Preface ...................................................... XIII
1 General Properties of Nitrides ............................. 1
1.1 Crystal Structure of Nitrides .............................. 1
1.2 Gallium Nitride ............................................ 5
1.3 Aluminum Nitride ........................................... 6
1.4 Indium Nitride ............................................ 10
1.5 AlGaN Alloy ............................................... 13
1.6 InGaN Alloy ............................................... 14
1.7 AlInN Alloy ............................................... 14
1.8 InAlGaN Quaternary Alloy .................................. 15
1.9 Electronic Band Structure and Polarization Effects ........ 15
1.9.1 Introduction ....................................... 18
1.9.2 General Strain Considerations ...................... 22
1.9.3 k-p Theory and the Quasicubic Model ................ 23
1.9.4 Temperature Dependence of Wurtzite GaN Bandgap ..... 26
1.9.5 Sphalerite (Zincblende) GaN ........................ 26
1.9.6 A1N ................................................ 28
1.9.6.1 Wurtzite AlN ................................... 28
1.9.6.2 Zincblende AlN ................................. 28
1.9.7 InN ................................................ 29
1.10 Polarization Effects ...................................... 31
1.10.1 Piezoelectric Polarization ......................... 32
1.10.2 Spontaneous Polarization ........................... 35
1.10.3 Nonlinearity of Polarization ....................... 35
1.10.3.1 Nonlinearities in Piezoelectric Polarization ... 42
1.10.4 Polarization in Heterostructures ................... 46
1.10.4.1 Ga-Polarity Single AlGaN-GaN Interface ......... 51
1.10.4.2 Polarization in Quantum Wells .................. 56
1.11 Nonpolar and Semipolar Orientations ....................... 59
Further Reading ........................................... 61
2 Doping: Determination of Impurity and Carrier
Concentrations ............................................ 63
2.1 Introduction .............................................. 63
2.2 Doping .................................................... 63
2.3 Formation Energy of Defects ............................... 65
2.3.1 Hydrogen and Impurity Trapping at Extended
Defects ............................................ 67
2.4 Doping Candidates ......................................... 69
2.5 Free Carriers ............................................. 70
2.6 Binding Energy ............................................ 70
2.7 Conductivity Type: Hot Probe and Hall Measurements ........ 71
2.8 Measurement of Mobility ................................... 71
2.9 Semiconductor Statistics, Density of States, and Carrier
Concentration ............................................. 74
2.10 Charge Balance Equation and Carrier Concentration ......... 78
2.10.1 n-Type Semiconductor .............................. 79
2.10.2 p-Type Semiconductor .............................. 84
2.11 Capacitance-Voltage Measurements .......................... 87
Appendix 2.A. Fermi Integral .............................. 94
Further Reading ........................................... 95
3 Metal Contacts ............................................ 97
3.1 Metal-Semiconductor Band Alignment ........................ 97
3.2 Current Flow in Metal-Semiconductor Junctions ............ 101
3.3 Ohmic Contact Resistance ................................. 107
3.3.1 Specific Contact Resistivity ...................... 107
3.4 Semiconductor Resistance ................................. 108
3.4.1 Determination of the Contact Resistivity .......... 109
Further Reading .......................................... 113
4 Carrier Transport ........................................ 115
4.1 Introduction ............................................. 115
4.2 Carrier Scattering ....................................... 117
4.2.1 Impurity Scattering ............................... 118
4.2.2 Acoustic Phonon Scattering ........................ 120
4.2.2.1 Deformation Potential Scattering .............. 121
4.2.2.2 Piezoelectric Scattering ...................... 124
4.2.3 Optical Phonon Scattering ......................... 126
4.2.3.1 Nonpolar Optical Phonon Scattering ............ 126
4.2.3.2 Polar Optical Phonon Scattering ............... 127
4.2.4 Alloy Scattering and Dislocation Scattering ....... 134
4.3 Calculated Mobility of GaN ............................... 143
4.4 Scattering at High Fields ................................ 147
