Quantum theory of solids

Quantum Theory of Solids

The Taylor & Francis Masters Series in Physics and Astronomy
Edited by David S. Betts Department of Physics and Astronomy, University of Sussex, Brighton, UK

Core Electrodynamics Sandra C. Chapman 0-7484-0622-0 (PB) 0-7484-0623-9 (HB) Atomic and Molecular Clusters Roy L. Johnston 0-7484-0931-9 (PB) 0-7484-0930-0 (HB) Quantum Theory of Solids Eoin P. O’Reilly0-7484-06271-1 (PB) 0-7484-0628-X (HB) Forthcoming titles in the series: Basic Superfluids Anthony M. Guénault 0-7484-0892-4 (PB) 0-7484-0891-6 (HB)

Quantum Theory of Solids

Eoin P. O’Reilly

London and New York

First published 2003 by RoutledgeCurzon 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by RoutledgeCurzon 29 West 35th Street, New York, NY10001 RoutledgeCurzon is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2005.

“To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.”
© 2003 Meredith L. Weiss and Saliha Hassan; individual chapters © the individual contributors All rights reserved. Nopart of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from theBritish Library Library of Congress Cataloging in Publication Data A catalog record for this book has been requested ISBN 0-203-21215-0 Master e-book ISBN

ISBN 0-203-26954-3 (Adobe eReader Format) ISBN 0–7007–1646–7

Contents

Series Preface Preface

ix xi

1

Introduction and review of quantum mechanics
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 Introduction 1 Wave–particle duality 2Wave quantisation 4 Heisenberg uncertainty principle 5 Schrödinger’s equation 6 Expectation values and the momentum operator 9 Some properties of wavefunctions 10 The variational principle 12 The variational method in an infinite square well 13 The finite square well 14

1

2

Bonding in molecules and solids
2.1 2.2 2.3 2.4 2.5 2.6 2.7 Introduction 19 Double square well potential 20 Thehydrogen molecule, H2 26 The diatomic LiH molecule 30 Tetrahedral bonding in Si crystals 33 Bonding in gallium arsenide 36 Trends in semiconductors 36

19

3

Band structure of solids
3.1 3.2 3.3 3.4 3.5 Introduction 41 Bloch’s theorem and band structure for a periodic solid 43 The Kronig–Penney model 46 The tight-binding method 51 The nearly free electron method 55

41

vi Contents

3.63.7

Band structure of tetrahedral semiconductors 61 The use of ‘pseudo’ potentials 63

4

Band structure and defects in bulk semiconductors
4.1 4.2 4.3 4.4 4.5 4.6 Introduction 72 k · p theory for semiconductors 76 Electron and hole effective masses 79 Trends in semiconductors 83 Impurities in semiconductors 84 Amorphous semiconductors 90

72

5

Physics and applications oflow-dimensional semiconductor structures
5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 Introduction 95 Confined states in quantum wells, wires, and dots 97 Density of states in quantum wells, wires, and dots 99 Modulation doping and heterojunctions 103 Quantum Hall effect 106 Semiconductor laser action 112 Strained-layer lasers 116 Tunnelling structures and devices 119

95

6

Diamagnetism and paramagnetism
6.16.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9

128

Introduction 128 Magnetisation 128 Magnetic moment of the electron 130 Diamagnetism in atoms and solids 132 Langevin (classical) theory of paramagnetism 133 Magnetic moments in isolated atoms and ions: Hund’s rules 136 Brillouin (quantum mechanical) theory of paramagnetism 139 Paramagnetism in metals 141 Floating frogs 143

7

Ferromagnetism and...