Physics of Solar Energy C. Julian Chen Department of Applied Physics and Applied Mathematics Columbia University 2 Contents Preface xvii Gallery xxi Chapter 1: Introduction 1 1.1Solarenergy............................ 1 1.2Gobeyondpetroleum...................... 5 1.3Otherrenewableenergyresources................ 8 1.3.1 Hydroelectricpower................... 9 1.3.2 Windpower........................ 11 1.3.3 Biomassandbioenergy................. 14 1.3.4 Shallowgeothermalenergy............... 19 1.3.5 Deepgeothermalenergy................. 20 1.4Asolarphotovoltaicsprimer................... 22 1.4.1 Birthofmodernsolarcells............... 22 1.4.2 Someconceptsonsolarcells............... 24 1.4.3 Typesofsolarcells.................... 25 1.4.4 Energybalance...................... 26 1.5Abovephysics........................... 27 1.5.1 Economicsofsolarenergy................ 27 1.5.2 Moralequivalenceofwar................ 29 1.5.3 Solar water heaters in other countries . 32 1.5.4 Photovoltaics:towardsgridparity........... 36 Chapter 2: Nature of Solar Radiation 43 2.1Lightaselectromagneticwaves................. 43 2.1.1 Maxwell’sequations................... 44 2.1.2 Vectorpotential..................... 45 2.1.3 Electromagneticwaves.................. 45 2.1.4 Planewaves........................ 46 2.1.5 Polarizationoflight................... 47 2.1.6 Motion of an electron in electric and magnetic fields . 48 2.2Opticsofthinfilms........................ 50 2.2.1 Relative dielectric constant and refractive index . 50 2.2.2 Energyflux:thePoyntingvector............ 52 2.2.3 Fresnelformulae..................... 52 2.3Black-bodyradiation....................... 54 2.3.1 TheRayleigh-Jeanslaw................. 55 2.3.2 Planck formula and Stefan-Boltzmann’s law . 58 ii Contents 2.4Photoelectriceffectandtheconceptofphotons........ 61 2.4.1 Einstein’stheoryofphotons............... 62 2.4.2 Millikan’s experimental verification . .......... 64 2.4.3 Wave-particleduality.................. 65 2.5Einstein’sderivationofblack-bodyformula.......... 66 Chapter 3: Origin of Solar Energy 71 3.1BasicparametersoftheSun................... 72 3.1.1 Distance.......................... 72 3.1.2 Mass............................ 72 3.1.3 Radius........................... 72 3.1.4 Emissionpower...................... 73 3.1.5 Surfacetemperature................... 73 3.1.6 Composition....................... 74 3.2TheKelvin-Helmholtztimescale................ 74 3.3EnergysourceoftheSun.................... 76 3.3.1 The p − p chain...................... 77 3.3.2 Thecarbonchain..................... 78 3.3.3 InternalstructureoftheSun.............. 78 Chapter 4: Tracking Sunlight 81 4.1RotationoftheEarth:latitudeandlongitude......... 81 4.2TheCelestialsphere....................... 82 4.2.1 Coordinate transformation: Cartesian coordinates . 84 4.2.2 Coordinate transformation: spherical trigonometry . 87 4.3Treatmentinsolartime..................... 88 4.3.1 Obliquity and the declination of the Sun . 88 4.3.2 Sunriseandsunsettime................. 90 4.3.3 Direct solar radiation on an arbitrary surface . 91 4.3.4 Directdailysolarradiationenergy........... 92 4.4Treatmentinstandardtime................... 97 4.4.1 Siderealtimeandsolartime............... 98 4.4.2 RightascensionoftheSun............... 99 4.4.3 Time difference originated from obliquity . 100 4.4.4 Aphelionandperihelion.................101 4.4.5 Time difference originated from eccentricity . 101 4.4.6 Equationoftime.....................103 4.4.7 DeclinationoftheSun..................104 4.4.8 Analemma........................105 4.5Solarcalenderandsolarclock..................106 Contents iii 4.5.1 TheColumbiaUniversitysundials...........106 4.5.2 Omnidirectionallens...................107 4.5.3 Thecrystal-ballsundial.................110 4.5.4 Thecrystal-ballsolarcompass.............111 Chapter 5: Interaction of sunlight with Earth 115 5.1Interactionofradiationwithmatter..............115 5.1.1 Absorptivity, reflectivity and transmittivity . 115 5.1.2 Emissivity and Kirchhoff’s law . ..........116 5.1.3 Bouguer-Lambert-Beer’slaw..............116 5.2Interactionofsunlightwithatmosphere............118 5.2.1 The AM1.5 reference solar spectral irradiance . 119 5.2.2 Annualinsolationmap..................121 5.2.3 Clearnessindex......................121 5.2.4 Beamanddiffusesolarradiation............122 5.3PenetrationofsolarenergyintotheEarth...........124 Chapter 6: Thermodynamics of Solar Energy 129 6.1Definitions.............................129 6.2Thefirstlawofthermodynamics................131 6.3Thesecondlawofthermodynamics...............133 6.3.1 TheCarnotcycle.....................133 6.3.2 Thethermodynamictemperature............136 6.3.3 Entropy..........................137 6.4Thethermodynamicfunctions..................138 6.4.1 Freeenergy........................138 6.4.2 Enthalpy.........................139 6.4.3 Gibbsfreeenergy.....................139 6.4.4 Chemicalpotential....................140 6.4.5 Maxwell’srelations....................140 6.5Theidealgas...........................141 6.6Ground-sourceheatpumpandairconditioning........144 6.6.1 PrincipleandtheCarnotlimit.............146 6.6.2 Coefficientofperformance................146 6.6.3 Vapor-compression heat pump and refrigerator . 