INTRODUCTION TO

APPLIED SOLID STATE PHYSICS TOPICS IN mE APPLICATIONS OF SEMICONDUCTORS, SUPERCONDUCTORS, FERROMAGNETISM, AND mE NONlINEAR OPTICAl PROPERTIES OF SOLIDS

SECOND EDITION

INTRODUCTION TO

APPLIED SOLID STATE PHYSICS TOPICS IN THE APPLICATIONS OF SEMICONDUCTORS, SUPERCONDUCTORS, FERROMAGNETISM, AND THE NONLINEAR OPTICAL PROPERTIES OF SOLIDS

SECOND EDITION

RICHARD DALVEN Department of Physics University of California Berkeley, California

PLENUM PRESS . NEW YORK AND LONDON

Softcover reprint of the hardcover 1st edition

LIbrary of Congress Cataloglng-ln-Publlcatlon Data

Dalven. RIchard. Introduct1on to appl1ed solId state physIcs: top1cs In the

applIcatIons of semIconductors. superconductors. ferromagnetIsm. and the nonl1near optIcal propert1es of sol1ds I RIchard Dalven. -- 2nd ed.

p. cm. Includes bIblIographIcal references. ISBN-l3: 978-1-4684-l332-8 e-ISBN-l3: 978-1-4684-l330-4 DOl: 10.1007/978-1-4684-l330-4 1. SolId state physICS. 2. Sem1conductors. I. TItle.

QC17S.D24 1990 530.4' l--dc20 89-72108

© 1990, 1980 Plenum Press, New York Softcover reprint of the hardcover 2nd edition 1990 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013

All rights reserved

CIP

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

To my father, JOSEPH DALVEN

and to the memory of my mother,

RUTH NEWTON DALVEN

Preface to the Second Edition

In addition to the topics discussed in the First Edition, this Second Edition contains introductory treatments of superconducting materials and of ferromagnetism. I think the book is now more balanced because it is divided perhaps 60% - 40% between devices (of all kinds) and materials (of all kinds). For the physicist interested in solid state applications, I suggest that this ratio is reasonable. I have also rewritten a number of sections in the interest of (hopefully) increased clarity.

The aims remain those stated in the Preface to the First Edition; the book is a survey of the physics of a number of solid state devices and ma­terials. Since my object is a discussion of the basic ideas in a number of fields, I have not tried to present the "state of the art," especially in semi­conductor devices. Applied solid state physics is too vast and rapidly changing to cover completely, and there are many references available to recent developments. For these reasons, I have not treated a number of interesting areas. Among the lacunae are superiattices, heterostructures, compound semiconductor devices, ballistic transistors, integrated optics, and light wave communications. (Suggested references to those subjects are given in an appendix.) I have tried to cover some of the recent revolutionary developments in superconducting materials. However, as of this writing, this field is still in ferment and the story is far from complete, so my pres­entation may well be obsolete in a short time. I have also elected to discuss only the physics of individual discrete devices, rather than the functions of the integrated circuits which serve as digital and analog building blocks. It seems to me that an applied physicist would probably be more concerned with, say, how field-effect transistors work than how they are used in an integrated circuit.

The prerequisites for reading this book remain the same as those for the First Edition, with the addition of a knowledge of ferromagnetism

vili Preface to the Second Edition

equivalent to that presented in an introductory solid state physics course. Many people have commented on the manuscript or have helped me

in other ways. My debts from the First Edition remain outstanding, and I have new debts to P. Berdahl, G. Y. Chin, J. Clarke, M. L. Cohen, L. M. Falicov, T. H. Geballe, E. L. Hahn, J. D. Jackson, T. W. Kenny, C. Kittel, R. U. MartineIli, A. M. Portis, A. C. Rose-Innes, M. Tinkham, and R. M. White. All have helped improve the book, but the responsibility for errors and obscurities remains mine alone. Thanks are also due the AAPT for permission to use some of the material in Chapter 8 which appeared in preliminary form in the American Journal of Physics. The text was typed by Rita Jones and Claudia Madison, both of whom were exceptionally skillful and patient. John Clarke's kind hospitality at the Lawrence Berkeley Laboratory was, as always, most helpful.

Last, I must thank D. for making this book possible, and G. for keep­ing it going.

RICHARD DALVEN

Berkeley, California

Preface to the First Edition

The aim of this book is a discussion, at the introductory level, of some applications of solid state physics.

The book evolved from notes written for a course offered three times in the Department of Physics of the University of California at Berkeley. The objects of the course were (a) to broaden the knowledge of graduate students in physics, especially those in solid state physics; (b) to provide a useful course covering the physics of a variety of solid state devices for students in several areas of physics; (c) to indicate some areas of research in applied solid state physics.

