The Physics of Solar Energy Conversion

Contents

Preface........................................................................................................................................................................xv

Acknowledgments....................................................................................................................................................xvii

Author.......................................................................................................................................................................xix

Chapter 1 Introduction to Energy Devices...............................................................................................................1

References...............................................................................................................................................9

PART I Equilibrium Concepts and Kinetics

Chapter 2 Electrostatic and Thermodynamic Potentials of Electrons in Materials...............................................13

2.1 Electrostatic Potential..................................................................................................................13

2.2 Energies of Free Electrons and Holes.......................................................................................... 14

2.3 Potential Energy of the Electrons in the Semiconductor............................................................. 17

2.4 The Vacuum Level....................................................................................................................... 17

2.5 The Fermi Level and the Work Function....................................................................................20

2.6 The Chemical Potential of Electrons........................................................................................... 21

2.7 Potential Step of a Dipole Layer or a Double Layer....................................................................23

2.8 Origin of Surface Dipoles............................................................................................................24

2.9 The Volta Potential......................................................................................................................25

2.10 Equalization of Fermi Levels of Two Electronic Conductors in Contact....................................27

2.11 Equilibration of Metal Junctions and the Contact Potential Difference......................................28

2.12 Equilibrium across the Semiconductor Junction.........................................................................29

General References............................................................................................................................... 31

References............................................................................................................................................. 31

Chapter 3 Voltage, Capacitors, and Batteries.........................................................................................................33

3.1 The Voltage in the Device...........................................................................................................33

3.2 Anode and Cathode.....................................................................................................................34

3.3 Applied Voltage and Potential Difference...................................................................................35

3.4 The Capacitor..............................................................................................................................37

3.5 Measurement of the Capacitance.................................................................................................38

3.6 Energy Storage in the Capacitor..................................................................................................40

3.7 Electrochemical Systems: Structure of the Metal/Solution Interface..........................................40

3.8 Electrode Potential and Reference Electrodes.............................................................................42

3.9 Redox Potential in Electrochemical Cells...................................................................................44

3.10 Electrochemical and Physical Scales of Electron Energy in Material Systems..........................45

3.11 Changes of Electrolyte Levels with pH.......................................................................................46

3.12 Principles of Electrochemical Batteries.......................................................................................47

3.13 Capacity and Energy Content......................................................................................................50

3.14 Practical Electrochemical Batteries............................................................................................. 51

3.14.1 Zinc-Silver Battery.......................................................................................................... 51

3.14.2 Sodium-Sulfur Battery....................................................................................................52

3.15 Li-Ion Battery.............................................................................................................................. 53

General References...............................................................................................................................57

References.............................................................................................................................................57

Chapter 4 Work Functions and Injection Barriers.................................................................................................59

4.1 Injection to Vacuum in Thermionic Emission.............................................................................59

4.2 Richardson-Dushman Equation..................................................................................................60

4.3 Kelvin Probe Method.................................................................................................................. 61

4.4 Photoelectron Emission Spectroscopy.........................................................................................63

4.5 Injection Barriers.........................................................................................................................66

4.6 Pinning of the Fermi Level and Charge-Neutrality Level...........................................................69

General References...............................................................................................................................73

References.............................................................................................................................................73

Chapter 5 Thermal Distribution of Electrons, Holes, and Ions in Solids............................................................... 75

5.1 Equilibration of the Electrochemical Potential of Electrons....................................................... 75

5.2 Configurational Entropy of Weakly Interacting Particles...........................................................76

5.3 Equilibrium Occupancy of Conduction Band and Valence Band States.....................................76

5.4 Equilibrium Fermi Level and the Carrier Number in Semiconductors.......................................79

5.5 Transparent Conducting Oxides.................................................................................................. 81

5.6 Hot Electrons...............................................................................................................................82

5.7 Screening.....................................................................................................................................84

5.8 The Rectifier at Forward and Reverse Voltage............................................................................85

5.9 Semiconductor Devices as Thermal Machines that Realize Useful Work..................................88

5.10 Cell Potential in the Lithium Ion Battery....................................................................................90

5.11 Insertion of Ions: The Lattice Gas Model....................................................................................94

General References...............................................................................................................................98

References.............................................................................................................................................98

Chapter 6 Interfacial Kinetics and Hopping Transitions...................................................................................... 101

6.1 Principle of Detailed Balance.................................................................................................... 101