147 6.6.4 Thegroundheatexchanger...............150 iv Contents Chapter 7: Quantum Transitions 155 7.1Basicsofquantummechanics..................155 7.1.1 Quantum states: energy levels and wavefunctions . 156 7.1.2 Dynamic variables and equation of motion . 157 7.1.3 One-dimensionalpotentialwell.............158 7.1.4 Thehydrogenatom...................160 7.2Many-electronsystems......................162 7.2.1 Single-electronapproximation..............163 7.2.2 Direct observation of quantum states by STM . 164 7.2.3 Quantum states of molecules: HOMO and LUMO . 164 7.2.4 Quantumstatesofananocrystal............165 7.2.5 Semiconductors: valence band and conduction band . 166 7.3TheGoldenRule.........................167 7.3.1 Time-dependent perturbation by a periodic disturbance168 7.3.2 Golden Rule for continuous spectrum . 170 7.3.3 Principleofdetailedbalance...............171 7.4Interactionswithphotons....................171 Chapter 8: pn-Junction 175 8.1 p-type and n-typesemiconductors...............175 8.2 Formation of a pn-junction...................176 8.2.1 Space charge at a pn-junction..............178 8.2.2 Quasi-Fermilevels....................180 8.3 Analysis of pn-junctions.....................181 8.3.1 Effectofbiasvoltage...................183 8.3.2 Lifetimeofexcessminoritycarriers...........183 8.3.3 Diffusion length of excess minority carriers . 184 8.3.4 Junctioncurrent.....................184 8.3.5 TheShockleyequation..................186 Chapter 9: Semiconductor Solar Cells 189 9.1Basicconcepts..........................190 9.1.1 Generationofelectricpower...............191 9.1.2 Thesolarcellequation..................191 9.1.3 Maximumpowerandfillfactor.............193 9.2TheShockley-Queisserlimit...................195 9.2.1 Theultimateefficiency..................196 9.2.2 Roleofrecombinationtime...............198 9.2.3 Adetailed-balancetreatment..............198 9.2.4 Nominalefficiency....................201 Contents v 9.2.5 The Shockley-Queisser efficiency limit . 201 9.2.6 EfficiencylimitforAM1.5radiation..........202 9.3Nonradiativerecombinationprocesses.............203 9.3.1 Augerrecombination...................204 9.3.2 Trap-staterecombination................205 9.3.3 Surface-staterecombination...............205 9.4Anti-reflectioncoatings......................206 9.4.1 Matrixmethod......................207 9.4.2 Single-layeranti-reflectioncoating...........210 9.4.3 Double-layeranti-reflectioncoatings..........211 9.5Crystallinesiliconsolarcells...................213 9.5.1 Productionofpuresilicon................213 9.5.2 Solarcelldesignandprocessing.............214 9.5.3 Modulefabrication....................216 9.6Thin-filmsolarcells.......................217 9.6.1 CdTesolarcells......................217 9.6.2 CIGSsolarcells......................218 9.6.3 Amorphoussiliconthin-filmsolarcells.........218 9.7Tandemsolarcells........................219 Chapter 10: Solar Electrochemistry 225 10.1Physicsofphotosynthesis....................225 10.1.1Chlorophyll........................226 10.1.2ATP:theuniversalenergycurrencyoflife. .228 10.1.3 NADPH and NADP+ ..................229 10.1.4TheCalvincycle.....................229 10.1.5C4plantsversusC3plants...............230 10.1.6Chloroplast........................231 10.1.7Efficiencyofphotosynthesis...............231 10.2Artificialphotosynthesis.....................233 10.3Geneticallyengineeredalgae...................233 10.4Dye-sensitizedsolarcells.....................234 10.5Bilayerorganicsolarcells....................236 Chapter 11: Solar Thermal Energy 241 11.1Earlysolarthermalapplications.................241 11.2SolarHeatCollectors.......................244 11.2.1Selectiveabsorptionsurface...............244 11.2.2Flat-platecollectors...................249 vi Contents 11.2.3All-glassvacuum-tubecollectors............252 11.2.4Thermosiphonsolarheatcollectors...........255 11.2.5 High-pressure vacuum-tube collectors . 256 11.3Solarwaterheaters........................257 11.3.1 System with thermosiphon solar heat collectors . 258 11.3.2 System with pressurized heat-exchange coils . 258 11.3.3 System with a separete heat-exchange tank . 258 11.4Solarthermalpowersystems..................259 11.4.1Parabolictroughconcentrator..............260 11.4.2Centralreceiverwithheliostats.............261 11.4.3Paraboloidaldishconcentrator.............262