Semiconductor Physical Electronics

MICRODEVICES Physics and Fabrication Technologies

Series Editors: Ivor Brodie and Julius J. Murayt

SRI International Menlo Park, California

ELECTRON AND ION OPTICS Miklos Szilagyi

GaAs DEVICES AND CIRCUITS Michael Shur

ORIENTED CRYSTALLIZATION ON AMORPHOUS SUBSTRATES E. I. Givargizov

THE PHYSICS OF MICROjNANO-FABRICATION Ivor Brodie and Julius J. Muray

PHYSICS OF SUBMICRON DEVICES David K. Ferry and Robert O. Grondin

THE PHYSICS OF SUBMICRON LITHOGRAPHY Kamil A. Valiev

SEMICONDUCTOR LITHOGRAPHY Principles, Practices, and Materials Wayne M. Moreau

SEMICONDUCTOR PHYSICAL ELECTRONICS Sheng S. Li

t Deceased.

A Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volume immediately upon publication. Volumes are billed only upon actual shipment. For further information please contact the publisher.

Semiconductor Physical Electronics

Sheng S. Li Department of Electrical Engineering University of Florida Gainesville, Florida

Plenum Press • New York and London

Ll, Shang S .. 1938-S .. lconductor physlc.' electronic. I Shlng S. L1.

p. c •• -- (Mlcrod,vlclS 1 Includ .. bl~llographlcal reflrenc .. and Indl ••

1. S,.lconductors. 2. Solid Uatl physics. 1. Tltll. II. Serl ••• TK7871.85.L495 1993 621.3815·2--dc20 92-28807

CIP

1098765432

ISBN-13: 978-1-4612-7635-7 DOl: 10.1007/978-1-4613-0489-0

e-ISBN-13: 978-1-4613-0489-0

© 1993 Plenum Press, New York

Softcover reprint of the hardcover 1st edition 1993 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. loon

All rights reserved

No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, e1ectronic, mechanical. photocopying. microfilming, recording. or otherwise, without written permission from the Publisher

Preface

The purpose of this book is to provide the reader with a self-contained treatment of fundamen­tal solid state and semiconductor device physics. The material presented in the text is based upon the lecture notes of a one-year graduate course sequence taught by this author for many years in the ·Department of Electrical Engineering of the University of Florida. It is intended as an introductory textbook for graduate students in electrical engineering. However, many students from other disciplines and backgrounds such as chemical engineering, materials science, and physics have also taken this course sequence, and will be interested in the material presented herein. This book may also serve as a general reference for device engineers in the semiconductor industry.

The present volume covers a wide variety of topics on basic solid state physics and physical principles of various semiconductor devices. The main subjects covered include crystal structures, lattice dynamics, semiconductor statistics, energy band theory, excess carrier phenomena and recombination mechanisms, carrier transport and scattering mechanisms, optical properties, photoelectric effects, metal-semiconductor devices, the p--n junction diode, bipolar junction transistor, MOS devices, photonic devices, quantum effect devices, and high­speed III-V semiconductor devices. The text presents a unified and balanced treatment of the physics of semiconductor materials and devices. It is intended to provide physicists and mat­erials scientists with more device backgrounds, and device engineers with a broader knowledge of fundamental solid state physics.

The contents of the text is divided into two parts. In Part I (Chapters 1-9), we cover subjects on fundamental solid state and semiconductor physics that are essential for device applications. In Part II (Chapters 10-15), we deal with basic device physics and structure, operation principles, general characteristics, and the applications of various semiconductor devices.

Chapter I presents the classification of solids, crystal structures, the concept of reciprocal lattice and Brillouin lone, the definition of Miller indices, chemical bondings, and crystal defects. Chapter 2 deals with the thermal properties and lattice dynamics of crystalline solids. The lattice specific heat, the dispersion relation of lattice vibrations, and the concept of phonons are also described. Chapter 3 is concerned with the derivation of the three semicon­ductor statistics, namely, the Maxwell-Boltzmann (M-B), Bose-Einstein (B-E), and Fermi­Dirac (F-D) distribution functions. Chapter 4 covers energy band theory, the concept of effective mass, and the density-of-states function for the bulk semiconductor and the superlat­tice. Chapter 5 describes the equilibrium properties of both the intrinsic and extrinsic semicond­uctors. Derivation of electron and hole densities, and a discussion of the properties of shallow­and deep-level impurities are also covered. Chapter 6 presents the excess carrier phenomenon and recombination mechanisms in a semiconductor. The six basic equations which govern the transport of excess electrons and holes in a semiconductor are described. Chapter 7 is con-

