Thermoelectrics

Preface to the Second Edition xvii Preface to the First Edition xix About the Companion Website xxi 1 Introduction 1 1.1 Introduction 1 1.2 Thermoelectric Effect 3 1.2.1 Seebeck Effect 3 1.2.2 Peltier Effect 4 1.2.3 Thomson Effect 4 1.2.4 Thomson (or Kelvin) Relationships 4 1.3 The Figure of Merit 5 1.3.1 New Generation Thermoelectrics 5 Problems 7 References 8 2 Thermoelectric Generators 9 2.1 Ideal Equations 9 2.2 Performance Parameters of a Thermoelectric Module 12 2.3 Maximum Parameters for a Thermoelectric Module 13 2.4 Normalized Parameters 14 Example 2.1 Estimate Heat Flow 16 Example 2.2 Using Ideal Equations 18 2.5 Effective Material Properties 20 2.6 Comparison of Calculations with a Commercial Product 21 Example 2.3 Exhaust Waste Heat Recovery 24 2.7 Figure of Merit and Optimum Geometry 26 Problems 27 References 30 3 Thermoelectric Coolers and Heat Pumps 31 3.1 Ideal Equations 31 3.2 Maximum Parameters 34 3.3 Normalized Parameters for Thermoelectric Coolers 36 Example 3.1 Thermoelectric Cooler 39 3.4 Normalized Parameters for Thermoelectric Heat Pumps 40 Example 3.2 Thermoelectric Heat Pump 42 Example 3.3 Thermoelectric Cooler and Heat Pump 44 Example 3.4 Thermoelectric Air Conditioner 46 3.5 Effective Material Properties 50 3.6 Comparison of Calculations with a Commercial Product 51 3.7 Multistage Modules 52 3.7.1 Commercial Multistage Peltier Modules 55 Problems 55 References 58 4 Optimal System Design 59 4.1 Introduction 59 4.2 Optimal System Design for Thermoelectric Generators 59 4.2.1 Basic Equations 59 4.2.2 Instability and Maximum Efficiency 62 4.2.3 Dimensionless Characteristics 64 4.2.4 Effect of Convection Conductance 66 4.2.5 Dimensionless Characteristics 67 Example 4.1 Waste Heat Recovery System 70 Example 4.2 Thermoelectric Generator System in a Nuclear Reactor 75 Example 4.3 Thermoelectric Generator on a Wood Stove 78 4.3 Thermoelectric Generator System with Thermal Radiation 81 4.3.1 Dimensional Analysis 82 4.3.2 Instability and Maximum Efficiency with Radiation 84 4.3.3 Dimensionless Characteristics 85 4.3.4 Heat Flux Conversion to Dimensionless Surrounding Temperature 86 Example 4.4 Thermoelectric Generator System for an Offshore Fusion Nuclear Reactor 88 4.4 Optimal System Design of Thermoelectric Coolers and Heat Pumps 92 4.4.1 Basic Equations 92 4.4.2 Instability 94 4.4.3 Dimensionless Optimal Cooling Power 95 4.4.4 Effect of Convection Conductance N h 97 4.4.5 Dimensionless Characteristics for Optimal Cooling and Half Optimal Cooling 99 Example 4.5 Thermoelectric Cooler System 102 4.4.6 Micro Cooler System 107 Example 4.6 Micro Cooling System 108 4.4.7 Thermoelectric Heat Pumps 112 4.4.8 Heat Sinks Without Thermoelectric Cooler 112 Example 4.7 Thermoelectric Cooler and Heat Pump 115 4.5 Thermoelectric Cooler System with Heat Flux 120 4.5.1 Basic Equations 120 4.5.2 Dimensional Analysis 121 4.5.3 Instability 122 4.5.4 Optimal Cooling 123 4.5.5 Dimensionless Characteristics 123 Example 4.8 Thermoelectric Cooler System with Heat Flux 126 Example 4.9 Isotherm Instrument 130 Example 4.10 Car Seat Climate Control 135 Problems 140 Thermoelectric Generator System 140 Computer Programming 147 Thermoelectric Cooler System 149 Computer Programming 154 Projects 154 References 156 5 Thomson Effect, Exact Solution, and Compatibility Factor 159 5.1 Thermodynamics of the Thomson Effect 159 5.1.1 Seebeck Effect 159 5.1.2 Peltier Effect 159 5.1.3 Thomson Effect 160 5.1.4 Thomson (or Kelvin) Relationships 161 5.2 Exact Solutions 163 5.2.1 Equations for the Exact Solutions and the Ideal Equation 163 5.2.2 Thermoelectric Generator 165 5.2.3 Thermoelectric Coolers 166 5.3 Compatibility Factor 168 5.3.1 Reduced Current Density 168 5.3.2 Heat Balance Equation 169 5.3.3 Numerical