Strain Effect in Semiconductors (eBook)

Contents 5
Preface 10
1 Overview: The Age of Strained Devices 12
1.1 Origin of the Strained-Si Technology 12
1.2 Strain in Semiconductor Devices 12
1.2.1 Conventional Simple Scaling 13
1.2.2 Feature-Enhanced CMOS 13
1.2.3 Variable Strain Sensors 15
1.2.4 Strained Quantum Well Optoelectronics 15
1.3 Organization 16
Part I Band Structures of Strained Semiconductors 18
2 Stress, Strain, Piezoresistivity, and Piezoelectricity 19
2.1 Strain Tensor 19
2.2 Stress Tensor 21
2.3 Elastic Compliance and Stiffness Constants 24
2.4 Examples of Stress--Strain Relations 26
2.4.1 Hydrostatic and Shear Strain 28
2.5 Piezoresistivity 29
2.6 Piezoelectricity 30
3 Strain and Semiconductor Crystal Symmetry 32
3.1 Introduction 32
3.2 Symmetry and Strain: Overview 33
3.2.1 Examples of Crystal Lattices 33
3.2.2 Crystal Symmetry 35
3.2.3 Energy Band Symmetry 36
3.2.4 Strain Effects on Energy Bands 39
3.3 Symmetry Effects in Determining Electronic States 43
3.3.1 Translational Symmetry and Reciprocal Space 44
3.3.2 Bloch Theorem 46
3.3.3 Point Symmetry Effects on Electronic States 47
3.4 Semiconductor Crystal Classes and Systems 50
3.4.1 Crystal Classes and Systems 50
3.4.2 Cubic Semiconductors 52
3.5 Strain Effects on Electronic Band Structures 54
3.5.1 Evolution of Crystal Systems with Strain 54
3.5.2 Strained Band Structures 56
3.6 Summary of Symmetry, and Its Limitation 58
4 Band Structures of Strained Semiconductors 59
4.1 Introduction 59
4.2 Strain Effects on Semiconductor Band Structures:A Qualitative Overview 60
4.2.1 Tight-Binding Formation of Semiconductor Crystals 61
4.2.2 Overlap Integrals 64
4.2.3 Properties of Electronic Wave Functions 66
4.2.4 Strain Effects on Tight-Binding Band Structures 69
4.2.5 Determining Deformation PotentialsUsing Tight-Binding Method 71
4.2.6 Summary for the Qualitative Overview 72
4.3 Brief Introduction to Plane Wave Expansion Method 72
4.4 Tight-Binding Method 75
4.4.1 A General Introduction 75
4.4.2 The sp3 Tight-Binding Model 80
4.4.3 Tight-Binding Band Structure 84
4.4.4 The sp3 Hybridization and Bond Orbital Approximation 90
4.5 Strain Effects in Tight-Binding Framework 92
4.5.1 Hydrostatic Strain: d-2 Principle 92
4.5.2 Shear Strain: Bond Rotation 95
4.6 Summary for the Tight-Binding Method 97
4.7 The kp Method 98
4.7.1 Effective Mass 98
4.7.2 kp Hamiltonian 100
4.7.3 Single Band Perturbation Expansion 101
4.7.4 Degenerate Band Perturbation Expansion 104
4.8 Luttinger Hamiltonian 106
4.8.1 Luttinger Hamiltonian Without Spin--orbit Coupling 106
4.8.2 Luttinger Hamiltonian with Spin--Orbit Coupling 108
4.8.3 44 Analytical Energy Dispersion 111
4.8.4 Coordinate Transformation 112
4.9 Kane's Model with Remote Band Coupling 113
4.10 Band Structure of Selected Semiconductors 115
4.11 Density of States and Conductivity Mass 120
4.12 Pikus--Bir Strain Hamiltonian 126
4.13 Strained Band Structures 132
4.13.1 Conduction Band 132
4.13.2 Analytical Results for Valence Bandswith 44 Hamiltonian 135
4.13.3 Valence Bands of Strained Semiconductorswith Split-Off Band Coupling 138
4.13.4 Band Gap Shift with Strain 141
5 Low-Dimensional Semiconductor Structures 144
5.1 Introduction 144
5.2 Overview: Low-Dimensional Semiconductor Structures 145
5.2.1 MOS Structure and MOSFET Channel 146
5.2.2 Heterojunction 147
5.2.3 Square Quantum Well 149
5.2.4 Nanowire 151
5.3 Electronic Properties of Low-Dimensional Structures 152
5.3.1 Envelope Function Theory 152
5.3.2 Triangular Potential Well Approximation 155
5.3.3 Quantum Well and Quantum Wire Band Structures 158
