The Physics of Solar Energy Conversion

<p>Research on advanced energy conversion devices such as solar cells has intensified in the last two decades. A broad landscape of candidate materials and devices were discovered and systematically studied for effective solar energy conversion and utilization. New concepts have emerged forming a rather powerful picture embracing the mechanisms and limitation to efficiencies of different types of devices. <strong><em>The Physics of Solar Energy Conversion</em></strong> introduces the main physico-chemical principles that govern the operation of energy devices for energy conversion and storage, with a detailed view of the principles of solar energy conversion using advanced materials.</p><p>Key Features include:</p><ul> <li>Highlights recent rapid advances with the discovery of perovskite solar cells and their development.</li> <li>Analyzes the properties of organic solar cells, lithium ion batteries, light emitting diodes and the semiconductor materials for hydrogen production by water splitting.</li> <li>Embraces concepts from nanostructured and highly disordered materials to lead halide perovskite solar cells </li> <li>Takes a broad perspective and comprehensively addresses the fundamentals so that the reader can apply these and assess future developments and technologies in the field.</li> <li>Introduces basic techniques and methods for understanding the materials and interfaces that compose operative energy devices such as solar cells and solar fuel converters.</li> </ul> <p><strong>Contents</strong></p><p>Preface........................................................................................................................................................................xv</p><p>Acknowledgments....................................................................................................................................................xvii</p><p>Author.......................................................................................................................................................................xix</p><p>Chapter 1 Introduction to Energy Devices...............................................................................................................1</p><p>References...............................................................................................................................................9</p><p>PART I Equilibrium Concepts and Kinetics</p><p>Chapter 2 Electrostatic and Thermodynamic Potentials of Electrons in Materials...............................................13</p><p>2.1 Electrostatic Potential..................................................................................................................13</p><p>2.2 Energies of Free Electrons and Holes.......................................................................................... 14</p><p>2.3 Potential Energy of the Electrons in the Semiconductor............................................................. 17</p><p>2.4 The Vacuum Level....................................................................................................................... 17</p><p>2.5 The Fermi Level and the Work Function....................................................................................20</p><p>2.6 The Chemical Potential of Electrons........................................................................................... 21</p><p>2.7 Potential Step of a Dipole Layer or a Double Layer....................................................................23</p><p>2.8 Origin of Surface Dipoles............................................................................................................24</p><p>2.9 The Volta Potential......................................................................................................................25</p><p>2.10 Equalization of Fermi Levels of Two Electronic Conductors in Contact....................................27</p><p>2.11 Equilibration of Metal Junctions and the Contact Potential Difference......................................28</p><p>2.12 Equilibrium across the Semiconductor Junction.........................................................................29</p><p>General References............................................................................................................................... 31</p><p>References............................................................................................................................................. 31</p><p>Chapter 3 Voltage, Capacitors, and Batteries.........................................................................................................33</p><p>3.1 The Voltage in the Device...........................................................................................................33</p><p>3.2 Anode and Cathode.....................................................................................................................34</p><p>3.3 Applied Voltage and Potential Difference...................................................................................35</p><p>3.4 The Capacitor..............................................................................................................................37</p><p>3.5 Measurement of the Capacitance.................................................................................................38</p><p>3.6 Energy Storage in the Capacitor..................................................................................................40</p><p>3.7 Electrochemical Systems: Structure of the Metal/Solution Interface..........................................40</p><p>3.8 Electrode Potential and Reference Electrodes.............................................................................42</p><p>3.9 Redox Potential in Electrochemical Cells...................................................................................44</p><p>3.10 Electrochemical and Physical Scales of Electron Energy in Material Systems..........................45</p><p>3.11 Changes of Electrolyte Levels with pH.......................................................................................46</p><p>3.12 Principles of Electrochemical Batteries.......................................................................................47</p><p>3.13 Capacity and Energy Content......................................................................................................50</p><p>3.14 Practical Electrochemical Batteries............................................................................................. 51</p><p>3.14.1 Zinc-Silver Battery.......................................................................................................... 51</p><p>3.14.2 Sodium-Sulfur Battery....................................................................................................52</p><p>3.15 Li-Ion Battery.............................................................................................................................. 53</p><p>General References...............................................................................................................................57</p><p>References.............................................................................................................................................57</p><p>Chapter 4 Work Functions and Injection Barriers.................................................................................................59</p><p>4.1 Injection to Vacuum in Thermionic Emission.............................................................................59</p><p>4.2 Richardson–Dushman Equation..................................................................................................60</p><p>4.3 Kelvin Probe Method.................................................................................................................. 