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SECOND EDITION ThermaPl hysic·s CHARLES KITTEL/ HERBERT KROEMER Thermal Physics SECOND EDITION Thermal Physics Charles Kittel Herbert Kroemer University of California [E W. H. Freeman and Company New York Sponsoring Editor: Peter Renz Project Editor: Nancy Flight Manuscript Editor: Ruth Veres Designers: Gary A. Head and Sharon H. Smith Production Coordinator: Frank Mitchell Illustration Coordinator: Batyah Janowski Anist: Felix Cooper Compositor: Syntax International Printer and Binder: Halliday Litho Library of Congress Cataloging in Publication Data Kittel, Charles. Thermal physics. Bibliography: p. Includes index. I. Statistical thermodynamics. I. Kroemer, Herbert, 1928- joint author. II. Title. QC31 l.5.K52 1980 536'.7 79-16677 ISBN 0-7167-1088-9 Copyright© 1980 by W. H. Freeman and Company No part of this book may be reproduced by any mechanical, photographic, or electronic process, or in the form of a phonographic recording, nor may it be stored in a retrieval system, transmitted, or otherwise copied for public or private use, without written permission from the publisher. Printed in the United State of America 11 12 13 14 15 16 VB 9 9 8 7 6 5 4 3 2 1 0 About the Authors Charles Kittel has taught solid state physics at the University of California at Berkeley since 1951, having previously been at the Bell Laboratories. His undergraduate work in physics was done at M.I.T. and at the Cavendish Laboratory of Cambridge University. His Ph.D. research was in theoretical nuclear physics with Professor Gregory Breit at the University of Wisconsin. He has been awarded three Guggenheim fellowships, the Oliver Buckley Prize for Solid State Physics, and, for contributions to teaching, the Oersted Medal of the American Association of Physics Teachers. He is a member of the National Academy of Science and of the American Academy of Arts and Sciences. His research has been in magnetism, magnetic resonance, semicon ductors, and the statistical mechanics of solids. Herbert Kroemer is Professor of Electrical Engineering at the University of California at Santa Barbara. His background and training are in solid state physics. He received a Ph.D. in physics in 1952f rom the University of Gottingen in Germany with a thesis on hot electron effects in the then new transistor. From 1952 through 1968 he worked in several semiconductor research labora tories in Germany and the United States. In 1968 he became Professor of Electrical Engineering at the University of Colorado; he came to UCSB in 1976. His research has been in the physics and technology of semiconductors and semiconductor devices, including high-frequency transistors, negative mass effects in semiconductors, injection lasers, the Gunn effect, electron-hole drops, and semiconductor heterojunctions. V Preface This book gives an elementary account of thermal physics. The subject is simple, the methods are powerful, and the results have broad applications. Probably no other physical theory is used more widely throughout science and engineering. We have written for undergraduate students of physics and astronomy, and for electrical engineering students generally. These fields for our purposes have strong common bonds, most notably a concern with Fermi gases, whether in semiconductors, metals, stars, or nuclei. We develop methods (not original, but not easily accessible elsewhere) that are well suited to these fields. We wrote the book in the first place because we were delighted by the clarity of the "new" methods as compared to those we were taught when we were students ourselves. The second edition is substantially rewritten and revised from the first edition, which, although warmly accepted, suffered from the concentration of abstract ideas at the beginning. In the new structure the free energy, the partition function, and the Planck distribution are developed before the chem ical potential. Real problems can now be solved much earlier. We have added chapters on applications to semiconductors, binary mixtures, transport theory, cryogenics, and propagation. The treatment of heat and work is new and will be helpful to those concerned with energy conversion processes. Many more examples and problems are given, but we have not introduced problems where they do not contribute to the main line of advance. For this edition an instructor's guide is available from the publisher, upon request from the instructor. This edition has been tested extensively over the past few years in classroom use. We have not emphasized several traditional topics, some because they are no longer useful and some because their reliance on classical statistical me chanics would make the course more difficult than we believe a first course should be. Also, we have avoided the use of combinatorial methods where they are unnecessary. For a one quarter course for physics undergraduates, we suggest most of Chapters 1 through 10, plus 14. The Debye theory could be omitted from "" viii Preface Chapter 4 and the Boltzmann transport equation from Chapter 14. For a one quarter course for electrical engineers, we suggest Chapter 13 at any time after the discussion of the Fermi gas in Chapter 7. The material of Chapter 13 does not draw on Chapter 4. The scope of the book is ample for a one semester course, and here the pace can be relaxed. Notation and units: We generally use the SI and CGS systems in parallel. We do not use the calorie. The kelvin temperature T is related to the funda mental temperature r by r = k8 T, and the conventional entropy S is related to the fundamental entropy a by S = k8a. The symbol log will denote natural logarithm throughout, simply because In is less expressive when set in type. The notation (18) refers to Equation (18) of the current chapter, but (3.18) refers to Equation (18) of Chapter 3. The book is the successor to course notes developed with the assistance of grants by the University of California. Edward M. Purcell contributed many ideas to the first edition. We benefited from review of the second edition by Seymour Geller, Paul L. Richards, and Nicholas Wheeler. Help was given by Ibrahim Adawi, Bernard Black, G. Domokos, Margaret Geller, Cameron Hayne, K. A. Jackson, S. Justi, Peter Kittel, Richard Kittler, Martin J. Klein, Ellen Leverenz, Bruce H.J. McKellar, F. E. O'Meara, Norman E. Phillips, B. Roswell Russell, T. M. Sanders, B. Stoeckly, John Verhoogen, John Wheatley, and Eyvind Wichmann. We thank Carol Tung for the typed manuscript and Sari Wilde for her help with the index. Berkeley and Santa Barbara Charles Kittel H erhert Kroemer Note to the Student For minimum coverage of the concepts presented in each chapter, the authors recommend the following exercises. Chapter 2: 1, 2, 3; Chapter 3: 1, 2, 3, 4, 8, 11; Chapter 4: 1, 2, 4, 5, 6, 8; Chapter 5: 1, 3, 4, 6, 8; Chapter 6: 1, 2, 3, 6, 12, 14, 15; Chapter 7: 2, 3, 5, 6, 7, 11; Chapter 8: 1, 2, 3, 5, 6, 7; Chapter 9: l, 2, 3: Chapter 10: l, 2, 3; Chapter 11: 1, 2, 3; Chapter 12: 3, 4, 5; Chapter 13: 1, 2, 3, 7, 8, 10; Chapter 14: 1, 3, 4, 5; Chapter 15: 2, 3, 4, 6. ix Contents Guide to Fundamental Definitions xm General References xv Introduction Chapter 1 States of a Model System 5 Chapter 2 Entropy and Temperature 27 Chapter 3 Boltzmann Distribution and Helmholtz Free Energy 55 Chapter 4 Thermal Radiation and Planck Distribution 87 Chapter 5 Chemical Potential and Gibbs Distribution 117 Chapter 6 Ideal Gas 151 Chapter 7 Fermi and Bose Gases 181 Chapter 8 Heat and Work 225 Chapter 9 Gibbs Free Energy and Chemical Reactions 261 Chapter 10 Phase Transformations 275 Chapter 11 Binary Mixtures 309 Chapter 12 Cryogenics 333 Chapter 13 Semiconductor Statistics 353 Chapter 14 Kinetic Theory 389 Chapter 15 Propagation 423 Appendix A Some Integrals Containing Exponentials 439 Appendix B Temperature Scales 445 xi