation compared to the experiment for a typical bulk heterojunction solarcell in the dark and under light. Excellent agreement is found, justifying thesuitability of this model for describing the performance of a bulk heterojunc-tion solar cell. An important lesson can be learned from these simulations: thenature of the rectification (the diode principle) in bulk heterojunction solarcells can be explained by the selectivity of the individual contacts, e.g., thespecific permeability of the individual electrodes for just one type of carrier.


Further, the model allows us to estimate electrical losses in the device.Figures 5.18c and d show the local variations in the energy levels and thecarrier densities for the bulk heterojunction solar cell for different mobilities.In Fig. 5.18c, balanced mobilities for electrons and holes are assumed, whileFig. 5.18d describes the situation for the case where the electron mobility ishigher than the hole mobility. In the latter case recombination is enhancedas seen from the carrier densities, and the performance of the device (Isc) issignificantly lowered.

5.3 Performance Analysisof Bulk Heterojunction Solar Cells

The previous section gave an overview of the transport and junction prop-erties of conjugated materials regarding their importance for photovoltaicdevices. In this chapter, the bulk heterojunction device itself will be in thespotlight. Device properties will be discussed and evaluated as for classicalinorganic solar cells, concentrating on the short-circuit current Isc, the open-circuit voltage Voc, the fill factor FF, and the spectral sensitivity.

Generally, the operation of a photovoltaic device may be visualized astaking place in three consecutive fundamental steps:

• absorption of light,• creation of separate charges at the donor–acceptor interfaces,• selective transport of the charges through the bulk of the device to theappropriate collecting electrodes.

A prerequisite for highly efficient conversion of photons into electrical cur-rent is that holes and electrons do not recombine before being swept outof the device into the external circuit. Therefore, a metastable photoin-duced charge-separated state and high charge carrier mobilities are importantfactors. The ultrafast photoinduced charge transfer in conjugated polymer–methanofullerene blends and the subsequent rather slow recombination canprovide both of these characteristics [8]. The time-resolved measurements [86]in Chap. 1 of this book (Sect. 1.4) have shown that the initial photoinducedelectron transfer from a conjugated polymer to a soluble methanofullerene oc-curs on a timescale of less than 40 fs, whereas the timescale for back-transferto the neutral state is very long and extends into the microsecond range.Once this metastable charge-separated state is formed, the free charges aretransported through the device by diffusion and/or drift processes. The lat-ter is induced by using top and bottom layer electrodes that have differentwork functions, thus providing a built-in electric field across the active layer,similar to the intrinsic layer in p–i–n solar cells.

In the active layer of the device, positive carriers (holes) are transportedthrough the conjugated polymer matrix, and negative carriers (electrons) aretransported by hopping between fullerene molecules. Importantly, these two


different charge transport processes do not interfere with each other, as hasbeen proved by recent mobility measurements [97].

The overall efficiency ηeff of a solar cell is calculated from

ηeff =VocIscFF

Ilight, (5.16)

where Voc is the open-circuit voltage, typically measured in V, Isc the short-circuit current in A/m2, FF the fill factor, and Ilight the incident solar radi-ation in W/m2.

5.3.1 Precise Calibration of Solar Cells

An accurate determination of the photovoltaic conversion efficiency is essen-tial for an international comparison of results and product compatibility. Upto now, a lot of experience has been built up in the characterisation of es-tablished inorganic solar cell technologies such as crystalline silicon, GaAs,and so on. For these technologies, a high accuracy is not only of academicinterest but can also prevent developments in the wrong direction, becauseimprovements resulting from one process step are usually in the range of0.1%.

For novel devices like the polymer solar cells described in this chapter,measurement procedures are not nearly so well-established as for inorganicdevices. It was reported earlier that all kinds of ill-defined efficiencies can befound in the literature [87]. This makes a meaningful comparison of efficiencyvalues extremely difficult or even impossible, when they are measured atdifferent institutes and using different measuring techniques. This sectiondescribes a procedure for obtaining better defined polychromatic efficiencies.

The efficiency of a solar cell is strongly dependent on conditions such ascell temperature, and incident light intensity and spectral content. Standardreporting conditions (SRC) have therefore been defined so that the perfor-mance of a solar cell can be quantified in a reproducible way. The standardreporting conditions are specified as:

light intensity 1 000 W/m2 ,

sun spectrum AM1.5 global (IEC 904-3) ,

sample temperature 25◦C .

The most direct way to carry out the measurements is in places where themeasured solar spectrum is found to be nearly identical to the standardAM1.5G spectrum. By measuring the temperature dependence and irradi-ance dependence of the I/V curve parameters, cell properties may be adjustedto the SRC. Since in most places around the world these SRC conditions can-not be met, characterisation laboratories have been set up with suitable ap-paratus and procedures to do accurate indoor efficiency measurements underSRC according to international standard norms (ASTM, IEC). This involves


using solar simulators with a light spectrum that approximates the AM1.5global spectrum and a calibrated reference cell. Measurement procedures areextensively described elsewhere [88] and are summarized below.

Measurements can be divided into two steps:

• determination of the spectral mismatch factor M ,• measurement of the I/V characteristic of the solar cell at SRC.

The match between a simulator spectrum ES(λ) and the reference AM1.5Gspectrum ER(λ) is never perfect, even for the best solar simulators. Further-more, a spectral mismatch is introduced because the spectral responses ST(λ)of the device under test and SR(λ) of the reference cell are not identical. Inorder to correct for this, a spectral mismatch factor M can be computed from

M =∫

ER(λ)SR(λ)dλ∫ES(λ)SR(λ)dλ

∫ES(λ)ST(λ)dλ∫ER(λ)ST(λ)dλ

. (5.17)

For each test cell, the spectral response ST has to be measured relative tothe known spectral response SR of the reference cell. The relative spectralirradiance ES of the simulator should be measured in regular intervals on aregular basis. The mismatch factor can be calculated by taking the values ofthe reference cell and spectrum from the tables.

The next step in the procedure is to adjust the solar simulator so thatthe reference cell reads an Isc of I0/M , where I0 is its calibration value forSRC. This establishes SRC for the test cell. Then the I/V characteristic ismeasured and the efficiency η can be calculated using (5.16).

For the highest accuracy (M ≈ 1) it is important that the test cell shouldhave the same geometrical design and spectral response as the calibratedcell. If this is not the case, it can result in larger mismatch factors and alarger uncertainty in the efficiency values. Furthermore, other parametersare important for an accurate measurement, such as the homogeneity of theilluminated area and temperature control during the measurement. For crys-talline silicon solar cells, M lies in the range 0.98–1.02, since stable calibratedsolar cells can be constructed from the same materials.

However, for relatively new types of solar cells such as the polymer-basedsolar cells described here, suitable stable reference cells cannot yet be fabri-cated. This implies that, for measurements concerning these cells, calibratedreference cells are used (Si, GaAs) with a different spectral response to thedevice under test, resulting in mismatch factors that deviate significantlyfrom 1. It is therefore of the utmost importance to carry out the procedureas precisely as possible in order to minimise measurement errors.

For bulk heterojunction solar cells made from MDMO–PPV/PCBM, mea-sured under metal halogenide lamps, a mismatch factor of M ≈ 0.76 has beendetermined, while for xenon high-pressure lamps, M ≈ 0.9 is used.


5.3.2 Production: Device Geometry

The chemical structure of the compounds and the device structure is shownin Figs. 5.19 and 5.3, respectively. For the devices discussed in this chap-ter, poly(2-methoxy-5-(3′, 7′-dimethyloctyloxy)-1,4-phenylene-vinylene) (ab-breviated to MDMO–PPV) was used as electron donor and p-type semicon-ductor, while the electron acceptor was [6,6]-phenyl C61-butyric acid methylester (PCBM) [28]. MDMO–PPV and PCBM are prototype organic semicon-ductors which fulfil the basic requirements for organic photovoltaics. Bothsemiconductors can be produced with high purity and low defect density.They are truly intrinsic, typically with a carrier concentration much lessthan 1015 cm3, and show satisfactory solubility in a large number of organicsolvents. Their film-producing properties are good, and their chemical simi-larity is sufficient to form an interpenetrating network (as will be discussedlater).

Fig. 5.19. Abbreviation and structure of common conjugated polymers andacceptor-type molecules

Indium-doped tin oxide (ITO) glasses are commonly used as semi-transparent substrates with a transmission of around 90% in the visiblerange and a conductivity of around 20 ohm/square. The glass substrates


are typically cleaned in ultrasonic baths of acetone, NMP or isopropanol,followed by oxygen plasma treatment. Poly(ethylene dioxythiophene) dopedwith polystyrene sulphonic acid (PEDOT:PSS, Bayer AG) is spin-coated toa thickness of 100 nm on top of the ITO from a water solution, giving a con-ductive layer (≈ 10−3 S/cm) which prevents shorts and allows us to increasethe shunt resistivity of thin film devices. The photoactive layer consisting ofMDMO–PPV:PCBM (1:4 by wt. ratio) is again spin-coated on top of thePEDOT to a thickness of about 100 nm from solution.

The negative electrode (cathode, typically Ca/Al, Ba/Al or LiF/Al) isthermally deposited through a shadow mask. The geometrical overlap be-tween the positive electrode and the negative electrode defines the activearea. For the LiF/Al cathode, a specific two-layer deposition is performed.This technique has been shown to enhance the interface between the activelayer and the cathode in organic light-emitting diodes [89,90]. A small amountof LiF is first thermally deposited (10−6 torr) onto the active layer, with anaverage thickness of 0.6 nm. In the second step, Al is thermally evaporatedto a thickness of more than 100 nm.

In the following, we discuss strategies for optimizing the power efficiencyof polymeric solar cells based upon bulk heterojunctions.

Short-Circuit Current. Key parameters for efficient charge collection byplastic solar cells are the hole and electron mobilities of the interpenetrat-ing networks and the lifetime of the carriers within this network. While thelifetime of the carriers in the bulk heterojunction blends has already been dis-cussed as a peculiarity of the interpenetrating network, the mobility of theindividual components is a true material parameter. The interplay betweennetwork quality and mobility and their impact on the short-circuit currentwill be discussed by means of a simple model in this section.

Open-Circuit Voltage. A particularly interesting phenomenon in bulk het-erojunction cells based on organic (polymeric) semiconductors, i.e., plasticsolar cells (PSC), is the observation of unusually high open-circuit voltages.Before discussing PSC observations, the findings for pristine conjugated poly-mer PV elements are briefly reviewed.

For single-layer polymer PV elements, produced by spin-casting fromalkoxy PPV solutions, a consistent picture is found for experimental observa-tions and an explanation of the open-circuit voltage can be given. For deviceswith high purity (Nd � 1017 cm−3), it is argued that a single-layer polymerdevice works as a metal–insulator–metal (MIM) diode [91]. Typically, suchdevices exhibit a Voc determined by the difference between the work func-tions of the two metal electrodes. On the other hand, for diodes preparedfrom pristine conjugated polymers (e.g., precursor-PPV), deviations from theMIM picture can be observed. Several reports [92] on the observation of Vocin the range 1.2–1.5 V for ITO/precursor-PPV/Al devices and the formation


of a Schottky junction at the precursor-PPV/Al interface can be found inthe literature. Obviously, the MIM picture is reasonable for pristine polymerPV devices as long as the impurity density does not favor the formation ofSchottky barriers.

The experimentally observed Voc of PSC cannot be explained by theMIM picture alone. For typical devices, based on ITO/conjugated polymer–fullerene/Al, values of Voc can be observed in a range of 800 mV and higherfor several polymer/fullerene mixtures, in contrast to the 400 mV expectedfrom the MIM picture. The origin of the open-circuit voltage in plastic solarcells will be discussed and explained in Sect. 5.3.4.

Fill Factor. The fill factor of solar cells is determined by

FF =ImppVmpp

IscVoc, (5.18)

where Impp and Vmpp are the current and voltage at the maximum powerpoint of the I/V curve in the fourth quadrant. This fill factor reflects thediode properties of the solar cells.

In general, a large serial resistance and an over-small parallel resistance(shunt) tend to reduce the FF. Strategies for reducing the serial resistivity byimproving the quality of the Ohmic contact will be discussed. The insertionof very thin polar layers like LiF have been shown to reduce the interfacebarrier at the cathode in bulk heterojunction solar cells, if they are evaporatedbetween the photoactive material and an Al electrode [93,94].

Spectral Sensitization. One of the limiting factors in plastic solar cellsis their mismatch with regard to the solar spectrum. Typically, conjugatedpolymers like MDMO–PPV, used for photovoltaics, have their peak absorp-tion around 500 nm. This is significantly offset from the maximum in thephoto-flux of the sun, which peaks around 700 nm.

The use of low bandgap polymers (Eg < 1.8 eV) to extend the spectralsensitivity of bulk heterojunction solar cells is a real solution to this problem.These polymers can either substitute one of the two components in the bulkheterojunction (if their transport properties match) or they can be mixedinto the blend. Such a three-component layer, comprising semiconductorswith different bandgaps in a single layer, can be visualized as a variation of atandem cell in which only the current and not the voltage can be added up.

5.3.3 Short-Circuit Current

The interpenetrating network in bulk heterojunction solar cells [9] helps toovercome the limitations of bilayer systems [25,95] with low mobility mate-rials. However, less is known about the nanometer morphology of an inter-penetrating network or the optimum density of donor/acceptor interfacial


contacts that facilitate both the photoinduced creation of mobile charge car-riers and transport of the carriers to the electrodes. In this section we discussthe importance of network morphology and the effect on the Isc of the in-dividual component’s morphology in the blends. Structuring of the blend toform a more intimate mixture that contains less phase-segregation of themethanofullerene species, thereby simultaneously increasing the degree of in-teraction between conjugated polymer chains, is a straightforward matter.Improving the mobility of the polymeric semiconductor (obviously the com-ponent with the lower mobility in the blend, as discussed in the last section)is another important step towards Isc improvement.

Once this metastable charge-separated state is formed, the free charges aretransported through the device by diffusion and drift processes. The latterare induced by using top and bottom layer electrodes with different workfunctions, thus providing a built-in electric field over the active layer [96]. Inthe active layer of the device, holes are transported through the conjugatedpolymer matrix and electrons are transported by hopping between fullerenemolecules. Importantly, these two different charge transport processes do notinterfere with each other. Field-effect mobility measurements have shown thatmixing a methanofullerene into a conjugated polymer matrix (using the samematerials and doping level as in the devices presented in this work) does notreduce hole mobility [97].

Figure 5.20 shows AFM images of the surfaces of MDMO–PPV:PCBMblend films spin-coated using either toluene or chlorobenzene. The imagesshow significantly different surface morphologies. The surface of the toluene-cast film contains structures with horizontal dimensions of order 0.5 μm. Sincethe horizontal dimensions of these features are much larger than the thicknessof the film (100 nm), it can be concluded that the morphology seen on thesurface is representative of that throughout the bulk. Measurements of themechanical stiffness and adhesion properties of the surface (performed simul-taneously with the topographic imaging) are shown in Fig. 5.21. Stiffness andadhesion are material rather than topographic properties. The nearly perfectcoincidence between topography, stiffness and adhesion clearly indicates thatthese vertical features have a different chemical composition to the surround-ing valleys. Since such features are not observed in films of pristine MDMO–PPV spin-coated from toluene, they are assigned to phase-segregated regionsthat contain higher concentrations of fullerenes.

In contrast, the chlorobenzene-cast film contains structures with hori-zontal dimensions of the order of only 0.1 μm. This indicates a much moreuniform mixing of the constituents. Furthermore, the toluene-cast film hasheight variations of the order of 10 nm, whereas the chlorobenzene-cast film isextremely smooth, with height variations of the order of 1 nm. This contrastin film morphologies is mainly attributed to the fact that PCBM is morethan twice as soluble in chlorobenzene as in toluene. However, the solubilityof the polymer in these two solvents also changes.


b

0.5 μm

0.0 0.5 1.0 1.5 2.0 2.5-4

0

4

8

Sur

face

Hei

ght (

nm)

Distance (μm)

(a)

0.0 0.5 1.0 1.5 2.0 2.5-4

0

4

8

Sur

face

Hei

ght

(nm

)

Distance (μm)

(b)

a

0.5 μm

Fig. 5.20. AFM images (acquired in the tapping mode) showing the surface mor-phology of MDMO–PPV:PCBM blend films (1:4 by wt.) with a thickness of approx-imately 100 nm and the corresponding cross-sections. (a) Film spin-coated from atoluene solution. (b) Film spin-coated from a chlorobenzene solution. The imagesshow the first derivative of the actual surface heights. The cross-sections of the truesurface heights for the films were taken horizontally along the dashed lines

Results from AFM studies are supported by light-scattering data. Theparticle size distribution in the MDMO–PPV solutions can be analyzed bymeans of light-scattering measurements using a Microtrac Ultrafine ParticleAnalyzer. This technique allows us to determine the particle size (PS) in solu-tions. It can be expressed as a number distribution or a volume distribution.The results for MDMO–PPV dissolved in toluene and chlorobenzene withdifferent concentrations (0.0625%, 0.125% and 0.25%) are given in Table 5.1.

The PS values shown in Table 5.1 signify that 90% of the number (orvolume) of particles is below the given value. Rows entitled ‘Volume/fraction


(a)

(b)

Fig. 5.21. AFM images (acquired in the pulsed force mode) showing the physicalsurface properties of MDMO–PPV:PCBM blend films (1:4 by wt.) with a thicknessof approximately 100 nm and the corresponding cross-sections. (a) Film spin-coatedfrom a toluene solution. (b) Film spin-coated from a chlorobenzene solution. Thepulsed force mode allows us to acquire the mechanical properties of the surface.The top left image shows the topography, the top right image shows the errorpicture, and the bottom left and bottom right images show the stiffness and adhesion,respectively


Table 5.1. Overview of light-scattering measurements on toluene and chloroben-zene solutions of MDMO–PPV. Particle sizes [nm] are shown for different concen-trations (0.25%, 0.125% and 0.0625%): 90% of the number or volume are below thegiven value. More details are given in the text

0.25% 0.125% 0.0625%

Toluene Number distribution 35 6 6 240Volume distribution 2 265 3 240 > 6 000Volume/fraction 30, 1 050 6, 1 000–3 000 > 6 000average

Chlorobenzene Number distribution 66 8 8Volume distribution 1 565 8 5 585Volume/fraction 40, 70, 120, 1 200 8 8, 5 500average

average’ indicate the average PS in several (if present) distinct fractions ofthe volume distribution. It can be seen from Table 5.1 that, in toluene, thenumber PS develops upon dilution from 35 nm through 6 nm to more than6 μm. The volume PS increases from 2.2 μm through 3.2 μm to > 6 μm. At thehighest concentration (0.25%), two fractions can be distinguished from whichthe smaller decreases further in the first dilution and completely vanishes atthe lowest concentration (0.0625%). The latter is indicative of a true solution.At a concentration of 0.25%, toluene provides at least a partial solubility forMDMO–PPV. In this case, vacancies are created within the polymer coilthat can be occupied by toluene molecules, in this way possibly hinderinginterchain interactions.

In chlorobenzene, the number PS decreases from 66 nm down to 8 nmupon dilution. The volume PS first decreases from 1 565 nm to 8 nm, thenrises again to 5 585 nm. At a concentration of 0.25%, there are four (partiallyoverlapping) PS fractions, which are reduced to just one fraction at mediumconcentration. At the lowest concentration, a new fraction develops arounda PS of 5.5 μm. These data indicate that chlorobenzene solutions with highand medium concentrations form a colloidal system, rather than a solution.It is reasonable to assume that, in these colloids, chromophore aggregationand thus interchain interactions are promoted. As the degree of aggregation isknown to be preserved throughout the spin-casting process, we can concludethat the solution aggregation will also be mirrored in thin film systems.

To compare the impact of these different morphologies on photovoltaicperformance, devices are fabricated in an identical manner except for thechoice of solvent (either toluene or chlorobenzene) used for spin-coating theactive layer (MDMO–PPV:PCBM, 1:4 by wt.). Characterization of the de-vices is performed under illumination by a solar simulator. The AM1.5 power


conversion efficiency ηAM 1.5 of the photovoltaic devices measured with a solarsimulator is given by

ηAM 1.5 =Pout

PinM = FF

VocJsc

PinM , (5.19)

where Pout is the output electrical power of the device under illumination,Pin is the light intensity incident on the device as measured by a calibratedreference cell, Voc is the open-circuit voltage, and Jsc is the short-circuitcurrent density. M is the spectral mismatch factor accounting for deviationsin the spectral output of the solar simulator with respect to the standardAM1.5 spectrum and deviations in the spectral response of the device beingmeasured with respect to that of the reference cell [98], as defined in (5.17).For measurements with solar simulators using a metal-halogenide lamp, themismatch factor is determined as M ≈ 0.76, while a solar simulator usinga xenon lamp typically has a mismatch factor of M ≈ 0.9 under Pin =80 mW/cm2.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-6

-5

-4

-3

-2

-1

0

from toluene from chlorobenzeneC

urre

nt D

ens

ity (

mA

/cm

2 )

Voltage (V)

Fig. 5.22. Characteristics for devices with an active layer that is spin-coatedfrom a toluene solution (open squares): Jsc = 2.33 mA/cm2, Voc = 0.82 V,FF = 0.50, ηAM 1.5 = 0.9%, and from a chlorobenzene solution (open circles):Jsc = 5.25 mA/cm2, Voc = 0.82 V, FF = 0.61, ηAM 1.5 = 2.5%. Data are for devicesilluminated with an intensity of 80 mW/cm2 and an AM 1.5 spectral mismatchfactor of 0.753. The temperature of the samples during measurement was 50◦C

A plot of the current density versus voltage for the two devices is shownin Fig. 5.22. The open-circuit voltages of the cells are identical (0.82 V).However, the chlorobenzene-based device exhibits a more than twofold in-crease in the short-circuit current density as compared to the toluene-based


device (5.25 mA/cm2 versus 2.33 mA/cm2). As shown in Fig. 5.23a, theoptical transmission spectra of the active layer films are nearly identical, ex-cept for a small redshift in the MDMO–PPV absorption (425–575 nm) in thechlorobenzene-cast film, as expected for the case of increased interchain inter-actions. Thus, the chlorobenzene-based device is much more efficient at con-verting photons to electrons. This is explicitly demonstrated in Fig. 5.23b, inthe plot of external quantum efficiency, or incident photon to converted elec-tron (IPCE) ratio, as a function of wavelength. The fill factor also increases(0.50 versus 0.61) upon changing the solvent from toluene to chlorobenzene.The increased short-circuit current density and fill factor combine to yielda nearly threefold increase in the AM1.5 power conversion efficiency (0.9%versus 2.5%).

a

b

400 450 500 550 600 650 7000

102030405060

IPCE

(%)

Wavelength (nm)

50

60

70

80

90

100

Tran

smiss

ion

(%)

Fig. 5.23. (a) Optical absorption spectra of 100 nm thick MDMO–PPV:PCBMfilms (1:4 by wt.) spin-coated onto glass substrates from either toluene (dash-dottedline) or chlorobenzene (solid line) solutions. (b) IPCE spectra for photovoltaicdevices using these films as the active layer

The IPCE plot in Fig. 5.23b shows a maximum value of 50% in the wave-length range of 460–480 nm. This spectral response is not well matched tothe spectrum of the sun. In fact, 50% of the power in the AM1.5 spectrumis above 685 nm in wavelength. This obviously limits the ultimate efficiencyobtainable from a device based on MDMO–PPV and PCBM. However, the


efficiency for the conversion of absorbed photons to electrons in this deviceis extremely high. The light absorption of the device is measured (using areflection geometry) to be less than 60% at 460 nm. This yields an internalquantum efficiency, or absorbed photon to converted electron, of greater than83%. Since the Jsc of the devices was measured to have a linear dependenceon the incident light intensity for values up to 80 mW/cm2, monochromaticpower conversion efficiencies can be calculated from the IPCE data. AssumingVoc = 0.82 V and FF = 0.61, this yields a power conversion efficiency of 9.5%at 488 nm for the chlorobenzene-based device, an impressive demonstrationof the potential of organic solar cells.

The observed increase in the fill factor of the devices can also be explainedby an increased charge carrier mobility, as well as the much smoother surfaceof the chlorobenzene-cast active layer that leads to better interfacial contactwith the cathode. In addition, the enhancements seen in the short-circuit cur-rent density and the IPCE can be partially explained by an increased chargecarrier mobility for both holes and electrons in the chlorobenzene-cast activelayer. As illustrated earlier with the AFM images, the tendency of the PCBMmolecules to phase-segregate into clusters is suppressed when chlorobenzeneis used as the solvent. Clustering of the PCBM molecules is expected to de-crease the charge carrier mobility for electrons, since the voids between theclusters present large barriers to the hopping process. Monte Carlo simula-tions of transport in a disordered medium have shown that charge carriermobility is very sensitive to inhomogeneous density variations of the hoppingsites [99].

The charge carrier mobility for holes is also affected by the morphologyof the film, since the relative orientation of the conjugated polymer chainsdetermines the degree of interchain interactions. This is also evidenced bytheoretical studies on interchain interactions in conjugated polymers [100]and experimental studies on conjugated polymer-based organic light-emittingdiodes [101]. The ability of the solvent to affect the degree of interchain in-teractions can be shown using light-scattering, and also spectroscopy exper-iments [102]. For p-type semiconductors with a chemical structure similar toMDMO–PPV (alkoxy PPVs), it is found that the polymer chains assume anopen conformation, leading to a high degree of interchain interaction. In filmsspin-coated using chlorobenzene, aggregates are observed.