Solution 169 5.3.4 Infinitesimal Efficiency 170 5.3.5 Reduced Efficiency 170 5.3.6 Reduced Efficiency 170 5.3.7 Compatibility Factor 171 5.3.8 Segmented Thermoelements 171 5.3.9 Thermoelectric Potential 173 5.4 Thomson Effect 174 5.4.1 Formulation of Basic Equations 175 5.4.2 Numeric Solutions of the Thomson Effect 178 5.4.3 Comparison Between the Thomson Effect and Ideal Equation 180 Problems 183 References 183 6 Thermal and Electrical Contact Resistances for Micro and Macro Devices 185 6.1 Modeling and Validation 185 6.1.1 Cancellation of Spreading Resistance with Thermal Contact Resistance 186 6.1.2 Thermoelectric Coolers 187 6.1.3 Thermoelectric Generators 187 6.1.4 Validation of Model 187 6.2 Micro and Macro Thermoelectric Coolers 188 6.2.1 Effect of Leg Length 190 6.2.2 Effect of Material on Ceramic Plate 191 6.3 Micro and Macro Thermoelectric Generators 191 6.3.1 Model and Verification for Macro TE Generators 191 6.3.2 Effect of Load Resistance 191 6.3.3 Effect of Leg Length and Ceramic Material 194 Problems 194 References 195 7 Modeling of Thermoelectric Generators and Coolers with Heat Sinks 197 7.1 Modeling of Thermoelectric Generators with Heat Sinks 197 7.1.1 Modeling 197 7.2 Plate-Fin Heat Sinks 206 7.2.1 Nusselt Number for Air 207 7.2.2 Turbulent Flow for Gases and Liquids 208 7.2.3 Optimal Design of Heat Sink 208 7.2.4 Single Fin Efficiency 209 7.2.5 Overall Fin Efficiency 210 7.3 Modeling of Thermoelectric Coolers with Heat Sinks 210 7.3.1 Modeling 210 Problems 218 References 218 8 Applications 219 8.1 Exhaust Waste Heat Recovery 219 8.1.1 Recent Studies 219 8.1.2 Modeling of Module Tests 221 8.1.3 Modeling of TEG 226 8.1.4 New Design of TEG 234 8.2 Solar Thermoelectric Generators (STEGs) 237 8.2.1 Recent Studies 237 8.2.2 Modeling of a STEG 238 8.2.3 Optimal Design of STEG (Dimensional Analysis) 246 8.2.4 New Design of STEG 248 8.3 Automotive Thermoelectric Air Conditioner (TEAC) 251 8.3.1 Recent Studies 251 8.3.2 Modeling of Air-to-Air TEAC 254 8.3.3 Optimal Design of TEAC 260 8.3.4 New Design of TEAC 262 Problems 266 References 267 9 Crystal Structure 269 9.1 Atomic Mass 269 9.1.1 Avogadro’s Number 269 Example 9.1 Mass of One Atom 269 9.2 Unit Cells of a Crystal 269 9.2.1 Bravais Lattices 272 Example 9.2 Gold Au Forms an FCC Unit Cell. Its Atomic Radius is 1.44 Å. Calculate the Lattice Constant of the Gold, and Also Calculate the Density of Gold 274 9.3 Crystal Planes 275 Example 9.3 Indices of a Plane 276 Problems 277 References 277 10 Physics of Electrons 279 10.1 Quantum Mechanics 279 10.1.1 Electromagnetic Wave 279 10.1.2 Atomic Structure 281 10.1.3 Bohr’s Model 282 10.1.4 Line Spectra 283 10.1.5 De Broglie Wave 285 10.1.6 Heisenberg Uncertainty Principle 285 10.1.7 Schrödinger Equation 286 10.1.8 A Particle in a One-Dimensional Box 286 10.1.9 Quantum Numbers 289 10.1.10 Electron Configurations 291 Example 10.1 Electronic Configuration of a Silicon Atom 292 10.2 Band Theory and Doping 293 10.2.1 Covalent Bonding 293 10.2.2 Energy Band 294 10.2.3 Pseudo-Potential Well 295 10.2.4 Doping, Donors, and Acceptors 295 Problems 296 References 297 11 Density of States, Fermi Energy, and Energy Bands 299 11.1 Current and Energy Transport 299 11.2 Electron Density of States 300 11.2.1 Dispersion Relation 300 11.2.2 Effective Mass 300 11.2.3 Density of States 301 11.3 Fermi–Dirac Distribution 303 11.4 Electron Concentration 304 11.5 Fermi Energy in Metals 305 Example 11.1 Fermi Energy in Gold 306 11.6 Fermi Energy in Semiconductors 307 Example 11.2 Fermi Energy in Doped Semiconductors 308 11.7 Energy Bands 309 11.7.1 Multiple Bands 310 11.7.2 Direct and Indirect Semiconductors 310 11.7.3 Periodic Potential (Kronig–Penney Model) 311 Problems 317 References 318 12 Thermoelectric Transport Properties for