Metals: the Drude and Sommerfeld models p. 1 Introduction p. 1 What do we know about metals? p. 1 The Drude model p. 2 Assumptions p.

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1 Metals: the Drude and Sommerfeld models p. 1 Introduction p. 1 What do we know about metals? p. 1 The Drude model p. 2 Assumptions p. 2 The relaxation-time approximation p. 3 The failure of the Drude model p. 4 Electronic heat capacity p. 4 Thermal conductivity and the Wiedemann-Franz ratio p. 4 Hall effect p. 6 Summary p. 7 The Sommerfeld model p. 7 The introduction of quantum mechanics p. 7 The Fermi-Dirac distribution function p. 9 The electronic density of states p. 9 The electronic density of states at E [approximate] E[subscript F] p. 10 The electronic heat capacity p. 11 Successes and failures of the Sommerfeld model p. 13 The quantum mechanics of particles in a periodic potential: Bloch's theorem p. 16 Introduction and health warning p. 16 Introducing the periodic potential p. 16 Born-von Karman boundary conditions p. 17 The Schrodinger equation in a periodic potential p. 18 Bloch's theorem p. 19 Electronic bandstructure p. 20 The nearly-free electron model p. 23 Introduction p. 23 Vanishing potential p. 23 Single electron energy state p. 23 Several degenerate energy levels p. 24 Two degenerate free-electron levels p. 24 Consequences of the nearly-free-electron model p. 26 The alkali metals p. 27 Elements with even numbers of valence electrons p. 27 More complex Fermi surface shapes p. 29 The tight-binding model p. 32 Introduction p. 32 Band arising from a single electronic level p. 32 Electronic wavefunctions p. 32 Simple crystal structure p. 33 The potential and Hamiltonian p. 33

2 General points about the formation of tight-binding bands p. 35 The group IA and IIA metals; the tight-binding model viewpoint p. 36 The Group IV elements p. 36 The transition metals p. 37 Some general points about bandstructure p. 41 Comparison of tight-binding and nearly-free-electron bandstructure p. 41 The importance of k p. 42 hk is not the momentum p. 42 Group velocity p. 42 The effective mass p. 42 The effective mass and the density of states p. 43 Summary of the properties of k p. 44 Scattering in the Bloch approach p. 45 Holes p. 45 Postscript p. 46 Semiconductors and Insulators p. 49 Introduction p. 49 Bandstructure of Si and Ge p. 50 General points p. 50 Heavy and light holes p. 51 Optical absorption p. 51 Constant energy surfaces in the conduction bands of Si and Ge p. 52 Bandstructure of the direct-gap III-V and II-VI semiconductors p. 53 Introduction p. 53 General points p. 53 Optical absorption and excitons p. 54 Excitons p. 55 Constant energy surfaces in direct-gap III-V semiconductors p. 56 Thermal population of bands in semiconductors p. 56 The law of mass action p. 56 The motion of the chemical potential p. 58 Intrinsic carrier density p. 58 Impurities and extrinsic carriers p. 59 Extrinsic carrier density p. 60 Degenerate semiconductors p. 62 Impurity bands p. 62 Is it a semiconductor or an insulator? p. 62 A note on photoconductivity p. 63 Bandstructure engineering p. 65 Introduction p. 65 Semiconductor alloys p. 65

3 Artificial structures p. 66 Growth of semiconductor multilayers p. 66 Substrate and buffer layer p. 68 Quantum wells p. 68 Optical properties of quantum wells p. 69 Use of quantum wells in opto-electronics p. 70 Superlattices p. 71 Type I and type II superlattices p. 71 Heterojunctions and modulation doping p. 73 The envelope-function approximation p. 74 Band engineering using organic molecules p. 75 Introduction p. 75 Molecular building blocks p. 75 Typical Fermi surfaces p. 77 A note on the effective dimensionality of Fermi-surface sections p. 78 Layered conducting oxides p. 78 The Peierls transition p. 81 Measurement of bandstructure p. 85 Introduction p. 85 Lorentz force and orbits p. 85 General considerations p. 85 The cyclotron frequency p. 85 Orbits on a Fermi surface p. 87 The introduction of quantum mechanics p. 87 Landau levels p. 87 Application of Bohr's correspondence principle to arbitrarily-shaped Fermi surfaces in a magnetic field p. 89 Quantisation of the orbit area p. 90 The electronic density of states in a magnetic field p. 91 Quantum oscillatory phenomena p. 91 Types of quantum oscillation p. 93 The de Haas-van Alphen effect p. 94 Other parameters which can be deduced from quantum oscillations p. 96 Magnetic breakdown p. 97 Cyclotron resonance p. 97 Cyclotron resonance in metals p. 98 Cyclotron resonance in semiconductors p. 98 Interband magneto-optics in semiconductors p. 100 Other techniques p. 102 Angle-resolved photoelectron spectroscopy (ARPES) p. 103 Electroreflectance spectroscopy p. 104 Some case studies p. 105

