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1 Charge and Current in Solids: The Classical Drift-Diffusion Model |
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1 | (34) |
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1 | (3) |
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1.2 Drift-Diffusion Model |
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4 | (1) |
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1.3 The Drude Model and Ohm's Law |
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5 | (6) |
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11 | (2) |
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1.5 Electron and Hole Currents |
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13 | (1) |
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1.6 Conservation of Charge and the Continuity Equation |
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14 | (2) |
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1.7 Determining Transport Variables: The "Equations of State" or "Drift-Diffusion Equations" |
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16 | (1) |
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1.8 Generation and Recombination Processes |
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17 | (3) |
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1.9 Nonlinear but Local Effects: The Drift-Diffusion Model Holds |
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20 | (1) |
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1.10 Nonlocal Effects: Invalidity of Drift-Diffusion Model |
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21 | (6) |
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27 | (6) |
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33 | (2) |
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2 Boltzmann Transport: Beyond the Drift-Diffusion Model |
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35 | (56) |
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2.1 Transport in the Presence of Nonlocal Effects: The Carrier Distribution Function |
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35 | (2) |
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2.2 Boltzmann Transport Equation for the Carrier Distribution Function |
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37 | (4) |
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2.2.1 Limitations of the BTE |
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39 | (1) |
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2.2.2 Limits of Validity of the BTE |
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40 | (1) |
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2.3 The Generalized Moment Equation or Hydrodynamic Balance Equation |
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41 | (4) |
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2.4 Deriving the Drift-Diffusion Equations from the Generalized Moment Equation |
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45 | (5) |
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45 | (2) |
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47 | (3) |
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50 | (1) |
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2.6 Finding the Mobility and Diffusion Coefficient from the Carrier Distribution Function |
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51 | (7) |
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2.7 Methods of Solving the Boltzmann Transport Equation |
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58 | (1) |
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2.8 Relaxation Time Approximation Method |
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58 | (2) |
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2.9 When Can We Define a Constant Relaxation Time? |
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60 | (6) |
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63 | (2) |
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2.9.2 Isotropic Scattering in a Nondegenerate Carrier Population |
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65 | (1) |
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2.10 Low Field Steady-State Conductivity in a Homogeneous Nondegenerate Electron Gas |
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66 | (5) |
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2.11 The Monte Carlo Simulation Method for Evaluating the Distribution Function |
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71 | (10) |
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2.11.1 Initial Conditions in the Simulation |
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72 | (1) |
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2.11.2 Determination of the Duration of Free Flight |
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73 | (3) |
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2.11.3 Updating the Electron Trajectory at the End of Free Flight and Beginning of the Collision Event |
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76 | (1) |
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2.11.4 Updating the Electron State After the Collision Event |
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76 | (2) |
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2.11.5 Terminating a Trajectory |
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78 | (1) |
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2.11.6 Collecting Statistics and Evaluating the Distribution Function |
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78 | (2) |
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80 | (1) |
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81 | (8) |
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89 | (2) |
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3 Some Essential Elements of Quantum Mechanics |
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91 | (56) |
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91 | (1) |
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3.2 The Schrodinger Picture |
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91 | (2) |
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3.2.1 Calculating Expectation Values |
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92 | (1) |
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3.3 The Wavefunction and the Schrodinger Equation |
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93 | (5) |
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3.3.1 Schrodinger Equation in a Time-Independent Potential |
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95 | (1) |
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3.3.2 Wavefunction of a Free Electron |
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96 | (1) |
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3.3.3 Electron Wave and Electron Waveguide |
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97 | (1) |
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3.4 How to Find the Quantum-Mechanical Operator for a Physical Quantity |
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98 | (9) |
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3.4.1 Rectangular Potential Well |
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104 | (2) |
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106 | (1) |
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107 | (10) |
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3.5.1 Time-Independent Perturbation Theory |
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108 | (6) |
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3.5.2 Time-Dependent Perturbation Theory |
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114 | (3) |