To achieve these ends, this book is designed to be a survey of the physics of a number of solid state devices. As the italics indicate, the key words in this description are physics and survey. Physics is a key word because the book stresses the basic qualitative physics of the applications, in enough depth to explain the essentials of how a device works but not deeply enough to allow the reader to design one. The question emphasized is how the solid state physics of the application results in the basic useful property of the device. An example is how the physics of the tunnel diode results in a negative dynamic resistance. Specific circuit applications of devices are mentioned, but not emphasized, since expositions are available in the elec­trical engineering textbooks given as references. To summarize, the aim of the book is the physics underlying the applications, rather than the applications themselves.

The second key word is survey. The book is designed to be broad rather than deep. Although the survey approach is not to everyone's taste, it has proved popular with the approximately 120 Berkeley graduate students (mostly in physics) who took or audited the course in 1973, 1974, and 1977. They seemed to want to learn something, but not everything, about the applications of the solid state physics they already knew. As a survey, the

ix

x Preface to tbe First Edition

selection of topics is a compromise between recognition of the overwhelming technological importance of semiconductor devices and a desire to have some breadth of coverage. To this end, about 70% of the material covers applications of semiconductors, and the remainder is divided about evenly between nonlinear optical devices and superconductive materials and devices. Since the physics of the applications is the central interest of the book, no special effort was made to select the latest devices or to indicate the present "state of the art."

The book is a textbook ("A textbook explains, a treatise expounds"­J. M. Ziman) in that its aim is frankly tutorial. The book is essentially a collection of material from a number of sources, ranging from introductory textbooks to research journals, organized and presented with the intent of emphasizing the basic physics involved. There is no original work in­cluded. More advanced treatments and discussions of fine points are left to the literature. However, the reader is provided with references where fuller and/or more advanced treatments may be found. Further, a special effort has been made to give very specific references, telling where values of parameters, etc., were obtained. A selection of problems can be found at the end of each chapter. These are derivations, illustrative calculations, or invitations to explore the physics of some application. It is believed that these points harmonize with the attempt to provide a broad selection of the applications of solid state physics, while telling the reader where further information may be found.

The order of the first seven chapters is more or less linear. After a first chapter that is partly review and partly new material that will be useful, Chapter 2 treats the semiconductor p-n junction in some detail. The third chapter exploits this treatment in a discussion of several device applications. Chapter 4 treats the physics of metal-semiconductor and metal-insulator­semiconductor junctions, and the results are used in Chapter 5 to explore a few applications. In Chapter 6, a potpourri of "other" devices is discussed; they were chosen principally on the basis of my own interests. The seventh chapter treats a number of detectors and generators (principally semi­conductors) of electromagnetic radiation. Chapter 8 is mostly concerned with the physics of Josephson junction devices, but concludes with a short discussion of the transition temperature in superconductors. Finally, Chap­ter 9 covers the interaction of electromagnetic waves in nonlinear solids, and concludes with a few applications.

In teaching a course on these topics, I have found that this book con­tains too much material for a one-quarter course. One semester would seem about right, particularly if appropriate review material were included. The notation used is standard, except perhaps that I have used ff' for the electric

Preface to the First Edition xi

field vector to avoid confusion with energy E, particularly in band dia­grams. The chapter on nonlinear optics reverts to the more common E for electric field because there seemed little possibility of ambiguity.

The presentation relies on a number of standard sources. Charles Kittel's classic introductory text on solid state physics is constantly quoted and used as a reference. Other books on which I have drawn particularly are Solid State Electronic Devices by B. G. Streetman; "Optical Second Har­monic Generation and Parametric Oscillation" by A. Yariv, in Topics in Solid State and Quantum Electronics, W. D. Hershberger (editor); The Feynman Lectures on Physics by R. P. Feynman, R. B. Leighton, and M. Sands; and Long-Range Order in Solids by R. M. White and T. H. Geballe.

This book is at the introductory level in that no particular prior knowledge of solid state device physics is assumed. However, the introduc­tory level is not the same for all topics. For example, the treatment of the applications of nonlinear optical effects in solids is more complex than the treatment of the p-n junction. As for prerequisites, it is assumed that the reader has had an introductory course in solid state physics at the level of Kittel's Introduction to Solid State Physics, Fifth Edition. In particular, it is assumed that the reader has a knowledge of energy bands, semiconduc­tors, and superconductivity equivalent to that covered in Chapters 7, 8, and 12 of Kittel's book. In addition, this book assumes a knowledge of electromagnetic theory at the level of Reitz and Milford's Foundations of Electromagnetic Theory, of optics at the level of Stone's Radiation and Optics or Fowles's Modern Optics, and of quantum mechanics at the level of Bohm's Quantum Theory.