4 Copper p. 105 Recent controversy: Sr[subscript 2]RuO[subscript 4] p. 106 Studies of the Fermi surface of an organic molecular metal p. 106 Quasiparticles: interactions between electrons p. 112 Transport of heat and electricity in metals and semiconductors p. 117 A brief digression; life without scattering would be difficult! p. 117 Thermal and electrical conductivity of metals p. 119 Metals: the 'Kinetic theory' of electron transport p. 119 What do [tau subscript [sigma] and [tau subscript [kappa] represent? p. 120 Matthiessen's rule p. 122 Emission and absorption of phonons p. 122 What is the characteristic energy of the phonons involved? p. 123 Electron-phonon scattering at room temperature p. 123 Electron-phonon scattering at T [double less-than sign] [theta subscript D] p. 123 Departures from the low temperature [sigma] [proportional to] T[superscript -5] dependence p. 124 Very low temperatures and/or very dirty metals p. 124 Summary p. 125 Electron-electron scattering p. 125 Electrical conductivity of semiconductors p. 127 Temperature dependence of the carrier densities p. 127 The temperature dependence of the mobility p. 128 Disordered systems and hopping conduction p. 129 Thermally-activated hopping p. 129 Variable range hopping p. 130 Magnetoresistance in three-dimensional systems p. 133 Introduction p. 133 Hall effect with more than one type of carrier p. 133 General considerations p. 133 Hall effect in the presence of electrons and holes p. 135 A clue about the origins of magnetoresistance p. 135 Magnetoresistance in metals p. 135 The absence of magnetoresistance in the Sommerfeld model of metals p. 135 The presence of magnetoresistance in real metals p. 137 The use of magnetoresistance in finding the Fermi-surface shape p. 138 The magnetophonon effect p. 139 Magnetoresistance in two-dimensional systems and the quantum Hall effect p. 143 Introduction: two-dimensional systems p. 143 Two-dimensional Landau-level density of states p. 144 Resistivity and conductivity tensors for a two-dimensional system p. 145 Quantisation of the Hall resistivity p. 147 Localised and extended states p. 148

5 A further refinement- spin splitting p. 148 Summary p. 149 The fractional quantum Hall effect p. 150 More than one subband populated p. 151 Inhomogeneous and hot carrier distributions in semiconductors p. 154 Introduction: inhomogeneous carrier distributions p. 154 The excitation of minority carriers p. 154 Recombination p. 155 Diffusion and recombination p. 155 Drift, diffusion and the Einstein equations p. 156 Characterisation of minority carriers; the Shockley-Haynes experiment p. 156 Hot carrier effects and ballistic transport p. 158 Drift velocity saturation and the Gunn effect p. 158 Avalanching p. 160 A simple resonant tunnelling structure p. 160 Ballistic transport and the quantum point contact p. 161 Useful terminology in condensed matter physics p. 165 Introduction p. 165 Crystal p. 165 Lattice p. 165 Basis p. 165 Physical properties of crystals p. 166 Unit cell p. 166 Wigner-Seitz cell p. 167 Designation of directions p. 167 Designation of planes; Miller indices p. 168 Conventional or primitive? p. 169 The 14 Bravais lattices p. 171 Derivation of density of states in k-space p. 172 Introduction p. 172 Density of states p. 173 Reading p. 174 Derivation of distribution functions p. 175 Introduction p. 175 Bosons p. 178 Fermions p. 178 The Maxwell-Boltzmann distribution function p. 178 Mean energy and heat capacity of the classical gas p. 179 Phonons p. 181 Introduction p. 181 A simple model p. 182

6 Extension to three dimensions p. 183 The Debye model p. 185 Phonon number p. 187 Summary; the Debye temperature as a useful energy scale in solids p. 188 A note on the effect of dimensionality p. 188 The Bohr model of hydrogen p. 191 Introduction p. 191 Hydrogenic impurities p. 192 Excitons p. 192 Experimental considerations in measuring resistivity and Hall effect p. 194 Introduction p. 194 The four-wire method p. 194 Sample geometries p. 196 The van der Pauw method p. 197 Mobility spectrum analysis p. 198 The resistivity of layered samples p. 198 Canonical momentum p. 200 Superconductivity p. 201 Introduction p. 201 Pairing p. 201 Pairing and the Meissner effect p. 203 List of selected symbols p. 205 Solutions and additional hints for selected exercises p. 209 Index p. 217 Table of Contents provided by Blackwell's Book Services and R.R. Bowker. Used with permission.

Basic Semiconductor Physics

Chihiro Hamaguchi Basic Semiconductor Physics With 177 Figures and 25 Tables Springer 1. Energy Band Structures of Semiconductors 1 1.1 Free-Electron Model 1 1.2 Bloch Theorem 3 1.3 Nearly Free Electron