4.4.1 Transport at High Fields: Energy and Momentum
Relaxation Times .................................. 152
4.4.2 Energy-Dependent Relaxation Time and Large В ...... 153
4.4.3 Hall Factor ....................................... 155
4.5 Delineation of Multiple Conduction Layer Mobilities ...... 156
4.6 Carrier Transport in InN ................................. 158
4.7 Carrier Transport in AlN ................................. 159
4.8 Carrier Transport in Alloys .............................. 161
4.9 Two-Dimensional Transport in n-Type GaN .................. 164
4.9.1 Scattering in 2D Systems .......................... 166
4.9.1.1 Electron Mobility in AlGaN/GaN 2D System ...... 168
4.9.1.2 Numerical Two-Dimensional Electron Gas
Mobility Calculations ......................... 170
4.9.1.3 Magnetotransport and Mobility Spectram ........ 173
Further Reading ............................... 174
5 The p-n junction ......................................... 177
5.1 Introduction ............................................. 177
5.2 Band Alignment ........................................... 177
5.3 Electrostatic Characteristics of p-n Heterojunctions ..... 179
5.4 Current-Voltage Characteristics of p-n Junctions ......... 185
5.4.1 Diode Current under Reverse Bias .................. 186
5.4.1.1 Poole-Frenkel and Schottky Effects ............ 187
5.4.1.2 Avalanching ................................... 188
5.4.2 Diffusion Current ................................. 189
5.4.2.1 Diffusion Current under Reverse Bias .......... 190
5.4.2.2 Diffusion Current under Forward Bias .......... 190
Further Reading .......................................... 191
6 Optical Processes ........................................ 193
6.1 Introduction ............................................. 193
6.2 Einstein's A and В Coefficients .......................... 194
6.3 Absorption and Emission .................................. 196
6.4 Band-to-Band Transitions and Efficiency .................. 198
6.5 Optical Transitions in GaN ............................... 200
6.5.1 Excitonic Transitions in GaN ...................... 200
6.5.1.1 Strain Effects ................................ 203
6.5.1.2 Bound Excitons ................................ 204
6.6 Free-to-Bound Transitions ................................ 205
6.7 Donor-Acceptor Transitions ............................... 206
Further Reading .......................................... 207
7 Light-Emitting Diodes and Lighting ....................... 209
7.1 Introduction ............................................. 209
7.2 Current Conduction Mechanism in LED-Like Structures ...... 211
7.3 Optical Output Power and Efficiency ...................... 214
7.3.1 Efficiency and Other LED Relevant Terms ........... 215
7.3.2 Optical Power and External Efficiency ............. 217
7.3.3 Internal Quantum Efficiency ....................... 218
7.3.3.1 Auger Recombination ........................... 219
7.3.3.2 SRH Recombination ............................. 220
7.3.3.3 Radiative Recombination ....................... 222
7.3.3.4 Continuity or Rate Equations as Pertained to
Efficiency .................................... 223
7.3.3.5 Carrier Overflow (Spillover, Flyover,
Leakage) ...................................... 231
7.4 Effect of Surface Recombination .......................... 244
7.5 Effect of Threading Dislocation on LEDs .................. 247
7.6 Current Crowding ......................................... 247
7.7 Perception of Color ...................................... 250
7.8 Chromaticity Coordinates and Color Temperature ........... 251
7.9 LED Degradation .......................................... 253
7.10 Packaging ................................................ 255
7.11 Luminescence Conversion and White Light Generation ....... 257
7.11.1 Color-Rendering Index ............................ 258
7.11.2 White Light from Multichip LEDs .................. 259
7.11.3 Combining LEDs and Phosphor(s) ................... 262
Further Reading .......................................... 266
8 Semiconductor Lasers: Light Amplification by Stimulated
Emission of Radiation .................................... 267
8.1 Introduction ............................................. 267
8.2 A Primer to the Principles of Lasers ..................... 268
8.2.1 Waveguiding ....................................... 270
8.2.2 Analytical Solution to the Waveguide Problem ...... 273
8.2.2.1 ТЕ Mode .................................. 274
8.2.2.2 TM Mode .................................. 276