6.2 Form of the Transition Rates.....................................................................................................104

6.3 Kinetics of Localized States: Shockley-Read-Hall Recombination Model...............................106

6.4 Reorganization Effects in Charge Transfer: The Marcus Model............................................... 107

6.5 Polaron Hopping........................................................................................................................ 112

6.6 Rate of Electrode Reaction: Butler-Volmer Equation................................................................ 115

6.6.1 Availability of Electronic Species................................................................................. 116

6.6.2 Availability of Redox Species........................................................................................ 116

6.6.3 The Kinetic Constant for Charge Transfer.................................................................... 117

6.7 Electron Transfer at Metal-Semiconductor Contact..................................................................120

6.8 Electron Transfer at the Semiconductor/Electrolyte Interface.................................................. 121

General References.............................................................................................................................126

References...........................................................................................................................................127

Chapter 7 The Chemical Capacitance.................................................................................................................. 131

7.1 Carrier Accumulation and Energy Storage in the Chemical Capacitance................................. 131

7.2 Localized Electronic States in Disordered Materials and Surface States................................. 133

7.3 Chemical Capacitance of a Single State.................................................................................... 135

7.4 Chemical Capacitance of a Broad DOS.................................................................................... 136

7.5 Filling a DOS with Carriers: The Voltage and the Conductivity.............................................. 138

7.6 Chemical Capacitance of Li Intercalation Materials................................................................. 139

7.7 Chemical Capacitance of Graphene.......................................................................................... 140

General References............................................................................................................................. 142

References........................................................................................................................................... 143

Chapter 8 The Density of States in Disordered Inorganic and Organic Conductors........................................... 145

8.1 Capacitive and Reactive Current in Cyclic Voltammetry.......................................................... 145

8.2 Kinetic Effects in CV Response................................................................................................ 149

8.3 The Exponential DOS in Amorphous Semiconductors.............................................................150

8.4 The Exponential DOS in Nanocrystalline Metal Oxides.......................................................... 152

8.5 Basic Properties of Organic Layers........................................................................................... 156

8.6 The Gaussian DOS.................................................................................................................... 160

General References............................................................................................................................. 162

References........................................................................................................................................... 163

Chapter 9 Planar and Nanostructured Semiconductor Junctions......................................................................... 167

9.1 Structure of the Schottky Barrier at a Metal/Semiconductor Contacts..................................... 167

9.2 Changes of the Schottky Barrier by the Applied Voltage.......................................................... 168

9.3 Properties of the Planar Depletion Layer.................................................................................. 170

9.4 Mott-Schottky Plots.................................................................................................................. 171

9.5 Capacitance Response of Defect Levels and Surface States..................................................... 172

9.6 Semiconductor Electrodes and the Flatband Potential.............................................................. 173

9.7 Changes of Redox Level and Band Unpinning.......................................................................... 176

9.8 Inversion and Accumulation Layer............................................................................................ 180

9.9 Heterojunctions.......................................................................................................................... 181

9.10 Effect of Voltage on Highly Doped Nanocrystalline Semiconductors...................................... 183

9.11 Homogeneous Carrier Accumulation in Low-Doped Nanocrystalline Semiconductors........... 188

General References............................................................................................................................. 192

References........................................................................................................................................... 192

PART II Foundations of Carrier Transport

Chapter 10 Carrier Injection and Drift Transport.................................................................................................. 197

10.1 Transport by Drift in the Electrical Field.................................................................................. 197

10.2 Injection at Contacts.................................................................................................................. 198

10.3 The Metal-Insulator-Metal Model.............................................................................................202

10.4 The Time-of-Flight Method......................................................................................................205

General References.............................................................................................................................206

References...........................................................................................................................................206

Chapter 11 Diffusion Transport.............................................................................................................................209

11.1 Diffusion in the Random Walk Model......................................................................................209

11.2 Macroscopic Diffusion Equation............................................................................................... 211

11.3 The Diffusion Length................................................................................................................ 212

11.4 Chemical Diffusion Coefficient and the Thermodynamic Factor............................................. 213

General References............................................................................................................................. 215

References........................................................................................................................................... 215

Chapter 12 Drift-Diffusion Transport.................................................................................................................... 217

12.1 General Transport Equation in Terms of Electrochemical Potential......................................... 217

12.2 The Transport Resistance.......................................................................................................... 217

12.3 The Einstein Relation................................................................................................................ 219