Many people have shared their expertise with me and have commented on the manuscript at various stages. I would like to thank N. Amer, T. Andrade, B. Black, R. W. Boyd, J. Clarke, M. L. Cohen, L. M. Falicov, L. T. Greenberg, E. L. Hahn, G. I. Hoffer, M. B. Ketch.en, A. F. Kip, R. U. Martinelli, R. S. Muller, W. G. Oldham, and P. L. Richards for helping me improve the book. However, the responsibility for errors and misconceptions is mine alone. Special thanks are due M. L. Cohen and C. Kittel for their encouragement during the development of the course. T. H. Geballe kindly provided me with a prepublication copy of his work. I would like to thank M. L. Cohen, D. Long, G. S. Kino, W. G. Oldham, J. Tauc, D. Adler, E. Gutsche, J. Millman, B. G. Streetman, T. C. Harman, H. Y. Fan, and J. Clarke for permission to use figures from their publica­tions. The hospitality extended by John Clarke was invaluable and is sincerely appreciated. Linda Billard typed part of the manuscript with great

xii Preface to the First Edition

skill, and Leslie Hausman typed the first draft. Gloria Pelatowski executed the drawings with exceptional skill and enthusiasm.

Last, but also first, I would like to thank D. and G. for making this book a reality.

RICHARD DALVEN

Contents

1. Review of Semiconductor Physics

Introduction. . . . . . . . . . . . Metals, Insulators, and Semiconductors Band Structure Diagrams . . . . . . Holes in Semiconductors ...... . Effective Mass of Carriers in Semiconductors Conductivity of Semiconductors . . . . . . Carrier Density in an Instrinsic Semiconductor . Impurity Conductivity (Extrinsic Conductivity) . Fermi Level Position in Extrinsic Semiconductors. Carrier Lifetime in Semiconductors . Problems ....... . References and Comments . Suggested Reading . . . .

2. The Semiconductor p-n Junction

Introduction. . . . . . . . . . . Qualitative Discussion of the p-n Junction in Equilibrium . Quantitative Treatment of the p-n Junction in Equilibrium. Effect of an Applied Potential on Electron Energy Bands . Diffusion and Recombination of Excess Carriers . . . . . Qualitative Discussion of a Junction under an Applied Potential Qualitative Discussion of Current Flow in the Biased Junction Quantitative Treatment of Carrier Injection in the Junction . . Calculation of the Current through the Junction . . . . . . . Majority and Minority Carrier Components of the Junction Current Summary of the Basic Physics of the p-n Junction Reverse Breakdown in p-n Junctions Other Topics on p-n Junctions . Problems ....... . References and Comments. Suggested Reading . . . .

xiii

1 3 6 7

10 12 14 17 21 22 23 24

27 27 35 50 51 55 59 61 64 71 74 75 77 77 78 79

xiv Contents

3. Semiconductor p-n Junction Devices

Introduction. . . . . . . . . . . 81 Semiconductor p-n Junction Diodes. . 81 The Bipolar Junction Transistor . . . 83 Amplification in the Bipolar Transistor 87 Current Gain in the Bipolar Transistor 88 Circuit Configurations for Amplification with the Bipolar Transistor 90 Quantitative Discussion of the Bipolar Transistor. . . . . . . . . 93 Summary of the Physics of Amplification in the Bipolar Transistor . 98 Tunnel Diodes . . . . . . . . . . . . . . . . . . . . . . . . 98 The Junction Field Effect Transistor (JFET) • • • • • • • • • 103 Physical Basis of the Current-Voltage Characteristic of the JFET 104 Problems. . . . . . . . 108 References and Comments 108 Suggested Reading. . . . 110

4. Physics of Metal-Semiconductor and Metal-Insulator-Semiconductor Junctions

Introduction . . . . . . . . . . . . . . . . . . . . . . . .. 111 The Metal-Semiconductor Junction at Equilibrium. . . . . . . .. 111 Effect of an Applied Potential on the Metal-Semiconductor Junction. 118 Physics of the Metal-Insulator-Semiconductor Structure 121 Problems. . . . . . . . 126 References and Comments 126 Suggested Reading. . . . 127

s. Metal-Semiconductor and Metal-Insulator-Semiconductor Devices

Introduction . . . . . . . . . . . . . . . . Metal-Semiconductor (Schottky) Diodes . . . . The Insulated-Gate Field-Effect Transistor (IGFET)

The Induced-Channel MOSFET • • • • • • • • •

Summary of the Physics of Field-Effect Transistors Applications of the MOSFET

Charge-Coupled Devices . Problems ....... . References and Comments Suggested Reading. . . .