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3.6 Wavefunction Engineering: Device Applications of Perturbation Theory |
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117 | (7) |
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3.6.1 The Velocity Modulation Transistor |
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117 | (2) |
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3.6.2 The Electro-Optic Modulator Based on the Quantum-Confined Stark Effect |
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119 | (5) |
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3.7 Multi-Electron Schrodinger Equation |
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124 | (9) |
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3.7.1 Hartree and Exchange Potentials |
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128 | (2) |
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3.7.2 Self-Consistent Schrodinger-Poisson Solution |
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130 | (3) |
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133 | (12) |
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145 | (2) |
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4 Band Structures of Crystalline Solids |
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147 | (62) |
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147 | (2) |
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4.2 The Schrodinger Equation in a Crystal |
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149 | (2) |
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4.2.1 Crystallographic Directions and Miller Indices |
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150 | (1) |
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4.3 The Nearly Free Electron Method for Calculating Bandstructure |
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151 | (4) |
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4.3.1 Why Do Energy Gaps Appear in the Bandstructure? |
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154 | (1) |
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4.3.2 Designation of Conduction and Valence Bands |
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155 | (1) |
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4.4 The Orthogonalized Plane Wave Expansion Method |
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155 | (5) |
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4.4.1 The Pseudopotential Method |
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159 | (1) |
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4.5 The Tight-Binding Approximation Method |
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160 | (5) |
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4.6 The k . p Perturbation Method |
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165 | (19) |
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4.6.1 Application of Perturbation Theory to Calculate Bandstructure |
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167 | (1) |
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4.6.2 A Simple Two-Band Theory: Neglecting the Remote Bands |
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168 | (4) |
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4.6.3 The Effect of Spin-Orbit Interaction on Bandstructure |
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172 | (3) |
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4.6.4 The 8-band k . p Perturbation Theory |
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175 | (3) |
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4.6.5 The 6x6 Hamiltonian: Neglecting the Split-Off Valence Band |
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178 | (1) |
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4.6.6 The 4x4 Hamiltonian: Neglecting Spin-Orbit Interaction |
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179 | (5) |
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4.7 Density of States of Electrons and Holes in a Crystal |
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184 | (13) |
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4.7.1 Equilibrium Electron Concentrations at Absolute Zero of Temperature |
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188 | (1) |
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4.7.2 Density of States as a Function of Kinetic Energy |
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189 | (3) |
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4.7.3 Calculating the Electron and Hole Concentrations in a Crystal Using the Density of States in Kinetic Energy Space |
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192 | (3) |
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4.7.4 Expressions for the Carrier Concentrations at Nonzero Temperatures |
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195 | (2) |
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4.8 Density of States of Phonons and Photons |
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197 | (5) |
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4.8.1 Density of Modes or Density of States of Phonons |
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200 | (1) |
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4.8.2 Density of States of Photons |
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201 | (1) |
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202 | (5) |
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207 | (2) |
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5 Carrier Scattering in Solids |
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209 | (48) |
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5.1 Charge Carrier Scattering |
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209 | (1) |
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5.2 Fermi's Golden Rule for Calculating Carrier Scattering Rates |
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209 | (7) |
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5.2.1 Derivation of Fermi's Golden Rule |
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210 | (6) |
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5.3 Dressed Electron States and Second Quantization Operators |
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216 | (3) |
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5.3.1 Matrix Elements with Dressed States |
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218 | (1) |
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5.4 Applying Fermi's Golden Rule to Calculate Phonon Scattering Rates |
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219 | (9) |
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5.4.1 Einstein's Thermodynamic Balance Argument |
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221 | (7) |
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5.5 Calculation of Relaxation Rates |
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228 | (18) |
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5.5.1 Scattering Rates in 3-D (Bulk) Systems |
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228 | (9) |
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5.5.2 Scattering Rates in 2-D (Quantum Well) Systems |
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237 | (5) |
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5.5.3 Scattering Rates in 1-D (Quantum Wire) Systems |
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242 | (4) |
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246 | (4) |
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5.6.1 Phonon Confinement Effects |
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246 | (3) |
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5.6.2 Phonon Bottleneck Effects |
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249 | (1) |
