1 Introduction to Semiconductor Heterostructures ............... 1
1.1 Introduction ............................................ 1
1.2 Electronic States of Bulk Semiconductors ................ 3
1.2.1 Fundamental Concepts ............................. 3
1.2.2 The k→ p→ Method ................................. 8
1.3 Envelope Function Model ................................ 12
References .................................................. 17
2 Theory and Modelling for the Nanoscale: The spds*
Tight Binding Approach ...................................... 19
2.1 Introduction: A Snapshot View of Theoretical Methods
for Nanosciences ....................................... 20
2.2 The Empirical Tight Binding Formalism .................. 21
2.3 Band Structure of Bulk Materials: From
sp3 to sp3 d5 s* ........................................ 22
2.4 Strain Effects: The Tight Binding Point of View ........ 24
2.5 Tight Binding as a Parameter Provider: Inversion
Asymmetry and Parameters of the 14-Band k.p Model ...... 25
2.6 Quantum Confinement and Atomistic Symmetries:
Interface Rotational Symmetry Breakdown ................ 26
2.7 Quantum Confinement and Valley Mixing: X-valley
and L-valley Quantum Wells ............................. 28
2.8 Three-Dimensional Confinement: Symmetry Mistake
in Current Theories of Impurity States ................. 29
2.9 Alloys, Beyond the Virtual Crystal Approximation:
Dilute Nitrides ........................................ 31
2.10 Full-Band Calculations: Dielectric Function
and Piezo-Optical Constants ............................ 32
2.11 Surface Physics and Modeling of STM Images ............. 34
2.12 Back to Theory: Local Wavefunction
in the Tight Binding Approach .......................... 36
2.13 Conclusion ............................................. 38
References .................................................. 38
3 Theory of Electronic Transport in Nanostructures ............ 41
3.1 Introduction ........................................... 41
3.1.1 Scope and Overview ............................... 42
3.2 Macroscopic Transport Models ........................... 43
3.2.1 Carrier Effective Mass .......................... 43
3.2.2 Carrier Mobility ................................ 46
3.2.3 Carrier Scattering Mechanisms ................... 47
3.2.4 Carrier Scattering Rates and Boltzmann
Transport Equation .............................. 48
3.2.5 Mobility in Bulk Semiconductors
and Heterostructures ............................ 49
3.3 Scattering in Dilute Nitrides: Beyond Fermi's
Golden Rule ............................................ 51
3.4 Quantum Hall effect .................................... 54
3.5 Spin Quantum Hall Effect ............................... 57
3.6 Quantised Conduction Through Wires and Dots ............ 60
3.7 Graphene ............................................... 62
3.8 Junctionless Transistor ................................ 66
3.9 Summary and Conclusions ................................ 67
References .................................................. 68
4 Hot Electron Transport ...................................... 71
4.1 Introduction ........................................... 71
4.1.1 The Lattice Temperature T0 ...................... 72
4.1.2 Electrons in Thermal Equilibrium ................ 73
4.1.3 Hot Electrons ................................... 73
4.1.4 Scope and Overview .............................. 73
4.2 Basic Concepts ......................................... 74
4.2.1 Ballistic Transport ............................. 74
4.2.2 Energy and Momentum Relaxation .................. 75
4.2.3 Describing Energy Bands ......................... 77
4.2.4 Group Velocity and the Density of States ........ 80
4.2.5 The Non-Equilibrium Distribution Function ....... 81
4.2.6 Transport Properties ............................ 82
4.2.7 The Conservation Equations ...................... 83
4.3 Scattering Mechanisms .................................. 86
4.3.1 General Comments ................................ 86
4.3.2 Electron-Electron Scattering .................... 87
4.3.3 Alloy Scattering ................................ 88
4.3.4 Phonons ......................................... 90
4.4 High-Field Phenomena ................................... 95
4.4.1 Impact Ionisation and Avalanche Breakdown ....... 95
4.4.2 Negative Differential Resistance ................ 98
4.5 The Boltzmann Transport Equation ...................... 101
4.5.1 General Form of the BTE ........................ 101
4.5.2 The Linearized Distribution Function ........... 102
4.5.3 Low Field Solution and the Ladder Method ....... 103
4.5.4 High-Field Solution ............................ 108
References ................................................. 112
5 Monte Carlo Techniques for Carrier Transport
in Semiconductor Materials ................................. 115
5.1 Introduction to Monte Carlo ........................... 115
5.1.1 Historical Review .............................. 116
5.1.2 Simple Examples of Monte Carlo ................. 116
5.2 Carrier Transport in Semiconductors ................... 119
5.3 Single Electron Monte Carlo ........................... 121
5.3.1 Scattering Processes ........................... 121
