Electrical properties of materials NINTH EDITION L. Solymar Department of Electrical and Electronic Engineering Imperial College, London D. Walsh Department of Engineering Science University of Oxford R. R. A. Syms Department of Electrical and Electronic Engineering Imperial College, London 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Oxford University Press, 1970, 1979, 1984, 1988, 1993, 1998, 2004, 2010, 2014 The moral rights of the authors have been asserted First edition 1970 Second edition 1979 Third edition 1984 Fourth edition 1988 Fifth edition 1993 Sixth edition 1998 Seventh edition 2004 Eighth edition 2010 Ninth edition 2014 Impression: 1 All rights reserved. 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Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work. Preface to the ninth edition The major change relative to all of the previous editions is that Professor Richard Syms of Imperial College has joined us as an author. There are new topics added and old topics updated, but the style remains as light as ever. Topics that needed considerable updating are semiconductor technology, semiconductor devices, nanoelectronics, plasma etching, ferroelectric materi- als, and spintronics. We have been aware of many physical phenomena of interest, which we have failed to include in the past because, in our opinion at the time, their application prospects were not strong enough. Some of these have now come to the fore and we have included them; they are dielectrophoresis, Raman spectroscopy, thermoelectricity, and pyroelectricity. We believe that one of the most important applications of the electrical properties of materials is in the field of memory elements. We have previ- ously described these in the respective chapters, e.g. semiconductor memories in the chapter on semiconductor devices and magnetic memories in the chapter on magnetism. We felt that this time, in order to emphasise their similarities and differences, we needed to collect them into a separate chapter, which has turned out to be an appendix. We have also added another appendix describing the two major directions in medical imaging: computed tomography (CT) and magnetic resonance imaging (MRI). We have to express here our gratitude to our wives who were willing to put up with the long hours we spent bringing this edition up to date. Contents Data on specific materials in text xiii Introduction xv 1 The electron as a particle 1.1 Introduction 1 1.2 The effect of an electric field—conductivity and Ohm’s law 2 1.3 The hydrodynamic model of electron flow 4 1.4 The Hall effect 5 1.5 Electromagnetic waves in solids 6 1.6 Waves in the presence of an applied magnetic field: cyclotron resonance 13 1.7 Plasma waves 16 1.8 Johnson noise 19 1.9 Heat 21 Exercises 23 2 The electron as a wave 2.1 Introduction 25 2.2 The electron microscope 28 2.3 Some properties of waves 29 2.4 Applications to electrons 31 2.5 Two analogies 33 Exercises 34 3 The electron 3.1 Introduction 36 3.2 Schrödinger’s equation 38 3.3 Solutions of Schrödinger’s equation 39 3.4 The electron as a wave 40 3.5 The electron as a particle 41 3.6 The electron meeting a potential barrier 41 3.7 Two analogies 44 3.8 The electron in a potential well 45 3.9 The potential well with a rigid wall 47 3.10 The uncertainty relationship 47 3.11 Philosophical implications 48 Exercises 50 vi Contents 4 The hydrogen atom and the periodic table 4.1 The hydrogen atom 53 4.2 Quantum numbers 58 4.3 Electron spin and Pauli’s exclusion principle 59 4.4 The periodic table 59 Exercises 64 5Bonds 5.1 Introduction 66 5.2 General mechanical properties of bonds 67 5.3 Bond types 69 5.3.1 Ionic bonds 69 5.3.2 Metallic bonds 70 5.3.3 The covalent bond 70 5.3.4 The van der Waals bond 73 5.3.5 Mixed bonds 74 5.3.6 Carbon again 74 5.4 Feynman’s coupled mode approach 75 5.5 Nuclear forces 80 5.6 The hydrogen molecule 81 5.7 An analogy 82 Exercises 82 6 The free electron theory of metals 6.1 Free electrons 84 6.2 The density of states and the Fermi–Dirac distribution 85 6.3 The specific heat of electrons 88 6.4 The work function 89 6.5 Thermionic emission 89 6.6 The