Band Theory and Electronic Properties of Solids

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ISBN: 9780198506447 | 0198506449
Cover: Paperback
Copyright: 10/24/2001

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This latest text in the new Oxford Master Series in Physics provides a much need introduction to band theory and the electronic properties of materials. Written for students in physics and material science, the book takes a pedagogical approach to the subject through the extensive use of illustrations, examples and problem sets. The author draws on his extensive experience teaching band theory to provide the reader with a thorough understanding of the field. Considerable attention is paid to the vocabulary and quantum-mechanical training necessary to learn about the electronic, optical and structural properties of materials in science and technology. The text also offers several chapters on the newest experimental techniques used to study band structure. Concise yet rigorous, it fills a long overdue gap between student texts and current research activities.

Metals: the Drude and Sommerfeld models

(15)

Introduction

(1)

What do we know about metals?

(1)

The Drude model

(2)

Assumptions

(1)

The relaxation-time approximation

(1)

The failure of the Drude model

(3)

Electronic heat capacity

(1)

Thermal conductivity and the Wiedemann-Franz ratio

(2)

Hall effect

(1)

Summary

(1)

The Sommerfeld model

(6)

The introduction of quantum mechanics

(2)

The Fermi-Dirac distribution function

(1)

The electronic density of states

(1)

The electronic density of states at E ≈ EF

(1)

The electronic heat capacity

(2)

Successes and failures of the Sommerfeld model

(3)

The quantum mechanics of particles in a periodic potential: Bloch's theorem

(7)

Introduction and health warning

(1)

Introducing the periodic potential

(1)

Born-von Karman boundary conditions

(1)

The Schrodinger equation in a periodic potential

(1)

Bloch's theorem

(1)

Electronic bandstructure

(3)

The nearly-free electron model

(9)

Introduction

(1)

Vanishing potential

(3)

Single electron energy state

(1)

Several degenerate energy levels

(1)

Two degenerate free-electron levels

(2)

Consequences of the nearly-free-electron model

(6)

The alkali metals

(1)

Elements with even numbers of valence electrons

(2)

More complex Fermi surface shapes

(3)

The tight-binding model

(9)

Introduction

(1)

Band arising from a single electronic level

(3)

Electronic wavefunctions

(1)

Simple crystal structure

(1)

The potential and Hamiltonian

(2)

General points about the formation of tight-binding bands

(6)

The group IA and IIA metals; the tight-binding model viewpoint

(1)

The Group IV elements

(1)

The transition metals

(4)

Some general points about bandstructure

(8)

Comparison of tight-binding and nearly-free-electron bandstructure

(1)

The importance of K

(3)

hk is not the momentum

(1)

Group velocity

(1)

The effective mass

(1)

The effective mass and the density of states

(1)

Summary of the properties of k

(1)

Scattering in the Block approach

(1)

Holes

(1)

Postscript

(3)

Semiconductors and Insulators

(16)

Introduction

(1)

Bandstructure of Si and Ge

(3)

General points

(1)

Heavy and light holes

(1)

Optical absorption

(1)

Constant energy surfaces in the conduction bands of Si and Ge

(1)

Bandstructure of the direct-gap III-V and II-VI semiconductors

(3)

Introduction

(1)

General points

(1)

Optical absorption and excitons

(1)

Excitons

(1)

Constant energy surfaces in direct-gap III-V semiconductors

(1)

Thermal population of bands in semiconductors

(9)

The law of mass action

(2)

The motion of the chemical potential

(1)

Intrinsic carrier density

(1)

Impurities and extrinsic carriers

(1)

Extrinsic carrier density

(2)

Degenerate semiconductors

(1)

Impurity bands

(1)

Is it a semiconductor or an insulator?

(1)

A note on photoconductivity

(2)

Bandstructure engineering

(20)

Introduction

(1)

Semiconductor alloys

(1)

Artificial structures

(9)

Growth of semiconductor multilayers

(2)

Substrate and buffer layer

(1)

Quantum wells

(1)

Optical properties of quantum wells

(1)

Use of quantum wells in opto-electronics

(1)

Superlattices

(1)

Type I and type II superlattices

(2)

Heterojunctions and modulation doping

(1)

The envelope-function approximation

(1)

Band engineering using organic molecules

(3)

Introduction

(1)

Molecular building blocks

(2)

Typical Fermi surfaces

(1)

A note on the effective dimensionality of Fermi-surface sections

(1)

Layered conducting oxides

(3)

The Peierls transition

(4)

Measurement of bandstructure

(32)

Introduction

(1)

Lorentz force and orbits

(2)

General considerations

(1)

The cyclotron frequency

(2)

Orbits on a Fermi surface

(1)

The introduction of quantum mechanics

(4)

Landau levels

(2)

Application of Bohr's correspondence principle to arbitrarily-shaped Fermi surfaces in a magnetic field

(1)

Quantisation of the orbit area

(1)

The electronic density of states in a magnetic field

(1)

Quantum oscillatory phenomena

(6)

Types of quantum oscillation

(1)

The de Haas-van Alphen effect

(2)

Other parameters which can be deduced from quantum oscillations

(1)

Magnetic breakdown

(1)

Cyclotron resonance

(3)

Cyclotron resonance in metals

(1)

Cyclotron resonance in semiconductors

(2)

Interband magneto-optics in semiconductors

100

(2)

Other techniques

102

(3)

Angle-resolved photoelectron spectroscopy (ARPES)

103

(1)

Electroreflectance spectroscopy

104

(1)

Some case studies

105

(7)

Copper

105

(1)

Recent controversy: Sr2RuO4

106

(1)

Studies of the Fermi surface of an organic molecular metal

106

(6)

Quasiparticles: interactions between electrons

112

(5)

Transport of heat and electricity in metals and semiconductors

117

(16)

A brief digression; life without scattering would be difficult!