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250 | (4) |
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254 | (3) |
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6 Optical Properties of Solids |
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257 | (84) |
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6.1 Interaction of Light with Matter: Absorption and Emission Processes |
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257 | (8) |
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6.1.1 The k-selection Rule |
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260 | (4) |
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6.1.2 Optical Processes in Direct-Gap and Indirect-Gap Semiconductors |
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264 | (1) |
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6.2 Rate Equation in Two-Level Systems |
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265 | (5) |
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6.2.1 Gain Medium and Lasing |
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269 | (1) |
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6.3 The Three Important Optical Processes |
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270 | (3) |
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6.4 Van Roosbroeck-Shockley Relation |
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273 | (3) |
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276 | (1) |
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276 | (6) |
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6.5.1 Threshold Condition for Lasing |
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277 | (5) |
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6.6 Different Types of Semiconductor Lasers |
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282 | (7) |
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6.6.1 Double Heterostructure Lasers |
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283 | (1) |
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6.6.2 Quantum Well Lasers |
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283 | (1) |
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6.6.3 Quantum Cascade Lasers |
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283 | (2) |
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6.6.4 Graded Index Separate Confinement Heterostructure Lasers |
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285 | (1) |
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6.6.5 Distributed Feedback Lasers |
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286 | (1) |
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6.6.6 Vertical Cavity Surface Emitting Lasers |
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287 | (1) |
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287 | (2) |
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6.7 Calculation of K p.ω1 (m, n) in Bulk Semiconductor |
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289 | (11) |
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6.7.1 The Electron-Photon Interaction Hamiltonian |
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293 | (5) |
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6.7.2 Polarization Dependence of Absorption and Emission |
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298 | (2) |
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6.8 Absorption and Emission in Semiconductor Nanostructures (Quantum Wells and Wires) |
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300 | (14) |
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301 | (8) |
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309 | (5) |
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314 | (7) |
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6.9.1 Excitons in Quantum-Confined Nanostructures |
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318 | (2) |
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6.9.2 Bleaching of Exciton Absorption: Nonlinear Optical Properties |
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320 | (1) |
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321 | (2) |
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323 | (2) |
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325 | (3) |
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326 | (1) |
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6.12.2 Invisibility Cloaking |
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327 | (1) |
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328 | (11) |
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339 | (2) |
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7 Magnetic Field Effects in a Nanostructured Device |
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341 | (54) |
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7.1 Electrons in a Magnetic Field |
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341 | (1) |
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7.2 Dirac's Equation and Pauli's Equation |
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342 | (3) |
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7.3 The "Spinless" Electron in a Magnetic Field |
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345 | (1) |
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7.4 An Electron in a Two-Dimensional Electron Gas (Quantum Well) Placed in a Static and Uniform Magnetic Field |
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345 | (16) |
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7.4.1 Landau Levels and Landau Orbits |
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349 | (6) |
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7.4.2 Density of States in a Two-Dimensional Electron Gas in a Perpendicular Magnetic Field |
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355 | (3) |
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7.4.3 Shubnikov-deHaas Oscillations in a Two-Dimensional Electron Gas |
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358 | (3) |
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7.5 An Electron in a One-Dimensional Electron Gas (Quantum Wire) Placed in a Static and Uniform Magnetic Field |
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361 | (14) |
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7.5.1 Quantum Wire with Parabolic Confinement Potential Along the Width |
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361 | (7) |
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7.5.2 Quantum Wire with Rectangular Confinement Potential Along the Width |
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368 | (5) |
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7.5.3 Edge State Phenomena |
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373 | (1) |
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7.5.4 Shubnikov-deHaas Oscillations in a Quasi One-Dimensional Electron Gas |
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374 | (1) |
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7.6 The Quantum-Confined Lorentz Effect |
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375 | (2) |
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7.7 The Hall Effect in a Two-Dimensional Electron Gas |
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377 | (5) |
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7.8 The Integer Quantum Hall Effect |
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382 | (1) |
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7.9 The Fractional Quantum Hall Effect |
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382 | (4) |
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386 | (7) |
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393 | (2) |