Schottky effect 92 6.7 Field emission 95 6.8 The field-emission microscope 95 6.9 The photoelectric effect 97 6.10 Quartz–halogen lamps 97 6.11 The junction between two metals 98 Exercises 99 7 The band theory of solids 7.1 Introduction 101 7.2 The Kronig–Penney model 102 7.3 The Ziman model 106 7.4 The Feynman model 109 Contents vii 7.5 The effective mass 112 7.6 The effective number of free electrons 114 7.7 The number of possible states per band 115 7.8 Metals and insulators 117 7.9 Holes 117 7.10 Divalent metals 119 7.11 Finite temperatures 120 7.12 Concluding remarks 121 Exercises 122 8 Semiconductors 8.1 Introduction 123 8.2 Intrinsic semiconductors 123 8.3 Extrinsic semiconductors 128 8.4 Scattering 132 8.5 A relationship between electron and hole densities 134 8.6 III–V and II–VI compounds 136 8.7 Non-equilibrium processes 140 8.8 Real semiconductors 141 8.9 Amorphous semiconductors 143 8.10 Measurement of semiconductor properties 143 8.10.1 Mobility 143 8.10.2 Hall coefficient 146 8.10.3 Effective mass 146 8.10.4 Energy gap 147 8.10.5 Carrier lifetime 151 8.11 Preparation of pure and controlled-impurity single-crystal semiconductors 151 8.11.1 Crystal growth from the melt 151 8.11.2 Zone refining 152 8.11.3 Modern methods of silicon purification 154 8.11.4 Epitaxial growth 154 8.11.5 Molecular beam epitaxy 156 8.11.6 Metal–organic chemical vapour deposition 156 8.11.7 Hydride vapour phase epitaxy (HVPE) for nitride devices 157 Exercises 158 9 Principles of semiconductor devices 9.1 Introduction 161 9.2 The p–n junction in equilibrium 161 9.3 Rectification 166 9.4 Injection 168 9.5 Junction capacity 170 9.6 The transistor 171 9.7 Metal–semiconductor junctions 176 9.8 The role of surface states; real metal–semiconductor junctions 178 9.9 Metal–insulator–semiconductor junctions 180 9.10 The tunnel diode 183 9.11 The backward diode 186 viii Contents 9.12 The Zener diode and the avalanche diode 186 9.12.1 Zener breakdown 187 9.12.2 Avalanche breakdown 187 9.13 Varactor diodes 188 9.14 Field-effect transistors 189 9.15 Heterostructures 194 9.16 Charge-coupled devices 198 9.17 Silicon controlled rectifier 200 9.18 The Gunn effect 201 9.19 Strain gauges 204 9.20 Measurement of magnetic field by the Hall effect 205 9.21 Gas sensors 205 9.22 Microelectronic circuits 206 9.23 Plasma etching 210 9.24 Recent techniques for overcoming limitations 212 9.25 Building in the third dimension 213 9.26 Microelectro-mechanical systems (MEMS) 215 9.26.1 A movable mirror 215 9.26.2 A mass spectrometer on a chip 216 9.27 Nanoelectronics 218 9.28 Social implications 222 Exercises 223 10 Dielectric materials 10.1 Introduction 225 10.2 Macroscopic approach 225 10.3 Microscopic approach 226 10.4 Types of polarization 227 10.5 The complex dielectric constant and the refractive index 228 10.6 Frequency response 229 10.7 Anomalous dispersion 230 10.8 Polar and non-polar materials 231 10.9 The Debye equation 233 10.10 The effective field 234 10.11 Acoustic waves 236 10.12 Dielectric breakdown 240 10.12.1 Intrinsic breakdown 240 10.12.2 Thermal breakdown 240 10.12.3 Discharge breakdown 241 10.13 Piezoelectricity, pyroelectricity, and ferroelectricity 241 10.13.1 Piezoelectricity 241 10.13.2 Pyroelectricity 247 10.13.3 Ferroelectrics 248 10.14 Interaction of optical phonons with drifting electrons 249 10.15 Optical fibres 250 10.16 The Xerox process 252 10.17 Liquid crystals 252 10.18 Dielectrophoresis 254 Exercises 256 Contents ix 11 Magnetic materials 11.1 Introduction 259 11.2 Macroscopic approach 260 11.3 Microscopic theory (phenomenological) 260 11.4 Domains and the hysteresis curve 264 11.5 Soft magnetic materials 268 11.6 Hard magnetic materials (permanent magnets) 270 11.7 Microscopic theory (quantum-mechanical) 273 11.7.1 The Stern–Gerlach experiment 278 11.7.2 Paramagnetism 278 11.7.3 Paramagnetic solids 280 11.7.4 Antiferromagnetism 281 11.7.5 Ferromagnetism 281 11.7.6 Ferrimagnetism 282 11.7.7 Garnets 282 11.7.8 Helimagnetism 282 11.8 Magnetic resonance 282 11.8.1 Paramagnetic resonance 282 11.8.2 Electron spin resonance 283 11.8.3 Ferromagnetic, antiferromagnetic, and ferrimagnetic