v

PREFACE

cerned with the derivation of transport coefficients from the Boltzmann equation, and low­field galvanomagnetic effects in a semiconductor. Chapter 8 deals with various scattering mechanisms in a semiconductor. The relaxation time and mobility expressions for ionized and neutral impurity scattering, acoustic and optical phonon scattering are derived. Chapter 9 is concerned with the optical properties and photoelectric effects in a semiconductor. The fundamental optical absorption and free carrier absorption processes, the photoconductive, photovoltaic, and photomagnetoelectric effects in a semiconductor are also discussed. Chapter 10 covers the basic physical principles and properties of metal-semiconductor contacts. Both the Schottky barrier and ohmic contacts on a semiconductor are discussed. Carrier transport in a Schottky barrier diode, methods of determining and modifying the barrier height, and the formation of ohmic contacts are presented. Chapter II deals with the basic device theory and properties of a p-n junction diode and a junction-field effect transistor (JFET). Chapter 12 is concerned with the device physics, the structure and characteristics of various photonic devices such as photodetectors, solar cells, light emitting diodes (LEOs) and diode lasers. Chapter 13 describes the bipolar junction transistor (BJTs) and p-n-p-n four-layer devices (e.g., SCRs or thyristers). Chapter 14 presents the silicon-based metal-oxide-semiconductor (MOS) devices. The device physics and characteristics for both the MOS field-effect transistors (MOSFETs) and charge-coupled devices (CCDs) are also described. Finally, in Chapter IS. we cover some novel high-speed devices using GaAs and other III-V compound semiconduc­tors. These include GaAs-based metal-semiconductor field effect transistors (MESFETs). high electron mobility transistors (HEMTs), heterojunction bipolar transistors (HBTs), and trans­ferred electrC?n devices (TEDs).

Throughout the text. the author stresses the importance of relating fundamental solid state physics to the properties and performance of various semiconductor devices. Without a good grasp of the physical concepts and an understanding of the underlying device physics. it would be difficult to tackle the problems encountered in material growth and device fabrica­tion. The information presented in this book should provide a solid background for under­standing the fundamental physical limitations of semiconductor materials and devices. This book is especially useful for those who are interested in itrengthening and broadening their basic knowledge of solid state and semiconductor device physics.

The author would like to acknowledge his former students for the many useful discussions and comments on the text. In particular. he is grateful to Drs. D. H. Lee and C. S. Yeh. and Robert Huang, for their assistance in the preparation of illustrations and the solutions manual, and the proofreading of the manuscript. He is indebted to his son. Jim, for setting up the MicroTex and TEXtures programs with which this book was prepared, and to his wife, Jean, and daughters Grace and Jeanette for their love and support during the course of preparing this book.

Sheng S. Li Gainesville, Florida

Contents

CHAPTER 1. Classification of Solids and Crystal Structure

1.1. Introduction ........................................................ I 1.2. The Bravais Lattice .................................................. 2 1.3. The Crystal Structure ................................................ 5 1.4. Miller Indices and the Unit Cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5. The Reciprocal Lattice and Brillouin Zone .............................. 8 1.6. Types of Crystal Bindings ............................................ II 1.7. Defects in a Crystalline Solid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13

1.7.1. Vacancies and Interstitials ...................................... 13 1.7.2. Line and Surface Defects. . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Problems .......................................................... 18 Bibliography ........................................................ 18

CHAPTER 2. Lattice Dynamics

2.1. Introduction ........................................................ 21 2.2. The One-Dimensional Linear Chain. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. 22 2.3. Dispersion Relation for a Three-Dimensional Lattice .................... 27 2.4. Concept of Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29 2.5. The Density of States and Lattice Spectrum ............................ 30 2.6. Lattice Specific Heat .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32 2.7. Elastic Constants and Velocity of Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35

Problems .......................................................... 37 References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39 Bibliography ........................................................ 39

CHAPTER 3_ Semiconductor Statistics

3.1. Introduction ........................................................ 41 3.2. Maxwell-Boltzmann (M-B) Statistics .................................. 42 3.3. Fermi-Dirac (F-D) Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 45

vii

viii CONTENTS

3.4. Bose-Einstein (B-E) Statistics ........................................ 50 3.5. Statistics in the Shallow-Impurity States ................................ 52

