Band theory and electronic properties of solids / John Singleton.

Format:

Book

Author/Creator:

Singleton, John, 1960 December 11-

Series:

Oxford master series in condensed matter physics

Language:

English

Subjects (All):

Energy-band theory of solids.

Solids--Electric properties.

Solids.

Physical Description:

xvi, 222 pages : illustrations ; 25 cm.

Place of Publication:

Oxford ; New York : Oxford University Press, 2001.

Summary:

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.

Contents:

1 Metals: the Drude and Sommerfeld models 1

1.2 What do we know about metals? 1

1.3 The Drude model 2

1.3.2 The relaxation-time approximation 3

1.4 The failure of the Drude model 4

1.4.1 Electronic heat capacity 4

1.4.2 Thermal conductivity and the Wiedemann-Franz ratio 4

1.4.3 Hall effect 6

1.5 The Sommerfeld model 7

1.5.1 The introduction of quantum mechanics 7

1.5.2 The Fermi-Dirac distribution function 9

1.5.3 The electronic density of states 9

1.5.4 The electronic density of states at E [approximate] E[subscript F] 10

1.5.5 The electronic heat capacity 11

1.6 Successes and failures of the Sommerfeld model 13

2 The quantum mechanics of particles in a periodic potential: Bloch's theorem 16

2.1 Introduction and health warning 16

2.2 Introducing the periodic potential 16

2.3 Born-von Karman boundary conditions 17

2.4 The Schrodinger equation in a periodic potential 18

2.5 Bloch's theorem 19

2.6 Electronic bandstructure 20

3 The nearly-free electron model 23

3.2 Vanishing potential 23

3.2.1 Single electron energy state 23

3.2.2 Several degenerate energy levels 24

3.2.3 Two degenerate free-electron levels 24

3.3 Consequences of the nearly-free-electron model 26

3.3.1 The alkali metals 27

3.3.2 Elements with even numbers of valence electrons 27

3.3.3 More complex Fermi surface shapes 29

4 The tight-binding model 32

4.2 Band arising from a single electronic level 32

4.2.1 Electronic wavefunctions 32

4.2.2 Simple crystal structure 33

4.2.3 The potential and Hamiltonian 33

4.3 General points about the formation of tight-binding bands 35

4.3.1 The group IA and IIA metals; the tight-binding model viewpoint 36

4.3.2 The Group IV elements 36

4.3.3 The transition metals 37

5 Some general points about bandstructure 41

5.1 Comparison of tight-binding and nearly-free-electron bandstructure 41

5.2 The importance of k 42

5.2.1 hk is not the momentum 42

5.2.2 Group velocity 42

5.2.3 The effective mass 42

5.2.4 The effective mass and the density of states 43

5.2.5 Summary of the properties of k 44

5.2.6 Scattering in the Bloch approach 45

5.3 Holes 45

6 Semiconductors and Insulators 49

6.2 Bandstructure of Si and Ge 50

6.2.1 General points 50

6.2.2 Heavy and light holes 51

6.2.3 Optical absorption 51

6.2.4 Constant energy surfaces in the conduction bands of Si and Ge 52

6.3 Bandstructure of the direct-gap III-V and II-VI semiconductors 53

6.3.3 Optical absorption and excitons 54

6.3.4 Excitons 55

6.3.5 Constant energy surfaces in direct-gap III-V semiconductors 56

6.4 Thermal population of bands in semiconductors 56

6.4.1 The law of mass action 56

6.4.2 The motion of the chemical potential 58

6.4.3 Intrinsic carrier density 58

6.4.4 Impurities and extrinsic carriers 59

6.4.5 Extrinsic carrier density 60

6.4.6 Degenerate semiconductors 62

6.4.7 Impurity bands 62

6.4.8 Is it a semiconductor or an insulator? 62

6.4.9 A note on photoconductivity 63

7 Bandstructure engineering 65

7.2 Semiconductor alloys 65

7.3 Artificial structures 66

7.3.1 Growth of semiconductor multilayers 66

7.3.2 Substrate and buffer layer 68

7.3.3 Quantum wells 68

7.3.4 Optical properties of quantum wells 69

7.3.5 Use of quantum wells in opto-electronics 70

7.3.6 Superlattices 71

7.3.7 Type I and type II superlattices 71

7.3.8 Heterojunctions and modulation doping 73

7.3.9 The envelope-function approximation 74

7.4 Band engineering using organic molecules 75

7.4.2 Molecular building blocks 75

7.4.3 Typical Fermi surfaces 77

7.4.4 A note on the effective dimensionality of Fermi-surface sections 78

7.5 Layered conducting oxides 78

7.6 The Peierls transition 81

8 Measurement of bandstructure 85

8.2 Lorentz force and orbits 85

8.2.1 General considerations 85

8.2.2 The cyclotron frequency 85

8.2.3 Orbits on a Fermi surface 87

8.3 The introduction of quantum mechanics 87

8.3.1 Landau levels 87

8.3.2 Application of Bohr's correspondence principle to arbitrarily-shaped Fermi surfaces in a magnetic field 89

8.3.3 Quantisation of the orbit area 90

8.3.4 The electronic density of states in a magnetic field 91

8.4 Quantum oscillatory phenomena 91

8.4.1 Types of quantum oscillation 93

8.4.2 The de Haas-van Alphen effect 94