It is generally accepted that charge transport along one polymer chainis a fast process. Measurements of one-dimensional intrachain mobilities ofholes and electrons in dilute solutions of an alkoxy PPV which is nearlyidentical to MDMO–PPV, namely, poly(2-methoxy-5-[2′-ethyl-hexyloxy]-1,4-phenylene vinylene) (MEH–PPV), yield values between 0.2 and 0.5 cm2/V s[103]. However, interchain transport relies on the hopping process, and mea-surements of charge carrier mobilities in films of MEH–PPV typically yieldvalues four to five orders of magnitude lower than this. Unlike the chargetransport, it has been demonstrated that interchain energy transfer occurs


two orders of magnitude faster than intrachain exciton migration in MEH–PPV [104]. It is thus clear that the optical and electronic properties of a bulkconjugated polymer medium are strongly affected by morphology [104,105].As a result, MEH–PPV films cast from CB (hence with a higher density ofthese 2-dimensional interchain aggregates) possess a higher interchain chargetransport than films deposited from a non-aromatic solvent such as THF[106].

FET mobilities of conjugated systems are limited in the same way by theπ–π interchain interactions of neighboring polymer chains, even though thetransport situation in the thin film transistor geometry is eased due to thethin accumulation layer responsible for carrier transport. Charge modulationspectroscopy (CMS) has revealed that the contribution of charge transfertransitions becomes stronger with increasing regioregularity, thus resulting inhigher mobility values [107]. In this way the hole mobilities of the thiophene-based p-type semiconductor poly(3-hexylthiophene) (P3HT) reach values upto 0.1 cm2/V s [108,109]. Interestingly, the dependence of FET mobilities onthe spin-casting solvent was also reported for P3HT [110].

FET mobility measurements thus constitute a sound method for investi-gating changes in the mobility of an organic semiconductor due to morphol-ogy variations. On the basis of the FET characteristics of MDMO–PPV filmsspin-cast from different solvents, we will discuss the influence of interchainpolymer aggregates on the hole field-effect mobility and further consequencesfor the short-circuiting of solar cells.

Figure 5.24 shows the layout of the FET structures used for mobilitymeasurements. Field-effect mobilities μFE can be calculated either from thesaturation regime or from the linear regime of the drain–source current Idsusing the following equations [111]:

Ids sat =μFEWCox

2L(Vgs − Vt)2 , (5.20)

Ids lin =μFEWCox

L(Vgs − Vt)Vds , (5.21)

where W and L are the conduction channel width and length, respectively,Cox is the capacitance of the insulating SiO2 layer, Vgs is the gate voltage,and Vt is the threshold voltage. Equation (5.20) is commonly used to estimatemobility values from organic FET characteristics. This equation predicts thatthe square root of Ids sat as a function of Vgs should give a straight line.However, OFETs often deviate from this behavior, especially at low Vgs.The latter can either be attributed to a sub-threshold regime or a gate bias-dependent mobility [112]. In order to distinguish between these two effects,(5.21) can be applied. The mobility is then calculated by differentiating Idsat low Vds as a function of Vgs, thereby eliminating the threshold voltage.

Figure 5.25 shows the FET characteristics of a device in p-channel modewith MDMO–PPV as the channel material. Figures 5.25a and b show the sit-uation for MDMO–PPV spin-cast from a toluene solution. The hole current


Fig. 5.24. FETs were assembled on highly doped p+ Si-substrates. An insulatingoxide (232 nm) was thermally grown on one side of the substrate, and the rearside was covered with an Al layer as the gate electrode. A structure of TiW/Auinterdigitating fingers, forming the source and drain electrodes, was realized ontop of the insulating SiO2 layer with a combination of photolithography and alift-off process. The following combinations of conduction channel width (W ) andlength (L) were produced: W/L = 1 075 μm/10 μm, W/L = 1 035 μm/5 μm, andW/L = 550 μm/3 μm. Finally, after cleaning the substrate, the organic semicon-ducting layer was spin-cast to fill the channel. Pristine MDMO–PPV was depositedfrom 0.5% (1% = 10 mg/ml) toluene and chlorobenzene solutions. The measurementmode of the FET is determined by the gate voltage, which induces an accumulationlayer of charges in the region of the conduction channel adjacent to the interfacewith the SiO2. For p-channel operation, a negative gate voltage is applied to in-duce an accumulation layer of holes, allowing the measurement of the hole mobility.Au source and drain electrodes were used for p-channel mode measurements in or-der to facilitate the injection of holes into the highest occupied molecular orbital(HOMO) level of the channel material. FET characterization was performed usingan HP4156A analyzer, with the source contact earthed. Measurements were per-formed with a long integration time (320 ms) in order to prevent capacitive chargingof the transistor channel during sweeps of the drain–source voltage. This capacitiveeffect was observed when using a short integration time (640 μs), leading to anoverestimate of the mobility values [97]. All measurements were performed under anitrogen flow

Ids reaches saturation for negative applied Vds and Vgs (Fig. 5.25a). The satu-ration point of Vds = −90 V is used to plot the Vgs dependence in Fig. 5.25b.From the slope of the linear fit at high negative Vgs, a field-effect hole mo-bility of μFE = 5 × 10−6 cm2/V s is calculated using (5.20) and (5.21). Thesame procedure is followed to derive the FET parameters of MDMO–PPVdeposited from a chlorobenzene solution (Figs. 5.25c and d). A hole mobilityof 3 × 10−5 cm2/V s is obtained in this case. The use of chlorobenzene assolvent clearly enhances the hole mobility of MDMO–PPV as compared totoluene. The increased mobility in the chlorobenzene-cast film is attributedto a modification of the polymer morphology [104]. This higher field mobil-ity of the p-type semiconductor MDMO–PPV can be explained by increasedintermolecular coupling and a larger number of chromophore aggregates, as


Fig. 5.25. (a) Ids versus Vds characteristics of a toluene-based MDMO–PPV FETwith Au contacts and L = 3 μm. (c) The same for chlorobenzene-based MDMO–PPV. (b) Right hand axis, circles: Ids plotted as a function of Vgs for Vds = −90 V ona logarithmic scale. Left hand axis, triangles: I1/2

ds plotted as a function of Vgs. Fromthe slope at high negative Vgs, the field-effect mobility of toluene-based MDMO–PPV for holes is calculated to be μFE = 5 × 10−6 cm2/V s. (d) The same forchlorobenzene-based MDMO–PPV with μFE = 3 × 10−5 cm2/V s

discussed earlier. The larger number of chromophores is induced by changingthe casting solvent from toluene to chlorobenzene, and the mobility is foundto be enhanced by nearly one order of magnitude (μFE = 5 × 10−6 cm2/V sfor toluene and μFE = 3 × 10−5 cm2/V s for chlorobenzene).

To obtain a better understanding of the effect of the mobility on theperformance of a solar cell, a simplified model is introduced to provide ananalytical description of the dependence of the short-circuit on the materialparameters of the semiconductor for thin film bulk heterojunction solar cells.The following assumptions are suggested to give separate descriptions of thefield current and diffusion current:

• There is no recombination of excess carriers at the surfaces nor in thearea of a possible space-charge region.


• The recombination of volume carriers in the field-free regions is diffusion-controlled.

• The extraction of carriers at the semiconductor interface is infinitely fast.• The electrical field in a possible space-charge region is only taken intoaccount as a mechanism to sweep out minority carriers.

The starting point for the mathematical treatment is the continuity equation:

1edivj +

∂ρ

∂t= 0 . (5.22)

In the 1-dimensional case, the equation reduces to

1e

∂j

∂x+

∂ρ

∂t= 0 . (5.23)

Illumination of the semiconductor leads to charge carrier generation p∗, whichis enhanced by a carrier concentration Δp over the dark carrier concentrationp0, for a given generation rate G and recombination rate U :

∂ρ

∂t=

∂p∗

∂t− (G − U) . (5.24)

Combining (5.23) and (5.24) yields

1e

∂j

∂x+ G − U = 0 . (5.25)

When the minority concentration in the dark is small compared to the photo-generated and majority carriers, first order recombination is reasonable andthe recombination rate U is given by U = Δp/τ .

First, the drift current is calculated in the case of a constant electricalfield, as one would expect for very thin bulk heterojunction solar cells. If thewidth W of the active layer is similar to the drift length of the carrier, thedevice will behave as a MIM junction, where the intrinsic semiconductor isfully depleted. The current is then determined by integrating the generationrate G = −dP/dx over the active layer, where P is the photon flux:

P = P0e−αx , G = αP0e−αx , Pdr = P0 − P0e−αW ,

Pd = αP0

∫ W

0e−αxdx = P0

(−e−αW + 1

). (5.26)

Assuming loss-free sweep-out of the carriers due to the driving force of theelectrical field, the drift current is given by

jdr = eP0(1 − e−αW

). (5.27)

In the second stage, the diffusion current is taken into account. When thewidth of the active layer is increased beyond the field-driven regime, contri-


butions from diffusion processes will become more relevant. For the photo-generated diffusion current, the following equations are valid:

jdiff = −eDpdp∗

dx, Dp

d2p∗

dx2 + G − U = 0 ,

Dpd2p∗

dx2 + αP0e−αx − Δp

τ= 0 . (5.28)

The boundary conditions for the diffusion-controlled regime are p∗ = 0 atx = W and p∗ = p0 at x = ∞. With this set of boundary conditions, ananalytical solution is possible:

jdiff = −eP0αLp

1 + αLpeαW − ep0

Dp

Lp, (5.29)

where Lp = (Dpτ)1/2 is the minority carrier diffusion length and Dp is thediffusion coefficient.

Fig. 5.26. Schematic drawingof the absorption profile, en-ergy bands and diffusion anddrift current contributions, to-gether with the minority car-rier concentration of an n-type semiconductor under il-lumination

Figure 5.26 sumarizes the findings. Bulk heterojunction solar cells, espe-cially in the thin film limit, are expected to be dominated by the drift current.


However, for a realistic description, one must take into account both contri-butions, i.e., the drift and the diffusion current. In the following, a model forthe overall current will be discussed. Once again, assumptions are made toallow an analytical solution:

• There is no bimolecular recombination. This assumption is in good agree-ment with experimental data for the solar cells. Combined with the as-sumption that both components (p- and n-type semiconductors) havecomparable transport properties, hole and electron contributions to theoverall current can be treated separately.

• The electrical field across the junction is constant. The effect of photoin-duced charge carriers on the field distribution is neglected and calcula-tions are not performed self-consistently with the field.

• Boundary conditions are set to ensure that there is no hole current to thenegative electrode and no electron current to the positive electrode. It isfurther assumed that the current at the collecting electrode is dominatedby a field contribution and not by a diffusion current.

• The quantum efficiency for charge generation is taken as unity, in goodagreement with experimental data.

• Once again, the set of equations is only solved in one dimension, wherethe coordinate x represents the height of the device.

Under these assumptions, the transport equation can be solved analytically.The set of equations describing such a situation is:

transport equation: Dn′′[x] + μV

ln′[x] − n[x]

τ+ αNe−αx = 0 , (5.30)

boundary conditions: n[0] = −n′[0]0.025V/d

, n′[∞] = 0 . (5.31)

The following material parameters were used for the calculations:

α = 5 × 104 cm−1 , N = 3 × 1021 , V = 0.8 V ,

D =kT

qμ(T = 298 K) , (5.32)

where D is the diffusion coefficient, n[x] the local carrier concentration, μ themobility, V the built-in voltage, τ the recombination time, α the absorptioncoefficient, and d the total thickness of the device. The parameters d andμ are free variables and are varied for the calculations. Figure 5.27 showsa calculation of the possible short-circuit current in plastic solar cells. Thecalculations show a clearly observable peak for the maximum short-circuitcurrent versus the device thickness. Depending on the given mobility, thepeak shifts to larger values in the device thickness, thereby allowing theabsorption of more photons and yielding a larger total short-circuit current.

The calculations demonstrate a fundamental property of thin film solarcells made from low mobility materials: the film thickness has to match theproduct of the mobility and the lifetime (μτ) for the semiconductor.


0 100 200 300 400 5000

5

10

15

20

25

30

35

40 10-4 cm2/Vs

5*10-4 cm2/Vs

10-3 cm2/Vs

5*10-3 cm2/Vs

10-2 cm2/Vs

I sc [m

A/c

m2 ]

Device Thickness [nm]

Fig. 5.27. Calculated short-ciruit current for a drift-controlled device. The lifetimeof the carriers was kept constant while the mobility of the p-type semiconductorwas varied. The correlation between mobility and performance is plotted againstthe total thickness of the active layer. Isc(d) is calculated for the following mo-bility values: 10−4 cm2/V s, 5 × 10−4 cm2/V s, 10−3 cm2/V s, 5 × 10−3 cm2/V s,10−2 cm2/V s

• If the device is too thin, no losses will occur. On the other hand, a filmwhich is too thin will not absorb a sufficient fraction of the incominglight.

• If the device becomes too thick, all the light can be absorbed. However,the thickness of the device will exceed the free carrier length of the chargesand losses will occur.

Consequently, there has to be an optimum thickness for this type of device.The optimum thickness will depend on the transport properties of the semi-conductor. Semiconductors with better transport properties allow us to createthicker (more highly absorbing) devices without losses.

Combining the results from morphology and transport studies, the in-crease in interchain aggregates strongly affects the performance of photo-voltaic cells. The enhanced carrier mobility of the polymeric p-type semicon-ductor, together with the more intimate mixture of donors and acceptors inthe blend which leads to a higher density of charge generation centers, en-hance the power efficiency by a factor of 3. It is important to note that theinternal quantum efficiency of these solar cells is over 80%. This can be calleda nearly loss-free device. An important consequence of these considerationsis that the spectral mismatch between the polymeric semiconductors and thesolar spectrum is the most serious limitation. An expansion of the bandgaptowards lower energies is essential.


Fig. 5.28. Density of States in a semiconductor under illumination

5.3.4 Open-Circuit Voltage Voc

Solar cells are semiconductors under illumination, where the absorption oflight leads to a generation of carriers. After carrier generation, the excessenergy of the carriers (in the case of photons with energies larger than thebandgap of the carrier) will be lost by interaction with the lattice (phonons).After this thermalization process, the carriers are in equilibrium in theirbands before they are lost by recombination. Therefore the carriers will oc-cupy the available states of different energies according to a Fermi distribu-tion. However, this situation leads to a dilemma [113]. Under illumination,the electron and hole densities are larger than the corresponding dark carrierdensities. The increased electron density tends to shift the Fermi level closerto the conduction band, while the increased hole density tends to shift thecarrier density closer to the valence band. The solution to this dilemma is theintroduction of two Fermi distributions, one for the electrons and one for theholes. This concept is strictly valid for the semiconductor under illumination.The electron and hole densities are then given by

ne = NC exp(

−εC − εF,C

kT

), nh = NV exp

(−εF,V − εV

kT

), (5.33)

where NC and NV are the effective densities of states of the conduction andvalence bands, respectively. The product nenh then becomes

nenh = n2i exp

(εF,C − εF,V

kT

). (5.34)

Note that under these conditions the product nenh can exceed n2I , leading to

a situation which would be impossible for a dark semiconductor even underdoping. Figure 5.28 shows the two Fermi distributions in a semiconductorunder illumination. The discrepancy of the model becomes obvious in theenergy region between εF,C and εF,V, where the electron Fermi distributionfC demands the occupation of intraband states, while the hole Fermi dis-tribution fV demands the vacancy of such states. The model is neverthelessvery useful for obtaining a better understanding of the origin of the open-circuit potential in solar cells. Figure 5.29 shows the energy situation for an


illuminated semiconductor p–n junction in equilibrium (no current flowing).One can immediately see that the maximum available potential from such asemiconductor junction is limited by the difference between the two quasi-Fermi levels. This difference, εF,C − εF,V, will therefore be an upper limit forthe open-circuit voltage. Phenomena like surface recombination can result ina reduction of the open-circuit voltage, as depicted in Fig. 5.29.

Fig. 5.29. Energy bands and quasi-fermi levels of a p–n junction under illumination

For thin film photovoltaic devices, the built-in potential is an essential pa-rameter for several reasons: it influences charge dissociation, charge transportand charge collection. A generally accepted estimate for the built-in poten-tial is given by the open-circuit voltage Voc, which underestimates the built-inpotential at room temperature and converges to the correct value at low tem-peratures. Therefore, the question of the built-in potential is directly relatedto an extensively discussed phenomenon, the origin of the open-circuit voltageVoc. Mixing fullerenes with conjugated polymers into a composite active layercompletely modifies the nature of thin film devices compared to those madewith conjugated polymers alone [114,115]. Naturally, it also modifies the Vocof the corresponding solar cells. Therefore, it is not surprising that modelssuccessfully describing the situation in pristine conjugated polymer photodi-odes, like the MIM [116] or the Schottky junction [117,118] pictures, cannotsatisfactorily explain the observed Voc in conjugated polymer/fullerene-based(bulk heterojunction) solar cells.

In order to carry out a systematic investigation of the critical parame-ters influencing the built-in potential in conjugated polymer/fullerene bulkheterojunction solar cells, a series of highly soluble fullerene derivatives withvarying acceptor strength (i.e., first reduction potential) were tested. Theopen-circuit voltage of the corresponding devices as a function of the acceptorstrength can then be analyzed. These fullerene derivatives, methanofullerenePCBM [28], an azafulleroid and a ketolactam quasi-fullerene (Fig. 5.30), showa variation of almost 200 mV in their first reduction potential. Additionally,


O

O n

FullerenesMDMO-PPV

ITOPlastic foil

Ca, Ag, Al, Au

PEDOT-PSS

O

N

O

ONO

O

O

Light

Fig. 5.30. Chemical structures and device layout of investigated compounds andsolar cells

cells made with fullerene C60 were compared. It is important to emphasizethat, apart from C60, these acceptors have a comparable size to the solubi-lizing group. In this way, effects due to different donor–acceptor distancesand/or different morphologies should be minimized, as required for a com-parative study. Nevertheless, it is highly unlikely that the morphologies ofthe various active layers are identical. (This is unavoidable, however, since itis obviously impossible to alter the electron affinity of an acceptor componentwithout altering its structure!)

In the second part of this section, we investigate the possibility of influenc-ing the built-in potential of the photodiodes by varying the work function ofthe top (negative) electrode (i.e., the negative electrode, collecting electronsfrom the active layer). Four different metal electrodes are selected for thispurpose: calcium, silver, aluminum and gold, thus varying the work function


by more than 2 eV, while keeping the transparent positive front electrodematerial constant (i.e., a PEDOT:PSS layer on an ITO-coated support ma-terial).

0.0 -0.5 -1.0 -1.5 -2.0 -2.5

1.0x10-5

0.0

-1.0x10-5

-2.0x10-5

-3.0x10-5

-4.0x10-5

fulleroid 5

I (A

)

E (V)

ketolactam 6

PCBM

Fig. 5.31. Cyclic voltammograms of PCBM, azafulleroid 5 and ketolactam 6. Ex-perimental conditions were as follows: V vs. Ag wire, working electrode GCE,supporting electrolyte Bu4NPF6 (0.1 M), solvent ODCB/MeCN (4/1), scan rate100 mV/s

The variation of the energy position of the conduction band (LUMO ofthe molecules) of the different fullerenes can be monitored by electrochem-istry. The redox behavior of the various fullerene derivatives is determinedby cyclic voltammetry (CV), together with that of parent C60 and PCBM,all measured under identical conditions. The voltammograms are shown inFig. 5.31, and the data are tabulated in Table 5.2 for numerical comparison.All four CVs show four reversible reduction waves corresponding to the re-duction of the fullerene cage. However, the first reduction waves – indicativeof the electron acceptor strength of the compounds – show distinctive differ-ences. Ketolactam 6 (−0.53 V) appears to be a substantially better electronacceptor than C60 (−0.60 V) [119], whereas azafulleroid 5 (−0.67 V) is closeto C60, and PCBM (−0.69 V) shows a clearly diminished electron affinity.Hence, a difference of 160 mV is observed between the strongest and weakestacceptors. Since the reduction potential of a compound is generally solventdependent, it is the relative differences between the acceptor strengths of thefullerene derivatives that are important, rather than their absolute values. Inthe discussion below we will assume that the trend we found working withsolutions is also representative for fullerene derivatives in the solid state.

Variation of Acceptor Strength. Photovoltaic parameters were deter-mined under illumination with 60 mW/cm2 white light from a halogen lamp.


Table 5.2. Redox potentials (V vs. NHE) of C60 and fullerene derivatives. Ex-perimental conditions: reference electrode quasi-Ag/AgCl wire (calibrated with fer-rocene), working and counter electrodes Pt foils, supporting electrolyte Bu4NPF6(0.1 M), solvent ODCB/MeCN (4/1), scan rate 100 mV/s, room temperature

Compound E1red E2

red E3red

PCBM −0.69 −1.09 −1.57Azafulleroid (5) −0.67 −1.07 −1.52Ketolactam (6) −0.53 −0.93 −1.41C60 −0.60 −1.01 −1.46

0.55

0.60

0.65

0.70

0.75

0.80

0.85

V

oc [

V]

PCBM azafulleroid 5 ketolactam 6

Fig. 5.32. Voc for solar cells using PCBM, azafulleroid 5 and ketolactam 6 as theacceptor component in bulk heterojunction solar cells comprising MDMO–PPV aselectron donor

The value of Voc for a given device depends critically on the diode quality(i.e., film homogeneity, pin holes, shunts, and so on), so that statistical eval-uation is needed in order to find a representative value. More than 80 deviceswere produced from each acceptor type to allow a statistical evaluation ofthe observed open-circuit voltage. A box plot diagram was chosen to presentthe results from current/voltage (I/V ) measurements for the Voc (Fig. 5.32).The horizontal lines in the box denote the 25th, 50th, and 75th percentile val-ues. Error bars denote the 5th and 95th percentile values. The two symbolsbelow and above the 5th/95th percentile error bar denote the highest andthe lowest observed values, respectively. For all three acceptors presented, arelatively narrow distribution of the open-circuit voltage is observed, indi-cating excellent reproducibility: 75% of the devices made from each acceptorare distributed less than 40 mV from their average value. The highest andlowest average open-circuit voltages are observed for PCBM-containing cellsand for ketolactam-containing cells with 760 mV and 560 mV, respectively.


-1,5 -1,0 -0,5 0,0 0,5 1,0 1,51x10

-4

1x10-3

1x10-2

1x10-1

1x100 Al Electrode

Ca Electrode Au Electrode Ag Electrode

Pho

tocu

rre

nt [

mA

/cm

2]

Voltage [V]

0,0 0,5 1,0-1x10-1

0

1x10-1

2x10-1

3x10-1

4x10-1

5x10-1

Ph

oto

curr

ent [

mA

/cm

2 ]

Voltage [V]

Fig. 5.33. I/V curves for MDMO–PPV/PCBM photovoltaic devices with differentmetal electrodes. The inset shows the I/V curves on a linear scale

Variation of Top Electrode Material. PCBM was chosen as referenceelectron acceptor to investigate the influence of top (negative) electrodeswith different work functions on the built-in potential of conjugated poly-mer/fullerene bulk heterojunction plastic solar cells. Figure 5.33 shows theI/V curves of four typical devices using Ca (φMe = 2.87 eV), Al (φMe =4.28 eV), Ag (φMe = 4.26 eV) and Au (φMe = 5.1 eV) [120] as negative elec-trodes on a logarithmic scale. A total variation of less than 200 mV of Vocis observed for a variation of the negative electrode work function by morethan 2.2 eV. For devices with an Au electrode, Voc is found to be slightlylower than the average value, but still as high as 650 mV. The Ca devicesexhibit a Voc value of 814 mV. It is interesting to note that the flow directionof the short-circuit current (i.e., the polarity of the device) is not reversedin the case of the Au electrode, as would be expected for a MIM devicedue to the nominally slightly higher work function of Au compared to theITO/PEDOT:PSS electrode on the other side. In this device, holes still flowtowards the ITO/PEDOT:PSS electrode (positive electrode), while electronsare still collected at the Au electrode (negative electrode). The observationthat the short-circuit current Isc for the Au devices is clearly lower than forcomparable devices with other electrodes will be discussed later.

Experimental results on the variation of the acceptor strength and on thevariation of the top electrode work function are summarized in Figs. 5.34a


-0.70 -0.65 -0.60 -0.55

0.55

0.60

0.65

0.70

0.75

0.80

0.85

S1 = 0.95

Vo

ltag

e [V

]

E1Red [V]

PCBM

azafulleroid 5 C60

ketolactam 6

(a)

2.5 3.0 3.5 4.0 4.5 5.0 5.50.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

S2 ~ 0.1

Vo

ltag

e [V

]

Work function [eV]

(b)

Fig. 5.34. (a) Voc versus acceptor strength and (b) Voc versus negative electrodework function. The slopes S1 and S2 of the linear fits to the data are indicated

and b. Figure 5.34a shows the highest observed Voc value versus the acceptorstrength for devices using PCBM, C60, azafulleroid 5 and ketolactam 6 aselectron acceptors. The data points are fitted to a linear model, and a slopeof S1 ≈ 1 is derived from the fitting procedure. The fact that a slope of unityis observed emphasizes the strong coupling of Voc to the reduction strength ofthe acceptors, as expected for the ideal case of Ohmic contacts between thevarious fullerenes and the Al contact. Deviations from this ‘ideal behavior’might occur since the reduction strength of the acceptors plotted on the x-axis in Fig. 5.34a are taken from electrochemical data in solution and notfrom thin solid films.