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8 Quantum Transport Formalisms |
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395 | (96) |
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8.1 When Is a Quantum-Mechanical Model for Transport Necessary? |
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395 | (5) |
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8.2 Quantum Mechanical Model to Calculate Transport Variables |
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400 | (28) |
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8.2.1 How to Calculate the Wavefunction |
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402 | (5) |
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8.2.2 The Transmission Matrix Method |
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407 | (2) |
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8.2.3 The Scattering Matrix |
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409 | (6) |
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8.2.4 Finding the Composite Current Scattering Matrix of a Disordered Region |
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415 | (1) |
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8.2.5 The Scattering Matrix for an Elastic Scatterer |
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416 | (3) |
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8.2.6 Finding the Coefficients Am,p;m',p'(x), Bm,p;m',p'(x), Cm,p;m',p'(x), and Dm,p;m',p'(x) at Some Location Within the Device |
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419 | (9) |
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8.3 The Importance of Evanescent Modes |
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428 | (4) |
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8.4 Spatially Varying Potential and Self-Consistent Solutions |
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432 | (2) |
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434 | (17) |
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8.5.1 A Two-Terminal Device and Tsu-Esaki Equation |
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434 | (9) |
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8.5.2 When Is Response Linear? |
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443 | (3) |
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8.5.3 Landauer Formula and Quantized Conductance of Point Contacts |
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446 | (2) |
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8.5.4 The Buttiker Multiprobe Formula |
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448 | (3) |
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8.6 The 2-probe and 4-probe Landauer Formulas |
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451 | (8) |
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8.6.1 The Contact Resistance |
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455 | (1) |
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8.6.2 The Addition Law of Series Resistance |
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456 | (2) |
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8.6.3 Computing the Landauer Resistances by Finding the Transmission Probability Through a Device |
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458 | (1) |
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8.7 The Landau-Vlasov Equation or the Collisionless Quantum Boltzmann Transport Equation |
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459 | (5) |
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8.8 A More Useful Collisionless Boltzmann Transport Equation |
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464 | (2) |
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466 | (7) |
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8.10 Quantum Transport in an Open System with Device-Contact Coupling and the Self-Energy Potential |
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473 | (5) |
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8.10.1 Coupling of a Device to a Single Contact |
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474 | (4) |
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8.11 The Nonequilibrium Green's Function Formalism |
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478 | (2) |
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480 | (8) |
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488 | (3) |
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9 Quantum Devices and Mesoscopic Phenomena |
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491 | (56) |
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491 | (1) |
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9.2 Double Barrier Resonant Tunneling Diodes |
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491 | (14) |
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9.2.1 Current-Voltage Characteristic of a Double Barrier Resonant Tunneling Diode |
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499 | (1) |
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9.2.2 Space Charge Effects and Self-Consistent Solution |
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499 | (1) |
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9.2.3 The Effect of Nonidealities on the Double-Barrier Resonant Tunneling Diode |
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500 | (2) |
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9.2.4 Other Mechanisms for Negative Differential Resistance in a DBRTD |
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502 | (1) |
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503 | (2) |
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9.3 The Stub-Tuned Transistor |
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505 | (4) |
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9.4 Aharonov-Bohm Quantum Interferometric Devices |
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509 | (11) |
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9.4.1 The Altshuler-Aronov-Spivak Effect |
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512 | (4) |
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9.4.2 More on the Ballistic Aharonov-Bohm Conductance Oscillations |
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516 | (1) |
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9.4.3 Magnetostatic Aharonov-Bohm Effect in Quantum Wire Rings |
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517 | (3) |
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9.5 The Electrostatic Aharonov-Bohm Effect |
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520 | (10) |
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9.5.1 The Effect of Multiple Reflections |
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524 | (6) |
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9.6 Mesoscopic Phenomena: Applications of Buttiker's Multiprobe Formula |
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530 | (10) |
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9.6.1 Hall Resistance of a Cross and Quenching of Hall Resistance |
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531 | (4) |
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9.6.2 Bend Resistance of a Cross |
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535 | (1) |
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9.6.3 An Alternate Explanation of the Integer Quantum Hall Effect |
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535 | (5) |
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540 | (5) |
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545 | (2) |
| Index |
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547 | |
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