8.4.3 Other parameters which can be deduced from quantum oscillations 96

8.4.4 Magnetic breakdown 97

8.5 Cyclotron resonance 97

8.5.1 Cyclotron resonance in metals 98

8.5.2 Cyclotron resonance in semiconductors 98

8.6 Interband magneto-optics in semiconductors 100

8.7 Other techniques 102

8.7.1 Angle-resolved photoelectron spectroscopy (ARPES) 103

8.7.2 Electroreflectance spectroscopy 104

8.8.1 Copper 105

8.8.2 Recent controversy: Sr[subscript 2]RuO[subscript 4] 106

8.8.3 Studies of the Fermi surface of an organic molecular metal 106

8.9 Quasiparticles: interactions between electrons 112

9 Transport of heat and electricity in metals and semiconductors 117

9.1 A brief digression; life without scattering would be difficult! 117

9.2 Thermal and electrical conductivity of metals 119

9.2.1 Metals: the 'Kinetic theory' of electron transport 119

9.2.2 What do [tau subscript [sigma] and [tau subscript [kappa] represent? 120

9.2.3 Matthiessen's rule 122

9.2.4 Emission and absorption of phonons 122

9.2.5 What is the characteristic energy of the phonons involved? 123

9.2.6 Electron-phonon scattering at room temperature 123

9.2.7 Electron-phonon scattering at T [double less-than sign] [theta subscript D] 123

9.2.8 Departures from the low temperature [sigma] [proportional to] T[superscript -5] dependence 124

9.2.9 Very low temperatures and/or very dirty metals 124

9.2.11 Electron-electron scattering 125

9.3 Electrical conductivity of semiconductors 127

9.3.1 Temperature dependence of the carrier densities 127

9.3.2 The temperature dependence of the mobility 128

9.4 Disordered systems and hopping conduction 129

9.4.1 Thermally-activated hopping 129

9.4.2 Variable range hopping 130

10 Magnetoresistance in three-dimensional systems 133

10.2 Hall effect with more than one type of carrier 133

10.2.1 General considerations 133

10.2.2 Hall effect in the presence of electrons and holes 135

10.2.3 A clue about the origins of magnetoresistance 135

10.3 Magnetoresistance in metals 135

10.3.1 The absence of magnetoresistance in the Sommerfeld model of metals 135

10.3.2 The presence of magnetoresistance in real metals 137

10.3.3 The use of magnetoresistance in finding the Fermi-surface shape 138

10.4 The magnetophonon effect 139

11 Magnetoresistance in two-dimensional systems and the quantum Hall effect 143

11.1 Introduction: two-dimensional systems 143

11.2 Two-dimensional Landau-level density of states 144

11.2.1 Resistivity and conductivity tensors for a two-dimensional system 145

11.3 Quantisation of the Hall resistivity 147

11.3.1 Localised and extended states 148

11.3.2 A further refinement- spin splitting 148

11.5 The fractional quantum Hall effect 150

11.6 More than one subband populated 151

12 Inhomogeneous and hot carrier distributions in semiconductors 154

12.1 Introduction: inhomogeneous carrier distributions 154

12.1.1 The excitation of minority carriers 154

12.1.2 Recombination 155

12.1.3 Diffusion and recombination 155

12.2 Drift, diffusion and the Einstein equations 156

12.2.1 Characterisation of minority carriers; the Shockley-Haynes experiment 156

12.3 Hot carrier effects and ballistic transport 158

12.3.1 Drift velocity saturation and the Gunn effect 158

12.3.2 Avalanching 160

12.3.3 A simple resonant tunnelling structure 160

12.3.4 Ballistic transport and the quantum point contact 161

A Useful terminology in

condensed matter physics 165

A.2 Crystal 165

A.3 Lattice 165

A.4 Basis 165

A.5 Physical properties of crystals 166

A.6 Unit cell 166

A.7 Wigner-Seitz cell 167

A.8 Designation of directions 167

A.9 Designation of planes; Miller indices 168

A.10 Conventional or primitive? 169

A.11 The 14 Bravais lattices 171

B Derivation of density of states in k-space 172

B.1.1 Density of states 173

C Derivation of distribution functions 175

C.1.1 Bosons 178

C.1.2 Fermions 178

C.1.3 The Maxwell-Boltzmann distribution function 178

C.1.4 Mean energy and heat capacity of the classical gas 179

D Phonons 181

D.2 A simple model 182

D.2.1 Extension to three dimensions 183

D.3 The Debye model 185

D.3.1 Phonon number 187

D.3.2 Summary; the Debye temperature as a useful energy scale in solids 188

D.3.3 A note on the effect of dimensionality 188

E The Bohr model of hydrogen 191

E.2 Hydrogenic impurities 192

E.3 Excitons 192

F Experimental considerations in measuring resistivity and Hall effect 194

F.2 The four-wire method 194

F.3 Sample geometries 196

F.4 The van der Pauw method 197

F.5 Mobility spectrum analysis 198

F.6 The resistivity of layered samples 198

G Canonical momentum 200

H Superconductivity 201

H.2 Pairing 201

H.3 Pairing and the Meissner effect 203.

ISBN:

0198506457

0198506449

OCLC:

46937594