The influence of the work function of the negative electrode on the value ofVoc for MDMO–PPV/PCBM solar cells is shown in Fig. 5.34b. It is importantto note that the x-axis now covers more than 2 eV. Once again, a linear modelis fitted to the experimental data and a slope of S2 ≈ 0.1 is calculated asthe best fit. This result shows that the work function of the metal has aconsiderably weaker effect on the Voc values than the reduction potential.

In order to understand this behavior, we introduce a concept developedto explain the built-in potential for inorganic semiconductor/metal interfacesand which is based on the index of interface behavior S [121]. This parameterS is defined as the slope in a diagram, where the blockade potential of asemiconductor/metal interface is plotted against the work function of themetal:

qVB = S(φM − φSC) + C , (5.35)

where qVB is the interface barrier, φM and φSC are the work functions of themetal and the semiconductor, respectively, and C is a constant describingthe interface potential for the ideal Ohmic contact. From the results pre-sented above (Fig. 5.34), the following equation for the open-circuit voltageis proposed:

Voc =(Aox − S1Ered(A)

)− S2

(φM − Ered(A)

)+ C , (5.36)


where Ered(A) is the reduction potential of the acceptor (fullerene derivative)and S1 and S2 are the slopes calculated from Fig. 5.34. Aox is a constant rep-resenting all the contributions from the positive electrode to Voc, expected tobe properly described by the oxidation potential of the conjugated polymer.The negative sign in front of the second term of (5.36) takes into account thefact that this contribution works as a counter diode. Since the parameter S2is found to be sufficiently small (S2 < 0.1), it can also be neglected for theopen-circuit voltage. This leads to

Voc =(Aox − S1Ered(A)

)+ C , (5.37)

which yields a good estimate for the experimental results. Comparing equa-tions (5.36) and (5.37), the slope S2 of the linear fit calculated from Fig. 5.34bresembles the index of interface behavior S. According to this idea, the obser-vation of a slope as low as 0.1 in Fig. 5.34b suggests a mechanism called Fermi-level pinning [121]. In such cases, the work function of the metal is pinned tothe work function of the semiconductor (typically via surface states), regard-less of whether the work function of the metal is higher or lower than theFermi level of the semiconductor. Figure 5.35 summarizes the classificationof inorganic semiconductors.

Fig. 5.35. Interface behavior of various semiconductors

In addition, the presence of surface charges leads to band bending at thesemiconductor–metal interface. For n-type semiconductors, these states areacceptor-like and the semiconductor at equilibrium may exhibit upward (neg-ative) band bending as the surface Fermi level moves towards the charged


states. For a p-type semiconductor with donor-like surface states, the semicon-ductor at equilibrium would exhibit downward band bending as the surfaceFermi level moves towards the charged states. For the photodiodes presentedin this study, it seems that the Fermi level of the negative electrode metal maybe pinned to the reduction potential of the fullerene. Firstly, the correlationbetween the open-circuit voltage and the reduction potential of the acceptor(Fig. 5.34a) proves that the energy alignment of the metal is related to thelowest unoccupied molecular orbital (LUMO) energy states of the acceptorand not those of the polymer. Secondly, recent XPS (X-ray photoemission) re-sults [122,123] on C60 mono- and multilayers on different metals with variouswork functions clearly demonstrate that there is considerable charge trans-fer to C60 adsorbed on metal surfaces. The alignment of the ground stateenergies is determined by the interface dipole, i.e., bond formation in thefirst layer, which produces the induced Fermi-level alignment of the chargedstate with the substrate. Surface states in organic semiconductors are un-likely, due to the weak bonding forces between molecular units. However,fullerenes with their cage-like π electron system and their strong tendencyto crystallize may be different, exhibiting strong charge transfer (up to 1.8electrons per fullerene) at fullerene/metal interfaces [124]. It is beyond theaim of this chapter to speculate on the nature of the charged states for thinspin-cast films of fullerenes, which is still under discussion for UHV grownfilms [125–127]. The presence of large interface dipoles between metals andorganic semiconductors is also relevant for many other small molecules [128].

Assuming that the mechanism of Fermi-level pinning dominates contactformation at the negative electrode of the photodiodes, the qualitative dif-ference between the Au electrode and Ca, Ag and Al electrons can be betterunderstood. While the low work function of Ca, Ag and Al (φME < 4.3 eV)will favor Ohmic contacts with fullerenes (EFermi C60 ≈ 4.7 eV), Au is theonly one to form Ohmic contacts with a hole-transporting conjugated poly-mer like MDMO–PPV, due to its high work function (φAu ≈ 5.1 eV). Theother three metals are known to form rectifying (blocking) contacts with theholes in a conjugated polymer [38,39].

For the devices presented in this study, it was shown above that the pin-ning of the metal work function to the fullerene reduction potential promotesa quasi-Ohmic contact between the metal and the fullerene even for a Au elec-trode (preceded by charge transfer between the metal and the first fullerenemonolayer, yielding an interfacial dipole layer). For the proper functioningof a photodiode, asymmetric contact conditions are essential. At the nega-tive electrode, an Ohmic contact with the electron-transporting phase of thedonor–acceptor composite is favorable, while the holes should be blocked (rec-tifying contact). This condition seems to be fulfilled for the photodiodes witha Ca, Ag or Al negative electrode, due to the low value of the work functioncompared to the Fermi level of the fullerenes. In the case of the Au nega-tive electrode, Ohmic contacts may be formed with both the fullerene phase


and the conjugated polymer phase. Such a contact will enhance surface re-combination, thereby reducing the short-circuit current and the open-circuitvoltage.

An interesting consequence of this explanation of the observation that theAu contact with the conjugated polymer phase is a rectifying contact for theAu-PSC is the occurrence of a dipole layer at this interface with a reversedsign compared to the Al, Ca, and Ag electrodes. This results in positivelycharged states on the fullerene for the Au contact and negatively chargedstates on the fullerene for the other contacts with higher work functions. Anopen question is the nature of the charges responsible for the alignment. Theformation of space-charge layers at the electrode/polymer interface [129] dueto doping of the semiconductor by metal ions can lead to these local potentialsinfluencing the open-circuit potential. Such ‘doping’ during the evaporationof the metal electrode is expected for reactive metals like Ca or Mg, whilstthis mechanism is unlikely for Au.

The experiments discussed here clearly motivate the idea that the open-circuit voltage in bulk heterojunction solar cells is directly related to theacceptor strength of the fullerenes. This result fully supports the view that theopen-circuit voltage of this type of donor–acceptor bulk heterojunction cell isrelated directly to the energy difference between the HOMO level of the donorand the LUMO level of the acceptor components. Furthermore, and also in fullagreement with this view, it is found that a variation of the negative electrodework function influences the open-circuit voltage only in a minor way. Thiselectrode-insensitive voltage behavior is specific to the negative electrode inpolymer/fullerene bulk heterojunction solar cells and is discussed in terms ofFermi-level pinning between the negative metal electrode and the fullerenereduction potential via charged interfacial states.

5.3.5 Fill Factor FF

For practical solar cells, the ideal equivalent circuit will be modified to includethe series resistance from Ohmic loss in the two electrodes and the shuntresistance from leakage currents (Fig. 5.36a). The diode current for a realisticsetup is then given by

ln(

I(V ) + Isc

I0− V − IRs

I0Rp+ 1

)=

q(V − IRs)nkT

, (5.38)

where I0, Rs, Rp, n and q/kT are the saturation current density, the serialand parallel resistivity, the diode ideality factor and the temperature poten-tial (25 mV at room temperature), respectively. Plots of this equation withdifferent combinations of Rs and Rp are shown in Fig. 5.36b–d. It can beseen that a low shunt resistance mainly influences the FF through a shiftof the MPP, but it also influences the open-circuit voltage if it leads to realshunting of the device. The influence of Rp on Isc is typically negligible. The


influence of the series resistance on the FF is generally more dramatic sinceit tilts the whole I/V curve around the Voc point. Voc remains unchanged. Ifthe series resistance becomes large enough, even Isc will be lowered.

-2 -1 0 1 2 3 4 5

-1,0

-0,5

0,0

0,5

1,0

1,5

JSC

VOC

V

J SC

Ideal case:RP=∞, RS=0Ω

(b)0 1 2 3 4 5

5

0

5

0

5

0

5

V1OC

V2OC

JSC

V

Reduced VOC :RP-small, RS=0Ω

(c)-1 0 1 2 3 4 5

,5

,0

,5

,0

,5

,0

J2SC

VOC

J1SC

V

Reduced JS C:RP=∞, RS =large

(d)

Rp

Rs

JL

JDiodeJRp

J

(a)

Fig. 5.36. (a) Equivalent circuit for a solar cell. The parallel resistivity Rp resem-bles all shunts while the serial resistivity resembles the bulk resistivity of the activearea, contact resistivity and circuit resistivity. (b) Ideal I/V characteristics in the4th quadrant for a solar cell with a negligible Rs and an infinite Rp. (c) I/V char-acteristics in the 4th quadrant for a solar cell with a small Rp and a negligible Rs.(d) I/V characteristics in the 4th quadrant for a solar cell with an infinite Rp anda large Rs

Recent advances in the development of electrodes for bulk heterojunctionsolar cells [130] involve a strategy of incorporating a small amount of LiF atthe interface between the photoactive layer and the aluminum cathode. Thistechnique has previously been used to enhance the performance of organiclight-emitting diodes for devices fabricated either by thermal deposition oflow-molecular-weight compounds [131–133] or by solution-casting of polymers[134,135]. In this section, the performance of bulk heterojunction photovoltaicdevices with respect to the FF is studied as a function of the LiF thickness.Emphasis is put on the quality of the contact. Insertion of thin layers ofLiF (< 15 A) are discussed as a way of increasing both the open-circuitvoltage and the fill factor of the device, yielding an increased power conversionefficiency.


Although LiF/Al electrodes are already widely used for enhancing the effi-ciency of electron injection electrodes for OLEDs, the underlying mechanismsare worth discussing. Several mechanisms can be suggested:

• lowering of the effective work function of the aluminum,• dissociation of the LiF and subsequent chemical reaction (doping) of theorganic layer,

• formation of a dipole layer leading to a vacuum level offset between theorganic layer and the Al,

• protection of the organic layer from hot Al atoms during thermal depo-sition.

For solar cells, the fill factor FF determines the position of the maximumpower point in the 4th I/V quadrant of the illuminated diode and is thereforea quality sign of the photodiode. Besides the increased efficiency, the FF ofa photodiode is also important when evaluating the proper function of thediode. High FF values are expected only for diodes with a strict selectionprinciple for the separation of positive and negative carriers. There are severalloss mechanisms for photodiodes that can reduce the FF in a photodiode:

• counter diodes, leading to a negative curvature of the I/V line in the 4thquadrant and resulting in an FF below 25%,

• high serial resistivities lower the FF by flattening the I/V curve in the4th quadrant, thereby reducing the short-circuit current but leaving theopen-circuit voltage unchanged,

• low parallel resistivities, resulting in reduced open-circuit voltages andlower FF.

A significant increase in the forward current and in the FF is observed forconjugated polymer/fullerene bulk heterojunction solar cells upon insertionof a thin layer of LiF between the organic layer and the Al electrode (negativeelectrode of the solar cell), as shown in Fig. 5.37a and b.

Once again, a box plot diagram is chosen to present the results from cur-rent/voltage (I/V ) measurements for the FF (Fig. 5.37b) and Voc (Fig. 5.37c).At least 6 different devices were evaluated for each LiF thickness, the latterbeing varied between 0 A and 15 A. Upon insertion of only 3 A of LiF, theFF already increased by about 20% compared to otherwise identical referencedevices with a pristine Al electrode. Together with an Isc of 5.25 mA/cm2 anda Voc of 825 mV, the white light power conversion efficiency under 800 W/m2

at 50◦C is calculated to be 3.3%. (Note that this is a white light efficiencywhich is not corrected by a spectral mismatch factor M .)

Further increase of the layer thickness (up to 9 A) does not change theaverage value of the FF, but considerably narrows the distribution of the FFof the individual devices. At a LiF layer thickness of 12 A, a slight decreaseis observed in the FF and at a layer thickness exceeding 20 A, the beneficialinfluence of the LiF layer on the FF is lost due to the high resistivity of theLiF layer.


0.0 0.2 0.4 0.6 0.8 1.0-6

-4

-2

0

2

4

6

3 Ang. 6 Ang. 12 Ang. No LiFC

urre

nt D

ensi

ty [m

A/c

m²]

Voltage [V]

(a)

1.0 1.2 1.4 1.6 1.8 2.00

50

100

150

200

250

Cur

ren

t De

nsi

ty [m

A/c

m²]

Voltage [V]

LiF-3A LiF-6A LiF-12A No LiF0.48

0.50

0.52

0.54

0.56

0.58

0.60

0.62

0.64

LiF Thickness [A]

Fill

Fac

tor

[%]

(b)

LiF-3A LiF-6A LiF-12A No LiF

760

780

800

820

840

LiF Thickness [A]

Vo

c [mV

]

(c)

Fig. 5.37. (a) I/V characteristics of typical MDMO–PPV/PCBM solar cells witha LiF/Al electrode of various LiF thicknesses (� 3 A, • 6 A, � 12 A) compared to theperformance of a MDMO–PPV/PCBM solar cell with a pristine Al electrode (�).(b) and (c) are box plots with the statistics of the FF and Voc from 6 separate solarcells. LiF or SiOx were thermally deposited at a rate of 1–2 A/min from a tungstenboat in a vacuum system with a base pressure of 10−4 Pa. We emphasize that,for thickness values of the order of 1 nm, LiF/SiOx does not form a continuous,fully covering layer, but instead consists of island clusters on the surface of thephotoactive layer. Slow evaporation conditions are essential for more homogenousdistribution of the LiF on the organic surface. The nominal thickness values givenhere represent an average value across the surface of the substrate. The metalelectrode (either aluminum or gold) was thermally deposited with a thickness of80 nm


SiOx-3A SiOx-3A SiOx-3A LiF-6A760

780

800

820

840

SiOx Thickness [A]

Vo

c [mV

]

(c)

SiOx-3A SiOx-6A SiOx-12A LiF-6A0.45

0.50

0.55

0.60

0.65

SiOx Thickness [A]

Fill

Fac

tor

[%]

(b)

0.0 0.2 0.4 0.6 0.8 1.0-6

-4

-2

0

2

4

6

3A SiOx 6A SiOx 12A SiOx 6A LiFC

urr

en

t de

nsi

ty [

mA

/cm

²]

Voltage [V]

(a)

1.0 1.2 1.4 1.6 1.8 2.00

50

100

150

200

Cur

rent

den

sity

[mA

/cm

²]

Voltage [V]

Fig. 5.38. (a) I/V characteristics of typical MDMO–PPV/PCBM solar cells withSiOx/Al electrodes with various SiOx thicknesses (� 3 A, • 6 A, � 12 A) comparedto the performance of an MDMO–PPV/PCBM solar cell with an LiF/Al electrode(� 6 A LiF). (b) and (c) are box plots with the statistics of the FF and Voc from6 separate solar cells

Thin layers of SiOx were evaporated as an inert reference interfacial layerbetween the organic layer and the Al electrode, in order to investigate theimportance of the interfacial layer as a buffer preventing reactions betweenthe hot, incoming Al atoms and the organic compounds during thermal de-position of the Al. Figure 5.38 shows the I/V behavior under illuminationand the statistics on the FF and Voc for devices with SiOx layers between 3 Aand 12 A. As a reference, results are compared with those for the 6 A LiF/Alelectrode in Fig. 5.37. No enhancement of any of the power characteristics ofthe photodiode is observed upon insertion of a SiOx layer as an inert buffer.From this one can conclude that the beneficial effects of LiF insertion cannotbe explained by an insulating buffer function.

The question arises as to whether Al is a necessary component in theenhancement of the photodiode properties upon insertion of a thin LiF layer.


-1 0 110-5

10-4

10-3

10-2

10-1

100

101

102

103

LiF, darkLiF, illuminated

Cur

rent

den

sity

[mA

cm

-2]

Voltage [V]

Fig. 5.39. I/V plot of a typical MDMO–PPV/PCBM bulk heterojunction solarcell with a Au electrode (continuous line) and an LiF/Au electrode (dotted line),respectively, in the dark and under illumination

This can be investigated by comparing devices where the LiF layer is coveredby a Au electrode instead of an Al electrode. The typical I/V characteristicshown in Fig. 5.39 reveals a clear difference upon insertion of a 6 A thinLiF layer beneath the Au electrode. Most strikingly, Voc is found to increaseto values as high as 770 mV, which are otherwise only obtained when us-ing metals with a lower work function. The FF increases from about 50%up to > 55%. In addition, the short-circuit current is observed to increase(4.1 mA/cm2), in good agreement with the expectations for a more selectivediode contact, i.e., better Ohmic resistance to electrons (PCBM) and betterblocking to holes (MDMO–PPV) [136]. The white light power efficiency ofthe MDMO–PPV/PCBM diodes with a LiF/Au electrode under 800 W/m2

at 50◦C is calculated to be 2.3%. Table 5.3 summarizes the average FF andVoc for the various diodes.

A numerical fitting analysis to the I/V curves can be applied to evaluatethe observations in terms of diode parameters. The current equation of anideal Schottky diode [137] is rewritten from (5.38), viz.,

I(V ) = I0

[exp

q(V − IRs)nkT

− 1]+

V − IRs

Rp+ Isc , (5.39)

and fitted to measured I/V curves by a recursive algorithm, allowing us toextract the diode parameters. For all diodes, excellent fits can be generatedwith this diode model. The calculated values for the serial resistivity Rs andthe shunt resistivity Rp are also summarized in Table 5.3. While there islittle or no change in the shunt resistivity for any of the diodes, their serialresistivities are lowered by a factor of 3–4 upon insertion of a thin LiF layer,regardless of the evaporated metal. This lowering of the serial resistivity isresponsible for the increase in the FF due to formation of a better Ohmiccontact, as discussed previously.


Table 5.3. Solar cell characteristics (FF and Voc) of MDMO–PPV/PCBM bulkheterojunction devices for various interfacial layers (LiF, SiOx) with different thick-nesses compared to a solar cell with a pristine Al electrode, and also calculated diodecharacteristics Rs and Rp found using (5.39) for the various interfacial layers

Voc [mV] FF [%] Rs [kΩ] Rp [kΩ]

No spacer 759 53 1.0e-002 1.2LiF [A]3 821 61.1 4.0e-003 1.16 834 63.2 3.8e-003 1.39 814 59.2 4.2e-003 1.212 832 58.8 5.1e-003 1.215 791 49 4.9e-003 1.2SiOx [A]3 794 52.2 1.7e-002 1.16 788 51.5 1.6e-002 0.912 796 49.8 1.7e-002 1.0Au 620 51 8.0e-003 0.7LiF(6 A)/Au 763 54 2.9e-003 0.9

While it is essential for OLEDs to form a low-barrier, efficient electron-injecting contact with the conjugated polymer, this contact side is determinedin bulk heterojunction solar cells by the matching between the quasi-Fermilevel of the fullerene and the metal work function, as discussed previously. Analignment between the work function of the metal and the quasi-Fermi levelof the fullerene can be obtained irrespective of the work function of the evap-orated metal, and quasi-Ohmic contacts are formed with the fullerene phasevia surface state interaction. The quality of the contact is merely determinedby its contact resistivity and by hole-blocking properties. LiF has been shownin this chapter to significantly reduce the contact resistivity. In the following,a combined mechanism is proposed to obtain a better understanding of thisbehavior.

Due to the strong dipole moment of LiF (6.3 D) [138], even a monomolec-ular layer of LiF can cause a significant vacuum level offset [139]. This shift ofthe vacuum level is well known in the field of surface science for the depositionand adsorption of molecules on metal surfaces [139–141]. This phenomenonresults in a change in the work function (or surface potential) of the metal,as has been verified for LiF/Al electrodes by ultraviolet photon spectroscopy(UPS) [133] and Kelvin probe measurements [142]. It is important to notethat these techniques revealed a lowering of the Al work function, i.e., adipole moment directed from the metal, when LiF was evaporated on top ofAl under conditions in which a dissociation of the LiF is not expected (lowevaporation rates, UHV). The improved electrode properties (i.e., loweringof the metal work function or shifting of the molecular levels towards higherenergies) can thus be explained by an alignment of LiF resulting from the Li+


adhering preferentially to the organic surface and the F− pointing towardsthe metal surface. UPS studies confirm that such a mechanism exists for smallmolecule/LiF/Al interfaces [143]. It is important to note that embedding ofmolecular dipoles in the form of organic monolayers at metal/inorganic semi-conductor (e.g., Ge, Si or n-GaAs) interfaces shows qualitatively the sameeffect as insertion of LiF at the interface between a metal and an organicsemiconductor [144].

Additionally, the possibility has to be considered that some amount ofthe LiF dissociates during the subsequent thermal deposition of Al. Mea-surements on small molecule/LiF/Al interfaces using secondary ion massspectroscopy (SIMS) suggest that thermal deposition of Al onto LiF in thepresence of water results in several possible reaction pathways leading tothe formation of free Li [142]. This free Li can then diffuse into and dopethe underlying organic material, which reduces the interface barrier height.Whether or not this scenario occurs in addition to the formation of inter-face dipoles in the present material system of MDMO–PPV:PCBM/LiF/Alis difficult to say. Dissociation of the LiF by way of chemical reactions thatlead to charge transfer across the interface can produce an interface dipolein much the same way as intact LiF molecules. In the case of the LiF/Aucathode, the reaction pathways leading to the production of free Li are notclear, and it is possible that the observed enhancement is entirely due to thedipole moment of intact LiF molecules. However, it is interesting to realizethat doping of the underlying organic layer is not the only mechanism toincrease the fill factor – interface alignment via dipole formation can also beused as a method for improving the quality of a contact.

The white light efficiency of conjugated polymer/fullerene bulk hetero-junction solar cells can be significantly enhanced by using LiF/Al electrodesinstead of pristine Al electrodes alone, due to an increase in the FF of up to20%. The increase in the FF is explained by a lowering of the contact resis-tivity between the organic layer and the negative metal electrode. A similarenhancement is observed for LiF/Au electrodes. The formation of a dipolemoment across the junction, due to either orientation of the LiF or chem-ical reactions and subsequent doping leading to charge transfer across theinterface, are identified as possible mechanisms for enhancing the FF of bulkheterojunction solar cells.

5.3.6 Spectral Response

Efficient harvesting of the terrestrial solar spectrum by conjugated polymer-based solar cells requires low bandgap polymers with a bandgap < 1.8 eVto guarantee further progress in organic photovoltaics [1,3,6,8,9,29,86,145–147]. Figure 5.40 shows the solar spectrum and the absorption spectrum ofa bulk heterojunction solar cell comprising MDMO–PPV and PCBM. Thespectral mismatch between the bandgap of organic semiconductors and thesolar spectrum is obvious and provides strong motivation for exploring the


potential of low bandgap systems. The photophysics of such low bandgapconjugated polymers and their excited state interactions with electron ac-ceptors like fullerenes are all-important when they are used in photovoltaicdevices.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.20

1x1021

2x1021

3x1021

4x1021

Spe

ctra

l pho

ton

flux

× 1

021

(n ph

s-1 m

2 μm

-1)

Wavelength (μm)

0

20

40

60

80

100AM1.5

MDMO-PPV:PCBM abs

% of total ph

oton flu

xin

teg

rate

d from 0 n

m

Fig. 5.40. Photon density and integrated photon density of the AM 1.5 spectrumcompared to the absorption spectrum (arbitrary units) of a MDMO–PPV/PCBMbulk heterojunction composite

Requirements for such polymers (either p- or n-type) are manifold:

• high absorption in the wavelength region of the solar spectrum,• high efficiency for production of photoinduced charges,• metastability for holes,• high mobility for holes.

Since a single polymer may not fulfill all these requirements, it is worth con-sidering the idea of transferring some of the tasks to other materials. In thissection we present a prototype p-type low bandgap polymer PTPTB, consist-ing of alternating electron-rich N -dodecyl-2,5-bis(2′-thienyl)pyrrole (TPT)and electron-deficient 2,1,3-benzothiadiazole (B) units. The bandgap of thispolymer, determined by electrochemistry and optical absorption, is 1.6 eV.The performance of the photovoltaic devices is discussed in terms of spectrallyresolved photocurrent measurements, AM1.5 measurements and temperaturedependent I/V spectroscopy. We discuss strategies for using this polymer inbulk heterojunction tandem solar cells either with a wide bandgap polymeror in conjunction with strongly absorbing small-molecule dyes.


