Thermoelectrics

Preface xiii
1 Introduction 1
1.1 Introduction 1
1.2 Thermoelectric Effect 3
1.2.1 Seebeck Effect 3
1.2.2 Peltier Effect 3
1.2.3 Thomson Effect 4
1.2.4 Thomson (or Kelvin) Relationships 4
1.3 The Figure of Merit 4
1.3.1 New-Generation Thermoelectrics 5
Problems 7
References 7
2 Thermoelectric Generators 8
2.1 Ideal Equations 8
2.2 Performance Parameters of a Thermoelectric Module 11
2.3 Maximum Parameters for a Thermoelectric Module 12
2.4 Normalized Parameters 13
Example 2.1 Exhaust Waste Heat Recovery 15
2.5 Effective Material Properties 17
2.6 Comparison of Calculations with a Commercial Product 18
Problems 19
Computer Assignment 21
References 22
3 Thermoelectric Coolers 23
3.1 Ideal Equations 23
3.2 Maximum Parameters 26
3.3 Normalized Parameters 27
Example 3.1 Thermoelectric Air Conditioner 29
3.4 Effective Material Properties 33
3.4.1 Comparison of Calculations with a Commercial Product 34
Problems 36
Reference 37
4 Optimal Design 38
4.1 Introduction 38
4.2 Optimal Design for Thermoelectric Generators 38
Example 4.1 Exhaust Thermoelectric Generators 46
4.3 Optimal Design of Thermoelectric Coolers 49
Example 4.2 Automotive Thermoelectric Air Conditioner 57
Problems 61
References 63
5 Thomson Effect, Exact Solution, and Compatibility Factor 64
5.1 Thermodynamics of Thomson Effect 64
5.2 Exact Solutions 68
5.2.1 Equations for the Exact Solutions and the Ideal Equation 68
5.2.2 Thermoelectric Generator 70
5.2.3 Thermoelectric Coolers 71
5.3 Compatibility Factor 71
5.4 Thomson Effects 79
5.4.1 Formulation of Basic Equations 79
5.4.2 Numeric Solutions of Thomson Effect 83
5.4.3 Comparison between Thomson Effect and Ideal Equation 85
Problems 87
Projects 88
References 88
6 Thermal and Electrical Contact Resistances for Micro and Macro Devices 89
6.1 Modeling and Validation 89
6.2 Micro and Macro Thermoelectric Coolers 92
6.3 Micro and Macro Thermoelectric Generators 94
Problems 97
Computer Assignment 97
References 98
7 Modeling of Thermoelectric Generators and Coolers With Heat Sinks 99
7.1 Modeling of Thermoelectric Generators With Heat Sinks 99
7.2 Plate Fin Heat Sinks 108
7.3 Modeling of Thermoelectric Coolers With Heat Sinks 111
Problems 119
References 119
8 Applications 120
8.1 Exhaust Waste Heat Recovery 120
8.1.1 Recent Studies 120
8.1.2 Modeling of Module Tests 122
8.1.3 Modeling of a TEG 126
8.1.4 New Design of a TEG 133
8.2 Solar Thermoelectric Generators 138
8.2.1 Recent Studies 138
8.2.2 Modeling of a STEG 138
8.2.3 Optimal Design of a STEG (Dimensional Analysis) 144
8.2.4 New Design of a STEG 146
8.3 Automotive Thermoelectric Air Conditioner 149
8.3.1 Recent Studies 149
8.3.2 Modeling of an Air-to-Air TEAC 150
8.3.3 Optimal Design of a TEAC 157
8.3.4 New Design of a TEAC 160
Problems 162
References 163
9 Crystal Structure 164
9.1 Atomic Mass 164
9.1.1 Avogadro's Number 164
Example 9.1 Mass of One Atom 164
9.2 Unit Cells of a Crystal 165
9.2.1 Bravais Lattices 166
Example 9.2 Lattice Constant of Gold 169
9.3 Crystal Planes 170
Example 9.3 Indices of a Plane 171
Problems 171
10 Physics of Electrons 172
10.1 Quantum Mechanics 172
10.1.1 Electromagnetic Wave 172
10.1.2 Atomic Structure 174
10.1.3 Bohr's Model 174
10.1.4 Line Spectra 176
10.1.5 De Broglie Wave 177
10.1.6 Heisenberg Uncertainty Principle 178
10.1.7 Schrödinger Equation 178
10.1.8 A Particle in a One-Dimensional Box 179
10.1.9 Quantum Numbers 181
10.1.10 Electron Configurations 183
Example 10.1 Electronic Configuration of a Silicon Atom 184
10.2 Band Theory and Doping 185
10.2.1 Covalent Bonding 185
10.2.2 Energy Band 186
10.2.3 Pseudo-Potential Well 186
10.2.4 Doping, Donors, and Acceptors 187
Problems 188
References 188
11 Density of States, Fermi Energy, and Energy Bands 189
11.1 Current and Energy Transport 189
11.2 Electron Density of States 190
11.2.1 Dispersion Relation 190
11.2.2 Effective Mass 190
11.2.3 Density of States 191
11.3 Fermi-Dirac Distribution 193
11.4 Electron Concentration 194
11.5 Fermi Energy in Metals 195