12.4 Drift-Diffusion Equations..........................................................................................................220

12.5 Ambipolar Diffusion Transport................................................................................................221

12.6 Relaxation of Injected Charge..................................................................................................222

12.7 Transient Current in Insulator Layers.......................................................................................223

12.8 Modeling Transport Problems..................................................................................................224

General References.............................................................................................................................227

References...........................................................................................................................................227

Chapter 13 Transport in Disordered Media...........................................................................................................229

13.1 Multiple Trapping and Hopping Transport...............................................................................229

13.2 Transport by Hopping in a Single Level...................................................................................231

13.3 Trapping Factors in the Kinetic Constants...............................................................................233

13.4 Two-Level (Single-Trap) Model................................................................................................235

13.5 Multiple Trapping in Exponential DOS....................................................................................237

13.6 Activated Transport in a Gaussian DOS...................................................................................237

13.7 Multiple Trapping in the Time Domain....................................................................................239

13.8 Hopping Conductivity...............................................................................................................241

13.9 The Transport Energy...............................................................................................................242

13.10 Variable Range Hopping...........................................................................................................243

General References.............................................................................................................................245

References...........................................................................................................................................245

Chapter 14 Thin Film Transistors..........................................................................................................................249

14.1 Organic Thin Film Transistors.................................................................................................249

14.2 Carrier Density in the Channel.................................................................................................250

14.3 Determination of the DOS in Thin Film Transistor Configuration..........................................252

14.4 Current-Voltage Characteristics................................................................................................255

14.5 The Mobility in Disordered Semiconductors............................................................................257

14.6 Electrochemical Transistor.......................................................................................................258

General References.............................................................................................................................259

References...........................................................................................................................................259

Chapter 15 Space-Charge-Limited Transport........................................................................................................263

15.1 Space-Charge-Limited Current................................................................................................263

15.2 Injected Carrier Capacitance in SCLC.....................................................................................265

15.3 Space Charge in Double Injection............................................................................................267

General References.............................................................................................................................269

References...........................................................................................................................................269

Chapter 16 Impedance and Capacitance Spectroscopies....................................................................................... 271

16.1 Frequency Domain Measurements...........................................................................................271

16.2 Dielectric Relaxation Functions................................................................................................272

16.3 Resistance and Capacitance in Equivalent Circuit Models.......................................................274

16.4 Relaxation in Time Domain......................................................................................................279

16.5 Universal Properties of the Frequency-Dependent Conductivity..............................................281

16.6 Electrode Polarization...............................................................................................................283

General References.............................................................................................................................284

References...........................................................................................................................................284

PART III Radiation, Light, and Semiconductors

Chapter 17 Blackbody Radiation and Light...........................................................................................................289

17.1 Photons and Light......................................................................................................................289

17.2 Spread and Direction of Radiation............................................................................................289

17.3 Color and Photometry................................................................................................................ 291

17.4 Blackbody Radiation.................................................................................................................293

17.5 The Planck Spectrum................................................................................................................294

17.6 The Energy Density of The Distribution of Photons in Blackbody Radiation..........................295

17.7 The Photon and Energy Fluxes in Blackbody Radiation...........................................................297

17.8 The Solar Spectrum...................................................................................................................299

General References.............................................................................................................................302

References...........................................................................................................................................302

Chapter 18 Light Absorption, Carrier Recombination, and Luminescence...........................................................305

18.1 Absorption of Incident Radiation..............................................................................................305

18.2 Luminescence and Energy Transfer..........................................................................................307

18.3 The Quantum Efficiency........................................................................................................... 310

18.4 The Recombination of Carriers in Semiconductors.................................................................. 311

18.5 Recombination Lifetime............................................................................................................ 314

General References............................................................................................................................. 316

References........................................................................................................................................... 316

Chapter 19 Optical Transitions in Organic and Inorganic Semiconductors.......................................................... 319

19.1 Light Absorption in Inorganic Solids........................................................................................ 319

19.2 Free Carrier Phenomena............................................................................................................323

19.3 Excitons.....................................................................................................................................325

19.4 Quantum Dots...........................................................................................................................328

19.5 Organic Molecules and Materials..............................................................................................330

19.6 The CT Band in Organic Blends and Heterojunctions.............................................................. 333

General References............................................................................................................................. 336

References........................................................................................................................................... 336