Also very attractive is the idea of blending polymers with different band-gaps within one single layer, thus producing a variation on the tandem cell.In contrast to classical tandem cells, only the current would be added up insuch a multiple bandgap blended device, while the open-circuit voltage wouldbe determined by the polymer with the smaller bandgap. Further, we discussthe possibility of spectrally doping the low bandgap polymer by mixing witha strongly absorbing dye. This idea is attractive due to the large absorptioncoefficient of the dopant dyes. Absorption coefficients of 2 × 105 cm−1 arecommon for such dyes, allowing us to cast ultrathin films (30 nm or less) whichabsorb 100% of the incoming light. Nile red is used as dopant dye in this study.Figure 5.41 summarizes desirable photophysical processes in such blendedcomposites. From the scheme it is clear that transport properties of the lowbandgap polymer (LBP) are decisive for device performance, regardless ofwhether sensitization is performed via energy or electron transfer reactionsfrom the dye.

Dye + LBP +

(b) Charge transfer:

Dye LBPHOMO

LUMO

HOMO

LUMO

SDye* + acceptor Dye+ + acceptor– Dye+ + LBP

transport out of device - holes along LBP - electrons along acceptor

SDye* + LBP Dye + SLBP* SLBP* + acceptor LBP+ + acceptor–

Dye LBP

HOMO

LUMO

HOMO

LUMO transport out of device - holes along LBP - electrons along acceptor

(a) Energy transfer:

( )61 /rRk odFet−=τ νννενα d)()(FR ado

4

0

6 −∞

∫=

Fig. 5.41. Schematic overview of different strategies for spectral sensitization ofbulk heterojunction solar cells utilizing a low bandgap polymer. (a) shows thescenario for an energy transfer between the dye and the low bandgap polymer,while (b) illustrates the scenario for an electron transfer between the dye and thelow bandgap polymer


The structure of the low bandgap polymeric semiconductor and the dop-ant dye is plotted in Fig. 5.19. The average thickness of the active layers,determined by AFM measurements, is between 80 and 110 nm. In order toobtain a better understanding of the transport behavior of polymer blends,low temperature studies of cells with pristine MDMO–PPV and MDMO–PPV/PTPTB 1:1 (wt.%) with Au electrodes were carried out. Au has ahigh work function and should therefore be a good hole injection contact andprovide a high barrier for electron injection. The device will therefore be ahole-only device, as described earlier in this chapter [14].

10-2

10-1

100

101

102

under AM 1.5 condition

PTPTB/PCBM PTPTB/PCBM +10 % nile red PTPTB/PPV/PCBM 0.5/0.5/4

Cu

rre

nt [

mA

/cm

2 ]

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.010-5

10-4

10-3

10-2

10-1

100

101

102

in the dark

Voltage [V]

Fig. 5.42. I/V curves under AM 1.5 conditions (top) and in the dark (bottom)for a device with PTPTB/PCBM 1/3, PTPTB/PCBM 1/3 +10% Nile red, andPTPTB/MDMO–PPV/PCBM 0.5/0.5/4, as indicated

Figure 5.42 shows the I/V curves of a bulk heterojunction device madefrom PTPTB/PCBM (1:3 wt. ratio). The low rectification of the device(around 100 at ±2 V) reflects the rather poor film-forming properties ofPTPTB, which are induced by the low average polymer length distribution(5–16 aromatic units, as determined by size-exclusion chromatography). Un-der simulated AM1.5 illumination, a strong photoeffect is observed in theI/V curve. The open-circuit voltage of 0.72 V is just 0.1 V less than inthe highest values observed for MDMO–PPV/fullerene devices, although thebandgap of PTPTB is reduced by 0.6 eV compared to MDMO–PPV. The ob-


servation of similar open-circuit voltages for devices with identical acceptorsbut polymers with different HOMO levels (around 0.4 eV offset) indicates aninfluence of the metal electrode (ITO/PEDOT) on the electrical potentialsat the positive electrode/semiconductor interface. Therefore no limitation inthe use of low bandgap materials in polymer solar cells can be seen as long asthe right electrodes are provided. The short-circuit current Isc is measuredwith 3 mAcm−2 and the fill factor FF is calculated to be 0.37. From thesevalues, the power conversion efficiency ηAM 1.5 is calculated to be about 1%.The photovoltaic parameters of all devices are also summarized in Table 5.4.

Table 5.4. PV performance parameters of various bulk heterojunction devicescomprising a low bandagap p-type polymer PTPTB under AM 1.5 conditions

Active layer Voc [V] Isc FF R [±1 V] ηe(AM 1.5)[mA cm−2] (dark) [%]

PTPTB/PCBM 1/3 0.72 2.95 0.37 23 1

PTPTB/PCBM + 0.53 2.25 0.32 55 0.4810% Nile red 1/3

PTPTB/PPV/PCBM 0.51 1.0 0.3 2 008 0.20.5/0.5/4

PPV/PCBM 1/4 0.81 4.9 0.6 140 3.0

While the short-circuit current of the device is already satisfyingly high,the overall efficiency of the device is limited by the low fill factor. Gener-ally, low FF values can be induced by high series resistances or by smallshunt resistances. For PTPTB/PCBM devices, the series resistance is below10 ohmcm−2, which cannot explain the low FF. Therefore, the low FF isexplained by the fact that the parallel resistance in the device is too low.The nature of the shunt is still under discussion, but AFM measurements(Fig. 5.43) on the surface of the photoactive layer show films with a surfaceroughness of around 5 nm, i.e., one order of magnitude higher than observedfor MDMO–PPV/PCBM devices [146]. Most probably, it is the low molecularweight of the polymer, together with partial phase incompatibility betweenPTPTB and PCBM, which induces the low film quality. Other mechanismsresponsible for the reduction of the FF include field dependent recombinationprocesses, probably induced by the energetically close positions of PTPTB−

and PCBM−, thereby reducing the selectivity of the negative contact in sep-arating holes and electrons.

Figure 5.44a compares the spectrally resolved photocurrent IPCE and thequantity of absorbed photons. The spectral photocurrent of PTPTB/PCBMpeaks at 600 nm and contributions to the IPCE are observed down to 750 nm,evidencing the low bandgap of PTPTB.


Fig. 5.43. AFM picture of PTPTB/PCBM 1/3 blend with highest efficiency. AFMin tapping mode

0

5

10

15

20

25400 500 600 700 800

spectral photocurrent

IPC

E [%

]

0

20

PTPTB/PCBM 1/3

(a) absorbed photons

Absorbed P

hotons [%]

0

2

4

6

8

10

PTPTB/PCBM 1/3+ 10 % nile red

(b)

0

20

400 500 600 700 8000

2

4

6

8

10

PTPTB/PPV/PCBM 0.5/0.5/4

(c)

wavelength [nm]

0

20

40

Fig. 5.44. Spectrally resolved photocurrent (IPCE) (continuous curve) and ab-sorbed photons (dot-dashed curve) of the active layer (measured in transmis-sion) of (a) PTPTB/PCBM 1/3, (b) PTPTB/PCBM 1/3 +10% Nile red, (c)PTPTB/PPV/PCBM 0.5/0.5/4


Upon blending 10 wt.% of a highly absorbing, small molecular dye (Nilered) into the photoactive PTPTB/PCBM blend, no major changes are ob-served in the dark I/V characteristics (Fig. 5.42b). Only the onset for in-jection in the forward direction is slightly lowered. Under illumination, theopen-circuit voltage is found to be reduced from 0.72 to 0.53 V with addi-tion of the dye. The photoactivity of the dye is evidenced by the spectralphotocurrent measurements (Fig. 5.44b). The maximum of the spectrally re-solved photocurrent and the maximum absorption are both shifted to 550 nm,i.e., the absorption maximum of the dye. The contribution of PTPTB to thephotocurrent is still in the region between 600 to 750 nm, which is strikinglysimilar in shape to the PTPTB/PCBM device. Although it can be shown thatthe absorbing compounds, the conjugated polymer and the small moleculardye, both contribute to the photocurrent, the overall performance of the de-vice is slightly lowered. The primary photoreaction in this three-componentsystem, either energy transfer from Nile red to PTPTB and subsequent elec-tron transfer from PTPTB to PCBM or mutual electron transfer from bothabsorbers (Nile red and PTPTB) to PCBM, is still under investigation. It isclear, however, that positive charges on Nile red photogenerated in the sec-ond reaction pathway would demand at least one additional transport stepvia an inefficient hopping process.

A blended composite of MDMO–PPV, PTPTB and PCBM in a wt. ratioof 0.5:0.5:4 is used as photoactive layer to investigate the polymer mixtureapproach. The beneficial effect on the diode quality of mixing MDMO–PPVinto the PTPTB/PCBM composite (Fig. 5.42b) is demonstrated by a higherforward and lower reverse current. This leads to an overall increase in the rec-tification for this device by more than an order of magnitude. However, underillumination this device shows reduced Voc, Isc and even FF as compared tothe PTPTB/PCBM reference device. The spectrally resolved photocurrentof the polymer mixture device (Fig. 5.44c) is dominated by the contributionof MDMO–PPV around 500 nm, and only the weak near-IR part may beattributed to PTPTB. Interestingly, the shoulder in the absorption spectrumaround 600 nm, originating from PTPTB, has no pendant in the spectralphotocurrent. Obviously, in the blend, excited PTPTB does not contributeto the photocurrent to the same extent as MDMO–PPV.

In order to understand the performance of the tandem device, low tem-perature transport studies are a valuable tool. Diodes made from pristineMDMO–PPV and in composites with PTPTB are compared. ITO/PEDOTand Au electrodes are chosen to guarantee hole-only devices. This specialchoice of the electrodes is a successful technique for improving our under-standing of transport failures. The proper choice of contacts allows us toproduce p-type or n-type diodes from the same semiconductor, dependingon the selectivity of the contact. For instance, Au is a hole-injection contactfor most of the polymeric semiconductors, while Ca is an electron-injection


10-1110-1010-910

-810

-710

-610

-510-4-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

294 K

ITO / PEDOT / MDMO-PPV / Au ITO / PEDOT / MDMO-PPV:PTPTB(1:1) / Au

Cur

rent

[mA

]

10-11

10-10

10-9

10-810

-710-610-510

-4

167 K

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 610

-1110-1010-910

-810-710

-610

-510

-4

Voltage [V]

75 K

Fig. 5.45. I/V curves in the dark for a ITO-PEDOT/PPV/Au device (continu-ous curve) and a ITO-PEDOT/PPV-PTPTB 1:1/Au device (dot-dashed curve) at296 K (upper), 167 K (middle) and 75 K (lower). The thickness of both deviceswas determined to be about 115 nm by AFM tapping mode

contact. The dark I/V curves of the two devices are compared at differenttemperatures in Fig. 5.45.

For p-type MDMO–PPV diodes at room temperature, the forward currentscales as V α, where α > 2, indicating space-charge-limiting current SCLCtransport in the presence of traps [15]. At lower temperatures (167 K and75 K), traps no longer influence the transport mechanisms (e.g., as if alltrap levels were filled or all electron contributions to the current had beenfrozen out) and trap-free SCLC transport is observed (α ≈ 2), allowing usto estimate a hole mobility of around 10−8 cm2V−1s−1 for T < 200 K. Forthe MDMO–PPV/PTPTB composite, even at such low temperatures, trap-free SCLC is not observed. Obviously, trapping is more significant in blendsof these two polymers than in pristine MDMO–PPV. Thus the reduced PVperformance of the polymer mixture devices can originate in the presence ofhole traps in the composite. Besides the presence of traps in the individualcomponents, the blending of two polymers with different energy positions ofthe valence/conduction band can also lead to trapping between the polymers.


Polymeric solar cells with a bandgap > 2 eV are spectrally so badly mis-matched to the solar spectrum that their efficiency is severely restricted.It is essential to develop polymeric semiconductors with lower bandgap.Low bandgap polymeric semiconductors behave similarly in conjunction withfullerenes as n-type semiconductors (acceptors).

5.3.7 Temperature Behavior of Bulk Heterojunction Solar Cells

The significance of temperature information for bulk heterojunction solarcells can provide insights into the mechanisms governing photovoltage gener-ation and charge collection, as will be discussed in greater detail below. Atthe practical level there is a twofold importance. Firstly, such informationenables one to optimize the operation of such cells. But no less important, ithelps one to quantify cell performance in a manner that may be comparedfrom one laboratory to another. In the case of conventional inorganic solarcells, a set of standard test conditions (STC) have been defined. These cor-respond to a radiant intensity of 1 000 W/m2 with a spectral distributiondefined as AM1.5G IEC 904-3 and a cell temperature of 25◦C.

-2 -1 0 1 2

1

10

100

aftersealing before sealing

Ph

otoc

urr

ent D

ensi

ty (

mA

/cm

2 )

Voltage (V)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-6

-4

-2

0

2 before sealing after sealing

Ph

otoc

urr

en

t De

nsity

(m

A/c

m2 )

Voltage (V)

Fig. 5.46. Typical I/V curves for an as-produced polymer–fullerene solar cell be-fore and after sealing. Measurements were performed with a solar simulator (Steuer-nagel Solar Constant 575) at an irradiance level of 800 W/m2 and a cell temperatureof 55◦C. Measured data were corrected to the plotted AM 1.5 values using a calcu-lated mismatch factor of 0.76

In spite of the existence of such a standard, all kinds of efficiencies havebeen reported for organic solar cells, based on measurements performed undera wide variety of test conditions [148]. This section reports a detailed study of


the resulting temperature dependence for solar cells based on interpenetratingnetworks of conjugated polymers with fullerenes. We can then discuss possiblephysical mechanisms which may be responsible for the observed temperaturedependence.

Table 5.5. Photovoltaic parameters of conjugated polymer–fullerene solar cellsmeasured under simulated AM 1.5 conditions before sealing. Measurements wereperformed with a solar simulator (Steuernagel Solar Constant 575) at an irradiancelevel of 800 W/m2 and a cell temperature of 55◦C. Measured data were correctedto the plotted AM 1.5 values using a calculated mismatch factor of 0.76

Voc [mV] Jsc [mA/cm2] FF Efficiency [%] Area [mm2]

Cell 26 856 3.85 0.598 2.47 6.75839 3.9 0.601 2.45 6.9837 3.92 0.598 2.46 7.05

Cell 40 858 4.02 0.567 2.46 6.3845 3.99 0.585 2.47 6.2844 3.90 0.606 2.49 6.15

Table 5.5 summarizes the results for a series of solar cells, measured di-rectly after production under inert conditions, before sealing and packaging.Current–voltage measurements are performed under irradiation by a metal-halide solar simulator at light intensity 800 W/m2 and a cell temperatureof 55◦C. I/V curves for a typical cell before and after sealing are plotted inFig. 5.46. Table 5.5 shows that for the various solar cells short-circuit cur-rent densities Jsc are found to be between 3.85 and 4.02 mA/cm2 and thecorresponding open-circuit voltages, fill factors, and energy conversion effi-ciencies are in the respective ranges: Voc: 837–858 mV, FF: 0.567–0.606, andη: 2.45–2.49%. Reproducibility of these cells is satisfactory, and good enoughto discuss physical phenomena.

After sealing and packaging, these devices are delivered to the differentlaboratories where they are subjected to outdoor I/V measurements andfurther indoor measurements, at a variety of cell temperatures. Generally, aqualitatively similar temperature behavior is observed in indoor and outdoorI/V measurements of all devices studied. Figures 5.47 and 5.48 summarizethe temperature dependence of the principal cell parameters (Voc, Jsc, η, andFF) derived from indoor and outdoor I/V measurements of typical devices.Outdoor and simulator measurements of Voc show a linear decrease withincreasing temperature (Figs. 5.47b and 5.48).

Additional outdoor measurements of Voc made while continuously vary-ing the cell temperature, without recording the entire I/V curve, confirmthis behavior (Fig. 5.49). For all samples, the observed linear decrease hasa temperature coefficient in the range dVoc/dT ≈ 1.40–1.65 mV/K. This iscomparable with corresponding values observed for familiar inorganic solar


Fig. 5.47. Temperature dependence of the principal photovoltaic parameters for atypical polymer–fullerene solar cell derived from outdoor measurements of its I/Vcurves. Plotted values of efficiency and Isc have been adjusted to the STC irradiancelevel of 1 000 W/m2

25 30 35 40 45 50 55 600.8

0.9

1.0

1.1

1.2

ISC VOC FF

η

Cell temperature (0C)

Nor

mal

ized

cel

l par

amet

er

Fig. 5.48. Temperature dependence of normalized photovoltaic parameters for atypical polymer–fullerene solar cell derived from indoor measurements of its I/Vcurves. The ordinate axis displays all parameters normalized to their measured val-ues at 25◦C, namely, Jsc: 3.1 mA/cm2, Voc: 840 mV, FF: 0.55, and η: 1.45%. Activecell area 7.5 mm2. Measurements were performed with a class A solar simulator(Spectrolab X-10). Measured data were corrected to their corresponding AM 1.5values using a mismatch factor of 0.9


Fig. 5.49. Outdoor measurement of Voc vs. temperature made by continuouslyvarying the cell temperature. The inset shows the same data extrapolated to 0 K

cells in this temperature range. Recent low temperature measurements onthe current–voltage behavior of conjugated polymer/fullerene bulk hetero-junction solar cells in the range 80–300 K show that this linear temperaturedependence of Voc is lost at temperatures below 200 K and that Voc beginsto saturate [149]. It is important to note that this T coefficient might bespecific to the semiconductor selection used for this device and not for bulkheterojunction solar cells in general. The linear temperature coefficient ob-tained from the present measurements is nevertheless used to extrapolate toT ≈ 0 K (inset in Fig. 5.49), in order to derive an upper limit for the valueof the open-circuit voltage at 0 K. The result is Voc(0 K) ≈ 1.33–1.40 V.

In order to try and understand the physical mechanisms which may beresponsible for the observed temperature dependence of Voc in the high andlow temperature ranges, it is instructive to start with an analysis of theVoc behavior of conventional inorganic semiconductor solar cells with a p–njunction [150]:

Voc =AkT

qln(

Isc

I0+ 1

), (5.40)

where A is a diode quality factor for the p–n junction and I0 is a reversesaturation current. According to Shockley’s diffusion theory, I0 is given by

I0 = qNvNc

(Ln

nnτn+

Lp

ppτp

)exp

(−Eg

kT

), (5.41)

where Nv and Nc are the effective densities of states in the valence andconduction band, Eg is the bandgap of the semiconductor, Ln, Lp, nn, pp,


τn, τp are the diffusion lengths, densities and lifetimes of electrons and holes,respectively. Using (5.41) and assuming Isc � I0, equation (5.40) implies

Voc =AEg

q− AkT

q

(Ln

nnτn+

Lp

ppτp

)ln(

1Isc

qNvNc

)= a − bT , (5.42)

where

a = Voc(0 K) =AEg

q,

and

b =dVoc

dT=

Ak

q

(Ln

nnτn+

Lp

ppτp

)ln(

1Isc

qNvNc

).

The observed experimental result that Voc decreases linearly for bulk hetero-junction solar cells allows us to conclude that, at least in the high temperaturerange (T > 200 K), these solar cells may be described by a diode model withI0 ∼ exp(E/kT ). Here E is a parameter analogous to Eg for conventionalsemiconductors. For conjugated polymer/fullerene bulk heterojunction solarcells, E should correspond to the energy difference between the HOMO levelof the donor and the LUMO level of the acceptor components of the activelayer [as also suggested by the extrapolated value of Voc(0 K)].

The observed Voc value of around 0.8 V is considerably higher than theVoc value of 0.53 V found for bilayer conjugated polymer/fullerene solar cellsunder intense illumination [151]. This result again strongly supports the con-clusion from the previous section that photovoltage generation in bulk donor–acceptor heterojunctions cannot be explained by a model of the work functiondifference of the two electrodes [152] (as is generally accepted for single-layerconjugated polymer devices [153,154]), or by a picture involving only bandbending at the ‘polymer/fullerene’ interface (which is adequate for bilayerconjugated polymer/fullerene solar cells with non-rectifying metal contacts[155]), but is related to the electronic position of the conduction and valenceband of the two semiconductors.

This view of Voc generation is additionally supported by the fact thatthe values of the temperature coefficient dVoc/dT = −(1.40–1.65) mVK−1

for the cells under the present study (with bilayer LiF/Al and ITO/PEDOTcontacts) coincide with those for polymer/fullerene bulk heterojunction solarcells of the ‘previous generation’ (with the same components of the activelayer but without LiF and PEDOT contact layers) [156]. In this picture, thetemperature dependence of Voc is directly correlated with the temperaturedependence of the quasi-Fermi levels of the components of the active layerunder illumination, i.e., of the polymer and the fullerene. Therefore, the tem-perature dependence of Voc over a wide range, and in particular Voc(0 K),are essential parameters for understanding bulk heterojunction solar cells.

Figures 5.47a and 5.48 show a relatively large monotonic increase in Iscwith temperature, followed by a saturation region. A slight increase in Isc


with temperature is also a common feature for inorganic solar cells [157].However, in the case of bulk heterojunction solar cells, the rate of increase isso dramatic that the increase in current with temperature overtakes the de-crease in voltage with temperature. As a result, there is an absolute increasein the power efficiency η with temperature, reaching a maximum value atTmax which, for different samples, lies in the range 47–60◦C (Fig. 5.47c).The temperature dependence of FF is quite similar to that of the current(Fig. 5.47d). The latter might be explained in terms of a temperature depen-dent series resistance Rs, as discussed in the previous section.

Fig. 5.50. Outdoor measurement of Isc vs. temperature made by continuously vary-ing the cell temperature. Plotted values have been adjusted to the STC irradiancelevel of 1 000 W/m2

In order to investigate the above-mentioned behavior more thoroughly,we measured Isc with continuous variation of the cell temperature, withoutrecording the entire I/V curve. The result is shown in Fig. 5.50 (for anothercell), where a clear indication of saturation sets in at around 60◦C. Togetherwith the continuing fall-off in Voc, this might result in a corresponding de-crease in the efficiency. A noteworthy point about this experiment is that,when the temperature was cycled back and forth, there was no hysteresis inthe Isc temperature dependence.

A positive temperature dependence of η is a remarkable peculiarity ofsolar cells, which is not observed for any kind of inorganic solar cell [157].It is important to note that heating the cells to such elevated temperaturesas Tmax may be achieved merely by the absorption of solar radiation, i.e.,without any additional heating.

In the previous section on the short-circuit current, it was demonstratedtheoretically and experimentally that Isc in conjugated polymer–fullerene so-lar cells is controlled to a considerable extent by mobility of the majoritycharge carriers in the cell’s active layer [158]. Moreover, activated behav-ior of charge carrier mobility in conjugated polymers is known to result inhigher mobility at higher temperatures (for a review, see [159]). Accordingly,


60050040030020010000.00

0.05

0.10

0.15

0.20

0.25

0.30

Isc (33 o C ) [m A]

Isc (25 o C ) [m A]

Isc (20 °C )[m A]

Isc (10 oC ) [m A]

Irra d ia nc e ( W/ m 2 )

I SC (

mA

)

Fig. 5.51. Short-circuit current (Isc) vs. irradiance level of solar simulator (Steuer-nagel Solar Constant 575), at various cell temperatures, for a typical cell sample

it is likely that our observed, unusually large, positive temperature coeffi-cient for Isc originates from the temperature dependence of the mobility ofthe conjugated polymer–fullerene composite. This hypothesis is also in ac-cord with the irradiance-resolved measurements performed at different celltemperatures using the solar simulator (Fig. 5.51). In those measurementsa linear increase is observed in Isc with light intensity for the whole rangeof irradiance and temperature. Moreover, it should be noted that the slopeof the irradiance dependence of Isc increases with increasing temperature. Inother words, the maximum temperature influence is observed at the highestlight intensities. At such intensities, a maximum quantity of photocarriers isgenerated and the limitation in carrier transport, caused by low mobility ofholes in the conjugated polymer and electrons in the fullerene channels, ismore obvious than for lower carrier densities.

The observed temperature dependence of Figs. 5.47d and 5.48 is quitesimilar to that of Isc. The former, however, can be qualitatively under-stood in terms of the temperature dependent series resistance Rs of the solarcell, as the following argument demonstrates. With familiar inorganic solarcells, the series resistance is determined principally by the contacts and con-tact/semiconductor interfaces, because the resistivity of the semiconductormaterial is relatively low. On the other hand, the organic active layer in bulkheterojunction solar cells has a relatively high resistivity, but one which de-creases with increasing temperature, owing to the increase in carrier mobility.It is this decrease in resistivity that manifests itself as an improvement in thefill factor with increased temperature.


A similar temperature dependence of Isc, Voc, and η is also reported for the‘lower mobility generation’ of solar cells, based on interpenetrating networksof conjugated polymers with fullerenes, but processed from solvents so thatthe initial efficiency is < 1% [156]. This behavior is discussed extensivelyin the section dealing with Isc. A positive temperature coefficient is alsoobserved for the efficiency of C60 single-crystal photoelectrochemical cells[160]. Finally, a temperature dependence of Isc qualitatively similar to thatshown in Fig. 5.47a and 5.48 is also observed for organic solar cells based onZn-phthalocyanine (ZnPc)/perylene (MPP) heterojunctions [161].

Furthermore, these data strongly suggest that the positive temperaturedependence of Isc, FF, and η may be characteristic for solar cells based on or-ganic semiconductors that show a temperature-activated behavior for chargetransport, resulting in higher mobility/conductivity at higher temperatures(as also observed, for example, for some types of amorphous silicon solar cells[162]).