Example 11.1 Fermi Energy in Gold 196
11.6 Fermi Energy in Semiconductors 197
Example 11.2 Fermi Energy in Doped Semiconductors 198
11.7 Energy Bands 199
11.7.1 Multiple Bands 200
11.7.2 Direct and Indirect Semiconductors 200
11.7.3 Periodic Potential (Kronig-Penney Model) 201
Problems 205
References 205
12 Thermoelectric Transport Properties for Electrons 206
12.1 Boltzmann Transport Equation 206
12.2 Simple Model of Metals 208
12.2.1 Electric Current Density 208
12.2.2 Electrical Conductivity 208
Example 12.1 Electron Relaxation Time of Gold 210
12.2.3 Seebeck Coefficient 210
Example 12.2 Seebeck Coefficient of Gold 212
12.2.4 Electronic Thermal Conductivity 212
Example 12.3 Electronic Thermal Conductivity of Gold 213
12.3 Power-Law Model for Metals and Semiconductors 213
12.3.1 Equipartition Principle 214
12.3.2 Parabolic Single-Band Model 215
Example 12.4 Seebeck Coefficient of PbTe 217
Example 12.5 Material Parameter 221
12.4 Electron Relaxation Time 222
12.4.1 Acoustic Phonon Scattering 222
12.4.2 Polar Optical Phonon Scattering 222
12.4.3 Ionized Impurity Scattering 223
Example 12.6 Electron Mobility 223
12.5 Multiband Effects 224
12.6 Nonparabolicity 225
Problems 228
References 229
13 Phonons 230
13.1 Crystal Vibration 230
13.1.1 One Atom in a Primitive Cell 230
13.1.2 Two Atoms in a Unit Cell 232
13.2 Specific Heat 234
13.2.1 Internal Energy 234
13.2.2 Debye Model 235
Example 13.1 Atomic Size and Specific Heat 239
13.3 Lattice Thermal Conductivity 241
13.3.1 Klemens-Callaway Model 241
13.3.2 Umklapp Processes 244
13.3.3 Callaway Model 244
13.3.4 Phonon Relaxation Times 245
Example 13.2 Lattice Thermal Conductivity 247
Problems 249
References 250
14 Low-Dimensional Nanostructures 251
14.1 Low-Dimensional Systems 251
14.1.1 Quantum Well (2D) 251
Example 14.1 Energy Levels of a Quantum Well 255
14.1.2 Quantum Wires (1D) 256
14.1.3 Quantum Dots (0D) 258
14.1.4 Thermoelectric Transport Properties of Quantum Wells 260
14.1.5 Thermoelectric Transport Properties of Quantum Wires 261
14.1.6 Proof-of-Principle Studies 263
14.1.7 Size Effects of Quantum Well on Lattice Thermal Conductivity 264
Problems 267
References 267
15 Generic Model of Bulk Silicon and Nanowires 268
15.1 Electron Density of States for Bulk and Nanowires 268
15.1.1 Density of States 268
15.2 Carrier Concentrations for Two-band Model 269
15.2.1 Bulk 269
15.2.2 Nanowires 269
15.2.3 Bipolar Effect and Fermi Energy 269
15.3 Electron Transport Properties for Bulk and Nanowires 270
15.3.1 Electrical Conductivity 270
15.3.2 Seebeck Coefficient 270
15.3.3 Electronic Thermal Conductivity 270
15.4 Electron Scattering Mechanisms 271
15.4.1 Acoustic-Phonon Scattering 271
15.4.2 Ionized Impurity Scattering 272
15.4.3 Polar Optical Phonon Scattering 272
15.5 Lattice Thermal Conductivity 273
15.6 Phonon Relaxation Time 273
15.7 Input Data for Bulk Si and Nanowires 275
15.8 Bulk Si 275
15.8.1 Fermi Energy 275
15.8.2 Electron Mobility 275
15.8.3 Thermoelectric Transport Properties 275
15.8.4 Dimensionless Figure of Merit 276
15.9 Si Nanowires 276
15.9.1 Electron Properties 276
15.9.2 Phonon Properties for Si Nanowires 280
Problems 282
References 284
16 Theoretical Model of Thermoelectric Transport Properties 286
16.1 Introduction 286
16.2 Theoretical Equatons 287
16.2.1 Carrier Transport Properties 287
16.2.2 Scattering Mechanisms for Electron Relaxation Times 290
16.2.3 Lattice Thermal Conductivity 293
16.2.4 Phonon Relaxation Times 293
16.2.5 Phonon Density of States and Specific Heat 295
16.2.6 Dimensionless Figure of Merit 295
16.3 Results and Discussion 295
16.3.1 Electron or Hole Scattering Mechanisms 295
16.3.2 Transport Properties 299
16.4 Summary 315
Problems 316
References 316
Appendix A Physical Properties 323
Appendix B Optimal Dimensionless Parameters for TEGs with ZT12=1 353
Appendix C ANSYS TEG Tutorial 365
Appendix D Periodic Table 376
Appendix E Thermoelectric Properties 391
Appendix F Fermi Integral 399
Appendix G Hall Factor 402
Appendix H Conversion Factors 405
Index 409