Table of Contents

List of Symbols ix

Preface xi

1 Problems of the Energy Economy 1

1.1 Energy Economy 1

1.2 Estimate of the Maximum Reserves of Fossil Energy 4

1.3 The Greenhouse Effect 6

1.3.1 Combustion 6

1.3.2 The Temperature of the Earth 7

1.4 Problems 9

2 Photons 11

2.1 Black-body Radiation 11

2.1.1 Photon Density nγ in a Cavity (Planck’s Law of Radiation) 12

2.1.2 Energy Current Through an Area dA into the Solid Angle dΩ16

2.1.3 Radiation from a Spherical Surface into the Solid Angle dΩ19

2.1.4 Radiation from a Surface Element into a Hemisphere (Stefan–Boltzmann Radiation Law) 20

2.2 Kirchhoff’s Law of Radiation for Nonblack Bodies 22

2.2.1 Absorption by Semiconductors 24

2.3 The Solar Spectrum 25

2.3.1 Air Mass 26

2.4 Concentration of the Solar Radiation 28

2.4.1 The Abb´e Sine Condition 29

2.4.2 Geometrical Optics 30

2.4.3 Concentration of Radiation Using the Sine Condition 32

2.5 Maximum Efficiency of Solar Energy Conversion 33

2.6 Problems 40

3 Semiconductors 43

3.1 Electrons in Semiconductors 44

3.1.1 Distribution Function for Electrons 45

3.1.2 Density of States De(εe) for Electrons 45

3.1.3 Density of Electrons 50

3.2 Holes 52

3.3 Doping 55

3.4 Quasi-Fermi Distributions 59

3.4.1 Fermi Energy and Electrochemical Potential 61

3.4.2 Work Function 66

3.5 Generation of Electrons and Holes 67

3.5.1 Absorption of Photons 67

3.5.2 Generation of Electron–Hole Pairs 71

3.6 Recombination of Electrons and Holes 74

3.6.1 Radiative Recombination, Emission of Photons 74

3.6.2 Nonradiative Recombination 77

3.6.3 Lifetimes 87

3.7 Light Emission by Semiconductors 90

3.7.1 Transition Rates and Absorption Coefficient 90

3.8 Problems 95

4 Conversion of Thermal Radiation into Chemical Energy 97

4.1 Maximum Efficiency for the Production of Chemical Energy 100

4.2 Problems 105

5 Conversion of Chemical Energy into Electrical Energy 107

5.1 Transport of Electrons and Holes 107

5.1.1 Field Current 108

5.1.2 Diffusion Current 109

5.1.3 Total Charge Current 111

5.2 Separation of Electrons and Holes 113

5.3 Diffusion Length of Minority Carriers 115

5.4 Dielectric Relaxation 117

5.5 Ambipolar Diffusion 118

5.6 Dember Effect 119

5.7 Mathematical Description 122

5.8 Problems 123

6 Basic Structure of Solar Cells 125

6.1 A Chemical Solar Cell 125

6.2 Basic Mechanisms in Solar Cells 129

6.3 Dye Solar Cell 131

6.4 The pn-Junction 132

6.4.1 Electrochemical Equilibrium of Electrons in a pn-Junction in the Dark 133

6.4.2 Potential Distribution across a pn-Junction 134

6.4.3 Current–Voltage Characteristic of the pn-Junction 137

6.5 pn-Junction with Impurity Recombination, Two-diodeModel 143

6.6 Heterojunctions 145

6.7 Semiconductor–Metal Contact 148

6.7.1 Schottky Contact 150

6.7.2 MIS Contact 151

6.8 The Role of the Electric Field in Solar Cells 151

6.9 Organic Solar Cells 155

6.9.1 Excitons 156

6.9.2 Structure of Organic Solar Cells 159

6.10 Light Emitting Diodes (LED) 163

6.11 Problems 164

7 Limitations on Energy Conversion in Solar Cells 167

7.1 Maximum Efficiency of Solar Cells 167

7.2 Efficiency of Solar Cells as a Function of Their Energy Gap 170

7.3 The Optimal Silicon Solar Cell 172

7.3.1 Light Trapping 173

7.4 Thin-film Solar Cells 178

7.4.1 Minimal Thickness of a Solar Cell 179

7.5 Equivalent Circuit 180

7.6 Temperature Dependence of the Open-circuit Voltage 181

7.7 Intensity Dependence of the Efficiency 182

7.8 Efficiencies of the Individual Energy Conversion Processes 183

7.9 Problems 185

8 Concepts for Improving the Efficiency of Solar Cells 187

8.1 Tandem Cells 187

8.1.1 The Electrical Interconnection of Tandem Cells 191

8.2 Concentrator Cells 192

8.3 Thermophotovoltaic Energy Conversion 194

8.4 Impact Ionization 195

8.4.1 Hot Electrons from Impact Ionization 198

8.4.2 Energy Conversion with Hot Electrons and Holes 198

8.5 Two-step Excitation in Three-level Systems 201

8.5.1 Impurity Photovoltaic Effect 202

8.5.2 Up- and Down-conversion of Photons 206

8.6 Problems 209

Prospects for the Future 211

Solutions 215

Appendix 235

References 239

Index 241

About the Author

Peter Würfel studied physics at the University of Karlsruhe where he attended lectures in the same lecture hall in which Heinrich Hertz discovered the electro-magnetic waves in 1888. He obtained his PhD from the University of Karlsruhe and later became a Professor at the same university himself. His research activities started with ferroelectric thin films, mostly for pyroelectric infrared detectors. He always kept an interest in photovoltaics and has concentrated his efforts in this field over the last 20 years.