The Manchester Physics Series General Editors D. J. SANDIFORD: F. MANDL: A. C. PHILLIPS

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4 Solid State Physics

5 The Manchester Physics Series General Editors D. J. SANDIFORD: F. MANDL: A. C. PHILLIPS Department of Physics and Astronomy, Faculty of Science, University of Manchester Properties of Matter: Statistical Physics: Second Edition Electromagnetism: Second Edition Statistics: Solid State Physics: Second Edition Quantum Mechanics: Particle Physics: Second Edition The Physics of Stars: Second Edition Computing for Scientists: Nuclear Physics: B. H. Flowers and E. Mendoza F. Mandl I. S. Grant and W. R. Phillips R. J. Barlow J. R. Hook and H. E. Hall F. Mandl B. R. Martin and G. Shaw A. C. Phillips R. J. Barlow and A. R. Barnett J. S. Lilley

6 SOLID STATE PHYSICS Second Edition J. R.Hook H. E. Hall Department of Physics. University of Manchester John Wiley & Sons CHICHESTER NEW YORK BRISBANE TORONTO SINGAPORE

7 Copyright 1974 by John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex P019 8SQ, England Telephone (+44) (for orders and customer service enquiries): Visit our Home Page or First edition 1974 Second edition 1991 Reprinted June and November 1994, July 1995, August 1996, February 1997, February 1998 and February 1999 Reprinted with corrections December 2000, November 2001, April2003, August 2004, April2005, October 2006, December 2007, October 2008, February 2010 All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1 T 4LP, UK, without the permission in writing of the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the publication. Neither the author(s) nor John Wiley & Sons, Ltd accept any responsibility or liability for loss or damage occasioned to any person or property through using the material, instructions, methods or ideas contained herein, or acting or refraining from acting as a result of such use. The author(s) and Publisher expressly disclaim all implied warranties, including merchantability of fitness for any particular purpose. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA , USA Wilcy-VCH Verlag GmbH, Boschstr. 12, D Weinheim, Germany John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, JinXing Distripark, Singapore John Wiley & Sons (Canada) Ltd, 22 Worcester Road, Etobicoke, Ontario M9W ILl Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Library of Congress Cataloging-in-Publication Data Hook, J. R. (John R.) Solid state physics I J. R. Hook, H. E. HalL-2nd ed. p. cm.-(the Manchester physics series) Rev. ed. of: Solid state physics I H. E. Hall, 1st ed Includes bibliographical references and index. ISBN (cloth)-isbn (paper) I. Solid state physics. I. Hall, H. E. (Henry Edgar), Il. Hall, H. E. (Henry Edgar), Solid state physics. III. Title. IV. Series. QC176.H dc CIP British Library Cataloguing in Publication Data Hook, J. R. Solid state physics. 1. Solids. Structure & physics properties I. Title II. Hall, H. E. (Henry Edgar) III. Series ISBN (hbk) ISBN (pbk) Typeset by APS, Salisbury, Wilts Printed and bound in Great Britain by TJ International Ltd, Padstow, Cornwall

8 To my family in partial compensation for taking so much of my time away from them

10 Contents Flow diagram Editor's preface to the Manchester Physics Series Foreword Author's preface to second edition Inside front cover XV xvii XlX 1 CRYSTAL STRUCTURE 1.1 Introduction 1.2 Elementary Crystallography The crystal lattice The basis Crystal planes and directions 1.3 Typical Crystal Structures Cubic and hexagonal close-packed structures The body-centred cubic structure Structures of ionic solids The diamond and zincblende structures 1.4 X-ray Crystallography The Bragg law Experimental arrangements for x-ray diffraction * Starred sections may be omitted as they are not required later in the book

11 viii Contents * 1.5 Quasi-crystals 1.6 Interatomic Forces Van der Waals bonding Ionic bonding Covalent bonding Metallic bonding Hydrogen bonding Mixed bonding PROBLEMS CRYSTAL DYNAMICS 2.1 Introduction 2.2 Sound Waves 2.3 Lattice Vibrations of One-dimensional Crystals Chain of identical atoms Chain of two types of atom 2.4 Lattice Vibrations of Three-dimensional Crystals 2.5 Phonons 2.6 Heat Capacity from Lattice Vibrations Energy and heat capacity of a harmonic oscillator The density of states The high- and low-temperature limits The Debye interpolation scheme 2. 7 Anharmonic Effects Thermal expansion Phonon-phonon collisions 2.8 Thermal Conduction by Phonons Kinetic theory Conduction at high temperatures Conduction at intermediate temperatures Conduction at low temperatures PROBLEMS FREE ELECTRONS IN METALS 3.1 Introduction 3.2 The Free Electron Model Ground state of the free electron gas The free electron gas at finite temperature Heat capacity of the free electron gas Soft x-ray emission spectrum Metallic binding

