Physics of Solar Cells

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.

• List of Symbols ixPreface xi1 Problems of the Energy Economy 11.1 Energy Economy 11.2 Estimate of the Maximum Reserves of Fossil Energy 41.3 The Greenhouse Effect 61.3.1 Combustion 61.3.2 The Temperature of the Earth 71.4 Problems 92 Photons 112.1 Black-body Radiation 112.1.1 Photon Density nγ in a Cavity (Planck’s Law of Radiation) 122.1.2 Energy Current Through an Area dA into the Solid Angle dΩ162.1.3 Radiation from a Spherical Surface into the Solid Angle dΩ192.1.4 Radiation from a Surface Element into a Hemisphere (Stefan–Boltzmann Radiation Law) 202.2 Kirchhoff’s Law of Radiation for Nonblack Bodies 222.2.1 Absorption by Semiconductors 242.3 The Solar Spectrum 252.3.1 Air Mass 262.4 Concentration of the Solar Radiation 282.4.1 The Abb´e Sine Condition 292.4.2 Geometrical Optics 302.4.3 Concentration of Radiation Using the Sine Condition 322.5 Maximum Efficiency of Solar Energy Conversion 332.6 Problems 403 Semiconductors 433.1 Electrons in Semiconductors 443.1.1 Distribution Function for Electrons 453.1.2 Density of States De(εe) for Electrons 453.1.3 Density of Electrons 503.2 Holes 523.3 Doping 553.4 Quasi-Fermi Distributions 593.4.1 Fermi Energy and Electrochemical Potential 613.4.2 Work Function 663.5 Generation of Electrons and Holes 673.5.1 Absorption of Photons 673.5.2 Generation of Electron–Hole Pairs 713.6 Recombination of Electrons and Holes 743.6.1 Radiative Recombination, Emission of Photons 743.6.2 Nonradiative Recombination 773.6.3 Lifetimes 873.7 Light Emission by Semiconductors 903.7.1 Transition Rates and Absorption Coefficient 903.8 Problems 954 Conversion of Thermal Radiation into Chemical Energy 974.1 Maximum Efficiency for the Production of Chemical Energy 1004.2 Problems 1055 Conversion of Chemical Energy into Electrical Energy 1075.1 Transport of Electrons and Holes 1075.1.1 Field Current 1085.1.2 Diffusion Current 1095.1.3 Total Charge Current 1115.2 Separation of Electrons and Holes 1135.3 Diffusion Length of Minority Carriers 1155.4 Dielectric Relaxation 1175.5 Ambipolar Diffusion 1185.6 Dember Effect 1195.7 Mathematical Description 1225.8 Problems 1236 Basic Structure of Solar Cells 1256.1 A Chemical Solar Cell 1256.2 Basic Mechanisms in Solar Cells 1296.3 Dye Solar Cell 1316.4 The pn-Junction 1326.4.1 Electrochemical Equilibrium of Electrons in a pn-Junction in the Dark 1336.4.2 Potential Distribution across a pn-Junction 1346.4.3 Current–Voltage Characteristic of the pn-Junction 1376.5 pn-Junction with Impurity Recombination, Two-diodeModel 1436.6 Heterojunctions 1456.7 Semiconductor–Metal Contact 1486.7.1 Schottky Contact 1506.7.2 MIS Contact 1516.8 The Role of the Electric Field in Solar Cells 1516.9 Organic Solar Cells 1556.9.1 Excitons 1566.9.2 Structure of Organic Solar Cells 1596.10 Light Emitting Diodes (LED) 1636.11 Problems 1647 Limitations on Energy Conversion in Solar Cells 1677.1 Maximum Efficiency of Solar Cells 1677.2 Efficiency of Solar Cells as a Function of Their Energy Gap 1707.3 The Optimal Silicon Solar Cell 1727.3.1 Light Trapping 1737.4 Thin-film Solar Cells 1787.4.1 Minimal Thickness of a Solar Cell 1797.5 Equivalent Circuit 1807.6 Temperature Dependence of the Open-circuit Voltage 1817.7 Intensity Dependence of the Efficiency 1827.8 Efficiencies of the Individual Energy Conversion Processes 1837.9 Problems 1858 Concepts for Improving the Efficiency of Solar Cells 1878.1 Tandem Cells 1878.1.1 The Electrical Interconnection of Tandem Cells 1918.2 Concentrator Cells 1928.3 Thermophotovoltaic Energy Conversion 1948.4 Impact Ionization 1958.4.1 Hot Electrons from Impact Ionization 1988.4.2 Energy Conversion with Hot Electrons and Holes 1988.5 Two-step Excitation in Three-level Systems 2018.5.1 Impurity Photovoltaic Effect 2028.5.2 Up- and Down-conversion of Photons 2068.6 Problems 209Prospects for the Future 211Solutions 215Appendix 235References 239Index 241