INTRODUCTION TP

SEMICONDUCTOR PHYSICS

Holger T Grahn Paul-Drude-Institut für Festkörperelektronik Berlin, Germany

m World Scientific • Singapore» NewJersey London »HongKong

CONTENTS

Preface v

Chapter 1. INTRODUCTION 1

1. What is a Semiconductor? 2 2. Classification of Semiconductors 4 3. A Brief History of Semiconductor Physics 9

Chapter 2. CRYSTAL STRUCTURE AND RECD7ROCAL LATTICE 11

1. Principles of Crystal Lattices 11 1.1. Thediamond structure 15 1.2. The zincblende structure 16 1.3. The graphite and hexagonal close-packed structures . . . . 17 1.4. The wurtzite structure 18

2. Symmetry Properties of Crystal Lattices 18 3. The Reciprocal Lattice 22 4. Miller Indices and Points of High Symmetry in the First Brillouin

Zone 24

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viii Introduction to Semiconductor Physics

Chapter 3. ELECTRONS IN A PERIODIC POTENTIAL 29

1. The Bloch Theorem 29 2. The Kronig-Penney Model 32

Chapter 4. MODELS OF BAND STRUCTURE: ELECTRONS AND HOLES 39

1. The Concept of the Effective Mass 39 2. Electrons and Holes 41 3. ThefcpModel 44 4. The Band Structure of Selected Semiconductors 48

Chapter 5. DENSITY OF STATES AND CARRffiR STATISTICS 55

1. The Density of States 55 2. Critical Points in the Density of States 60 3. The Fermi-Dirac Distribution 61 4. Intrinsic Semiconductors 65 5. Extrinsic Semiconductors 67

5.1. N-type semiconductors 68 5.2. P-type semiconductors 69 5.3. Compensated semiconductors 70 5.4. Low-temperature regime for n-doped semiconductors . . . 71

Chapter 6. CARRIER TRANSPORT 77

1. The Drude Model 78 2. The Boltzmann Equation 79 3. The Hall Effect 82 4. Mobilities of Selected Semiconductors 85

Contents ix

Chapter 7. PHONONS AND PHONON STATISTICS 87

1. Acoustic Phonons 87 2. Optic Phonons .' 90 3. Phonon Density of States and Statistics 96

3.1. Density of states 97 3.2. The Bose-Einstein distribution for phonons 98

Chapter 8. SCATTERING PROCESSES 101

1. Phonon Scattering 103 1.1. Acoustic phonons 103 1.2. Optic phonons 104

2. Impurity Scattering 107 2.1. Neutral impurities 107 2.2. Ionized impurities 108

3. Temperature Dependence of the Mobility 108 4. Carrier-Carrier Scattering 111 5. Intervalley Scattering 111

Chapter 9. EXCITONS 115

1. Exciton States 115 2. Exciton Binding Energies 117 3. Excitons in Lower Dimensions 122

Chapter 10. OPTICAL ABSORPTION AND EMISSION 123

1. Absorption without Excitons 123 1.1. Joint density of states 126 1.2. Direct energy gap 127 1.3. Indirect energy gap 128 1.4. Experimental determination of the optical energy gap . . . 130

2. Absorption Including Excitonic Effects 131

x Introduction to Semiconductor Physics

3. Absorption Coefficient in Lower Dimensions 135 3.1. Free carrier absorption coefficient 135 3.2. Excitonic absorption coefficient 135

4. Absorption at Finite Temperatures 139 5. Emission of Light 140

5.1. Excess energy 140 5.2. Spontaneous emission 141 5.3. Carrier dynamics 145

Chapter 11. ELECTROABSORPTION 149

1. Electroabsorption of Free Carriers 149 2. Electroabsorption of Free Carriers in Lower Dimensions . . . . 1 5 6

2.1. Electric field applied parallel to thelow-dimensional System . 156 2.2. Electric field applied perpendicular to the low-dimensional

System 159 3. Excitonic Effects in the Electroabsorption Coefficient 162

3.1. Three dimensions 162 3.2. Lower dimensions 163

Chapter 12. MAGNETOABSORPTION 165

1. Magnetoabsorption of Free Carriers 165 2. Three-Dimensional Excitons in a Magnetic Field 171 3. Two-Dimensional Excitons in a Magnetic Field 173

Chapter 13. REFERENCES 175

Chapter 14. FUNDAMENTAL CONSTANTS AND EQUrVALENT UNITS 177

Index 179