117

(2)

Thermal and electrical conductivity of metals

119

(8)

Metals: the `Kinetic theory' of electron transport

119

(1)

What do τ&sigma and τκ represent?

120

(2)

Matthiessen's rule

122

(1)

Emission and absorption of phonons

122

(1)

What is the characteristic energy of the phonons involved?

123

(1)

Electron-phonon scattering at room temperature

123

(1)

Electron-phonon scattering at T ≪ θD

123

(1)

Departures from the low temperature σα T-5 dependence

124

(1)

Very low temperatures and/or very dirty metals

124

(1)

Summary

125

(1)

Electron-electron scattering

125

(2)

Electrical conductivity of semiconductors

127

(2)

Temperature dependence of the carrier densities

127

(1)

The temperature dependence of the mobility

128

(1)

Disordered systems and hopping conduction

129

(4)

Thermally-activated hopping

129

(1)

Variable range hopping

130

(3)

Magnetoresistance in three-dimensional systems

133

(10)

Introduction

133

(1)

Hall effect with more than one type of carrier

133

(2)

General considerations

133

(2)

Hall effect in the presence of electrons and holes

135

(1)

A clue about the origins of magnetoresistance

135

(1)

Magnetoresistance in metals

135

(4)

The absence of magnetoresistance in the Sommerfeld model of metals

135

(2)

The presence of magnetoresistance in real metals

137

(1)

The use of magnetoresistance in finding the Fermi-surface shape

138

(1)

The magnetophonon effect

139

(4)

Magnetoresistance in two-dimensional systems and the quantum Hall effect

143

(11)

Introduction: two-dimensional systems

143

(1)

Two-dimensional Landau-level density of states

144

(3)

Resistivity and conductivity tensors for a two-dimensional system

145

(2)

Quantisation of the Hall resistivity

147

(2)

Localised and extended states

148

(1)

A further refinement- spin splitting

148

(1)

Summary

149

(1)

The fractional quantum Hall effect

150

(1)

More than one subband populated

151

(3)

Inhomogeneous and hot carrier distributions in semiconductors

154

(11)

Introduction: inhomogeneous carrier distributions

154

(2)

The excitation of minority carriers

154

(1)

Recombination

155

(1)

Diffusion and recombination

155

(1)

Drift, diffusion and the Einstein equations

156

(2)

Characterisation of minority carriers; the Shockley-Haynes experiment

156

(2)

Hot carrier effects and ballistic transport

158

(7)

Drift velocity saturation and the Gunn effect

158

(2)

Avalanching

160

(1)

A simple resonant tunnelling structure

160

(1)

Ballistic transport and the quantum point contact

161

(4)

A Useful terminology in condensed matter physics

165

(7)

Introduction

165

(1)

Crystal

165

(1)

Lattice

165

(1)

Basis

165

(1)

Physical properties of crystals

166

(1)

Unit cell

166

(1)

Wigner-Seitz cell

167

(1)

Designation of directions

167

(1)

Designation of planes; Miller indices

168

(1)

Conventional or primitive?

169

(2)

The 14 Bravais lattices

171

(1)

B Derivation of density of states in k-space

172

(3)

Introduction

172

(3)

Density of states

173

(1)

Reading

174

(1)

C Derivation of distribution functions

175

(6)

Introduction

175

(6)

Bosons

178

(1)

Fermions

178

(1)

The Maxwell-Boltzmann distribution function

178

(1)

Mean energy and heat capacity of the classical gas

179

(2)

D Phonons

181

(10)

Introduction

181

(1)

A simple model

182

(3)

Extension to three dimensions

183

(2)

The Debye model

185

(6)

Phonon number

187

(1)

Summary; the Debye temperature as a useful energy scale in solids

188

(1)

A note on the effect of dimensionality

188

(3)

E The Bohr model of hydrogen

191

(3)

Introduction

191

(1)

Hydrogenic impurities

192

(1)

Excitons

192

(2)

F Experimental considerations in measuring resistivity and Hall effect

194

(6)

Introduction

194

(1)

The four-wire method

194

(2)

Sample geometries

196

(1)

The van der Pauw method

197

(1)

Mobility spectrum analysis

198

(1)

The resistivity of layered samples

198

(2)

G Canonical momentum

200

(1)

H Superconductivity

201

(4)

Introduction

201

(1)

Pairing

201

(2)

Pairing and the Meissner effect

203

(2)

I List of selected symbols

205

(4)

J Solutions and additional hints for selected exercises

209

(8)

Index

217

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Band Theory and Electronic Properties of Solids

Summary

Author Biography

Table of Contents

Supplemental Materials

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Band Theory and Electronic Properties of Solids

Summary

Author Biography

Table of Contents

Supplemental Materials

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