Electrons 319 12.1 Boltzmann Transport Equation 319 12.2 Semiclassical Model of Metals 321 12.2.1 Electric Current Density 321 12.2.2 Electrical Conductivity 321 Example 12.1 Electron Relaxation Time of Gold 323 12.2.3 Seebeck Coefficient 323 Example 12.2 Seebeck Coefficient of Gold 325 12.2.4 Electronic Thermal Conductivity 325 Example 12.3 Electronic Thermal Conductivity of Gold 326 12.3 Power-Law Model for Metals and Semiconductors 326 12.3.1 Equipartition Principle 327 12.3.2 Parabolic Single-Band Model 328 Example 12.4 Seebeck coefficient of PbTe 330 Example 12.5 Material Parameter 334 12.4 Hall Effect 335 12.5 Electron Relaxation Time 339 12.5.1 Acoustic Phonon Scattering 339 12.5.2 Polar Optical Phonon Scattering 339 12.5.3 Ionized Impurity Scattering 340 12.5.4 Comparison Between the Semiclassical Model and Experiments 340 Example 12.6 Electron Mobility and Electrical Conductivity 340 12.6 Multiband Effects 342 12.7 Nonparabolicity 343 12.8 Comparison Between the Semiclassical Model and Experiments 346 Problems 348 Computer Program 349 References 349 13 Phonons 351 13.1 Vibration of Lattice 351 13.2 Crystal Vibration 351 13.2.1 One Atom in a Primitive cell 351 13.2.2 Two Atoms in a Unit cell 354 13.3 Specific Heat 356 13.3.1 Internal Energy 356 13.3.2 Debye Model 357 Example 13.1 Atomic Size and Specific Heat 361 13.4 Lattice Thermal Conduction 363 13.4.1 Debye–Callaway Model 363 13.4.2 Umklapp Processes 366 13.4.3 Callaway Model 366 13.4.4 Phonon Relaxation Times 368 Example 13.2 Lattice Thermal Conductivity 371 13.4.5 Lower Limit of Thermal Conductivity 372 Problems 373 References 375 14 Low-Dimensional Nanostructures 377 14.1 Low-Dimensional Systems 377 14.1.1 Quantum Well (2D) 377 Example 14.1 Energy Levels of a Quantum Well 381 14.1.2 Quantum Wires (1D) 382 14.1.3 Quantum Dots (0D) 384 14.1.4 Thermoelectric Transport Properties of Quantum Wells 386 14.1.5 Thermoelectric Transport Properties of Quantum Wires 387 14.1.6 Proof-of-Principle Studies 388 Problems 390 References 391 15 Generic Model of Bulk Silicon and Nanowires 393 15.1 Electron Density of States for Bulk and Nanowires 393 15.1.1 Density of States 393 15.2 Carrier Concentrations for Two-band Model 393 15.2.1 Bulk 393 15.2.2 Nanowires 394 15.2.3 Bipolar Effect and Fermi Energy 394 15.3 Electron Transport Properties for Bulk and Nanowires 394 15.3.1 Electrical Conductivity 394 15.3.2 Seebeck Coefficient 395 15.3.3 Electronic Thermal Conductivity 395 15.4 Electron Scattering Mechanisms 396 15.4.1 Acoustic-Phonon Scattering 396 15.4.2 Ionized Impurity Scattering 396 15.4.3 Polar Optical Phonon Scattering 397 15.4.4 Total Electron Relaxation Time 398 15.5 Lattice Thermal Conductivity 398 15.6 Phonon Relaxation Time 398 15.7 Input Data for Bulk Si and Nanowires 399 15.8 Bulk Si 399 15.8.1 Fermi Energy 400 15.8.2 Electron Mobility 401 15.8.3 Thermoelectric Transport Properties 401 15.8.4 Dimensionless Figure of Merit 402 15.9 Si Nanowires 403 15.9.1 Electron Properties 403 15.9.2 Phonon Properties for Si Nanowires 407 Problems 410 References 410 16 Theoreical Model of Thermoelectric Transport Properties 413 16.1 Introduction 413 16.2 Theoretical Equations 414 16.2.1 Carrier Transport Properties 414 16.2.2 Scattering Mechanisms for Electron Relaxation Times 417 16.2.3 Lattice Thermal Conductivity 419 16.2.4 Phonon Relaxation Times 420 16.2.5 Phonon Density of States and Specific Heat 422 16.2.6 Dimensionless Figure of Merit 422 16.3 Results and Discussion 423 16.3.1 Electron or Hole Scattering Mechanisms 423 16.3.2 Transport Properties 427 16.4 Summary 446 Problems 446 References 447 Appendix A Thermophysical Properties 453 Appendix B 475 Appendix C Fermi Integral 483 Appendix D Periodic Table 487 Appendix G Conversion Factors 503 Index 507