The observed temperature dependence is therefore a characteristic of solarcells based on amorphous semiconductors, where transport properties aredominated by hopping transport and not by bandlike transport. Generally, inorganic semiconductors, the nature of charge transport and, in particular, thetemperature dependence of mobility are known to depend strongly upon theircrystalline structure. For example, it was found that the activation energy formobility decreases with increased grain size in polycrystalline small-moleculesamples [160]. Similar behaviour is also stated for organic semiconductors.Consequently, in high quality single crystals of pentacene, the mobility ofelectrons and holes was even found to decrease with increasing temperature,following the familiar power law for inorganic semiconductors [163]. It isvery important that solar cells based on such single crystals [3] demonstrateconventional negative temperature coefficient for efficiency [161].

5.3.8 Stability of Polymeric Semiconductors and Devices:A Molecular View

Organic materials for use in photovoltaic devices require good chemical sta-bility together with high optical absorption in the visible range with respectto the AM1.5 spectrum. Apart from the need to improve efficiency, stabilityof organic devices is the essential challenge to be overcome before productscan be developed. Organic π-conjugated semiconductors are known for theirinstability under combined exposure to light and oxygen. Rapid degradationof the semiconductor occurs under these conditions. Protection from air andhumidity is absolutely necessary if we hope to achieve long lifetimes. Withregard to this point, organic devices are comparable to inorganic ones. Thequality of packaging and sealing will be decisive for the durability of the solarcell.

In the development stage of plastic solar cells, where a number of differentsemiconductors have to be characterized, a fast and reliable stability testing


procedure must be applied. Device lifetime measurements are not always sat-isfactory because they take such a long time. In order to obtain informationon lifetime performance, accelerated tests are frequently used. In these tests,devices are run at higher temperature and humidity in order to speed updegradation. An acceleration factor is then calculated and used to extrap-olate lifetimes under standard conditions (STC: 25◦C, 1 sun illumination).However, lifetime data do not give information on the underlying physics ofthe degradation. Consequently, two different types of lifetime test are desir-able. On the one hand, the kind of lifetime measurements described aboveare needed for product description. But in addition, a second lifetime test isrequired, allowing us to determine the physical mechanisms of degradation.

In this section we discuss a method of controlled material degradationfor individual organic semiconductors and also for the blends used in bulkheterojunction solar cells [37]. The degradation is studied using attenuatedtotal reflection Fourier transform infrared spectroscopy (ATR-FTIR) and bydetermining current/voltage characteristics (I/V measurements) of the de-vices.

ATR-FTIR spectra are measured using an FTIR spectrometer. Thin filmsamples are cast from solution onto the surface of a ZnSe ATR reflectionelement and dried under vacuum. The substrates are mounted in an environ-mental cell, which allows ATR spectra to be recorded simultaneously withlaser light illumination of the sample in a controlled atmosphere. FTIR spec-tra with a measurement time of several minutes are recorded consecutivelyduring a period of about 8 h to guarantee a high signal-to-noise ratio. For illu-mination, an intense light source like an argon-ion laser can be used, emittingin resonance with the semiconductor (e.g., at 488 nm). The setup for such anATR-FTIR environmental cell is shown in Fig. 5.52a.

Fig. 5.52. Environmental cells for degradation measurements under (a) light and(b) current stressing

In order to get a fast characterization of the degradation processes, theindividual semiconductors (MDMO–PPV and C60) and a blend of the twosemiconductors as used in bulk heterojunction solar cells are studied underillumination in pure oxygen. ATR-FTIR spectra before and after an 8 hdegradation process and difference spectra showing only the spectral changes


during degradation, are presented in Fig. 5.53 for MDMO–PPV, C60 and theblend.

Fig. 5.53. FTIR spectra of degradation in oxygen. Left column: dashed lines be-fore degradation, solid lines after degradation (reference spectra: reflection ele-ment without sample). Right column: difference spectra during degradation (refer-ence spectra at the beginning of the degradation process). (∗) 1 506 cm−1 band ofMDMO–PPV, ( ) 1 182 cm−1 band of C60

The characterization of the degradation process can be performed byanalysing the time dependence of the decay of specific absorption bands at1 506 cm−1 (MDMO–PPV) and 1 182 cm−1 (C60) using spectral fitting tech-niques. The results are shown in Fig. 5.54. For the individual components,


Fig. 5.54. Time dependence of specific IR absorption bands during degradationunder illumination in an oxygen atmosphere

the degradation in an oxygen atmosphere occurs much faster for MDMO–PPV than for C60 or PCBM. For long-term applications, the stability of thepolymeric electron donor in the mixture for solar cells must be improved.As has been shown in a previous paper, the degradation of MDMO–PPVcan be forced down to a very low level by performing the stability test in anargon atmosphere [164]. However, in the mixture, the degradation of MDMO–PPV is much slower than that of the pure polymer sample. The fast electrontransfer from the polymer to C60 after excitation, accompanied by the for-mation of positively charged polarons on the chain, significantly decreasesthe reactivity of the polymer with regard to oxygen, probably by quenchingtriplet formation on the polymer and avoiding a triplet–triplet annihilationreaction with oxygen under formation of reactive singlet oxygen [165,166].Further systematic studies show that, upon addition of fullerenes to the con-jugated polymer matrix, the stability of the matrix is increased [164,167].As degradation products, carbonylic structures can be seen with character-istic absorption bands between 1 600 and 1 800 cm−1 [168] (right column ofFig. 5.53). Aromatic and aliphatic ketones occur, with absorption between1 600 and 1 700 cm−1 for the former, and absorption above 1 700 cm−1 withadditional weaker absorption around 1 000–1 200 cm−1 for the latter [169].

An exciting property of the ATR degradation method is the possibility ofusing the same environmental cell to perform similar degradation cycles ofthe semiconductors under current stressing [170]. Degradation under current,light and ambient atmosphere can be measured using a conducting reflectionelement, like doped Ge or Si. As counter electrode, Au or Al are evaporated


Fig. 5.55. IR spectral changes during degradation of MDMO–PPV in oxygen under(a) light stressing and (b) current stressing

for p- and n-type semiconductors, respectively. Figure 5.52b shows the slightlyaltered setup of the ATR environmental cell that allows us to simultaneouslystress a polymeric semiconductor under current, light and atmosphere. Figure5.55 shows the photodegration of the p-type semiconductor MDMO–PPVunder oxygen stressing (a) and current stressing (b). The spectral changesduring current degradation are observed at 1 700 cm−1, 1 000–1 300 cm−1 and700 cm−1 and do not correlate with spectral changes during oxygen stressing.It seems likely that these bands are correlated with changes involving themetal/polymeric semiconductor interface. This comparison demonstrates thepower of the ATR method. A typical lifetime measurement cannot distinguishbetween oxygen degradation and current degradation.

5.3.9 Processing of Polymeric Semiconductors:Blending with Conventional Polymers

The importance of melt processing properties for conjugated polymers in de-vice construction was demonstrated recently [34]. However, most conjugatedpolymers show no glass transitions or only side-chain glass transitions. Theembedding of the photoactive conjugated polymer–fullerene blend into a con-ventional polymer matrix (guest–host approach) presented in recent studies[29,171] is a sound and promising method in this respect, with the possibilityof improving the photoactive sample quality. The reasons are as follows:

• The conjugated polymer diluted by a proper host matrix shows less in-terchain interaction than pure films.

• Macroscopic ordering of the conjugated polymer can be performed bymechanical stretching of the host polymer.

• The stability of conjugated polymer–fullerene devices embedded in con-ventional polymers (guest–host approach) are higher due to encapsulationagainst environmental influences.

• By the choice of a proper host matrix, charge transfer between conjugatedpolymer and fullerene may be advantageously tuned, by changing either


0 20 40 60 80

10-3

10-2

10-1

100

(a)

150 mW 80 mW 40 mW 20 mW 10 mW

I sc [

mA

/cm

2 ]

PS Concentration [wt%]

15 10010-3

10-2

10-1

100

10 mW/cm2

20 mW/cm2

40 mW/cm2

80 mW/cm2

150 mW/cm2

I sc [

mA

/cm2 ]

100% - PS wt %

101 10210-4

10-3

10-2

10-1

100

11 wt% PS 20 wt% PS 33 wt% PS 50 wt% PS 66 wt% PS 80 wt% PS 0 wt% PS

η e [%

]

Excitation Intensity [mW/cm²]

(b)

Fig. 5.56. (a) Isc of various PS/MDMO–PPV/PCBM devices under different exci-tation intensities vs. PS percentage. The inset shows the dependence of Isc on theelectroactive component concentrations (100% PS wt. %) in a log–log plot. Linesare power law fits according to Isc ∼ [wt. %]α. Best fits are obtained with α ≈ 3.(b) Power efficiency ηeff of various PS/MDMO–PPV/PCBM cells vs. excitationintensity. Lines are drawn as a guide to the eye. Excitation is provided by Ar+

laser at 488 nm

the intermolecular distances through morphology control or the overalldielectric constant of the system.

For large scale production of plastic solar cells, the rheological properties willalso become relevant. To this end, and for the reasons listed above, we stud-ied the behavior of highly efficient conjugated polymer/methanofullerene cells(ITO/MDMO–PPV:PCBM/Al) blended into a conventional polymer matrix[29,171]. Figures 5.56a and b show the dependence of Isc and the efficiency ηeffon the content of an inert, photoinactive conventional polymer (polystyrene,PS) under various illumination intensities. Introducing small amounts of PS(10 wt.%) does not significantly change the efficiency of the cells. Furtherincrease in the PS concentration results in a significant decrease in Isc. Thepercolation threshold for the interpenetrating network of the conjugated poly-mer/methanofullerene mixture in the host matrix determined the onset of astrongly enhanced photovoltaic response. The intensity dependence of thespectrally resolved photocurrent and the short-circuit current indicates that,at higher light intensities, enhanced annihilation of mobile charge carriersoccurs. This is also a side-effect of the increased thickness when blended witha further polymeric component. However, these results clearly demonstratethat it is possible to enhance the rheological and/or mechanical propertiesof the bulk heterojunction solar cells by addition of smaller (over 10 wt.%)amounts of photoinactive ‘additives’.


5.4 Conclusion

Bulk heterojunction composites have a huge potential for photovoltaic energyconversion. Their excellent photosensitivity and quantum efficiency for chargegeneration, combined with the long lifetimes of the individual carriers inthe devices, allows relatively high energy conversion efficiencies. Surprisingly,classical PV concepts transferred to the extreme thin film limit can be used todescribe the performance of bulk heterojunction solar cells. A more detailedunderstanding of the photophysics and device physics will help us to improvedevice performance. Optimization should concern the following aspects:

• The choice of metallic electrodes, so as to achieve good Ohmic contactson both sides for collection of the oppositely charged photocarriers.

• The choice of the D/A pair (energetics determine the open-circuit poten-tial). In addition, the bandgap of the semiconducting polymer should bechosen to ensure efficient harvesting of the solar spectrum.

• The network morphology of the phase-separated composite material forenhanced transport and carrier generation. Absorption and mobility ofcharge carriers has to be maximized within the different components ofthe bulk heterojunction.

In organic photovoltaic elements, two different tasks should be clearly dis-tinguished: photoinduced charge generation (electron transfer efficiency) andtransport of created charges to the electrodes (charge carrier mobility). Thesetwo different tasks are frequently mixed up, and expected to be simultane-ously fulfilled by one and the same material. Optimizing photoinduced chargegeneration does not necessarily optimize charge carrier transport. Indeed itis particularly the second point, transport properties, which set the perfor-mance limits of organic amorphous semiconductors at the present time. Ashas been shown in Chap. 1 (Sect. 1.4), photoinduced charge generation inconjugated polymer/fullerene bulk heterojunctions is approximately 100%(subpicosecond electron transfer rate, approximately 1 000 times faster thanany competing photophysical relaxation channel). However, sweep-out of thecreated charges is only possible in a very thin sample due to limited chargecarrier mobilities. One possible strategy is to separate the two tasks by usingseparate components in the device for charge transport and charge genera-tion.

As we enter the new millennium, photovoltaic energy conversion will gainin importance. This clean, regenerative energy source will exploit all possiblemechanisms, materials and devices. Estimates predict that PV will contributeabout 1–2% to world energy consumption in 2020 and about 15% in 2050.This is equivalent to more than 100 000 km2 of PV. It is clear that such hugeareas demand novel production and installation technologies, which may notbe compatible with conventional inorganic PV technologies.

This work summarizes the physics of a special area of photovoltaic energyconversion, i.e., polymer-based, bulk heterojunction solar cells. With about


3% power conversion efficiency already demonstrated and a large potentialfor improvement, this approach represents a viable starting point for realizinglarge-area ‘plastic solar cells’ which may significantly contribute to our futureenergy consumption habits.

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6 Organic Photodiodes:From Diodes to Blends

Olle Inganas and Lucimara Stolz Roman

Organic materials and polymers have been extensively studied for the pur-pose of extracting opto-electronic functions from devices based on them [1].Such materials are easily processed and can be chemically engineered to ob-tain absorption and emission bands covering the entire visible spectrum [2].The possibility of using the photovoltaic effect in organic devices for opticaldetection and energy conversion has increasingly motivated research in thisfield in recent years. Some of the driving force for this development has beenthe successful demonstration of high energy conversion efficiency in hybridorganic/inorganics, such as in the Gratzel cell.

Efficient organic photovoltaic devices have been demonstrated which in-volve photoinduced charge transfer across an internal or external donor–acceptor (D/A) heterojunction [3,4]. While photoinduced charge transfer mayalso occur with a low probability in the pristine polymer [5,6], efficient chargegeneration requires the addition of an acceptor. These junctions are formedby materials with different electroaffinity and/or ionization potentials, whichwill promote exciton dissociation at their interfaces. The interfaces can befound in a bilayer (two photoactive layers between the electrodes) or dis-tributed in the bulk of a blend film (mixture of two materials). Bilayer andblend devices can be formed in polymer/polymer [7–9], polymer/molecule[7,10,11] and molecule/molecule [12] junctions. One layer donates electronsto the other under optical excitation and these are called the donor and ac-ceptor layers, respectively. The photogenerated excitons are dissociated atthe junctions and the dissociated charges – a hole in the donor phase and anelectron in the acceptor phase – are transported through the relevant layer(or phase in a blend), driven by the internal electric field to the electrode.

Acceptor materials, which need to have a high electroaffinity value, arequite rare among polymers. Some of the best examples can be found in[7,9,13]. The best studied acceptor is the molecule buckminsterfullerene C60[14], pure or derivatized. It is an excellent electron acceptor and can be sub-limed onto the donor layer, or mixed in a common solvent with the donor. Ithas been found that electron transfer from conjugated polymers (D) to C60(A) occurs on a picosecond time scale [3], much faster than any competingprocess. (The luminescence lifetime is greater than 300 ps.) Upon photoexci-tation, the quasi-one-dimensional semiconducting polymers show a structuralrelaxation (polaron exciton), due to electron–phonon coupling, leading to sta-

250 Olle Inganas and Lucimara Stolz Roman

bilization of the charge-separated state, a necessary requirement for efficientcharge collection [10].

In this chapter we focus on the optical and electric modeling of organicphotodiode devices in order to understand and optimize organic photovoltaicdevices using conjugated polymers and molecules. There are good groundsfor emphasizing this approach. Firstly, the layers used in present day organicphotodiodes are extremely thin, normally of the order of a few wavelengthsof light in the visible range. These thin layers are normally semi-transparent,and a considerable fraction of light is not absorbed. Reflection at interfacesin the multilayered devices will therefore be of importance in determiningdevice performance. Secondly, electrical fields inside devices are high, butstill distributed within a sequence of layers (for the bi- or multilayer diode).Basic transport issues, eventually determining the performance of the pho-todiodes, can therefore be investigated in the bilayer devices, and modelingthese is helpful. Lessons from such devices can then be used for developingmore complex structures, as for instance in the vertically stratified blends ofpolymer/molecule or polymer/polymer junctions, or in the addition of sev-eral polymers to help collect energy from a broadband light source (such asthe sun).

6.1 Thin Film Organic Photodiodes

In general, organic photovoltaic devices are constructed in a sandwich struc-ture where the organic layer(s) are found between two highly conductingelectrodes. One of them is transparent to let the light in, normally indiumtin oxide (ITO), and the other mirror reflective, usually aluminum. The mech-anism of photocurrent generation includes four basic processes:

• light absorption and generation of excited states,• the diffusion of excited states to sites where dissociation of excitons mayoccur,

• dissociation of the excitons to form free charge carriers,• transport of the carriers by drift and diffusion to the respective electrodefor collection.

Exciton dissociation may occur in the strong electric fields that can normallybe found near the interfaces. It can also occur at internal sites such as adefect or an impurity. Finally, it may occur at our engineered donor/acceptorjunctions. In the case of a single-polymer layer, only a small fraction of theabsorbed light contributes to the photocurrent. This is because the generatedphotocurrent basically only comes from light absorbed where the createdexcited states can diffuse to the metal electrode, and there be dissociatedby the field, rather than quenched by the image field in the metal. In ablend, this picture is muddled by the multitude of geometrical arrangementsof donor/acceptor phases. It is therefore expected that a larger fraction of

6 Organic Photodiodes: From Diodes to Blends 251

light can be converted to dissociated charges. While this may be the case ina blend, it is very important that these charges should be able to transfer tothe electrodes without recombination losses.

6.2 Optical Mode Structure in Thin Film OrganicStructures. Optimization of Bilayer Geometries

The first event in the sequence of steps leading to a photocurrent is the for-mation of excited states in the organic layers in the photodiodes. In singleor bilayer photodiodes, there is expected to be a zone near the metal or bi-layer interface, respectively, given by the exciton diffusion length, which maybe called the active region of the device since only excited states generatedwithin this region can diffuse to the junction to generate dissociated carriers(stippled region in the devices of Fig. 6.1). The exciton diffusion length inconjugated polymers is quite small, around 10 nm, and because of this thepolymeric layer is not likely to be much thicker. Efficiency is compromised inthicker devices by charge transport due to the higher resistance of the layer.They lose light through the filter effect caused by light absorption into thenon-active region. For these devices an important issue is the optical elec-tric field distribution inside the device on illumination. The metallic mirrorelectrode sets the boundary condition for the optical electrical field upon il-lumination. We may derive information about the monochromatic standingwave in the thin multilayer device by considering the dielectric function ofthe assembly.

We assume that:

• layers included in the device are homogeneous and isotropic, so that theirlinear optical response can be described by a scalar complex index ofrefraction,

• interfaces are parallel and flat compared to the wavelength of the light,• the light incident at the device can be described by plane waves,• exciton diffusion is described by the diffusion equation (6.22),• excitons that contribute to the photocurrent dissociate into charge carri-ers at interfaces acting as dissociation sites,

• the diffusion range of excitons does not depend on excitation energy(wavelength),

• all generated charges contribute to the steady state photocurrent, i.e., notrapping of charges occurs inside the device.

We employ matrix methods in order to obtain the reflection and trans-mission coefficient of the electromagnetic field within the device. Stratifiedstructures with isotropic and homogeneous media and parallel-plane inter-faces can be described by 2× 2 matrices because the equations governing thepropagation of the electric field are linear and the tangential component of theelectric field is continuous [15,16]. We consider a plane wave incident from the


Fig. 6.1. Cross-section of (a) an ITO/polymer/Al device and (b) anITO/polymer/C60/Al device. This exemplifies the advantages of using bilayer de-vices as far as the position of the active region is concerned (stippled area of thepolymer), with the maximum optical field distribution inside the device due to thenode at the mirror electrode in Al. The bulk of the polymer is gray and the C60

molecule is white

left at a general multilayer structure having m layers between a semi-infinitetransparent ambient and a semi-infinite substrate, as shown schematicallyin Fig. 6.2. Each layer j (j = 1, 2, . . . , m) has thickness dj and its opticalproperties are described by its complex index of refraction nj = ηj + iκj (orcomplex dielectric function εj + iε′′

j = n2j ), a function of wavelength (energy)

of the incident light. The optical electric field at any point in the system canbe resolved into two components corresponding to the resultant total electricfield. One component propagates in the positive x direction and one in thenegative x direction, which are denoted E+

j (x) and E−j (x), respectively, at a


Fig. 6.2. A general multilayer structure with m layers between a semi-finite trans-parent ambient and a semi-infinite substrate. Each layer j (j = 1, 2, . . . ,m) hasthickness dj and its optical properties are described by its complex index of re-fraction. The optical electric field at any point in layer j is n represented by twocomponents: one propagating in the positive x direction and one propagating inthe negative x direction

position x in layer j. An interface matrix (matrix of refraction) then describeseach interface in the structure:

Ijk =1

tjk

(1 rjk

rjk 1

), (6.1)

where rjk and tjk are the Fresnel complex reflection and transmission coef-ficients at interface jk. For light with the electric field perpendicular to theplane of incidence (s-polarized or TE waves), the Fresnel complex reflectionand transmission coefficients are defined by

rjk =qj − qk

qj + qk, (6.2a)

tjk =2qj

qj + qk. (6.2b)

For light with the electric field parallel to the plane of incidence (p-polarizedor TM waves), they are defined by

rjk =n2

kqj − n2jqk

n2kqj + n2

jqk, (6.3a)

tjk =2nknjqj

n2kqj + n2

jqk, (6.3b)


where

qj = nj cosφj =(n2

j − η20 sinφ0

)1/2, (6.4)

and η0 is the refractive index of the transparent ambient, φ0 is the angle ofincidence and φj is the angle of refraction in layer j. The layer matrix (phasematrix) describing propagation through layer j is described by

Lj =(e−iξjdj 0

0 eiξjdj

), (6.5)

where

ξj =2πλ

qj , (6.6)

and ξjdj is the layer phase thickness corresponding to the phase change thewave experiences as it traverses layer j.

By using the interface matrix and the layer matrix of (6.1) and (6.5), thetotal system transfer matrix (scattering matrix) S, which relates the electricfield on the ambient and substrate sides by(

E+0

E−0

)= S

(E+

m+1E−

m+1

), (6.7)

can be written

S =(

S11 S12S21 S22

)=

(m∏

v=1

I(v−1)vLv

)Im(m+1) . (6.8)

When light is incident from the ambient side in the positive x direction, thereis no wave propagating in the negative x direction inside the substrate. Thismeans that E−

m+1 = 0. For the whole layered structure, the resulting complexreflection and transmission coefficients can be expressed by using the matrixelements of the total system transfer matrix of (6.8):

r =E−

0

E+0

=S21

S11, (6.9)

t =E+

m+1

E+0

=1

S11. (6.10)

In order to calculate the internal electric field in layer j, the layer system canbe divided into two subsets, separated by layer j, which means that the totalsystem transfer matrix can be written as

S = S′jLjS

′′j . (6.11)


The partial system transfer matrices for layer j (Fig. 6.2) are defined by(E+

0E−

0

)= S′

j

(E′+

j

E′−j

), (6.12)

S′j =

(S′

j11 S′j12

S′j21 S′

j22

)=

(j−1∏v=1

I(v−1)vLv

)I(j−1)j ,

where E′+j and E′−

j refer to the left boundary (j − 1)j of layer j, and(E′′+

j

E′′−j

)= S′′

j

(E+

m+1E−

m+1

), (6.13)

S′′j =

(S′′

j11 S′′j12

S′′j21 S′′

j22

)=

⎛⎝ m∏

v=j+1

I(v−1)vLv

⎞⎠ Im(m+1) ,

where E′′+j and E′′−

j refer to the right boundary (j + 1)j of layer j. Fur-thermore, for the partial systems S′

j and S′′j , it is possible to define complex

reflection and transmission coefficients for layer j in terms of the matrixelements

r′j =

S′j21

S′j11

, t′j =1

S′j11

, r′′j =

S′′j21

S′′j11

, t′′j =1

S′′j11

. (6.14)

Combining (6.9)–(6.14), an internal transfer coefficient can be derived, relat-ing the incident plane wave to the internal electric field propagating in thepositive x direction in layer j at interface (j − 1)j :

t+j =E+

j

E+0

=t′j

1 − r′j−r′′

j e2iξjdj, (6.15)

where r′j− = −S′

j12/S′j11. An internal transfer coefficient can also be derived

to relate the incident plane wave to the internal electric field propagating inthe negative x direction in layer j at interface (j − 1)j :

t−j =E−

j

E+0

=t′jr

′′j e

2iξjdj

1 − r′j−r′′

j e2iξjdj= t+j r′′

j e2iξjdj . (6.16)

Using (6.15) and (6.16), the total electric field in an arbitrary plane in layerj at a distance x to the right of boundary (j − 1)j in terms of the incidentplane wave E+

0 is given by

Ej(x) = E+j (x) + E−

j (x) (6.17)

=(t+j e

iξjx + t−j e−iξjx

)E+

0 = t+j

(eiξjx + r′′

j eiξj(2dj−x)

)E+

0 ,

for 0 < x < dj . The expression in (6.17) can also be expressed in terms ofthe matrix elements of the partial system transfer matrices as

Ej(x) =S′′

j11e−iξj(dj−x) + S′′

j21eiξj(dj−x)

S′j11S

′′j11e−iξjdj + S′

j12S′′j21eiξjdj

E+0 . (6.18)


Since the number of excited states at a given position in a structure is directlydependent on the energy absorbed by the material, the energy dissipation ofthe electromagnetic field in the material is the quantity that is of interest inthe case of photovoltaic devices. The time average of the energy dissipatedper second in layer j at position x is given by

Qj(x) =12cε0αjηj |Ej(x)|2 , (6.19)

where c is the speed of light and ε0 the permittivity of free space. This meansthat the energy absorbed at position x in the layered structure is proportionalto the product of the modulus squared of the electric field |Ej(x)|2, therefractive index ηj , and the absorption coefficient

αj =4πκj

λ, (6.20)

at position x. Therefore, the number of excited states in a layer is proportionalto the number of absorbed photons, and |E|2 as a function of the position xin the film directly represents the production of excited states at each point.Using (6.17) to expand (6.19), the result for light incident from air at normalincidence becomes

Qj(x) = αjTjI0

{e−αjx + ρ′′2

j e−αj(2dj−x) (6.21)

+2ρ′′j e

−αjdj cos[4πηj

λ(dj − x) + δ′′

j

]},

where I0 is the intensity of the incident light,

Tj =ηj

η0|t+j |2

is the internal intensity transmittance, and ρ′′j and δ′′

j are the absolute valueand the argument of the complex reflection coefficient for the second subsys-tem given by the third equation of (6.14). As can be seen in (6.21), the energydissipation in a layered structure at each position x in layer j is describedby three terms. The first term on the right originates from the optical elec-tric field propagating in the positive x direction, the direction in which theincident electromagnetic field is propagating. The second originates from thefield propagating in the negative x direction and the third is due to interfer-ence of the two waves. This interference term becomes especially importantfor optically thin layers and for a layered structure with a highly reflectinginterface in the structure, as for example in the case of metal electrodes. Thedistribution of the optical electric field is directly related to the distributionof the excited states in the device and thus describes the excitation profile ina layered structure.