12 Contents IX 3.3 Transport Properties of the Conduction Electrons The equation of motion of the electrons The electrical conductivity The thermal conductivity The Wiedemann-Franz law and the temperature dependence of the electrical and thermal conductivities The Hall effect 97 PROBLEMS THE EFFECT OF THE PERIODIC LATTICE POTENTIAL-ENERGY BANDS Nearly Free Electron Theory Classification of Crystalline Solids into Metals, Insulators and Semiconductors The Tight Binding Approach Coupled probability amplitudes The Hi ion -covalent bonding Electron states on a one-dimensional chain Electron states in diamond, silicon and germanium Band Structure Effective Masses 124 PROBLEMS SEMICONDUCTORS Introduction Holes Methods of Providing Electrons and Holes Donor and acceptor impurities Thermal excitation of carriers Intrinsic behaviour Extrinsic behaviour Absorption of Electromagnetic Radiation Transport Properties Electrical conductivity Hall effect Cyclotron resonance Non-equilibrium Carrier Densities The continuity equations Electrical neutrality Generation and recombination Injection of minority carriers at a steady rate Injection of a pulse of minority carriers 166 PROBLEMS 5 168

13 x Contents 6 SEMICONDUCTOR DEVICES Introduction The p-n Junction with Zero Applied Bias The p-n Junction with an Applied Bias Other Devices Based on the p-n Junction Light emitting diodes and lasers Solar cells The junction transistor The junction-gate field-effect transistor Metal-oxide-semiconductor technology and the MOSFET Molecular Beam Epitaxy and Semiconductor Heterojunctions 192 PROBLEMS DIAMAGNETISM AND PARAMAGNETISM Introduction Paramagnetism The origin of permanent dipole moments The interaction of a permanent dipole moment with an applied magnetic field Calculation of the magnetization of paramagnetic ions Conduction electron paramagnetism Diamagnetism Momentum in a magnetic field Screening by induced currents Calculation of the diamagnetic susceptibility 215 PROBLEMS MAGNETIC ORDER 21~ 8o1 Introduction The Exchange Interaction Ferromagnetism The Weiss molecular field Calculation of ferromagnetic properties using the mean field theory The Neel Model of Antiferromagnetism Spin Waves Ferromagnets at low temperatures Spin waves in a one-dimensional crystal Magnetization and heat capacity at low temperatures 236 *805.4 Ferromagnetic resonance and the experimental observation of spin waves 0 239

14 Contents XI *8.6 Other Types of Magnetic Order Ferrimagnetism Spin density wave antiferromagnetism in chromium Magnetic ordering in rare-earth metals Ferromagnetic Domains The energy and thickness of a Bloch wall Why do domains occur? Magnetization curves of ferromagnets 250 PROBLEMS ELECTRIC PROPERTIES OF INSULATORS Dielectrics Dielectric constant and susceptibility Polarization due to relative motion of electrons and nuclei Orientation of permanent dipole moments 260 *9.1.4 Dielectric constant and lattice vibrations of ionic crystals Pyroelectric Materials. 271 *9.2.1 The Landau model Piezoelectricity 275 PROBLEMS SUPERCONDUCTIVITY Introduction Magnetic Properties of Superconductors Type I superconductors Thermodynamics of the superconducting transition Type II superconductors The London Equation The Theory of Superconductivity The energy gap and electron pairing. 290 * The Cooper problem. 292 * Origin of the attractive interaction 293 * Nature of the superconducting ground state Explanation of infinite conductivity Macroscopic Quantum Phenomena The superconducting order parameter Flux quantization Quantized flux lines and type II superconductivity Josephson effects 304 * Quantum interference High-temperature Superconductors 310 PROBLEMS

15 xn Contents 11 WAVES IN CRYSTALS Introduction Elastic Scattering of Waves by a Crystal Amplitude of the scattered wave Laue conditions for diffraction and the reciprocal lattice Examples of reciprocal lattices The structure factor Wavelike Normal Modes-Bloch's Theorem Normal Modes and the Reciprocal Lattice Periodicity of the dispersion relation Brillouin zones and the plotting of dispersion relations 333 PROBLEMS SCATTERING OF NEUTRONS AND ELECTRONS FROM SOLIDS Introduction Comparison of X-rays, Neutrons and Electrons Interaction of x-rays, neutrons and electrons with atoms Inelastic scattering Neutron Scattering Techniques Neutron sources Neutron detectors Time-of-flight methods Crystal monochromators Determination of Phonon Spectra Magnetic Scattering Determination of magnetic structure Determination of magnon spectra Electron Scattering 355 PROBLEMS REAL METALS Introduction Fermi Surfaces Fermi surface of a nearly free electron two-dimensional metal Fermi surface of three-dimensional metals Density of states at the Fermi surface 366

SOLID STATE PHYSICS. Second Edition. John Wiley & Sons. J. R. Hook H. E. Hall. Department of Physics, University of Manchester

SOLID STATE PHYSICS. Second Edition. John Wiley & Sons. J. R. Hook H. E. Hall. Department of Physics, University of Manchester SOLID STATE PHYSICS Second Edition J. R. Hook H. E. Hall Department of Physics, University of Manchester John Wiley & Sons CHICHESTER NEW YORK BRISBANE TORONTO SINGAPORE Contents Flow diagram Inside front