Problems .......................................................... 53 Bibliography ........................................................ 54

CHAPTER 4. Energy Band Theory

4.1. Introduction ........................................................ 55 4.2. The Bloch-Floquet Theorem............ ................ .............. 56 4.3. The Kronig-Penney Model.............. .............................. 57 4.4. The Nearly-Free Electron Approximation .............................. 62 4.5. The Tight-Binding (LCAO) Approximation ............................ 68

4.5.1. The Simple Cubic Lattice. . . . . . . . . . . . .. . . . . .. . . .. . .. . .. .. . . . . . ... 71 4.5.2. The Body-Centered Cubic Lattice (the s-like states) ................ 72

4.6. Energy Band Structures for Semiconductors ............................ 73 4.7. The Effective Mass Concept .......................................... 78 4.8. Energy Band Structure and Density of States in a Superlattice ............ 80

Problems .......................................................... 83 References .......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85 Bibliography ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85

CHAPTER 5. Equilibrium Properties of Semiconductors

5.1. Introduction ........................................................ 87 5.2. Densities of Electrons and Holes in a Semiconductor .................... 88 5.3. Intrinsic Semiconductors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 94 5.4. Extrinsic Semiconductors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 96 5.5. Ionization Energy of a Shallow Impurity Level .......................... 102 5.6. Hall Effect, Hall Mobility, and Electrical Conductivity ............ '" ..... 104 5.7. Heavy Doping Effects in a Degenerate Semiconductor ................... , 107

Problems .......................................................... 109 Reference .......................................................... III Bibliography ........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. III

CHAPTER 6_ Excess Carrier Phenomenon in Semiconductors

6.1. Introduction ........................................................ 113 6.2. Nonradiative Recombination: Shockley-Read-Hall Model. . . . . . . . . . . . . . .. 114 6.3. Band-to-Band Radiative Recombination .............................. 118 6.4. Band-to-Band Auger Recombination .................................. 121 6.5. Basic Semiconductor Equations ...................................... 124 6.6. Charge-Neutrality Conditions ........................................ 126 6.7. The Haynes-Shockley Experiment .................................... 128 6.8. Minority Carrier Lifetimes and Photoconductivity Experiment ............ 130 6.9. Surface States and Surface Recombination Velocity. . . . . . . . . . . . . . . . . . . . .. 135 6.10. Deep-Level Transient Spectroscopy (DLTS) Technique .................. 138

CONTENTS Ix

6.11. Surface Photovoltage (SPV) Technique ................................ 141 Problems .......................................................... 143 References ........................................................ 145 Bibliography ...................................................... 145

CHAPTER 7. Transport Properties of Semiconductors

7.1. Introduction ........................................................ 147 7.2. Galvanomagnetic, Thermoelectric, and Thermomagnetic Effects ...... . . . . .. 149

7.2.1. Electrical Conductivity ITn .•••.•.•..•...••..•..••.•.••.••••.••.• 149 7.2.2. Electronic Thermal Conductivity Kn .............................. lSI 7.2.3. Thermoelectric Coefficients ...................................... 152 7.2.4. Galvanomagnetic and Thermomagnetic Coefficients ................ 153

7.3. Boltzmann Transport Equation ........................................ ISS 7.4. Derivation of Transport Coefficients. . . . . . .. . . . .. . . . . .. . . . . . . . . . . . . .. . .. 156

7.4.1. Electrical Conductivity IT. ...................................... 158 7.4.2. Hall Coefficient RH ............................................ 161 7.4.3. Seebeck Coefficient S ........................................... 164 7.4.4. Nernst Coefficient Qn .......................................... 164 7.4.5. Transverse Magnetoresistance .................................... 165

7.5. Transport Coefficients for the Mixed Conduction Case .................... 169 7.5.1. Electrical Conductivity IT ........................................ 169 7.5.2. Hall Coefficient RH ............................................ 169 7.5.3. Seebeck Coefficient S .......................................... 170 7.5.4. Nernst Coefficient Q ............................................ 171

7.6. Transport Coefficients for Some Semiconductors ........................ 171 Problems .......................................................... 179 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 181 Bibliography ........................................................ 181

CHAPTER 8. Scattering Mechanisms and Carrier Mobilities in Semiconductors

8.1. Introduction ........................................................ 183 8.2. Differential Scattering Cross Section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 186 8.3. Ionized Impurity Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 189 8.4. Neutral Impurity Scattering .......................................... 192 8.5. Acoustic Phonon Scattering .......................................... 193