5.3.4 P-Type Structures 159
5.3.5 2D and 1D Density of States 160
5.4 Self-Consistent Calculation 162
5.4.1 Self-Consistent Procedure 163
5.4.2 Variational Method 164
5.4.3 Finite Difference Method 167
5.5 Subband Structures of 2D Electron/Hole Gas 171
5.5.1 Self-Consistent Confining Potential 171
5.5.2 Charge Distribution vs. Material 173
5.5.3 Subband Structure in GaAs/AlGaAs Heterostructures 174
5.5.4 Subband Structure in Square Quantum Wells 177
5.5.5 Subband Energy vs. Well Width 179
5.5.6 In-Plane Energy Dispersion 180
5.6 Strain Effects on Subband Structures 183
5.6.1 GaAs Conduction Band 183
5.6.2 Si Conduction Band 186
5.6.3 Valence Band 187
Part II Transport Theory of Strained Semiconductors 190
6 Semiconductor Transport 191
6.1 Introduction 191
6.2 Carrier Transport: A Qualitative Overview 191
6.2.1 Drude's Electron Transport Model 192
6.2.2 Strain Effects on Electron/Hole Transport in MOSFETs 193
6.3 Scattering in Semiconductors: General Consideration 196
6.3.1 Scattering Rate 196
6.3.2 Momentum Relaxation Rate 198
6.4 Scattering Processes in Semiconductors 199
6.4.1 Lattice Scattering 199
6.4.2 Acoustic Phonon Scattering 201
6.4.3 Piezoelectric Scattering 202
6.4.4 Optical Phonon Scattering 203
6.4.5 Polar Optical Phonon Scattering 204
6.4.6 Impurity Scattering 206
6.5 Boltzmann Equation 208
6.5.1 Electron Conductivity Mass of Si 211
6.6 New Features in 2D Scattering 214
6.6.1 Broken Symmetry due to Confinement 214
6.6.2 Surface Roughness Scattering 216
6.7 Strain Effects on Carrier Transport 220
6.7.1 Piezoresistance 220
6.7.2 Electron Transport 222
6.7.3 Hole Transport 227
6.7.4 Strain on Surface Roughness Scattering 229
6.7.5 Transport in High Effective Field 231
6.7.6 Strain Effects in Ballistic Transport Regime 237
Part III Strain in Semiconductor Devices 239
7 Strain in Electron Devices 240
7.1 Strain-Si Technology 240
7.2 Strained Electron Devices 244
7.2.1 Strained Planar MOSFETs 244
7.2.2 Strained Si-on-Insulator (SOI)/SiGe-on-Insulator (SGOI) Devices 246
7.2.3 Strain in Other Electron Devices 249
7.3 Strain Enhanced Mobility 249
7.4 SiGe Devices 256
7.5 Leakage and Reliability of Strained-Si 260
7.5.1 Strain on Threshold Voltage 260
7.5.2 Leakage Current in Strained-Si Devices 262
7.5.3 Reliability of Strained-Si 264
7.6 Defects in Strained-Si 266
7.7 Scalability of Strain 269
8 Piezoresistive Strain Sensors 272
8.1 Introduction 272
8.2 Resistor as Discrete Strain Transducer 273
8.2.1 Gauge Factor 274
Metals 274
Semiconductors 274
8.2.2 Piezoresistance 275
8.2.3 Coordinate Transformation to Arbitrary Directions 278
8.3 Integrated Piezoresistive Stress Transducers 286
8.3.1 Canonical Cantilever-Based Piezoresistive Force Transducer 287
Structure Interactions 287
Piezoresistor Configuration 289
Sensitivity 291
Some Ramifications of Piezoresistive Stress Transducers 292
8.3.2 Circular Diaphragm MEMS Piezoresistive Microphone 293
9 Strain Effects on Optoelectronic Devices 296
9.1 Introduction 296
9.2 Strain Effects in Optoelectronic Devices: An Overview 297
9.2.1 Photon Emission and Absorption 297
9.2.2 Working Principles for Photodiodesand Quantum Well Lasers 299
9.2.3 Strain Applications in Optoelectronic Devices 303
9.3 Optical Processes in Semiconductors 311
9.3.1 Light Absorption Coefficient 311
9.3.2 Joint Density of States 316
9.3.3 Optical Transitions in Quantum Wells 318
9.3.4 Optical Matrix Elements 319
9.4 Nonequilibrium Carrier Distribution and Gain 322
9.5 Strained Quantum Well Lasers 326
9.5.1 Subband Structure and Modal Gain 326
Appendix: Effective Mass Theorem 331
References 335
Index 350