5.3.2 Drift Process .................................. 123
5.3.3 Description of the Algorithm ................... 126
5.4 Ensemble Electron Monte Carlo ......................... 137
5.4.1 Description of the Algorithm .................... 137
5.5 An Example: Electron Motion in Bulk GaAs .............. 139
5.6 Monte Carlo Simulation at Very High Fields ............ 142
5.7 Electron Transport in Dilute Nitrides ................. 144
5.7.1 Single Electron Monte Carlo in GaAsN ............ 145
5.8 Quantum Monte Carlo ................................... 147
5.9 Appendix: Random and Pseudorandom Numbers ............. 149
References ................................................. 150
6 Band Structure Engineering of Semiconductor Devices
for Optical Telecommunications ............................. 153
6.1 Basics of Band Structure Engineering .................. 153
6.1.1 What is a Strained Semiconductor Layer? ........ 154
6.1.2 Main Disadvantages of Lattice Matched
III-V Semiconductor Lasers and Solutions
Proposed by Band-Structure Engineering ........ 156
6.2 Effects of Strain on the Band Structure ............... 159
6.2.1 Bulk InGaAs Under Biaxial Compression .......... 159
6.2.2 Electronic Band Structure in Strained
Quantum Wells .................................. 162
6.2.3 Influence of Strain on the Loss Mechanisms ..... 168
6.2.4 Strain-Induced Changes of the Laser
Threshold Current .............................. 172
6.3 Gain Calculation in III-V Quantum Wells ............... 173
6.3.1 Device Geometry ................................ 173
6.3.2 Carrier Wavefunctions in Quantum Wells ......... 174
6.3.3 Light-Matter Interaction and Optical
Selection Rules ................................ 174
6.3.4 Gain Calculation ............................... 176
6.4 Uncooled Operation of 1.3 μm Lasers ................... 177
6.4.1 Conduction Band of InGaAsN ..................... 178
6.4.2 Gain Improvement of InGaAsN Structures
is Obtained by ................................. 180
6.5 Large Bandwidth Semiconductor Optical Amplifiers ...... 184
6.5.1 InGaAsP/InP Heterostructures ................... 184
6.5.2 How to Realize Polarisation-Independent
Gain? .......................................... 185
6.5.3 How to Increase Bandwidth? ..................... 187
6.5.4 Band Structure and Gain ........................ 189
References ................................................. 192
7 Fundamental Theory of Semiconductor Lasers
and SOAs ................................................... 195
7.1 Review of Key Concepts ................................ 195
7.1.1 Radiative Transitions .......................... 196
7.1.2 Spontaneous and Stimulated Emission ............ 196
7.1.3 Optical Gain ................................... 197
7.2 Semiconductor Laser Structures ........................ 199
7.2.1 Heterostructures ............................... 199
7.2.2 Optical Waveguides ............................. 200
7.3 Semiconductor Laser Cavities .......................... 202
7.3.1 Fabry-Perot Cavity ............................. 202
7.3.2 Lasing Threshold and Power Output .............. 204
7.3.3 Distributed Bragg Reflectors ................... 205
7.3.4 Distributed Feedback Lasers .................... 207
7.4 Transient Behaviour of Lasers ......................... 209
7.4.1 Static Properties .............................. 209
7.4.2 Rate Equations ................................. 209
7.4.3 Small-Signal Modulation ........................ 210
7.4.4 Large-Signal Modulation ........................ 212
7.4.5 Chirp .......................................... 214
7.5 Semiconductor Optical Amplifiers ...................... 215
7.5.1 Cavity Effects ................................. 215
7.5.2 Saturation ..................................... 217
7.5.3 Crosstalk ...................................... 218
7.5.4 Polarisation ................................... 220
7.6 Conclusion ............................................ 221
References ................................................. 222
8 Vertical Cavities and Micro-Ring Resonators ................ 225
8.1 Introduction .......................................... 225
8.2 Vertical Cavities ..................................... 227
8.2.1 Basic Design Concepts .......................... 227
8.2.2 Optical Feedback and DBRs ...................... 229
8.2.3 Material Gain .................................. 232
8.2.4 The Gain Enhancement Factor .................... 232
8.2.5 Vertical Cavity Semiconductor Optical
Amplifiers (VCSOA) ............................. 234
8.2.6 VCSEL Polarisation Properties and
Spin-VCSELs .................................... 237
8.3 Microring Resonators .................................. 240
8.3.1 Fundamental Concepts ........................... 240
8.3.2 Waveguiding Properties of Micro Ring
Resonators ..................................... 243
8.3.3 Single and Multi-Micro Ring Configurations ..... 244
8.3.4 Active Micro Ring Structures ................... 248
8.4 Conclusion ............................................ 252
References ................................................. 253
Index ......................................................... 255
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