6. Other Semiconductor Devices

Introduction . . . . . . . . . Semiconductor Surface States. . . . . . . Band Structure at the Semiconductor Surface

129 129 130 133 134 135 136 138 139 140

141 141 143

Contents

Calculation of the Amount of Band Bending . . . . . . Effect of Surface States on Metal-Semiconductor Contacts Photoemission from Semiconductors. . . . . Effect of the Surface on Photoemission. . . . . . Negative Electron Affinity in Semiconductors. . . Physics of the Transferred Electron (Gunn) Effect Physics of Amorphous Semiconductors. Amorphous Semiconductor Devices Problems ....... . References and Comments Suggested Reading. . . .

7. Detectors and Generators of Electromagnetic Radiation

xv

147 149 151 153 156 158 165 170 171 172 175

Introduction . . . . . . . . . . . . . . . . . . . . . . 177 Intrinsic Photon Absorption in Semiconductors . . . . . . . 177 Photon Absorption by Bound States of Impurities in Semiconductors 182 Threshold Energies for Photon Absorption 183 Photoconductivity in Semiconductors. 187 Photodiodes . . . . . . . . . . . . . 190 Photovoltaic Devices. . . . . . . . . . 192 Other Applications of Intrinsic Photoconductivity 194 Summary on Semiconductor Photon Detectors 197 Emission of Photons in Semiconductors . . . . 198 p-n Junction Luminescence. . . . . . . . . . 201 Light Amplification by Stimulated Emission of Radiation. 202 Solid State Lasers . . . . . . 206 Semiconductor Injection Lasers 208 Summary on Solid State Lasers 211 Problems. . . . . . . . 211 References and Comments 212 Suggested Reading. . . . 216

8. Superconductive Devices and Materials

Introduction . . . . . . . . . . . . . . Review of Some Aspects of Superconductivity. . Wave Function of the Condensed Phase of Pairs The Josephson Effects . . . . . . Physics of the DC Josephson Effect ..... . Physics of the AC Josephson Effect ..... . Voltage-Current Curves for Josephson Junctions. Effect of Electromagnetic Radiation on the Junction. Quantization of Magnetic Flux in a Superconducting Ring Superconducting Quantum Interference. . . . . . . . . The Superconducting Quantum Interference Device (SQUID) Superconducting Materials . . . . . . . . . . . . . . .

217 217 218 222 222 228 231 232 236 239 243 246

xvi

Problems ....... . References and Comments Suggested Reading. . . .

Contents

282 283 291

9. Physics and Applications of the Nonlinear Optical Properties of Solids

Introduction . . . . . . . . . . . . . . . . . . . 293 Review of Electromagnetic Wave Propagation in Solids. 293 Electric Polarization in a Dielectric Solid . . . . . 297 Nonlinear Polarization and Nonlinear Susceptibility . . 302 Anharmonic Oscillator Model of a Nonlinear Solid . . 303 Summary of the Physical Picture of Nonlinear Polarization. 308 Tensor Nature of the Nonlinear Susceptibility. . . . . . . 309 Solid State Physics Factors Affecting the Nonlinear Susceptibility 309 Magnitude of the Nonlinear Susceptibility. . . . . . . . 313 Wave Equation for the Nonlinear Crystal. . . . . . . . 314 Wave Propagation and Interaction in a Nonlinear Crystal. 316 Optical Second Harmonic Generation . . . . . . . . . 322 Phase Matching (Index Matching) in Second Harmonic Generation. 330 Frequency Mixing and Up-Conversion 331 Parametric Amplification . 336 Summary. . . . . . . . 340 Problems. . . . . . . . 340 References and Comments 341 Suggested Reading. . . . 345

10. Ferromagnetic Materials

Introduction . . . . Review of Magnetism . . Ferromagnetism ..... The Exchange Interaction. Magnetic Domains. . . . The Magnetization Curve and Hysteresis Materials for Permanent Magnets . . . Magnetic Materials for Other Applications Problems ....... . References and Comments Suggested Reading. . . .

Appendix: References on Some Other Topics

Index ....•..••..•.••.•..

347 347 349 351 358 367 376 381 383 384 389

391

393

INTRODUCTION TO

APPLIED SOLID STATE PHYSICS