8.5.1. Deformation Potential Scattering ................................ 194 8.5.2. Piezoelectric Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 196

8.6. Optical Phonon Scattering ............................. '" ............ 198 8.7. Scattering by Dislocations ............................................ 200 8.8. Electron and Hole Mobilities in Semiconductors ...... . . . . . . . . . . . . . . . . .. 20\ 8.9. Hot Electron Effects in a Semiconductor ................................ 204

Problems .......................................................... 209 References .......................................................... 210 Bibliography ........................................................ 211

x CONTENTS

CHAPTER 9. Optical Properties and Photoelectric Effects

9.1. Optical Constants of a Solid .......................................... 214 9.2. Free-Carrier Absorption Process ...................................... 219 9.3. Fundamental Absorption Process ...... , ......... , ..................... 222

9.3.1. Direct Transition Process ........................................ 224 9.3.2. Indirect Transition Process ...................................... 225

9.4. The Photoconductive Effect .......................................... 228 9.4.1. Kinetics of Photoconduction .................................... 235 9.4.2. Practical Applications of Photoconductivity. . . . . . . . . . . . . . . . . . . . . . .. 237

9.5. The Photovoltaic (Dember) Effect. ..................................... 238 9.6. The Photomagnetoelectric Effect ...................................... 240

Problems ........................................... . . . . . . . . . . . . . .. 244 References ........................................................ " 245 Bibliography ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 245

CHAPTER 10. Metal-Semiconductor Contacts

10.1. Introduction ...................................................... 247 10.2. Metal Work Function and Schottky Effect ............................ 248 10.3. Thermionic Emission Theory ........................................ 249 10.4. Ideal Schottky Barrier Contact ...................................... 252 10.5. Current Flow in a Schottky Barrier Diode ............................ 25(j

10.5.1. Thermionic Emission Model .................................. 257 10.5.2. Image Lowering Effect ...................................... 258 10.5.3. The Diffusion Model ........................................ 259

10.6. I-V Characteristics of a Silicon and a GaAs Schottky Diode ............ 261 10.7. Determination of Barrier Height .................................... 264 10.8. Enhancement of Effective Barrier Height . . .. . .. .. . . .. . . .. . .. . .. .. .. ... 269 10.9. Applications of Schottky Diodes .................................... 275

10.9.1. Photodetectors and Solar Cells ................................ 275 10.9.2. Schottky-Clamped Transistors ................................ 277 10.9.3. Microwave Mixers .......................................... 278

10.10. Ohmic Contacts .................................................. 279 Problems ........................................................ 284 References ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 285 Bibliography ...................................................... 285

CHAPTER 11. p-n Junction Diodes

11.1. Introduction...................................................... 287 11.2. Equilibrium Properties of a p-n Junction Diode. . . . . . . . . . . . . . . . . . . . . . .. 287 11.3. p-n Junction Under Bias Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 293 11.4. Minority Carrier Distribution and Current Flow ................ ..... 296 11.5. Diffusion Capacitance and Conductance .............................. 301 11.6. Minority Carrier Storage and Transient Behavior ...................... 304 II. 7. Zener and Avalanche Breakdowns. .. .. .. .. . .. . .. . . . . . .. .. . .. . .. . . .... 307 11.8. Tunnel Diode .................................................... 312 11.9. p-n Heterojunction Diodes ........... , ................................ 314

CONTENTS

11.10. Junction Field-Effect Transistors Problems ....................................................... . References ....................................................... . Bibliography ..................................................... .

CHAPTER 12. Photonic Devices

xl

318 324 325 326

12.1. Introduction ........................................................ 327 12.2. Photovoltaic Devices ................................................ 328

12.2.1. p-n Junction Solar Cells ...................................... 329 12.2.2. Schottky Barrier and MIS Solar Cells .......................... 338 12.2.3. Heterojunction Solar Cells .................................... 341 12.2.4. Thin Film Solar Cells ........................................ 343

12.3. Photodetectors ...................................................... 344 12.3.1. p-n Junction Photodiodes .................................... 348 12.3.2. p-i·n Photodiodes ............................................ 349 12.3.3. Avalanche Photodiodes ...................................... 353 12.3.4. Schottky Barrier Photodiodes ..................... '" .......... 357 12.3.5. Point-Contact Photodiodes .................................... 358 12.3.6. Heterojunction Photodiodes .................................. 358 12.3.7. Photomultipliers .............................................. 359 12.3.8. Long-Wavelength Infrared Detectors ............................ 360