The transmission of a beam of light through the glass support must betreated as incoherent with respect to other beams, due to the large thickness(1 mm) and non-uniformity across the thickness of the glass, and the finitebandwidth of the light source. This is accomplished by calculating the re-sultant transmission through the glass substrate, summing the transmittedenergies (intensities) rather than the complex amplitudes.

We can now couple our calculated monchromatic standing wave to theexciton diffusion process, as a source term in the diffusion equation for excitedstates. In this way we can obtain the photocurrent from the device under thegiven assumptions.

If n is the exciton density, the diffusion equation gives

∂n

∂t= D

∂2n

∂x2 − n

τ+

θ1

hνQ(x) , (6.22)

where D is the diffusion constant, τ is the mean lifetime of the exciton, θ1 isthe quantum efficiency of exciton generation, and hν is the excitation energyof the incident light. In (6.22), the first term on the right represents excitonsmoving away by diffusion, the second term is a recombination term, andthe third term represents the exciton generation rate (photogeneration). Atsteady state (equilibrium), the exciton density is time independent and (6.22)can be written

d2n

dx2 = β2n(x) − θ1

DhνQ(x) , (6.23)

where β = 1/L = 1/√

Dτ , i.e., the reciprocal of the diffusion length L. Thegeneral solution to (6.23) with the generation term given by (6.21) is

n(x) =θ1αTN

D(β2 − α2)

{Ae−βx + Beβx + e−αx + C1eαx (6.24)

+C2 cos[4πη

λ(d − x) + δ′′

]},

where N is the number of photons incident on the device per unit time andarea (incident photon flux). A and B are constants given by the boundaryconditions of the model and

C1 = ρ′′2e−2αd , (6.25)

C2 =β2 − α2

β2 + (4πη/λ)22ρ′′e−αd . (6.26)

Assuming that the interfaces of the active layer act as perfect sinks for theexcitons, i.e., all excitons can either recombine or dissociate into free chargesat the interfaces, the boundary conditions are n = 0 at x = 0 and x = d.


Solving for the two constants A and B using this boundary condition togetherwith (6.24), the result becomes

A =eβd − e−αd + C1

(eβd − eαd

)+ C2

[eβd cos

(4πη

λd + δ′′

)− cos δ′′

]e−βd − eβd

(6.27)

and

B =e−βd − e−αd + C1

[e−βd − eαd

]+ C2

[e−βd cos

[4πη

λd + δ′′

]− cos δ′′

]e−βd − eβd

.

(6.28)

The short-circuit exciton current density at the interface x = 0 is

Jexc = Ddn

dx

∣∣∣∣x=0

, (6.29)

which is related to the short-circuit photocurrent through Jphoto = qθ2Jexc,where q is the electron charge and θ2 the efficiency of exciton dissociation atthe interface. The resulting short-circuit photocurrent density generated atthis interface is therefore

Jphoto(x = 0) =qθαTN

β2 − α2

{− βA + βB − α + αC1 (6.30)

+4πη

λC2 sin

[4πη

λd + δ′′

]},

where the total quantum efficiency of the free charge generation is defined asθ = θ1θ2. In the same way for the interface at x = d, the exciton flow is

Jexc = −Ddn

dx

∣∣∣∣x=d

, (6.31)

resulting in the generated short-circuit photocurrent density

Jphoto(x = d) =qθαTN

β2 − α2

{βAe−βd − βBeβd + αe−αd − αC1eαd (6.32)

−4πη

λC2 sin δ′′

}.

From (6.30) and (6.32), it can be seen that the generated photocurrent isdirectly proportional to the incident light intensity I0 at the photovoltaicdevice, since I0 is related to the incident photon flux through I0 = hνN .


The generation of photoexcited species at a particular position in the filmstructure has been shown in (6.19) and (6.20) to be proportional to theproduct of the modulus squared of the electric field, the refractive index,and the absorption coefficient. The optical electric field is strongly influencedby the mirror electrode. In order to illustrate the difference between single(ITO/polymer/Al) and bilayer (ITO/polymer/C60/Al) devices, hypotheti-cal distributions of the optical field inside the device are indicated by thegray dashed line in Fig. 6.1. Simulation of a bilayer diode (Fig. 6.1b) clearlydemonstrates that geometries may now be chosen to optimize the device, bymoving the dissociation region from the node at the metal contact to the het-erojunction. Since the exciton dissociation in bilayer devices occurs near theinterface of the photoactive materials with distinct electroaffinity values, theboundary condition imposed by the mirror electrode can be used to maximizethe optical electric field |E|2 at this interface [17].

The organic heterojunction devices studied with this model were formedby PEOPT [poly(3-(4′-(1′′,4′′,7′′trioxaoctyl)phenyl)thiophene)] and C60 asthe active materials, donor and acceptor, respectively. The C60 layer wasdeposited by evaporation on top of the polymer layer, giving a well definedthickness that could be systematically varied. The optical functions, index ofrefraction and absorption coefficient, of all layers forming the diodes were de-termined from spectroscopic ellipsometry data. Figure 6.3 presents the calcu-lated distribution of the squared modulus of the optical electrical field |E|2 forthree device structures with three different thicknesses of C60, at λ = 460 nm(peak position of the absorption spectrum of the polymer, Fig. 6.5). The lightintensity in the active region (interface) changes significantly with the thick-ness of the molecular layer, being optimal when the thickness is around 35 nmfor this wavelength. Since the most dominant boundary condition inside thedevice is at the Al electrode, changes in the polymer thickness affect themagnitude of the light intensity but not the profile of the |E|2 distribution.

Figure 6.4 presents the calculated value of |E|2 at the PEOPT/C60 inter-face versus the thickness of the molecule for two polymer thicknesses (30 nmand 40 nm). The photocurrent measurements given by the external quantumefficiency η (see Sect. 6.3) of these devices reflect the predictions of the cal-culated optical field distribution. When the C60 thickness was fixed at 34 nmand the PEOPT thickness was chosen as 30 nm and 40 nm, the η value ofthe thinner device reached 23%, while that of the thicker one reached 17%(Fig. 6.5). The thicker polymer layer only acted as a filter to the active region,decreasing the intensity and hence also the photocurrent. It can be observedthat the ratio of |E|2 at the interface is 1.12 while the η measurement gives aratio of 23/17=1.35, which is quite similar considering possible experimentalerrors in thickness determination.

When the thickness of C60 was varied (31 nm, 72 nm, and 87 nm), theamount of light arriving at the PEOPT/C60 interface due to different distri-butions was not reflected in a linear production of photocurrent. To model the


Fig. 6.3. The optical field distribution in a ITO/PEDOT/PEOPT/C60/Al devicebased on different devices for 460 nm wavelength. The thickness of C60 was 20 nm(a), 35 nm (b), and 80 nm (c). The field at the active interface is maximum for35 nm thickness and minimum for 80 nm thickness


Fig. 6.4. Calculated value of the square of the normalized optical electric field |E|2at the C60/PEOPT interface for PEOPT thicknesses of 30 nm (solid line) and 40 nm(dashed line) versus thickness of the C60 layer at a wavelength of 460 nm. The insetshows the calculated distribution of the square of the normalized optical electricfield |E|2 inside an ITO (120 nm)/PEDOT-PSS (110 nm)/PEOPT (30 nm)/C60

(34 nm) device at the same wavelength

Fig. 6.5. Spectral response of devices made with two different PEOPT poly-mer thicknesses: Al/C60 (35 nm)/PEOPT (30 nm)/PEDOT-PSS (110 nm)/ITO(120 nm)/glass (dotted line) and Al/C60 (35 nm)/PEOPT (40 nm)/PEDOT-PSS(110 nm)/ITO (120 nm)/glass (solid gray line). The absorption spectrum of thePEOPT polymer is plotted for comparison (solid black line)


experimental short-circuit photocurrent action spectra, contributions to thephotocurrent from the C60 layer were needed as well as those from polymerabsorption. For this reason, both interfaces PEOPT/C60 and C60/Al wereconsidered as sites of exciton dissociation. Figure 6.6 shows the experimentaland calculated action spectra for three devices. The experimental curves havesimilar shape, but quite different absolute values. They present photocurrentabove the polymer absorption edge (620 nm), indicating a contribution fromthe molecule. The calculated action spectra were fitted to the experimentaldata using the Gauss–Newton algorithm, by varying the thickness of the C60layer and diffusion ranges of the PEOPT and C60 to ascertain the best fit tothe multiple sets of experimental data. There was good agreement betweenthe model and experimental data, resulting in diffusion ranges of 4.7 nm forPEOPT and 7.7 nm for C60.

Fig. 6.6. Spectral response of similar photodiodes ITO/PEDOT/PEOPT/C60/Alwith different thicknesses of the C60 layer: 31 nm (circles), 72 nm (squares), and87 nm (solid line), and the best fit to the model (dashed line). Spectra were takenfrom these devices under short-circuit conditions. Asterisks mark the prediction ofthe model in Fig. 6.4 at wavelength 460 nm

Such bilayers were studied by photoluminescence, with a view to extract-ing the degree of photoluminescence quenching induced by a thin acceptorlayer on the polymer [18]. Studies of photoluminescence quenching in bilayershave corroborated the picture derived from studies of photoelectrical perfor-mance. The short exciton diffusion length in PEOPT is 5 nm, consistent withboth PL quenching and photodiode performance.


6.3 Internal and External Quantum Efficienciesof Organic Photodiodes

The spectral response, or action spectrum, of a phototodiode is obtained bymeasuring the electrical response of the device upon monochromatic illumi-nation over a wide range of wavelengths. The external quantum efficiencyη, often also called the incident photon-to-current efficiency (IPCE) of thedevice, is the ratio of the measured photocurrent (in electrons per unit areaand time) to the intensity of incoming monochromatic light in photons perunit area and time. Explicitly,

η = 1240Jsc

λL0, (6.33)

where Jsc is the photocurrent density in μA/cm2, λ is the wavelength in nm,and L0 is the light intensity in W/m2.

In order to study the physics of charge generation and transport in devices,it is helpful to define an internal measure. The internal quantum efficiency(IQE) or quantum yield can be obtained from the external quantum efficiencyby considering only the light absorbed in the device. The sum of total absorp-tance A, transmittance T and reflectance R must be unity: A + T + R = 1.In the case of thick devices, the transmittance is zero. Therefore the internalquantum efficiency is

ηIQE =η

1 − R=

η

A. (6.34)

In the case of thin devices, the transmittance may not be zero and the conceptof IQE becomes less well defined. Most polymer photovoltaic cells are quitethin and only the photons absorbed in the active regions of the device cancontribute to the photocurrent. The useful absorptance in the cells is givenby

Aactive =∑

I

AI ,

where i denotes the photoactive layers in the device, in which absorption cangenerate charge carriers.

It is possible to define a quantum efficiency describing the true efficiency ofthe material in the photoactive layers, i.e., the efficiency of exciton-to-chargegeneration (QEC) [19]

ηQEC =η

Aactive. (6.35)

This quantity is mostly helpful in the comparative analysis of photodiodes.As action spectra are normally taken at monochromatic illumination of lowlight intensity, limitations to transport are not always evident in these mea-surements. They are, however, of great importance when using high intensitypolychromatic illumination.


For solar cells, we are interested in the power that can be extracted fromthe device. The quantity of interest is the power conversion efficiency (PCE),which is the ratio of output electrical power Pout to input optical power Pin :

ηPCE =Pout

Pin= FF

JscVoc

L0. (6.36)

A useful convention is the fill factor FF. It is related to the maximum quantityof electrical energy extracted from the solar cell, characterised by an open-circuit photovoltage of Voc and a short-circuit current density Jsc. The fillfactor for a device is described by

FF =(JV )max

JscVoc, (6.37)

where J and V are the values for the current density and voltage which maxi-mize their product. The fill factor thus incorporates all mechanisms reducingthe photogenerated current due to recombination, trapping, resistive losses,etc. While the FF is a real number, we may also evaluate the performanceof solar cells with a plot of the product JV versus voltage, a function whosemaximum is located at the FF. This plot may be helpful when classifyingdevices of different construction.

6.4 Electrical Transport in Photodiodes

Whether prepared in the form of blends or with sharp or diffuse multilayersof pure materials, the real aim of organic solar cells is to convert energy.The generation of charges by photoinduced charge separation may well reach100%, but current drawn from the cell could still be limited by recombinationlosses, resistive layers, traps and other problems. We may study the transportof photogenerated charge carriers in model experiments, where donor andacceptor phases are deposited as thin layers on top of each other. If we are ableto arrive at an optically sharp interface, we will be able to combine opticalmodelling (Sect. 6.2) with modeling of electrical transport in the device. Inprevious studies on PEOPT/C60 bilayers, we have neglected any influenceof electrical transport in the photodiodes under short-circuit conditions, anuntenable assumption. Applying a model of field dependent mobility for thepolymer layer and using the concepts of internal quantum efficiency discussedabove, we are able to fit multisample photocurrent data to a common model.This indicates that the C60 layer acts as a photoconductor, which limits thephotogenerated current for sufficiently thick C60 layers. When studing thecurrent density–voltage behavior of bilayer devices in the dark, we note thatthe applied voltage will drop mainly across the C60 layer. A space-charge-limited current is apparent, located within the C60 layer [20].


6.5 Nanostructure in Polymer/Moleculeand Polymer/Polymer Blends

Photovoltaic devices constructed with a photoactive layer from a blend ofmaterials with suitable electroaffinity values may give a very effective dis-sociation of excitons at interfaces distributed inside the bulk of the layer.Charges are then transported to the electrodes using the respective mate-rial phase (donor/acceptor) driven by the electric field. A common result forsolid-state polymer blends is a phase separation in discrete domains of thecompounds due to the low entropy of mixing of polymers. Therefore, the ef-ficiency of devices based on blends depends strongly on the miscibility of thecompounds, and the morphology of the phase-separated domains. The scaleof the phase separation – the size of the domains of the different polymers –span the nanometer to micrometer scales, and therefore dramatically changethe interface area. When domain sizes are on the same scale as the excitondiffusion length, generally 5–10 nm in conjugated polymers, the efficiencyof photoinduced charge separation in photovoltaic devices is significantly im-proved. The morphology of phase-separated domains can be influenced by thechoice of solvent and the kinetics of solid formation from polymer solution,i.e., the evaporation rate.

Fig. 6.7. SFM pictures with different ranges on the vertical scales:(a) POMeOPT+PTOPT+C60 (1:1:2), (b) PTOPT+C60 (1:1), and (c)POMeOPT+C60 (1:1) blends spin-coated onto ITO/glass substrates


Fig. 6.8. Optical absorption of PTOPT+POMeOPT+C60 (1:1:2) (continuous line)and spectral response for the Al/PTOPT+POMeOPT+C60 (1:1:2)/ITO diode(dashed line)

We studied polythiophenes (PT) decorated with side chains to make agood solid solvent for C60. Unfortunately, it was noted that layers preparedfrom such POMeOPT/C60 blends make poor devices [POMeOPT is poly(3-(2′-methoxy-5′-octylphenyl)thiophene]. Adding a second polythiophene toobtain PTOPT [3-(4-octylphenyl)-2,2′-bithiophene], which exhibits majorphase separation with C60 in blends (see Fig. 6.7b), as well as phase sep-arating with POMeOPT, we are unable to observe phase separation in thethree-component blend (see Fig. 6.7a). Since this was recorded with scanningforce microscopy, we are only able to conclude that phase separation is notvisible on the surface. In fact it may well be hidden under the surface. Butone conclusion from these studies is that this low degree of nanostructure for-mation is still sufficient to enhance the performance of polymer/C60 blends.Figure 6.8 shows action spectra for ITO/POMeOPT:PTOPT:C60 (1:1:2)/Aldevices with peak η around 15%, significantly better then a mixture of oneof the polymers with C60 [11].

Combining our optical modeling results with the use of polymer blends,we note that an alternative should be a combination of blend and bilayerdevices obtained by stratifying the layers. It is possible to change the sharpheterojunction of a bilayer device into a diffuse junction of donor and acceptormaterials. This will increase the area of the donor–acceptor interfaces but alsoallow us to locate the junction close to a maximum of the optical electricalfield, in order to use the active interfaces at the peak of light intensity. Thismay help in improving the efficiency of photovoltaic devices. Stratificationshould also ensure that none of the donor or acceptor phases are in contactwith both electrodes; only one electrode should be in contact. Our attemptsto build such structures by sequential spin coating of organic layers have


successfully enhanced the performance of photodiodes [21], but we have notyet found proof that the structure obtained in stratified multilayers depositedby sequential spin coating from solvents is suitable. The enhanced efficiency insuch devices is a good sign. We also note that the best performance reportedfrom polymer/molecule blends comes from a special choice of the commonsolvent for both species, deposited by spin coating from chlorobenzene to givea suitable nanostructure [22].

Fig. 6.9. Short-circuit action spectra of bilayer devices constructed with neat poly-mer and blends. (a) PBOPT, BEHP-PPV and PBOPT:BEHP-PPV blend (1:1). (b)P3HT, BEHP-PPV and P3HT:BEHP-PPV blend (1:1). (c) PTOPT, BEHP-PPVand PTOPT:BEHP-PPV blend (1:1)

A different combination of blend and bilayer structures can also be quiteefficient. Having a mixture of polymers in the donor layer and using C60 asthe acceptor provides a way of increasing the spectral range of absorption ofphotovoltaic cells while retaining good collection efficiency [23]. A blend donorlayer can also be used to mimic the process of photosynthesis where many


pigments with narrow absorption bands collect light that is transferred toa ‘reaction center’ through non-radiative excitation transfer, called Forstertransfer [24]. The Forster mechanism of excitation energy transfer, from adonor (D) to an acceptor (A), involves weak coupling between them, i.e.,long D–A distances. In this case the excitation (localized exciton) jumps fromone material to the other. By blending the right combination of polymers, asimilar process can be made to happen, where a high absorption coefficientpolymer improves the total device absorption and transfers the exciton toa polymer, with a better interface for exciton ionization and good chargetransport.

Fig. 6.10. Photoluminescence spectra of polymeric films of BEHP-PPV, PBOPTand the blend BEHP-PPV:PBOPT in the ratio 1:1

When studying photodiodes prepared as bilayers of poly(2-(2′,5′-bis-(2′′-ethylhexyloxy)phenyl)-1,4-phenylenevinylene) BEHP-PPV/C60, PTs/C60and blend (BEHP-PPV:PTs)/C60, we note that the external quantum ef-ficiency at short-circuit current shows values increasing in that sequencefor the three systems poly(3-(2′-butyloxy-5′-octylphenyl)thiophene) PBOPT,PTOPT, and poly(3-hexylthiophene) P3HT. The blend is always superior.Figure 6.9 shows the action spectra of ITO/PEDOT/PTs, BEHP-PPV andblend (1:1)/C60/Al devices, where the polythiophene is PBOPT in Fig. 6.9a,P3HT in Fig. 6.9b, and PTOPT in Fig. 6.9c. The spectral response of thediodes corresponds to the absorption of the materials and is given in terms ofthe monochromatic external quantum efficiency η. The diodes in Figs. 6.9aand b are thicker than in Fig. 6.9c. Therefore the shapes of the spectra of the


diode BEHP-PPV/C60 taken in Figs. 6.9a and b differ from that in Fig. 6.9cand the efficiency is lower.

Fig. 6.11. Tapping mode SFM pictures of BEHP-PPV:PBOPT (1:1) blend filmtaken in (a) height and (b) phase contrast

It was shown earlier that the efficiency of the diode depends significantlyon the thicknesses of the layers due to the optical field distribution inside thedevice, caused by the interference of the incoming light with light reflectedfrom the mirror cathode. The blend diode is always more efficient than theneat diode. The excitation created by absorption in the PPV phase is trans-ferred to the polythiophene, where a more efficient charge separation processis possible, as is clear from Figs. 6.10 and 6.11.

We have also studied photodiodes with the polymer blend (BEHP-PPV:polythiophene) but without C60. We find very small photocurrents and no ev-


idence for photoinduced charge transfer in the polymer blend. The absorptionbands of PTs and BEHP-PPV are well separated, which allows us to identifythe contribution of the two polymers to the photocurrent. Charge formationoccurs mainly by excited state dissociation at the polymer/C60 interface, butalso with a contribution to the photocurrent from light absorption in the C60layer, important mainly for thick C60 layers. The PTOPT/C60 diode is moreefficient than BEHP-PPV/C60, suggesting better exciton dissociation at thePTOPT/C60 interface or more efficient charge collection. For the photodiodefabricated with the polymer blend, both BEHP-PPV and PTOPT contributeto the photocurrent. When we decrease the amount of the polymer, as in theblend, the efficiency of the blend device is much higher than the average ofthe efficiency of the neat bilayer diodes. At 430 nm, the value of η for thediode reaches 38%, while the values of η for the neat polymers PTOPT andBEHP-PPV are 28% and 16%, respectively. Enhancement at this wavelengthcan be estimated at 1.7 times the average and can be understood as a con-sequence of the Forster transfer of excitons from BEHP-PPV to PTOPT.Excitons not dissociated at the BEHP-PPV/C60 interface are transferred bythe Forster mechanism to the PTOPT polymer, where they are dissociated ata more efficient interface, namely PTOPT/C60. This transfer is also evidentin the low photovoltage recorded with these devices, typical of polythiophenephotodiodes.

6.6 Conclusion

The physical performance of thin film organic photovoltaic devices is greatlymuch affected by very thin layers whose thickness is less than a few wave-lengths of the light absorbed in the organic materials. The short transportdistance of photogenerated charges is essential, due to the poor mobility ofcharge carriers in these solids. We have shown here how a detailed opticalmodel is needed to fully account for the reflection and interference of lightinside such thin multilayered devices. This may create good opportunitiesfor testing the basic hypotheses of device physics, but it rarely leads to highperformance because of the small interface area between donor and accep-tor layers. Still, they are also of considerable importance for understandingelectrical transport in multilayer photodiodes in the dark [20] and under il-lumination.

For devices where a large interface between donor and acceptor moleculesis created, such as in vertically stratified photodiodes and bulk heterojunc-tion materials, a more complex optical situation is now at hand, requiringextended models for these heterogeneous or graded materials. The hetero-geneity may also extend to the case where multiple polymers are broughttogether in a common donor phase, combined with an acceptor phase instratified or layered devices. Possibly of much greater importance than thefine details of optical profiles and generation of excited states is the nanos-


tructure of the photovoltaic donor –acceptor blend materials, where chargetransport, charge recombination and charge trapping are heavily influencedby the geometrical constraints of electrons and holes hopping on a mani-fold of materials in convoluted geometries. The opportunity for generatinga large interface between polymers and small molecules is much better thanin the case of two high molecular weight polymers, although the creation ofelectronic ‘cul-de-sacs’ is also very great. Much progress is to be expectedin the development of photovoltaic materials combining several phases in awell controlled geometry, a geometry that should also preferably be close to athermodynamic minimum in order to allow stable and continued operation.Both polymers and molecules are expected to contribute towards attainingthis goal.

Acknowledgements. Results reported in this chapter include contributionsfrom Drs. Leif A.A. Pettersson, Lichun Chen, and Dmitri Godovsky. Poly-mers were supplied by Mats Andersson’s group at Chalmers University ofTechnology, Sweden. Work was funded by the Goran Gustafsson founda-tion, the European Commission Joule 3 Project (Contr. JOR3CT980206),the Swedish Natural Science Research Council, and the Swedish ResearchCouncil for Engineering Sciences (TFR). The authors express their gratitudeto all concerned.

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7 Dye-Sensitized Solar Cells

Jan Kroon and Andreas Hinsch

Ever since the invention of the silicon solar cell in the 1940s, people haveacknowledged the enormous potential of photovoltaic systems for large scaleelectricity production. However, semiconductor grade silicon wafers are ex-pensive so great effort has been put into developing cheaper thin-film solarcells and modules. Such films may be purely inorganic (amorphous silicon,cadmium telluride, copper-indium-diselenide) or contain organic materials asan essential part of the device. Examples of the latter are:

1. dye-sensitized photoelectrochemical solar cells (nc-DSC),2. molecular organic solar cells (MOSC) made from relatively small organic

molecules,3. polymer organic solar cells mainly based on electrically conductive poly-

mers.

