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1 Problems of the Energy Economy 1.1 Energy economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Estimate of the maximum reserves of fossil energy . . . . . . . . . . . . . . 1.3 The greenhouse effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 The temperature of the earth . . . . . . . . . . . . . . . . . . . . . . 2 Photons 2.1 Black-body radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 .1 Photon density nl in a cavity (Planck's law of radiation) . . . . . . . 2.1.2 Energy current through an area dA into the solid angle di2 . . . . . . 2.1.3 Radiation from a spherical surface into the solid angle dC2 . . . . . . 2.1.4 Radiation from a surface element into a hemisphere (Stefan-Boltzmann radiation law) . . . . . . . . . . . . . . . . . . . 2.2 Kirchhoff's law of radiation for non-black bodies . . . . . . . . . . . . . . 2.2.1 Absorption by semiconductors . . . . . . . . . . . . . . . . . . . . . 2.3 The solar spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 AirMass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Concentration of the solar radiation . . . . . . . . . . . . . . . . . . . . . . 2.4.1 The Abbe sine condition . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Geometrical optics . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Concentration of radiation using the sine condition . . . . . . . . . . 2.5 Maximum efficiency of solar energy conversion . . . . . . . . . . . . . . . 3 Semiconductors 3.1 Electrons in serniconductors . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Distribution function for electrons . . . . . . . . . . . . . . . . . . . 3.1.2 Density of states D,(&,) for electrons . . . . . . . . . . . . . . . . . 3.1.3 Density of electrons . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Quasi-Fermi distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Fermi energy and electrochemical potential . . . . . . . . . . . . . . 3.4.2 Work function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Generation of electrons and holes . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Absorption of photons . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Generation of electron-hole pairs . . . . . . . . . . . . . . . . . . . 3.6 Recombination of electrons and holes . . . . . . . . . . . . . . . . . . . . . 3.6.1 Radiative recombination. emission of photons . . . . . . . . . . . . . 3.6.2 Non-radiative recombination . . . . . . . . . . . . . . . . . . . . . . 3.6.3 Lifetimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Light emission by semiconductors . . . . . . . . . . . . . . . . . . . . . . 3.7.1 Transition rates and absorption coefficient . . . . . . . . . . . . . . . 4 Conversion of Thermal Radiation into Chemical Energy 4.1 Maximum efficiency for the production of chemical energy . . . . . . . . . 5 Conversion of Chemical Energy into Electrical Energy 5.1 Transport of electrons and holes . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Field current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Diffusion current . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Total charge current . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Separation of electrons and holes . . . . . . . . . . . . . . . . . . . . . . . 5.3 Diffusion length of minority carriers . . . . . . . . . . . . . . . . . . . . . 5.4 Dielectric relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Ambipolar diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Dember effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Mathematical description . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Basic Structure of Solar Cells 6.1 A chemical solar cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Basic mechanisms in solar cells . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Dye solar cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 The pn-junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Electrochernical equilibrium of electrons in a pn-junction in the dark . 6.4.2 Potential distribution across a pn-junction . . . . . . . . . . . . . . . 6.4.3 Current-voltage characteristic of the pn-junction . . . . . . . . . . . 6.5 pn-junction with impurity recombination. two-diode model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Hetero-junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 Semiconductor-metal contact . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.1 Schottky contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.2 MIScontact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8 The role of the electric field in solar cells . . . . . . . . . . . . . . . . . . 7 Limitations on Energy Conversion in Solar Cells 137 7.1 Maximum efficiency of solar cells . . . . . . . . . . . . . . . . . . . . . . . 7.2 Efficiency of solar cells as a function of their energy gap . . . . . . . . . . . 7.3 The optimal silicon solar cell . . . . . . . . . . . . . . . . . . . . . 7.3.1 Light trapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Thin-film solar cells . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Minimal thickness of a solar cell . . . . . . . . . . . . . . . . . . . . 7.5 Equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Temperature dependence of the open-circuit voltage . . . . . . . . . . . . . 7.7 Intensity dependence of the efficiency . . . . . . . . . . . . . . . . . . . . . 7.8 Efficiencies of the individual energy conversion processes . . . . . . . . . . 8 Concepts for Improving the Efficiency of Solar Cells 155 8.1 Tandem cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 The electrical interconnection of tandem cells . . . . . . . . . . . . . 8.2 Concentrator cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Thermo-photovoltaic energy conversion . . . . . . . . . . . . . . . . . . . 8.4 Impact ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Hot electrons from impact ionization . . . . . . . . . . . . . . . . . 8.4.2 Energy conversion with hot electrons and holes . . . . . . . . . . . 8.5 Two-step excitation in three-level systems . . . . . . . . . . . . . . . . . 8.5.1 Impurity photovoltaic effect . . . . . . . . . . . . . . . . . . . . . . 8.5.2 Up- and down-conversion of photons . . . . . . . . . . . . . . . . . 9 Prospects for the Future 177 Appendix 181 Index 183 |
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