Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons

1  Introduction ......Page 27
1.1  There  Is  Plenty  of  Room  at  the  Bottom ......Page 28
1.3.1  Conduction ......Page 33
1.3.2  Convection ......Page 35
1.3.3  Radiation ......Page 37
1.3.4  Energy  Balance ......Page 40
1.3.6  Scaling  Trends  under  Macroscopic  Theories ......Page 41
1.4.1  Heat  Carriers ......Page 42
1.4.2  Allowable  Energy  Levels  of  Heat  Carriers ......Page 46
1.4.3  Statistical  Distribution  of  Energy  Carriers ......Page 47
1.4.4  Simple  Kinetic  Theory ......Page 49
1.4.5  Mean  Free  Path ......Page 51
1.5.1  Classical  Size  Effects ......Page 52
1.5.2  Quantum  Size  Effects ......Page 53
1.5.3  Fast  Transport  Phenomena ......Page 54
1.6  Philosophy  of  This  Book ......Page 56
1.7  Nomenclature  for  Chapter  1 ......Page 58
1.8  References ......Page 59
1.9  Exercises ......Page 61
2  Material  Waves  and  Energy  Quantization ......Page 67
2.1  Basic  Wave  Characteristics ......Page 68
2.2.1  Wave-Particle  Duality  of  Light ......Page 70
2.2.2  Material  Waves ......Page 72
2.2.3  The  Schrodinger  Equation ......Page 73
2.3.1  Free  Particles ......Page 76
2.3.2  Particle  in  a  One-Di  men  si  on  al  Potential  Well ......Page 77
2.3.3  Electron  Spin  and  the  Pauli  Exclusion  Principle ......Page 82
2.3.4  Harmonic  Oscillator ......Page 83
2.3.5  The  Rigid  Rotor ......Page 87
2.3.6  Electronic  Energy  Levels  of  the  Hydrogen  Atom ......Page 88
2.4  Summary  of  Chapter  2 ......Page 94
2.6  References ......Page 96
2.7  Exercises ......Page 97
3  Energy  States  in  Solids ......Page 101
3.1.1  Description  of  Lattices  in  Real  Space ......Page 102
3.1.2  Real  Crystals ......Page 105
3.1.3  Crystal  Bonding  Potential ......Page 108
3.1.4  Reciprocal  Lattice ......Page 111
3.2.1  One-Dimensional  Periodic  Potential  (Kronig-Penney  Model) ......Page 115
3.2.2  Electron  Energy  Bands  in  Real  Crystals ......Page 122
3.3.1  One-Dimensional  Monatomic  Lattice  Chains ......Page 124
3.3.2  Energy  Quantization  and  Phonons ......Page 127
3.3.3  One-Dimensional  Diatomic  and  Polyatomic  Lattice  Chains ......Page 128
3.4  Density  of  States ......Page 129
3.4.1  Electron  Density  of  States ......Page 131
3.4.2  Phonon  Density  of  States ......Page 133
3.4.3  Photon  Density  of  States ......Page 134
3.5.1  Quantum  Wells,  Wires,  Dots,  and  Carbon  Nanotubes ......Page 135
3.5.2  Artificial  Periodic  Structures ......Page 138
3.6  Summary  of  Chapter  3 ......Page 141
3.7  Nomenclature  for  Chapter  3 ......Page 142
3.8  References ......Page 143
3.9  Exercises ......Page 145
4  Statistical  Thermodynamics  and  Thermal  Energy  Storage ......Page 147
4.1.1  Microcanonical  Ensemble  and  Entropy ......Page 148
4.1.2  Canonical  and  Grand  Canonical  Ensembles ......Page 151
4.1.3  Molecular  Partition  Functions ......Page 154
4.1.4  Fermi-Dirac,  Bose-Einstein,  and  Boltzmann  Distributions ......Page 158
4.2  Internal  Energy  and  Specific  Heat ......Page 161
4.2.1  Gases ......Page 162
4.2.2  Electrons  in  Crystals ......Page 165
4.2.3  Phonons ......Page 168
4.2.4  Photons ......Page 170
4.3  Size  Effects  on  Internal  Energy  and  Specific  Heat ......Page 172
4.4  Summary  of  Chapter  4 ......Page 174
4.5  Nomenclature  for  Chapter  4 ......Page 177
4.6  References ......Page 178
4.7  Exercises ......Page 179
5  Energy  Transfer  by  Waves ......Page 183
5.1  Plane  Waves ......Page 184
5.1.2  Plane  Electromagnetic  Waves ......Page 185
5.1.3  Plane  Acoustic  Waves ......Page 191