These three types have an enormous potential for future photovoltaic appli-cations. There are several reasons for this:

• Reduction of production costs: amounts and required purity of organicmaterials are low and large scale production is considered to be relativelyeasy compared with most inorganic materials, involving low temperatureprocessing at atmospheric pressure, cheap materials and flexibility.

• They can in principle be tailored to all needs due to the infinite variabilityof organic compounds, and this makes them widely applicable.

The current status of research into the three above types can be summarisedas follows. The interest in nc-DSC has increased enormously since the re-port by O’Regan and Gratzel in 1991 [1]. This photoelectrochemical cell isbased on a charge transfer from light-excited dye molecules to an inorganicsemiconductor with a large bandgap. By using nanostructured TiO2 that haspores on the nanometer scale, enough light can be absorbed to achieve use-ful efficiencies. Indeed, these devices have shown efficiencies up to 11% oversmall areas (0.25 cm2) and 5–8% over somewhat larger areas (1–5 cm2) [2]. Atthis stage, fundamental and technologically oriented research are running inparallel. While many academic research groups are investigating the variousunknown aspects of this solar cell, several companies and institutes aroundthe world have concentrated their efforts on the technological developmentof efficient large-area multicell modules that are simple to make and stablein the long term.

274 Jan Kroon and Andreas Hinsch

Molecular organic solar cells, made in most cases from flat aromaticmolecules like phthalocyanines and perylenediimides, have been under inves-tigation since the early 1970s. In 1979 Kodak patented an organic two-layerp–n heterojunction with an efficiency of 0.95% and this remained valid fornearly 20 years. By then, the effect of doping with fullerene (C60) moleculeshad been investigated in a three-layer device and this resulted in an effi-ciency of 1.1% [4]. Very recently, a significant efficiency enhancement wasdemonstrated for a laboratory Schottky-type MOSC based on single crystalsof pentacene (η = 4.5%) after molecular doping with bromine [5].

The youngest and fastest growing field in organic solar cell research isbased on the use of electrically conducting polymers as photovoltaic ma-terials. The inherent processing advantages of this technology, already de-veloped for a number of thin film technologies (e.g., light-emitting displaysLED, field-effect transistors FET), combined with the flexible possibilitiesfor chemically tailoring desired properties, make polymer-based solar cellsvery attractive. Presently, external power conversion efficiencies of up to 3%have been achieved for laboratory cells consisting of a bulk heterojunctionof light-absorbing polymers such as phenylene-vinylene and fullerene (C60)molecules [6]. Although several aspects remain to be investigated (e.g., con-ducting polymers with better light absorbing properties, film morphology,device stability), these encouraging numbers promise a cheap production pro-cess for efficient ‘plastic’ solar cells in the future.

The photoelectrochemical (i.e., liquid-containing) nc-DSC is closer tomarket introduction than the fully organic/polymeric solar cells of types (2)and (3). For the short term (< 5 years), commercialisation of the nc-DSCtechnology is expected for low-power indoor applications such as calculators,watches, clocks, and electronic price tags. This should work as a steppingstone for the introduction of mid- and high power applications, which aremainly intended for outdoor use. In principle, the colour and design of theproducts for large area power applications can be varied to a larger extentthan with several other solar cells, but there is always an optimum in thefreedom of design and the performance of the cell.

For a successful market introduction of nc-DSC technology, several factorsstand out: technical performance and manufacturability, cost, design, marketdemand and, last but not least, long-term stability.

In order to transfer the results achieved for small laboratory cells to a fullproduction line for dye-sensitised solar modules to be used for indoor andoutdoor applications, all process steps and technological parameters relevantfor industrial production have to be investigated. Topics that are essentialfor reliable and cheap production technology are listed below:

• large-area deposition of uniform TiO2 layers,• development of methods for dye-staining and electrolyte-filling,• internal electrical interconnection of individual cells,• sealing of modules,

7 Dye-Sensitized Solar Cells 275

• long term stability,• evaluation of process steps in terms of costs.

In this chapter, we first describe the basic working principles and componentsof the nc-DSC, then address a number of technologically related issues likemanufacturing and long-term stability.

7.1 Operating Principlesand Cell Structure of the nc-DSC

A schematic representation of the construction and operating principles ofthe nc-DSC is shown in Fig. 7.1. In the basic version, the device consists oftwo glass substrates coated with a transparent conducting oxide (TCO) suchas SnO2:F, with high optical transmission and low resistance.

TiO2

TCO

glass

glassTCO

3I-

3I-

I3-

I3-

S S*

S+

e-

Pt

e-

dyelight

counter electrode

photoelectrode

Fig. 7.1. Schematic representation of the nc-DSC showing various components

On one side of the cell (the photoelectrode), a porous layer (5–15 μm) ofsome wide bandgap semiconductor is deposited. This is composed ofnanometer-sized particles (10–20 nm), connected to form a three-dimensionalconducting network. A typical material is TiO2. A monolayer of sensitizingdye is adsorbed on the nanocrystalline oxide film. On a flat substrate, a singledye monolayer should absorb less than 1% of the incident light, but due tothe nanocrystalline character of the film, the surface area of the photoelec-trode can be enlarged by a factor of about 1 000. The second TCO substrateis coated with a catalytic amount of platinum and serves as the counterelectrode. In a complete cell, photo- and counter electrode are clamped to-gether and the space between the electrodes and the voids between the TiO2


particles are filled with an electrolyte containing a redox couple, usually io-dide/triiodide (I−/I−3 ) in a non-viscous organic solvent. The general operatingprinciples of this photoelectrochemical dye solar cell are depicted in Fig. 7.2.

S/S+

S*/S+

e -

Load

(I-↔ I3-)ΔΔΔΔVmax

e- e-

(I3-↔I-)

1

23

4

567

TCO TiO2 Dye Electrolyte Cathode

Fig. 7.2. Schematic representation of the forward reactions (steps 1–4, indicatedby plain arrows) and recombination routes (steps 5–7, indicated by dotted arrows)taking place in the nc-DSC. (1) Optical excitation of the sensitizer. (2) Electron in-jection from the excited sensitizer (S∗) to the conduction band of TiO2. (3) Electronpercolation through the network of TiO2 particles. (4) regeneration of the oxidizedsensitizer (S+) by iodide (I−). (5) Deactivation of the excited state of the sensi-tizer (S∗). (6) Recombination of injected electrons with oxidised sensitizer (S+). (7)Recombination of conduction band electrons with triiodide (I−

3 ) in the electrolyte.ΔVmax is the maximum voltage that can be generated under illumination and cor-responds to the difference between the Fermi level of the conduction band of TiO2

under illumination and the electrochemical potential of the electrolyte

Photons enter through the photoactive electrode and can be absorbed bysensitizer molecules (S) at various depths in the film. The sensitizer molecules(S∗) excited in this way inject electrons into the conduction band of theadjacent TiO2 particles (e−

CB), leaving an oxidised sensitizer molecule (S+)on the TiO2 surface:

S∗ −→ S+ + e−CB .

The injected electrons percolate through via the interconnected TiO2 parti-cles to the TCO substrate and are fed into an electrical circuit, where work


can be delivered. The oxidised sensitizer is reduced by the electron donor(I−) present in the electrolyte, filling the pores:

2S+ + 3I− −→ 2S + I−3 .

The triiodide (I−3 ) produced in this way diffuses to the counter electrode,where it is reduced back to iodide by metallic platinum under uptake ofelectrons from the external circuit:

I−3 + 2e− −→ 3I− .

The maximum voltage ΔVmax that can be generated under illumination cor-responds to the difference between the Fermi level of the conduction band ofTiO2 under illumination and the electrochemical potential of the electrolyte.

Loss Routes. In the operation of the nc-DSC, there are three possible lossor recombination routes which could lead to lower performances than themaximum obtainable:

• the rate of deactivation of the excited state of the sensitizer could competewith the rate of electron injection (step 5 versus step 2 in Fig. 7.2),

• recombination of the injected electron with the oxidized sensitizer couldcompete with regeneration of the oxidized sensitizer by iodide (step 6versus step 4 in Fig. 7.2),

• during electron transport through the TiO2 film, electrons can recombinewith I−3 in the electrolyte present in the pores (step 3 versus step 7 inFig. 7.2). Clearly, either an increase in the recombination rate with I−3 , ora decrease in the electron transport rate will adversely affect photocurrentgeneration in the external circuit.

7.2 Manufacture of a Standard Glass/Glass nc-DSC

A general scheme of the main process steps used to manufacture a standardglass/glass nc-DSC can be described as follows:

1. structuring (electrical insulation) of the TCO–glass plates,2. hole-drilling on the counter electrode side,3. screen-printing of conductive silver lines for adequate current collection,4. screen-printing of colloidal TiO2 and platinum-containing pastes on the

front and counter electrodes,5. sintering of the TiO2 and platinum layers between 400 and 500◦C,6. coloration of the TiO2 electrode by chemical bath deposition,7. sealing/lamination of the front and counter electrodes,8. injection of electrolyte through filling holes and device closure,9. electrical contacting and wiring.


Fig. 7.3. Representative picture of a 7.5 × 10 cm2 plate containing five individualnc-DSCs (active area 4 cm2). The coloration step is shown, flushing the dye solutionafter sealing through holes on a filling unit [7]

Depending on the thermal stability of the dye, the duration of the seal-ing/lamination step and the sealing material, dye coloration (process step 6)can also be carried out after sealing (process step 7) by flushing the cell withdye-containing solution through the filling holes.

Following the described process steps, single cells can be made over rel-atively small areas (< 5 cm2) to optimize all the different elements in thedevice. A representative picture of a 7.5 × 10 cm2 SnO2:F plate containingfive individual cells of 5 × 0.8 cm2 is shown in Fig. 7.3.

7.3 Module Designs

For the production and upscaling of practical solar cells on large areas, mod-ules have to be constructed from individual cells. The relatively high sheetresistance of the SnO2:F coating (usually about 10 Ω/�), used as the currentcollector, limits the width of individual cells to less than 1 cm.

One way to avoid Ohmic losses due to the high sheet resistance of theSnO2:F coating is to apply a current collector grid to the conducting glass,similarly to the technique used for silicon technology. Since silver is usuallythe material of choice, it is of great importance to protect the silver grid ad-equately from the highly corrosive iodide-containing redox electrolyte, whichis currently used in dye solar cells.


Another strategy for reducing Ohmic resistance losses in a module is toconnect many parallel single cells in series. In practice this means that thephotovoltage of the modules increases while keeping the current constant.

7.3.1 Series Connection of Glass/Glass Devices:Z- and W-Type Interconnection

For the basic glass/glass configuration, two series connection designs are pos-sible. These are described below.

Figure 7.4a shows a schematic representation of a Z-type interconnectedmodule. The Z refers to the path that the current flows from one cell to theother via the SnO2:F coating. The SnO2:F coating is removed in parallellines by etching procedures, like laser scribing. Adjacent cells are electricallyinterconnected via conductive elements, which have to be protected by in-ternal sealing, preventing shunts and stopping the iodide/iodine-containingelectrolyte from moving from one cell to the other (electrophoresis).

glass Ru-dye on TiO2 SnO2:F coating

sealant Interconnect electrolyte Pt-deposit

-

-

+

+

A

B

Fig. 7.4. Schematic representation of (a) Z-type and (b) W-type interconnectedmodules

The second type is the W connection. As can be seen in Fig. 7.4b, it isimportant to be able to illuminate the module from both sides, since pho-toelectrode and counter electrode layers are alternately deposited on eachglass plate. An advantage over the Z design is that it does not require con-ductive elements between adjacent cells. A disadavantage, however, is thatlight illumination through the platinum counter electrodes, which must betransparent, normally leads to lower currents. This current deficit can becompensated to some extent by making the counter electrodes wider.


7.3.2 Series Connection: Three-Layer or Monolithic Module

An interesting and innovative approach to the industrial fabrication of nc-DSCs is to use a single-faced monolithic structure of consecutive porous lay-ers. In terms of production costs, the advantage of this concept over the‘standard’ glass/glass design is that only one TCO–glass plate is requiredfor a series connection of integrated cells, as is also known from amorphoussilicon technology. This construction principle was first suggested in the liter-ature by Kay and Gratzel [8]. An AM1.5 efficiency of 5.3% has been reportedfor a small module (20 cm2) containing 6 series-connected monolithic cells of4.7 × 0.7 cm2.

-+

back cover

SnO2:F

sealant porous spacer

Ru-dye on TiO2

porous carbon counterelectrode

glass

Fig. 7.5. Nc-DSC in the monolithic setup

Figure 7.5 illustrates the nc-DSC construction principle in the monolithicsetup. Firstly, a layer of nanocrystalline TiO2 is applied as the photoelec-trode. On top of this, a porous insulating oxide layer (ZrO2) acts as a spacer.Finally, a porous graphite layer activated by carbon black pigments serves ascounter electrode for the iodide/iodine-containing electrolyte. All three lay-ers of the cell can be deposited by screen or stencil printing techniques onprestructured TCO–glass. At this stage, the layers are sintered, after whichdye and electrolyte are applied, and finally a non-functional material, whichonly serves to seal and insulate the cell, covers the whole module.

7.4 Sealing Aspects

The presence of a liquid electrolyte requires hermetic sealing of the modulein order to prevent evaporation of the solvent as well as intrusion of waterand oxygen. The sealing materials have to meet several requirements:

• chemical stability in contact with the liquid electrolyte,• excellent barrier properties in order to minimise solvent losses (typicallynitriles) during the service time of the module, and intrusion of waterand oxygen,


• good and stable adhesion of substrates to the TCO and glass,• processing compatible with other components of the nc-DSC.

Inorganic glass frits can be used to seal glass/glass modules. Hermetic sealshave been achieved for module sizes up to 30 cm × 30 cm, by carefully se-lecting thermal expansion coefficients to match that of the standard floatglass [9]. High temperature profiles and equipment similar to those used inindustrial glass bending and glass hardening have proved necessary in thiscase. Consequently, the dye and electrolyte have to be filled through smallholes in the glass after the sealing process. These holes must then be closed(see Sect. 7.2), implying additional cost factors. For this reason, low-cost or-ganic adhesives, which can be applied at much lower temperatures, are stillvery attractive in relation to future industrial production, although organicmaterials are never completely tight.

Several organic sealants such as epoxy resins, butyl rubber or siliconesprove to be more or less permeable and the tiny amount of solvent in the cellis rapidly lost. Suitable organic sealing materials for this technology turn outto be thermoplastic materials, like polyethylene/carboxylate copolymers. Sofar, Surlyn 1702 ionomer from Dupont has been the main substance used tooptimize cell performance and build module prototypes. However, the soft-ening point of Surlyn is rather low (65◦C) and at elevated temperatures(> 70◦C), serious solvent loss is observed because the bond between Surlynand TCO-coated glass is substantially weakened [7].

For outdoor applications, solar cells/modules have to survive tempera-tures up to 80◦C, and Surlyn would not be the best material. Therefore,polymer-sealing materials with higher heat resistivity are needed. It has beenreported that some linear LDPEs (low-density polyethylenes) and HDPEs(high-density polyethylenes) have shown promising results [10–12]. Bynel (ananhydride modified LLDPE) from Dupont is now regularly used as a sealingmaterial in nc-DSCs.

In the monolithic setup, a non-active flexible foil, such as aluminium, canbe used to cover the module. This is impermeable to gases and vapors. Themetal foil is laminated with a thermoplastic layer (Surlyn), which is neededfor hot sealing, while an additional layer of polyester is used for corrosionprotection and electrical insulation.

7.5 Technological Developmentand the State of the Art

A number of groups are working on upscaling nc-DSC technology for indoorand outdoor applications. Details of technological processing are not normallyprovided at this stage, but some general information reported in variouspapers is summarised in this section.

The INAP/Germany consortium has been working on the upscaling andimprovement of nc-DSC technology since 1995 [10–12]. The goal of the work


at INAP is to reach the pilot production stage for modules > 100 cm2 forhigh power applications. Their focus is on automating most process steps andreducing fluctuations in module properties introduced by manual handlingand variable material quality. After the introduction of the monolithic conceptby Andreas Kay [8], INAP demonstrated the feasibility of monolithic moduleswith 30×30 cm2 panel sizes [10]. Since there were a lot of uncertainties at thatstage concerning the materials used in this design, they decided to focus onthe basic Z-type interconnected glass/glass module technology, described inSect. 7.3.1. In 1998, an energy conversion efficiency of 7.0% had already beenreported for a module with an active area of 112 cm2 containing 12 single cells[10]. Several sealing materials and interconnects were investigated in termsof permeability, heat resistivity, electrical properties and compatibility withnc-DSC technology. Working prototypes of 50×50 cm2 Z-type interconnectedmodules were demonstrated [13]. Technological details of the processing andperformance are not known.

Sustainable Technologies Australia (STA) Ltd. started in March 2000 withthe construction of the first manufacturing pilot plant for nc-DSCs basedon Z-type interconnected glass/glass module technology. They opened theirproduction facilities in May 2001. The building blocks for STA DSC productsare solar cells with a size of 10 cm×18 cm. These are assembled into four-cellmodules. Prototypes of these modules are shown on the STA website [14].

ECN (Netherlands), IVF (Sweden), Leclanche SA (Switzerland), EPFL(Switzerland), Uppsala University (Sweden), IPM (Italy), DSM Research(Netherlands) and Pricer AB (Sweden) collaborated in a two year Europeanproject (from 1997 to 1999) where the whole range of aspects related to theproduction and testing of nc-DSC for indoor applications was investigated[15]. Starting from lab-scale experience, the partners worked on the followingitems: evaluation of manufacturing concepts, development and preparation ofmaterials and components, large scale batch processing of modules, standardtesting and material characterisation, production line design including com-puter simulation and cost analysis. Since then, mechanisation of individualprocess steps has continued at ECN, resulting in the realisation of a completebaseline for nc-DSC in 2001. This baseline is now used to produce solar cellswith dimensions up to 10 cm × 10 cm for outdoor applications.

An interesting approach to applying nc-DSC technology on flexible sub-strates has been announced by Lindstrom et al. [16]. A new method wasintroduced which completely avoids the high-temperature sintering step bymechanically pressing the colloidal films. Efficiencies up to 5.2% have beenobtained at 0.1 sun using plastic substrates. This press technique, operatingat room temperature, offers the possibility of working on flexible substrates,and this provides the basis for a continuous production technique.


7.6 Large Scale Batch Processing of Mini-Modules

As mentioned in the introduction, nc-DSCs are expected in the short termto be available for low-power applications, competing with other thin filmtechnologies, among which amorphous silicon is already an established tech-nology.

One aspect of indoor applications which makes sealing somewhat lesscritical is the low temperature range under operation and storage, as well asthe possibility of using electrolytes with high viscosity and high boiling point.For commercialisation of indoor dye devices, it is of the utmost importanceto simplify and optimize the currently known process steps.

In the above-mentioned European project [15], a number of partners haveinvestigated every aspect of the production and testing of nc-DSC for indoorapplications. The goal of the project was to design a production line for in-door modules and to calculate the total cost. It was concluded that, amongthe various possible fabrication concepts, production of the monolithic con-cept described in Sect. 7.3.2 is in principle the most attractive for industrialproduction of Dye Indoor PV modules. A large part of the activity focusedon processing large batches of mini-modules, for which the individual processsteps have already been mentioned in Sect. 7.3.2.

(a) (b)

(c)

Fig. 7.6. (a) Standard screen-printing equipment. (b) Master plates leaving thein-line drying furnace after screen-printing. (c) Master plates after sintering in abatch oven


Since modules are prepared with several elements in series, the TCO onthe glass substrate must be structured in thin lines in order to separate in-dividual elements. Therefore, cleaned SnO2:F master plates with a size of10 × 10 cm2 are structured using a Nd:YAG laser. Three layers are subse-quently deposited on the TCO plate using standard screen-printing equip-ment in a clean room environment (Fig. 7.6a). Three different screen-printpastes have been developed for the monolithic cell design, containing TiO2,zirconium dioxide, and carbon black, respectively, as well as organic me-dia/binders.

After each printing step, the master plates are dried using an in-line IRbelt furnace (Fig. 7.6b). This involves levelling the layers, evaporating thepaste solvent and then substantially shrinking the layers. After the dryingstep, the layers are fired at 450◦C in a batch oven to burn out organic resid-uals (Fig. 7.6c). These processing steps are carried out with commerciallyavailable materials and equipment, e.g., laser structuring, screen-printing,and standard drying and sintering ovens.

Further process steps such as dye coloration, electrolyte filling and seal-ing/lamination, leading to sealed completed modules, have also been carriedout on 10× 10 cm2 substrates. For these process steps, dedicated equipmenthas been developed from the laboratory stage, since it is not commerciallyavailable. A photo of a fully processed master plate is shown in Fig. 7.7. Itcontains 4 modules of 5 cells each (total area of 1 module 20 cm2) on oneTCO plate of 100 cm2. These modules were intended for LCD powered pricetags on supermarket shelves.

The five-cell dye module with the design showed in Fig. 7.7 was comparedwith a commercially available amorphous Si module (for price tag applica-tion) and similar performance was demonstrated for the active module area.The I–V parameters are shown in Table 7.1.

Table 7.1. Comparison between I–V parameters of an amorphous silicon moduleand a five-cell dye module

Light intensity Isc Voc FF Pmax

[lux] [μA/cm2] [mV/cell] [μW]

Three-layer 50 4.9 502 0.56 12.6monolithic 250 26.1 574 0.52 69.8module

Amorphous 50 3.9 612 0.63 13.9silicon 250 18.5 677 0.62 70.1


Fig. 7.7. Fully processed master plate (10 × 10 cm2), containing 4 mini-modules.The dye used is N719 [Ru(NCS)2(2,2′-bipyridyl-4,4′-dicarboxylate)2]. A moltensalt, hexylmethylimidazolium iodide (HMII) containing 10 mM I2, was used asthe electrolyte

7.7 Long Term Stability

Besides the establishment of a reliable processing technology for nc-DSC, thelong term stability of the cells/modules has to be guaranteed. The overallstability of the cell is controlled by the intrinsic and extrinsic stability. Theintrinsic stability is related to irreversible (photo-)electrochemical degrada-tion of the dye and/or components of the electrolyte solution. Evaporationof the electrolyte solvent and intrusion of water and oxygen determine theextrinsic stability of the device. This requires hermetic sealing materials andreliable sealing methods, as discussed in Sect. 7.4. Standard testing accordingto IEC standards (environmental and accelerated) can be applied to nc-DSCs.It should be mentioned that these tests are mainly developed for inorganicsolar cells and have to be tuned so that they stress dye solar cells and modulesin a way which present standards do not.

7.7.1 Stability Tests on Indoor Dye PV Modules

Environmental and accelerated ageing tests were performed on the indoordye modules described in Sect. 7.6 in order to detect failure mechanisms.Contrary to expectations, many modules survived humidity/freeze cyclingtests (10 cycles, 85%, 20 h at 55◦C per cycle) without major degradation,demonstrating the capability of the sealing concept (see Fig. 7.8). This wasalso true for temperature cycling (between −5 and 55◦C). However, it has


28 30 32 34 36 38 40

Isc (μμμμA)1.6 1.7 1.8 1.9 2.0

Voc

26 28 30 32 34 36

Maximum Power (μμμμW)0.46 0.50 0.54 0.58

Fill Factor

Fig. 7.8. Frequency distribution of module performance (at 250 lux) before (con-tinuous lines) and after (dotted lines) environmental testing

been shown from accelerated testing (strong continuous illumination undera fluorescent lamp, including UV-B light) that UV light in particular is aserious degradation factor. Efficient UV filters are therefore recommended inorder to prevent fast degradation of UV critical components in the cell [17].

7.7.2 Long Term Stability Tests on High Power nc-DSC

In order to predict outdoor module lifetimes, appropriate accelerated ageingtests are needed to make useful extrapolations to realistic outdoor conditionsand to identify possible degradation mechanisms.

A systematic investigation of intrinsic chemical stability was carried outon devices specially designed for high power applications [7]. For this purpose,accelerated ageing test procedures were developed for nc-DSCs and it turnedout that, to first order, a separation can be made between the effects of visiblelight soaking, UV illumination and thermal treatment on long term stability.

• Visible light soaking alone is not a dominant stress factor, which meansthat the dye (a ruthenium bipyridyl complex) used in these tests is sur-prisingly stable [7,18,19].


• UV light exposure often leads to strong degradation due to loss of iodinein the electrolyte. A dramatic improvement in stability can be obtainedby using surface additives like MgI2 and CaI2 in the electrolyte [7].

• Thermal stress appears to be one of the most critical factors determiningthe long term stability of nc-DSCs and is strongly related to the chemicalcomposition and purity of electrolyte solvents and additives [7]. Continu-ous (1 000 h at 85◦C) and periodic (−40 to 85◦C, 200 cycles) thermal testsaccording to IEC norms appear promising since no leakage of electrolytesolvent was observed, but with 30–40% loss in efficiency still critical.