PART IV Photovoltaic Principles and Solar Energy Conversion

Chapter 20 Fundamental Model of a Solar Cell....................................................................................................343

20.1 Majority Carrier Injection Mechanisms....................................................................................343

20.2 Majority Carrier Devices...........................................................................................................344

20.3 Minority Carrier Devices..........................................................................................................345

20.4 Fundamental Properties of a Solar Cell.....................................................................................346

20.5 Physical Properties of Selective Contacts in Solar Cells...........................................................348

General References............................................................................................................................. 351

References........................................................................................................................................... 351

Chapter 21 Recombination Current in the Semiconductor Diode......................................................................... 353

21.1 Dark Equilibrium of Absorption and Emission of Radiation.................................................... 353

21.2 Recombination Current............................................................................................................. 355

21.3 Dark Characteristics of Diode Equation.................................................................................... 356

21.4 Light-Emitting Diodes............................................................................................................... 357

21.5 Dye Sensitization and Molecular Diodes...................................................................................360

General References.............................................................................................................................363

References...........................................................................................................................................363

Chapter 22 Radiative Equilibrium in a Semiconductor.........................................................................................365

22.1 Utilization of Solar Photons......................................................................................................365

22.2 Fundamental Radiative Carrier Lifetime..................................................................................368

22.3 Radiative Emission of a Semiconductor Layer..........................................................................369

22.4 Photons at Nonzero Chemical Potential.................................................................................... 370

General References............................................................................................................................. 373

References........................................................................................................................................... 373

Chapter 23 Reciprocity Relations in Solar Cells and Fundamental Limits to the Photovoltage ........................... 375

23.1 The Reciprocity between LED and Photovoltaic Performance Parameters.............................. 375

23.2 Factors Determining the Photovoltage...................................................................................... 378

23.3 External Radiative Efficiency....................................................................................................382

23.4 Photon Recycling.......................................................................................................................383

23.5 Radiative Cooling in EL and Photoluminescence.....................................................................386

23.6 Reciprocity of Absorption and Emission in a CT Band............................................................387

General References............................................................................................................................. 391

References...........................................................................................................................................392

Chapter 24 Charge Separation and Material Limits to the Photovoltage...............................................................395

24.1 Light Absorption........................................................................................................................395

24.2 Charge Separation.....................................................................................................................395

24.3 Materials Limits to the Photovoltage.........................................................................................398

General References.............................................................................................................................403

References...........................................................................................................................................404

Chapter 25 Operation of Solar Cells and Fundamental Limits to Their Performance..........................................407

25.1 Current-Voltage Characteristics.................................................................................................407

25.2 Power Conversion Efficiency.....................................................................................................408

25.3 Analysis of FF........................................................................................................................... 410

25.4 Shockley-Queisser Efficiency Limits........................................................................................ 412

25.5 Practical Solar Cells Efficiency Limits...................................................................................... 413

General References............................................................................................................................. 419

References........................................................................................................................................... 419

Chapter 26 Charge Collection in Solar Cells......................................................................................................... 421

26.1 Introduction to Charge Collection Properties............................................................................ 421

26.2 Charge Collection Distance.......................................................................................................422

26.3 General Modeling Equations.....................................................................................................424

26.4 The Boundary Conditions.........................................................................................................425

26.4.1 Charge Extraction Boundary Condition........................................................................426

26.4.2 Blocking Boundary Condition.......................................................................................427

26.4.3 Generalized Boundary Conditions................................................................................428

26.5 A Photovoltaic Model with Diffusion and Recombination........................................................429

26.6 The Gaertner Model.................................................................................................................... 433

26.7 Diffusion-Recombination and Collection in the Space-Charge Region.................................... 435

26.8 Solar Cell Simulation................................................................................................................. 436

26.9 Classification of Solar Cells....................................................................................................... 437

26.10 Measuring and Reporting Solar Cell Efficiencies..................................................................... 439

General References.............................................................................................................................442

References...........................................................................................................................................442

Chapter 27 Spectral Harvesting and Photoelectrochemical Conversion................................................................445

27.1 Conversion of Photon Frequencies for Solar Energy Harvesting..............................................445

27.2 Tandem Solar Cells....................................................................................................................448

27.3 Solar Fuel Generation................................................................................................................450

General References.............................................................................................................................456

References...........................................................................................................................................456

Appendix................................................................................................................................................................. 459

Index........................................................................................................................................................................463