Table of Contents
Preface vii
Acknowledgments ix
List of Available Video Lectures xi
Constants Used in This Book xv
Some Symbols Used xvii
1 Overview 1
1.1 Conductance 3
1.2 Ballistic Conductance 4
1.3 What Determines the Resistance? 5
1.4 Where is the Resistance? 6
1.5 But Where is the Heat? 8
1.6 Elastic Resistors 10
1.7 Transport Theories 13
1.7.1 Why elastic resistors are conceptually simpler 14
1.8 Is Transport Essentially a Many-body Process? 16
1.9 A Different Physical Picture 17
What Determines the Resistance 19
2 Why Electrons Flow 21
2.1 Two Key Concepts 22
2.1.1 Energy window for current flow 23
2.2 Fermi Function 24
2.2.1 Thermal broadening function 25
2.3 Non-equilibrium: Two Fermi Functions 26
2.4 Linear Response 27
2.5 Difference in "Agenda" Drives the Flow 29
2.5.1 Drude formula 29
2.5.2 Present approach 30
3 The Elastic Resistor 31
3.1 How an Elastic Resistor Dissipates Heat 33
3.2 Current in an Elastic Resistor 34
3.2.1 Exclusion principle? 36
3.2.2 Convention for current and voltage 37
3.3 Conductance of a Long Resistor 38
3.4 Degenerate and Non-degenerate Conductors 40
4 Ballistic and Diffusive Transport 43
4.1 Transit Times 45
4.2 Channels for Conduction 48
5 Conductance from Fluctuation 51
5.1 Introduction 51
5.2 Current Fluctuations in an Elastic Resistor 54
5.2.1 One-level resistor 54
5.2.2 Multi-level resistor 55
Simple Model for Density of States 57
6 Energy Band Model 59
6.1 Introduction 59
6.2 E(p) or E(k) Relation 63
6.3 Counting States 65
6.3.1 Density of states, D(E) 66
6.4 Number of Modes 67
6.4.1 Degeneracy factor 68
6.5 Electron Density, n 69
6.5.1 n-type conductors 70
6.5.2 p-type conductors 70
6.5.3 "Double-ended" density of states 71
6.6 Conductivity versus n 72
7 The Nanotransistor 75
7.1 Current-voltage Relation 76
7.2 Why the Current Saturates 78
7.3 Role of Charging 80
7.3.1 Quantum capacitance 83
7.4 "Rectifier" Based on Electrostatics 86
7.5 Extended Channel Model 88
7.5.1 Diffusion equation 90
7.5.2 Charging: Self-consistent solution 92
7.6 MATLAB Codes for Figs. 7.9 and 7.11 93
What and Where is the Voltage Drop 97
8 Diffusion Equation for Ballistic Transport 99
8.1 Introduction 99
8.1.1 A disclaimer 104
8.2 Electrochemical Potentials Out of Equilibrium 104
8.3 Current from QFL's 107
9 Boltzmanu Equation 109
9.1 Introduction 109
9.2 BTE from "Newton's Laws" 111
9.3 Diffusion Equation from BTE 113
9.3.1 Equilibrium fields can matter 116
9.4 The Two Potentials 116
10 Quasi-Fermi Levels 121
10.1 Introduction 121
10.2 The Landauer Formulas (Eqs. (10.1) and (10.2)) 126
10.3 Biittiker Formula (Eq. (10.3)) 129
10.3.1 Application 131
10.3.2 Is Eq. (10.3) obvious? 134
10.3.3 Non-reciprocal circuits 135
10.3.4 Onsager relations 136
11 Hall Effect 139
11.1 Introduction 139
11.2 Why n- and p-type Conductors are Different 143
11.3 Spatial Profile of Electrochemical Potential 145
11.3.1 Obtaining Eq. (11.14) from BTE 146
11.4 Edge States 148
12 Smart Contacts 151
12.1 p-n Junctions 153
12.1.1 Current-voltage characteristics 155
12.1.2 Contacts are fundamental 158
12.2 Spin Potentials 159
12.2.1 Spin valve 159
12.2.2 Measuring the spin voltage 162
12.2.3 Spin-momentum locking 163
12.3 Concluding Remarks 166
Heat and Electricity 169
13 Thermoelectricity 171
13.1 Introduction 171
13.2 Seebeck Coefficient 174
13.3 Thermoelectric Figures of Merit 176
13.4 Heat Current 178
13.4.1 Linear response 180
13.5 The Delta Function Thermoelectric 181
13.5.1 Optimizing power factor 184
14 Phonon Transport 187
14.1 Introduction 187
14.2 Phonon Heat Current 188
14.2.1 Ballistic phonon current 191
14.3 Thermal Conductivity 192
15 Second Law 195
15.1 Introduction 195
15.2 Asymmetry of Absorption and Emission 198
15.3 Entropy 200
15.3.1 Total entropy increases continually 203
15.3.2 Free energy decreases continually 203
15.4 Law of Equilibrium 205
15.5 Fock Space States 206
15.5.1 Bose function 207
15.5.2 Interacting electrons 208
15.6 Alternative Expression for Entropy 210
15.6.1 From Eq. (15.24) to Eq. (15.25) 211
15.6.2 Equilibrium distribution from minimizing free energy 212
16 Fuel Value of Information 215
16.1 Introduction 215
16.2 Information-driven Battery 218
16.3 Fuel Value Comes from Knowledge 221
16.4 Landauer's Principle 223
16.5 Maxwell's Demon 224
Suggested Reading 227
Appendices 235
Appendix A Derivatives of Fermi and Bose Functions 237
A.1 Fermi Function 237
A.2 Bose Function 238
Appendix B Angular Averaging 239
B.1 One Dimension 239
B.2 Two Dimensions 239
B.3 Three Dimensions 240
B.4 Summary 240
Appendix C Current at High Bias for Non-degenerate Resistors 241
Appendix D Semiclassical Dynamics 245
D.1 Serniclassical Laws of Motion 245
D.1.1 Proof 246
Appendix E Transmission Line Parameters from BTE 247
Index 249