• Several Surlyn-sealed cells were exposed to outdoor conditions over a pe-riod of one year. Major failures only occurred due to imperfect sealingand ageing effects on the electrical contacts. The results of the best per-forming cells are shown in Fig. 7.9 and it can be seen that the efficiencyremains remarkably constant after one year of outdoor exposure.

0

1

2

3

4

5

6

7

8

0 100 200 300 400

Days

Effi

cien

cy /

%

Fig. 7.9. Efficiency data for two test cells (active area 4 cm2) exposed to outdoorconditions for 1 year. The efficiencies of the cells were measured from time totime with an indoor solar simulator. The dye used is Ru(NCS)2(2,2′-bipyridyl-4,4′-dicarboxylate)2 (N719). 0.6 M hexylmethylimidazolium iodide (HMII), 0.1 M LiI,0.05 M I2, 0.5 M tert-butylpyridin (TBP) in propionitril was used as the electrolyte.Surlyn 1702 (Dupont) was used as the sealant. The cells were placed under a windowto protect them from rain. Test location INAP, Gelsenkirchen, Germany

Reference can be made to the standard test conditions required for thinfilm and crystalline silicon modules (IEC 1646:1996 and IEC 1215:1993). It isobvious that before nc-DSCs can be commercialized on a large scale, IEC 1646


has to be fulfilled in the current or a somewhat modified form. The ultimateanswer as to whether nc-DSCs can be produced with lifetimes > 20 yearscannot be given at this stage. However, on the basis of present results andknowledge, stability can certainly be improved by a better understandingof the degradation mechanisms and chemical balancing of the electrolytecomponents.

7.8 Outlook

Organic materials are generally considered to offer a range of new possibilitiesin terms of material use and device concepts. Although it is difficult to makefirm statements about the different technologies in this category, there isevery reason to believe that they may be produced at (very) low cost.

Compared to organic/polymeric solar cells, higher efficiency and stabilityare achieved for the dye-sensitized solar cell at the present stage of develop-ment. A number of license holders of EPFL patents and a large number ofother groups including several Japanese companies, research institutes anduniversities are now working towards commercializing nc-DSCs for indoorand outdoor applications and improving our basic understanding.

The first aim is to commercialise the nc-DSC for indoor applications andconsumer electronics. It has been demonstrated [15] that several products forthis type of application are technically capable of fulfilling all the require-ments, although more technological research is still required for large scaleproduction of these cells. For a successful introduction of nc-DSC technologyonto the market, the main challenge is (company) economics. Large through-puts in solar cell production are needed to be price competitive on the alreadyexisting (consumer electronics) market. Another route is to aim for a highervalue product. This means that dye PV products need to be developed whichhave a better performance or which permit broader operating conditions thanother thin film solar cells. Flexibility in the module design for dye PVs mightbe an advantage over other inorganic thin film solar cell technologies in termsof applicability and product diversity.

A pilot line for producing large numbers of small modules also providesimportant knowledge for the future production of much larger solar panels foroutdoor use, where the long term cost target should be less than 1 euro/Wp.The most important issue to be solved is intrinsic stability and particularlythermal stability. A major concern remains the use of a liquid electrolyte.Practical experience will have to demonstrate feasibility.

Long term research into sensitised oxide solar cells focuses on solid-statedevices, where the liquid electrolyte is replaced by a solid charge transportmaterial. As in ‘solid’ batteries, the electrolyte in the dye cell can be gela-tinised, which should obviate electrolyte leakage over long periods of use. Ithas been found that organic liquid-phase electrolytes could be gelled withamino acid derivatives showing comparable efficiencies to liquid electrolytes


[20]. However, at higher temperatures the quasi-solid gel reversibly changedback into a liquid.

Toshiba developed a novel solid state chemically cross-linked gel elec-trolyte, which makes an irreversible three-dimensional network in the poresof TiO2. Interestingly, no significant loss in photovoltaic performance wasfound compared with cells containing liquid electrolytes [21].

A second approach in the development of solid state dye sensitised solarcells is the use of solid p-type hole conductors interpenetrating the nanocrys-talline TiO2 structure. Inorganic p-type semiconductors like CuI [22] andCuSCN [23], and amorphous organic/polymeric hole transport materials [24]have been tested in this regard but so far they have been less efficient (< 3–4%) than photoelectrochemical solar cells containing liquid phase electrolytes.Likewise, most research efforts on fully organic/polymeric solar cells focus onefficiency and stability and much more fundamental research is needed todevelop promising devices. The first applications for this type of solar cellare not expected within a time-frame of 10 years, although this field is cur-rently being explored by a large and rapidly expanding research community.This could lead to faster realisation of the ultimate goal: a very cheap, highlyefficient and stable organic thin film solar cell.

Acknowledgements. Some of the work described in this chapter was fi-nanced by the European Commission under contract numbers JOR3-CT97-0147 (‘Indoor Dye PV’) and JOR3-CT98-0261 (‘LOTS-DSC’). The collab-oration with the co-authors from the partners in the ‘Indoor Dye PV’ and‘LOTS-DSC’ projects listed in the references is gratefully acknowledged.

References

1. B. O’Regan, M. Gratzel: Nature 353, 737 (1991); for an extensive review onthis subject, see K. Kalyanasundaram, M. Gratzel: Coord. Chem. Rev. 117,347 (1998)

2. M.A. Green, K. Emery, K. Bucher, D.L. King, S. Igari: Progress in Photo-voltaics: Research and Applications 6, 35 (1998)

3. C.W. Tang: U.S. Patent 4, 164,431, 8/14/1979; C.E. Tang: Appl. Phys. Lett.48, 183 (1986)

4. J. Rostalski, D. Meissner: Solar Energy Material & Solar Cells, 61, 87 (2000)5. J.H. Schon, Ch. Kloc, B. Batlogg: Appl. Phys. Lett. 77, 2473 (2000)6. S.E. Shaheen, C.J. Brabec, F. Padinger, T. Fromherz, J.C. Hummelen, N.S.

Sariciftci: Appl. Phys. Lett. 78, 841 (2001)7. These plates are used as measurement objects for long-term stability tests of

nc-DSC in the framework of the EU project LOTS-DSC, EU contract no. JOR3-CT98-0261 (1.7.1998–1.7.2001). Collaborating partners are ECN (Netherlands),INAP (Germany), FMF-Freiburg (Germany) and Solaronix (Switzerland). Re-sults are described in: A. Hinsch, J.M. Kroon, R. Kern, I. Uhlendorf, J.Holzbock, A. Meyer: Progress in Photovoltaics: Research and Applications 9,425 (2001)


8. A. Kay, M. Gratzel: Solar Energy and Solar Materials 44, 99 (1996)9. A. Hinsch: private communication10. G. Chmiel, J. Gehring, I. Uhlendorf, D. Jestel: Proc. 2nd World conference on

PV Solar Energy Conversion (Vienna 1998) p. 5311. K.P. Hanke: Zeitschrift fur physikalische Chemie 212, 1 (1999)12. I. Lauermann, G. Chmiel, L. Dloczik, D. Jestel, A. Kuckelhaus, R. Niepmann,

I. Uhlendorf: Proc. 14th European conference on PV Solar Energy Conversion(Barcelona 1997) p. 973

13. I. Uhlendorf: in ESF Conference on Photovoltaic Devices: Thin Film Technology(Berlin 2000)

14. G. Tulloch: oral presentation held at IPS-12, Snowmass, Colorado USA, August2000; STA website www.sta.com.au

15. Indoor Dye PV, Dye Photovoltaic Cells for Indoor Applications: JOULE IIIprogramme, EU contract JOR3-CT97-0147, 1.5.97–30.4.99. Some of the resultsof this project are described in A. Hinsch, R. Kinderman, M. Wolf, C. Bradbury,A. Hagfeldt, S. Winkel, S. Burnside, M. Gratzel, H. Petterson, P. Johander:Proceedings book of extended abstracts, 11th International Photovoltaic Scienceand Engineering Conference (Sapporo City, Hokkaido, Japan September 1999);S. Burnside, S. Winkel, K. Brooks, V. Shklover, M. Gratzel, A. Hinsch, R.Kinderman, C. Bradbury, A. Hagfeldt, H. Petterson: J. of Materials Science:Materials in Electronics 11, 355 (2000)

16. H. Lindstrom, A. Holmberg, E. Magnusson, S-E. Lindquist, L. Malmqvist, A.Hagfeldt: Nanoletters 1, 97 ( 2001)

17. H. Pettersson, T. Gruszecki: Solar Energy Materials and Solar Cells 70, 203(2001)

18. O. Kohle, M. Gratzel, A.F. Meyer, T.B. Meyer: Advanced Materials 9, 904(1997)

19. E. Rijnberg, J.M. Kroon, J. Wienke, A. Hinsch, J.A.M. van Roosmalen, W.C.Sinke, B.J.R. Scholten, J.G. de Vries, C.G. de Koster, A.L.L. Duchateau, I.C.H.Maes, H.J.W. Hendricks: Proc. 2nd World PV Solar Energy conference (Vienna1998) p. 47

20. W. Kubo, K. Murakoshi, T. Kitamuta, Y. Wada, K. Hanabusa, H. Shirai, S.Yanagida: Chem. Lett. 1241 (1998)

21. S. Mikoshiba, H. Sumino, M. Yonetsu, S. Hayase: Proceedings 16th EuropeanPV Solar Energy conference (Glasgow 2000) p. 47

22. G.R. Tennakone, R.A. Kumara, I.R.M Kottegoda, K.G.U Wijayantha: J. ofPhys. D, Appl. Phys. 31, 1492 (1998)

23. B. O’Regan, D.T. Schwartz, S.M. Zakeeruddin, M. Gratzel: Advanced Materials12, 1263 (2000)

24. U. Bach, D. Lupo, P. Comte, J.E. Moser, F. Weissortel, J. Salbeck, H. Spreitzer,M. Gratzel: Nature 395, 583 (1998); J. Kruger, R. Plass, l. Cevey, M. Piccirelli,M. Gratzel: Appl. Phys. Lett. 79, 2085 (2001)

Index

absorptance 263absorption coefficient 124, 133, 203,

259absorptivity 134acceptor layer 249acceptor strength of fullerenes 214action spectrum 263, 268– of bilayer devices 267activation barrier for charge separation

49active interface 259, 260active layer 183, 185, 189, 191, 196,

197, 234, 251, 252, 263, 265– composite 206– thickness 204– width 201admittance spectroscopy 179AM 0 spectrum 119, 139– energy current density 119– photon current density 120AM 1.5 spectrum 119, 186, 195, 222,

225, 229, 230– energy current density 119– photon current density 120ambipolar semiconductor 168, 174,

175, 177anisotropic magnetoconductance 111anisotropy of conjugated polymers

65–67Arrhenius representation 180, 182atmospheric attenuation 119ATR-FTIR 237Auger recombination 136, 141azafulleroid 206, 208, 211– redox potential 209

band bending 178, 212bandwidth 96

BEHP–PPV 267– PL spectrum 268BEHP–PPV/PBOPT blend– PL spectrum 268– SFM image 269BEHP-PPV/C60 diode 269bilayer conjugated polymer–fullerene

solar cell 233bilayer photodiode 251, 252, 259bipolaron 8–11, 71blackbody 118, 139Bloch’s theorem 92Boltzmann distribution 122buckminsterfullerene 14, 16, 249built-in potential 185, 191, 206, 210,

211bulk heterojunction composites 1,

159, 162, 242bulk heterojunction solar cell 163–

168, 175– performance 185–241– simulation 183– temperature behavior 229–236

calibration of solar cells 186–187carrier mobility 146, 147, 169, 197, 234– in organic semiconductors 150– temperature dependence 236charge modulation spectroscopy (CMS)

198charge separation in solar cells

141–153charge transport– in low mobility materials 148–150– in solar cells 143–147charge-separated state 250Child’s law 170–172chlorobenzene 191, 194–196, 198–200

292 Index

condensed phase photophysics 77conduction band 121, 128, 205conductive polymers 4conductivity 98– of doped conjugated systems 97conjugated carbon chain 5conjugated oligomer 57conjugated polymer 1, 4, 57, 159, 188– anisotropy 65–67– charge detection 16–21– doping 10, 21, 22, 57– electron transfer 249– excited states 7– exciton diffusion length 251– in photodiode devices 250– interchain interactions 197– isolated 75– low bandgap 222– molecular structure 4–6– optical and electronic properties 6,

57–83– optical constants 57, 58– photoinduced electron transfer 10– semiconductivity 58– stability 57, 160conjugated polymer–fullerene blend

2–4, 14, 19–21, 160, 162, 167, 206, 240– photoinduced charge generation

21–25– photovoltaic parameters 230– temperature behavior 235conjugated polymer–methanofullerene

blend 185, 241continuity equation 201Coulomb gap 106critical regime 104current stressing 240current–voltage characteristic 125–

127, 139–140, 143, 151, 237– of bulk heterojunction diode 171– of MDMO–PPV/PCBM photovoltaic

device 210, 217–219– of PTPTB/PCBM device 224– of semiconductor diode 169– of solar cell 170, 187– temperature dependence 172, 174,

176CW–PIA 19

cyclic voltammetry 208

dark current 175decay kinetics 82deep trap 172defect 250degradation measurements 237, 239,

240device geometry 188dielectric constant 61, 62– spectroscopic determination 62–65diffusion current 147, 200–202diffusion equation 251, 257diode current 152, 214donor layer 249donor–acceptor heterojunction 233,

249donor–acceptor interactions 15–16,

29–51, 71, 80, 129, 164, 268doping 129–130, 216– of conjugated polymers 10, 21, 22,

57drift current 147, 201, 202drift-controlled device 204dye 275dye-sensitized solar cell 154, 222, 223,

227, 273–289– photoelectrochemical 273

e–e interaction 110, 111efficiency of solar cells 138–140, 186electrical transport in photodiodes

264electron membrane 126, 141, 142, 149,

153electron spin resonance (ESR) 26–29electron trap 169electron–hole interaction 9electron–hole pairs 121– free energy 124, 126– generation 135– non-radiative recombination 136– radiative recombination 125, 137,

138– recombination 136–138electron–phonon interaction 9, 71, 249ellipsometry 64–65, 67, 68, 259equivalent circuit for solar cell

151–153, 214, 215

Index 293

exciton 8–10, 15, 71, 162, 249– binding energy 11– decay 11, 12– diffusion 251, 257– diffusion length 251, 257, 262– dissociation 250, 251, 262– dissociation at interfaces 265– generation rate 257– intrachain 12, 198– mean lifetime 257– recombination 257external quantum efficiency 263, 268

Fermi distribution 122, 205– two-band system 128Fermi energy 122– in doped systems 129Fermi-level pinning 212, 213FET mobility 198, 199field current 200field emission 178fill factor 45, 186, 190, 197, 214–221,

225, 264– effect of LiF layer 215fluorescence quenching 47Forster transfer 268, 270free energy of e–h pairs 124, 126Frenkel exciton 9, 72Fresnel equations 132Fresnel reflection and transmission

coefficients 253, 254FTIR spectra 237, 238fullerene 2, 3, 14, 30, 207, 213, 239– acceptor strength 214– concentration 167– molecular orbital levels 4– redox potential 209fulleropyrrolidines 31

geminate polaron pair 12, 71generation rate 201glass transition 240Gratzel cell 249guest–host approach 240

heterojunction diode 162hole 121hole membrane 126, 141, 142, 149, 153hole-only device 172–174, 224, 227

HOMO states 121hopping transport 105–108, 185, 191,

197, 236

impurity 250impurity recombination 141indoor applications, low power 274indoor measurements 230intercalating membranes 154interchain transport 197interconnection, Z- and W-type 279interface matrix 253, 254internal conversion 75, 77internal quantum efficiency 263, 264internal transfer coefficient 255intramolecular vibrational relaxation

75inversion 124iodine-doped polyacetylene 100IPCE 196, 197, 225, 226, 263IRAV modes 21isolated conjugated molecule 75ITO substrate 188ITO/PEDOT/PEOPT/C60/Al device

260ITO/PEDOT/PEOPT/C60/Al

photodiode 262ITO/polymer/Al device 252, 259ITO/polymer/C60/Al 259

Kasha’s rule 24, 74ketolactam 206, 208, 211– redox potential 209Kramers–Kronig equations 62, 68

Lambert–Beer law 16, 17large area power applications 274lasing condition 124layer matrix 254LED 62, 67, 161, 162LiF layer 215–217, 220, 221LiF/Al electrode 217, 218, 221, 233LiF/Au electrode 219, 221lifetime of solar cells 237light stressing 240light trapping 134, 153light–matter interaction 131–134light-induced ESR 27–29linear optical response 251

294 Index

localization 93, 94localization–interaction model 102long term stability 285low bandgap polymer 190, 221, 223LUMO states 121

magnetoconductance 110– anisotropic 111magnetoresistance 108–112manufacture of standard glass/glass

nc-DSC 277Marcus region 50matrix of refraction 253maximum power point 140, 214, 216Maxwell’s equations 131MDMO–PPV 3, 19, 21, 23, 24, 169,

172, 188, 190, 224, 237, 239MDMO–PPV diode 174, 175, 228MDMO–PPV FET 198, 200MDMO–PPV solution 194MDMO–PPV/C60 165, 237MDMO–PPV/PCBM blend 23–25,

28, 29, 164, 187, 189– absorption spectrum 222– current–voltage characteristic 210– efficiency 196– film surface morphology 191, 192– optical absorption 196– physical surface properties 191, 193MDMO–PPV/PCBM solar cell 211,

217–219– characteristics 220MDMO–PPV/PTPTB blend 224, 228mean free path 93, 94MEH–PPV 3, 177, 197metal–insulator transition 95, 99–104metal/conjugated polymer contacts

177–183methanofullerene 191, 206MIM tunnel diode 162, 169, 170, 177,

189miscibility of polymer blends 265mLPPP 77, 79mobility 96– FET 198, 199– field dependent 169, 264– intrachain 197– relevance for solar cell 200mobility edge 94

module– large scale batch processing 283– monolithic 280– sealing 280molecular rectification 179monolithic module 280Monte Carlo simulation 197Mott–Hubbard transition 95Mott–Wannier exciton 9, 71MP–C60 32– excited energy levels 47– photoexcitation 33– redox potential 33multilayer structure 252, 253multispectral conversion 155

nanometer scale phase separation 265network morphology in blends 191neutral soliton 7, 8Nile red 223, 224, 227non-geminate polaron pair 12nonlinear optical response 72

ODCB 31, 38, 39, 46OLED 160, 197, 215, 220oligo-phenylene vinylene 29–51open-circuit voltage 45, 139, 140, 152,

175, 186, 189, 195, 205–214, 225, 264– outdoor measurements 230, 232– temperature dependence 230, 232,

233optical absorption– by polymer/molecule blends 266– by polymer/polymer blends 266optical constants of conjugated

polymers 57, 58optical electric field 251–253, 256, 259– at PEOPT/C60 interface 261optical mode structure 251–262optical quality of CP samples 60optically detected magnetic resonance

11, 14OPVn 30, 32– excited energy levels 47– photoexcitation 32– redox potential 33OPVn–C60 30, 31, 46– electrochemistry 32– energy levels 48

Index 295

– fluorescence spectra 34– intramolecular electron transfer

39–42, 50– intramolecular singlet-energy transfer

33–36– photoinduced electron transfer

42–44– PIA spectra 41– redox potential 33– UV/VIS spectra 31, 32, 35OPVn/MP–C60 36, 37– intermolecular electron transfer

38–39– intramolecular triplet-energy transfer

36–38organic semiconductors 1, 159– carrier mobility 150outdoor measurements 230– open-circuit voltage 230, 232– short-circuit current 234

P3HT 198, 267, 268P3HT/BEHP–PPV blend 267P3OT 3, 21, 22PBOPT 267, 268– PL spectrum 268PBOPT/BEHP–PPV blend 267PCBM 21, 208, 211, 239– redox potential 209PEDOT/PSS 44, 189Peierls distortion 6PEOPT 259PEOPT/C60 bilayer 264PEOPT/C60 interface 259, 261percolation threshold 108, 166, 167percolative transport 107, 167phase matrix 254phonon 136photobleaching 23, 73, 74, 76photocurrent generation 250, 258photodoping 11, 21photoinduced absorption 73, 74photoinduced absorption (PIA)

spectroscopy 16, 18photoinduced charge separation 264,

265photoinduced electron transfer 164– in organic molecules 15, 16photoluminescence 11

– quenching 166, 167, 262– spectra of polymeric films 268photon current density 119, 120photosynthesis 267plastic solar cell 189, 203, 210, 236,

243– large scale production 241plastics 57polar solvents 75polarization 70polaron 8, 9, 11, 27, 71, 161, 249– in magnetic field 11– recombination 71polaron pair 12–14, 71– geminate 12, 71– non-geminate 12polyacetylene 59, 60, 159, 160polyalkylthiophene 107polyaniline 103polydiacetylene 59, 60polyethylene 57polymer blend 167polymer film 71, 179polymer/molecule blends 265– optical absorption 266– spectral response 266polymer/polymer blends 265– optical absorption 266– spectral response 266polymeric bulk heterojunction 167polypyrrole 103polystyrene 241polythiophene 8, 21, 59, 60, 103, 159,

161, 266POMeOPT/C60 blend 266Poole–Frenkel effect 169, 181power conversion efficiency 195–197,

215, 216, 219, 225, 242, 264Poynting vector 132PPV 101, 159, 161PPV derivatives 70– blend in UHMW PE 71processing– large scale 283– of polymeric semiconductors

240–241– technology for nc-DSC 285PTDS 65

296 Index

PTFE 57PTOPT 266–268PTOPT/BEHP–PPV blend 267PTPTB 222PTPTB/MDMO–PPV/PCBM 224,

227PTPTB/PCBM device 224–227– IPCE 226pump–probe spectroscopy 16–21, 58,

72–75– sub-10-fs 80

quantum efficiency 62, 135, 183, 197,203, 204, 258, 263–264

– external 263, 268– internal 263, 264– of exciton generation 257quantum yield 263quasi-Fermi distribution 122– two-band system 130–131quinoid structure 8, 11

radiative limit for solar cell efficiency138–140

Raman– modes 21– scattering 33– spectrum 24, 25recombination– losses 251, 264– rate 201– time 203redox potential 209reflectance/transmittance 62–64, 67,

68, 263reflectivity 133refractive index 58, 62, 65, 133, 251,

259– anisotropy 67reverse current 126, 139, 153rheological properties 241

Schottky diode 219Schottky-type contacts 177Schottky-type junction 162SCLC 264sealing 280selection rules 133

semiconductivity of conjugatedpolymers 58

semiconductor– n-type 202– polymeric 160, 167, 169, 178, 191,

227, 236, 240– wide bandgap 275sensitizer 276series connection 279shallow trap 172Shockley diffusion theory 232short-circuit current 126, 139, 140,

152, 175, 186, 189–204, 225, 258, 262,264

– irradiance dependence 235– outdoor measurements 234– PS/MDMO–PPV/PCBM devices

241– temperature dependence 234short-circuit exciton current 258shunt current 152SIMS 221single-layer diode 160–162, 251single-layer polymer device 189single-polymer layer 250solar cell 121– bulk heterojunction 163–168, 175– calibration 186–187– characteristics 220– charge separation 141–153– charge transport 143–147– current–voltage characteristic 170,

187– dye-sensitised 154, 223, 227– efficiency 138–140, 186– equivalent circuit 151–153, 214, 215– ideal 142, 151, 214– lifetime 237– MDMO–PPV 211– organic 155, 159– plastic 189, 203, 210, 236, 243– semiconductor 127, 147, 149– specifications 153–156– spectral sensitisation 223– temperature behavior 229–236solar radiation 118–120– spectrum at Earth surface 119solar simulator 187, 194, 229, 230, 235

Index 297

soliton 7, 8, 71spectral mismatch 187, 190, 195, 229,

230spectral response 221–229, 261, 262– of photodiode 263– of polymer/molecule blends 266– of polymer/polymer blends 266spectral sensitization 190spontaneous emission 123– under solar excitation 125SSH model 6stability– long term 285– of conjugated polymers 57, 160– of polymeric semiconductors

236–240Standard Reporting Conditions (SRC)

186Standard Test Conditions (STC) 229stimulated emission 23, 73, 74, 123stretch-oriented PPV 67– ellipsometry 68, 69– KK analysis 69– refractive index 69superconductivity 57surface plasmon resonance 65, 67

tandem cell 156, 222, 227temperature behavior 229–236– of open-circuit voltage 230, 232, 233– short-circuit current 234thermal radiation 118thermalisation 135, 205thermionic field emission 178thermopower 113–115

thin film– organic photodiode 250– photovoltaic device 206TiO2 275toluene 33, 36, 46, 191, 194–196,

198–200trans-polyacetylene 5–8transmittance/reflectance 62–64, 67,

68, 263transport equation 147–148, 203trap 264trap-free SCLC 170, 174, 175, 228triple cell 156tunnelling 178two-band system 127–138– current–voltage characteristic 140two-level system 121– conversion efficiency 128– current–voltage characteristic 125

unipolar device 174, 175upscaling nc-DSC technology 281

valence band 121, 128, 205variable range hopping (VRH) 105Vavilov’s rule 74vibrational cooling 75

waveguide spectroscopy 65weak localization 110Weller equation 31, 45, 46wide bandgap polymer 222work function 162, 163, 170, 174, 177,

189, 207, 210, 211world energy consumption 242

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