5.2.1  Electron  Waves ......Page 193
5.2.2  Electromagnetic  Waves ......Page 195
5.2.3  Acoustic  Waves ......Page 202
5.2.4  Thermal  Boundary  Resistance ......Page 204
5.3  Wave  Propagation  in  Thin  Films ......Page 209
5.3.1  Propagation  of  EM  Waves ......Page 210
5.3.2  Phonons  and  Acoustic  Waves ......Page 215
5.3.3  Electron  Waves ......Page 217
5.4.1  Evanescent  Waves ......Page 218
5.4.2  Tunneling ......Page 219
5.5  Energy  Transfer  in  Nanostructures:  Landauer  Formalism ......Page 222
5.6.1  Wave  Packets  and  Group  Velocity ......Page 228
5.6.2  Coherence  and  Transition  to  Particle  Description ......Page 231
5.7  Summary  of  Chapter  5 ......Page 240
5.8  Nomenclature  for  Chapter  5 ......Page 242
5.9  References ......Page 244
5.10  Exercises ......Page 247
6  Particle  Description  of  Transport  Processes:  Classical  Laws ......Page 251
6.1.1  The  Phase  Space  and  Liouville’s  Equation ......Page 252
6.1.2  The  Boltzmann  Equation ......Page 254
6.2  Carrier  Scattering ......Page 257
6.2.1  Scattering  Integral  and  Relaxation  Time  Approximation ......Page 258
6.2.2  Scattering  of  Phonons ......Page 261
6.2.4  Scattering  of  Photons ......Page 264
6.3  Classical  Constitutive  Laws ......Page 266
6.3.1  Fourier  Law  and  Phonon  Thermal  Conductivity ......Page 267
6.3.2  Newton’s  Shear  Stress  Law ......Page 271
6.3.3  Ohm’s  Law  and  the  Wiedemann-Franz  Law ......Page 273
6.3.4  Thermoelectric  Effects  and  Onsager  Relations ......Page 278
6.3.5  Hyperpolic  Heat  Conduction  Equation  and  Its  Validity ......Page 282
6.3.6  Meaning  of  Local  Equilibrium  and  Validity  of  Diffusion  Theories ......Page 284
6.4  Conservative  Equations ......Page 286
6.4.1  Navier-Stokes  Equations ......Page 287
6.4.2  Electrohydrodynamic  Equation ......Page 290
6.4.3  Phonon  Hydrodynamic  Equations ......Page 292
6.5  Summary  of  Chapter  6 ......Page 297
6.7  Nomenclature  for  Chapter  6 ......Page 299
6.8  References ......Page 301
6.9  Exercises ......Page 303
7  Classical  Size  Effects ......Page 306
7.1  Size  Effects  on  Electron  and  Phonon  Conduction  Parallel to  Boundaries ......Page 307
7.1.1  Electrical  Conduction  along  Thin  Films ......Page 309
7.1.2  Phonon  Heat  Conduction  along  Thin  Films ......Page 312
7.2.1  Thermal  Radiation  between  Two  Parallel  Plates ......Page 316
7.2.2  Heat  Conduction  across  Thin  Films  and  Superlattices ......Page 323
7.2.3  Rarefied  Gas  Heat  Conduction  between  Two  Parallel  Plates ......Page 326
7.2.4  Current  Flow  across  Heterojunctions ......Page 331
7.3  Rarefied  Poiseuille  Flow  and  Knudsen  Minimum ......Page 332
7.4  Transport  in  Nonplanar  Structures ......Page 337
7.4.2  Rarefied  Gas  Flow  and  Convection ......Page 338
7.4.3  Phonon  Heat  Conduction ......Page 339
7.4.4  Multidimensional  Transport  Problems ......Page 340
7.5  Diffusion  Approximation  with  Diffusion-Transmission  Boundary Conditions ......Page 341
7.5.1  Thermal  Radiation  between  Two  Parallel  Plates ......Page 343
7.5.2  Heat  Conduction  in  Thin  Films ......Page 345
7.5.3  Electron  Transport  across  an  Interface:  Thermionic  Emission ......Page 346
7.5.4  Velocity  Slip  for  Rarefied  Gas  Flow ......Page 351
7.6.1  Modified  Differential  Approximation  for  Thermal  Radiation ......Page 355
7.6.2  Ballistic-Diffusive  Equations  for  Phonon  Transport ......Page 357
7.7  Summary  of  Chapter  7 ......Page 360
7.8  Nomenclature  for  Chapter  7 ......Page 362
7.9  References ......Page 364