12.4. Light-Emitting Diodes (LEDs) ........................................ 363 12.4.1. Injection Mechanisms ........................................ 364 12.4.2. Electronic Transitions ........................................ 365 12.4.3. Luminescent Efficiency and Injection Efficiency .................. 365 12.4.4. Application of LEDs ....................................... , 370

12.5. Semiconductor Laser Diodes ........................................ 375 12.5.1. Population Inversion .................. , ., ..................... 375 12.5.2. Oscillation Conditions ........................................ 377 12.5.3. Threshold Current Density ... " ............................... 378 12.5.4. GaAs Laser Diodes .......................................... 380 12.5.5. Semiconductor Laser Materials ................................ 384 12.5.6. Applications of Lasers ........................................ 386 Problems .......................................................... 387 References ........................................................ 388 Bibliography ...................................................... 389

CHAPTER 13. Bipolar Junction Transistor

13.1. Introduction ........................................................ 391 13.2. Basic Structures and Modes of Operation ............. " ............... 392 13.3. Current-Voltage Characteristics ...................................... 393 13.4. Current Gain, Base Transport Factor, and Emitter Injection Efficiency .... 401 13.5. Modeling of a Bipolar Junction Transistor ............................ 404 13.6. Switching Transistor ................................................ 409 13.7. Advanced Bipolar Transistor ........................................ 414

xli CONTENTS

13.8. Thyristors .......................................................... 415 Problems .......................................................... 420 References ........................................................ 421 Bibliography ......................................... . . . . . . . . . . . .. 422

CHAPTER 14. Metal-Oxide-Semiconductor Field-Effect Transistors

14. \. Introduction ........................................................ 423 14.2. An Ideal Metal-Oxide-Semiconductor System .......................... 423

14.2.\' Surface Space-Charge Region .................................. 426 14.2.2. Capacitance-Voltage Characteristics ............................ 427

14.3. Oxide Charges and Interface Traps .................................... 430 14.3.\. Interface Trap Charges ........................................ 431 14.3.2. Oxide Charges ................... : .......................... 433

14.4. The MOS Field-Effect Transistors .................................... 435 14.4. \. General Characteristics of a MOSFET .......................... 436 14.4.2. Channel Conductance ........................................ 437 14.4.3. Current-Voltage Characteristics ................................ 439 14.4.4. Small-Signal Equivalent Circuit ................................ 442 14.4.5. Scaled-Down MOSFETs ...................................... 444

14.5. Charge-Coupled Devices ............................................ 446 14.5.1. Charge Storage and Transfer .................................. 447 14.5.2. Charge Injection and Detection ................................ 450 14.5.3. Buried-Channel CCDs ........................................ 451 Problems .......................................................... 452 References ........................................................ 453 Bibliography ...................................................... 453

CHAPTER IS. Higb-Speed III-V Semiconductor Devices

15. \. Introduction........................................................ 455 15.2. Metal-Semiconductor Field-Effect Transistors .......................... 456

15.2. \. Basic Device Structure and Characteristics ...................... 456 15.2.2. Current-Voltage Characteristics ................................ 460 15.2.3. Small-Signal Device Parameters ................................ 463 15.2.4. Second-Order Effects in a GaAs MESFET ...................... 467

15.3. Modulation-Doped Field-Effect Transistors (MODFETs) ................ 468 15.3.\. Equilibrium Properties of the 2-DEG in GaAs .................. 470 15.3.2. 2-DEG Charge Control Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 474 15.3.3. Current-Voltage Characteristics ................................ 475

15.4. Heterojunction Bipolar Transistor .................................... 481 15.4.1. Device Structure and Fabrication Technology .................... 481 15.4.2. Current Gain and Device Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . .. 483 15.4.3. Current-Voltage Characteristics ................................ 485 15.4.4. High-Frequency Perfonnance .................................. 486

15.5. Hot Electron Transistors ............................................ 490 15.6. Resonant Tunneling Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 493

CONTENTS

15.7. Transferred-Electron Devices Problems ......................................................... . References ....................................................... . Bibliography ..................................................... .

xIII

495 499 501 501

Index ...................................................................... 503

Semiconductor Physical Electronics