8.2.3 Far-Field Pattern ................................. 280
8.3 Loss, Threshold, and Cavity Modes ........................ 281
8.4 Optical Gain ............................................. 283
8.5 A Glossary for Semiconductor Lasers ...................... 286
8.5.1 Optical Gain in Bulk Layers: a Semiconductor
Approach .......................................... 289
8.5.1.1 Relating Absorption Rate to Absorption
Coefficient ................................... 290
8.5.1.2 Relating Stimulated Emission Rate to
Absorption Coefficient ........................ 290
8.5.1.3 Relating Spontaneous Emission Rate to
Absorption Coefficient ........................ 290
8.5.2 Semiconductor Realm ............................... 291
8.5.3 Gain in Quantum Wells ............................. 299
8.5.3.1 Optical Gain .................................. 302
8.5.3.2 Measurement of Gain in Nitride Lasers ......... 304
8.5.4 Gain Measurement via Optical Pumping .............. 304
8.6 Threshold Current ........................................ 306
8.7 Analysis of Injection Lasers with Simplifying
Assumptions .............................................. 307
8.7.1 Recombination Lifetime ............................ 309
8.7.2 Quantum Efficiency ................................ 311
8.8 GaN-Based LD Design and Performance ...................... 312
8.8.1 Gain Spectra of InGaN Injection Lasers ............ 317
8.8.2 Mode Hopping ...................................... 321
8.9 Thermal Resistance ....................................... 322
8.10 Nonpolar and Semipolar Orientations ...................... 323
8.11 Vertical Cavity Surface-Emitting Lasers (VCSELs) ......... 325
8.11.1 Microcavity Fundamentals .......................... 328
8.11.2 Polariton Lasers .................................. 333
8.12 Degradation .............................................. 337
Appendix 8.A: Determination of the Photon Density and
Photon Energy Density in a Cavity ........................ 343
Further Reading .......................................... 348
9 Field Effect Transistors ................................. 349
9.1 Introduction ............................................. 349
9.2 Operation Principles of Heterojunction Field Effect
Transistors .............................................. 350
9.2.1 Heterointerface Charge ............................ 350
9.2.2 Analytical Description of HFETs ................... 358
9.3 GaN and InGaN Channel HFETs .............................. 364
9.4 Equivalent Circuit Models: De-embedding and Cutoff
Frequency ................................................ 366
9.4.1 Small-Signal Equivalent Circuit Modeling .......... 367
9.4.2 Cutoff Frequency .................................. 370
9.5 HFET Amplifier Classification and Efficiency ............. 373
9.6 Drain Voltage and Drain Breakdown Mechanisms ............. 378
9.7 Field Plate for Spreading Electric Field for Increasing
Breakdown Voltage ........................................ 383
9.8 Anomalies in GaN MESFETs and AlGaN/GaN HFETs ............. 384
9.8.1 Effect of the Traps in the Buffer Layer ........... 386
9.8.2 Effect of Barrier States .......................... 392
9.8.3 Correlation between Current Collapse and Surface
Charging .......................................... 393
9.9 Electronic Noise ......................................... 396
9.9.1 FET Equivalent Circuit with Noise ................. 398
9.9.2 High-Frequency Noise in Conjunction with GaN
FETs .............................................. 402
9.10 Self-Heating and Phonon Effects .......................... 405
9.10.1 Heat Dissipation and Junction Temperature ......... 406
9.10.2 Hot Phonon Effects ................................ 409
9.10.2.1 Phonon Decay Channels and Decay Time ......... 411
9.10.2.2 Implications for FETs ........................ 416
9.10.2.3 Heat Removal in View of Hot Phonons .......... 418
9.10.2.4 Tuning of the Hot Phonon Lifetime ............ 421
9.11 HFET Degradation ......................................... 427
9.11.1 Gated Structures: Reliability ..................... 434
9.11.2 Reliability Tests ................................. 438
9.12 HFETs for High-Power Switching ........................... 440
Appendix 9.A. Sheet Charge Calculation in AlGaN/GaN
Structures with A1N Interface Layer (AlGaN/AlN/GaN) ...... 444
Further Reading .......................................... 446
Index ......................................................... 449
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