Physics of Solar Cells

Peter Wurfel studied physics at the University of Karlsruhe where he later became Professor. His research activities started with ferroelectric thin films, mostly for pyroelectric infrared detectors. He has a keen interest in the physics of photovoltaics and has more than 25 years research and teaching experience in this field. Uli Wurfel studied physics at the Universities of Freiburg and Heidelberg. He received a PhD from the University of Freiburg in 2006. Since 2009 he is head of the group "dye and organic solar cells" at the Fraunhofer Institute for Solar Energy Systems (ISE) in Freiburg. Besides an ambition to realize low-cost organic solar cells, he is also highly interested in selective contacts and modelling solar cells.

• 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 dΩ 162.1.3 Radiation from a Spherical Surface into the Solid Angle dΩ 192.1.4 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 242.3.1 Air Mass 262.4 Concentration of the Solar Radiation 282.4.1 The Abbé Sine Condition 292.4.2 Geometrical Optics 302.4.3 Concentration of Radiation Using the Sine Condition 312.5 Maximum Efficiency of Solar Energy Conversion 332.6 Problems 393 Semiconductors 413.1 Electrons in Semiconductors 423.1.1 Distribution Function for Electrons 433.1.2 Density of States De(εe) for Electrons 433.1.3 Density of Electrons 483.2 Holes 503.3 Doping 523.4 Quasi-Fermi Distributions 573.4.1 Fermi Energy and Electrochemical Potential 593.4.2 Work Function 633.5 Generation of Electrons and Holes 653.5.1 Absorption of Photons 653.5.2 Generation of Electron–Hole Pairs 693.6 Recombination of Electrons and Holes 713.6.1 Radiative Recombination, Emission of Photons 723.6.2 Nonradiative Recombination 743.6.3 Lifetimes 853.7 Light Emission by Semiconductors 873.7.1 Transition Rates and Absorption Coefficient 883.8 Problems 924 Conversion of Thermal Radiation into Chemical Energy 954.1 Maximum Efficiency for the Production of Chemical Energy 984.2 Shockley–Queisser Limit 1034.3 Problems 1045 Conversion of Chemical Energy into Electrical Energy 1055.1 Transport of Electrons and Holes 1055.1.1 Field Current 1065.1.2 Diffusion Current 1075.1.3 Total Charge Current 1095.2 Separation of Electrons and Holes 1115.3 Diffusion Length of Minority Carriers 1135.4 Dielectric Relaxation 1155.5 Ambipolar Diffusion 1165.6 Dember Effect 1175.7 Mathematical Description 1205.8 Problems 1206 Basic Structure of Solar Cells 1236.1 A Chemical Solar Cell 1236.2 Basic Mechanisms in Solar Cells 1286.3 Dye Solar Cell 1316.4 The pn-Junction 1336.4.1 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 1386.5 pn-Junction with Impurity Recombination, Two-Diode Model 1436.6 Heterojunctions 1476.7 Semiconductor–Metal Contact 1506.7.1 Schottky Contact 1526.7.2 MIS Contact 1536.8 The Role of the Electric Field in Solar Cells 1546.9 Organic Solar Cells 1606.9.1 Excitons 1606.9.2 Structure of Organic Solar Cells 1636.10 Light Emitting Diodes (LED) 1676.11 Problems 1697 Limitations on Energy Conversion in Solar Cells 1717.1 Maximum Efficiency of Solar Cells 1717.2 Efficiency of Solar Cells as a Function of Their Energy Gap 1747.3 The Optimal Silicon Solar Cell 1757.3.1 Light Trapping 1767.4 Thin-film Solar Cells 1817.4.1 Minimal Thickness of a Solar Cell 1827.5 Equivalent Circuit 1837.6 Temperature Dependence of the Open-circuit Voltage 1857.7 Intensity Dependence of the Efficiency 1867.8 Efficiencies of the Individual Energy Conversion Processes 1867.9 Problems 1888 Concepts for Improving the Efficiency of Solar Cells 1898.1 Tandem Cells 1898.1.1 The Electrical Interconnection of Tandem Cells 1938.2 Concentrator Cells 1948.3 Thermophotovoltaic Energy Conversion 1968.4 Impact Ionization 1978.4.1 Hot Electrons from Impact Ionization 2008.4.2 Energy Conversion with Hot Electrons and Holes 2008.5 Two-step Excitation in Three-level Systems 2038.5.1 Impurity Photovoltaic Effect 2038.5.2 Up- and Down-conversion of Photons 2088.6 Problems 2119 Characterization of Solar Cells 2139.1 Spectral Response and Quantum Efficiency 2139.2 Quasi-Steady-State Photoconductance 2189.3 Luminescence 2209.3.1 Homogeneous Distribution of Electrons and Holes 2219.3.2 Inhomogeneous Distribution of Electrons and Holes 2229.3.3 Electroluminescence 2239.3.4 Photoluminescence 2249.3.5 Diffusion Length 2259.3.6 Series Resistance 2289.4 Thermography 2299.5 Light-Beam-Induced Current (LBIC) 2309.6 The Suns-VOC Method 2339.7 Transient Techniques 2379.7.1 Photovoltage Decay 2379.7.2 Transient Absorption 2389.7.3 Charge Carrier Extraction 2409.7.4 CELIV – Charge Extraction by Linearly Increasing Voltage 2419.7.5 Impedance Spectroscopy 241Solutions 245Appendix 263References 267Index 271