7.10  Exercises ......Page 368
8  Energy  Conversion  and  Coupled  Transport  Processes ......Page 372
8.1.1  Nonequilibrium  Electron-Phonon  Interactions ......Page 373
8.1.2  Photon  Absorption  and  Carrier  Excitation ......Page 382
8.1.3  Relaxation  and  Recombination  of  Excited  Carriers ......Page 387
8.1.4  Boltzmann  Equation  Revisited ......Page 390
8.2  Coupled  Nonequilibrium  Electron-Phonon  Transport  without Recombination ......Page 391
8.2.1  Hot  Electron  Effects  in  Short  Pulse  Laser  Heating  of  Metals ......Page 393
8.2.2  Hot  Electron  and  Hot  Phonon  Effects  in  Semiconductor  Devices ......Page 394
8.3.1  Energy  Source  Formulation ......Page 397
8.3.2  Energy  Conversion  in  a  p-n  Junction ......Page 400
8.3.3  Radiation  Heating  of  Semiconductors ......Page 408
8.4.1  Thermoelectric  Devices ......Page 410
8.4.2  Solar  Cells  and  Thermophotovoltaic  Power  Conversion ......Page 415
8.5  Summary  of  Chapter  8 ......Page 419
8.6  Nomenclature  for  Chapter  8 ......Page 420
8.7  References ......Page 422
8.8  Exercises ......Page 425
9  Liquids  and  Their  Interfaces ......Page 428
9.1.1  Radial  Distribution  Function  and  van  der  Waals  Equation  of  State ......Page 429
9.1.2  Kinetic  Theories  of  Liquids ......Page 432
9.1.3  Brownian  Motion  and  the  Langevin  Equation ......Page 435
9.2  Forces  and  Potentials  between  Particles  and  Surfaces ......Page 440
9.2.1  Intermolecular  Potentials ......Page 441
9.2.2  Van  der  Waals  Potential  and  Force  between  Surfaces ......Page 443
9.2.3  Electric  Double  Layer  Potential  and  Force  at  Interfaces ......Page 445
9.2.4  Surface  Forces  and  Potentials  Due  to  Molecular  Structures ......Page 451
9.2.5  Surface  Tension ......Page 452
9.3.1  Pressure-Driven  Flow  and  Heat  Transfer  in  Micro-  and  Nanochannels ......Page 457
9.3.2  Electrokinetic  Flows ......Page 460
9.4  Size  Effects  on  Phase  Transition ......Page 462
9.4.1  Curvature  Effect  on  Vapor  Pressure  of  Droplets ......Page 463
9.4.3  Extension  to  Solid  Particles ......Page 465
9.4.4  Curvature  Effect  on  Surface  Tension ......Page 466
9.5  Summary  of  Chapter  9 ......Page 467
9.6  Nomenclature  for  Chaper  9 ......Page 469
9.7  References ......Page 471
9.8  Exercises ......Page 473
10  Molecular  Dynamics  Simulation ......Page 476
10.1  The  Equations  of  Motion ......Page 477
10.2  Interatomic  Potential ......Page 482
10.3.1  Time  Average  versus  Ensemble  Average ......Page 486
10.3.2  Response  Function  and  Kramers-Kronig  Relations ......Page 488
10.3.3  Linear  Response  Theory ......Page 490
10.3.4  Linear  Response  to  Internal  Thermal  Disturbance ......Page 497
10.3.5  Microscopic  Expressions  of  Thermodynamic  and  Transport Properties ......Page 500
10.3.6  Thermostatted  Ensembles ......Page 503
10.4.1  Numerical  Integration  of  the  Equations  of  Motion ......Page 507
10.4.3  Periodic  Boundary  Condition ......Page 509
10.5.1  Equilibrium  Molecular  Dynamics  Simulation ......Page 510
10.5.2  Nonequilibrium  Molecular  Dynamics  Simulations ......Page 514
10.5.3  Molecular  Dynamics  Simulation  of  Nanoscale  Heat  Transfer ......Page 517
10.6  Summary  of  Chapter  10 ......Page 518
10.7  Nomenclature  for  Chapter  10 ......Page 520
10.8  References ......Page 522
10.9  Exercises ......Page 526
Appendix  A:  Homogeneous  Semiconductors ......Page 529
Appendix  B:  Seconductor  p-n  Junctions ......Page 533
Index ......Page 537
Units  and  Their  Conversions ......Page 554
Physical  Constants ......Page 555