61</p><p>4.4 Photoelectron Emission Spectroscopy.........................................................................................63</p><p>4.5 Injection Barriers.........................................................................................................................66</p><p>4.6 Pinning of the Fermi Level and Charge-Neutrality Level...........................................................69</p><p>General References...............................................................................................................................73</p><p>References.............................................................................................................................................73</p><p>Chapter 5 Thermal Distribution of Electrons, Holes, and Ions in Solids............................................................... 75</p><p>5.1 Equilibration of the Electrochemical Potential of Electrons....................................................... 75</p><p>5.2 Configurational Entropy of Weakly Interacting Particles...........................................................76</p><p>5.3 Equilibrium Occupancy of Conduction Band and Valence Band States.....................................76</p><p>5.4 Equilibrium Fermi Level and the Carrier Number in Semiconductors.......................................79</p><p>5.5 Transparent Conducting Oxides.................................................................................................. 81</p><p>5.6 Hot Electrons...............................................................................................................................82</p><p>5.7 Screening.....................................................................................................................................84</p><p>5.8 The Rectifier at Forward and Reverse Voltage............................................................................85</p><p>5.9 Semiconductor Devices as Thermal Machines that Realize Useful Work..................................88</p><p>5.10 Cell Potential in the Lithium Ion Battery....................................................................................90</p><p>5.11 Insertion of Ions: The Lattice Gas Model....................................................................................94</p><p>General References...............................................................................................................................98</p><p>References.............................................................................................................................................98</p><p>Chapter 6 Interfacial Kinetics and Hopping Transitions...................................................................................... 101</p><p>6.1 Principle of Detailed Balance.................................................................................................... 101</p><p>6.2 Form of the Transition Rates.....................................................................................................104</p><p>6.3 Kinetics of Localized States: Shockley-Read-Hall Recombination Model...............................106</p><p>6.4 Reorganization Effects in Charge Transfer: The Marcus Model............................................... 107</p><p>6.5 Polaron Hopping........................................................................................................................ 112</p><p>6.6 Rate of Electrode Reaction: Butler-Volmer Equation................................................................ 115</p><p>6.6.1 Availability of Electronic Species................................................................................. 116</p><p>6.6.2 Availability of Redox Species........................................................................................ 116</p><p>6.6.3 The Kinetic Constant for Charge Transfer.................................................................... 117</p><p>6.7 Electron Transfer at Metal-Semiconductor Contact..................................................................120</p><p>6.8 Electron Transfer at the Semiconductor/Electrolyte Interface.................................................. 121</p><p>General References.............................................................................................................................126</p><p>References...........................................................................................................................................127</p><p>Chapter 7 The Chemical Capacitance.................................................................................................................. 131</p><p>7.1 Carrier Accumulation and Energy Storage in the Chemical Capacitance................................. 131</p><p>7.2 Localized Electronic States in Disordered Materials and Surface States................................. 133</p><p>7.3 Chemical Capacitance of a Single State.................................................................................... 135</p><p>7.4 Chemical Capacitance of a Broad DOS.................................................................................... 136</p><p>7.5 Filling a DOS with Carriers: The Voltage and the Conductivity.............................................. 138</p><p>7.6 Chemical Capacitance of Li Intercalation Materials................................................................. 139</p><p>7.7 Chemical Capacitance of Graphene.......................................................................................... 140</p><p>General References............................................................................................................................. 142</p><p>References........................................................................................................................................... 143</p><p>Chapter 8 The Density of States in Disordered Inorganic and Organic Conductors........................................... 145</p><p>8.1 Capacitive and Reactive Current in Cyclic Voltammetry.......................................................... 145</p><p>8.2 Kinetic Effects in CV Response................................................................................................ 149</p><p>8.3 The Exponential DOS in Amorphous Semiconductors.............................................................150</p><p>8.4 The Exponential DOS in Nanocrystalline Metal Oxides.......................................................... 152</p><p>8.5 Basic Properties of Organic Layers........................................................................................... 156</p><p>8.6 The Gaussian DOS.................................................................................................................... 160</p><p>General References............................................................................................................................. 162</p><p>References........................................................................................................................................... 163</p><p>Chapter 9 Planar and Nanostructured Semiconductor Junctions......................................................................... 167</p><p>9.1 Structure of the Schottky Barrier at a Metal/Semiconductor Contacts..................................... 167</p><p>9.2 Changes of the Schottky Barrier by the Applied Voltage.......................................................... 168</p><p>9.3 Properties of the Planar Depletion Layer.................................................................................. 170</p><p>9.4 Mott–Schottky Plots.................................................................................................................. 171</p><p>9.5 Capacitance Response of Defect Levels and Surface States..................................................... 172</p><p>9.6 Semiconductor Electrodes and the Flatband Potential.............................................................. 173</p><p>9.7 Changes of Redox Level and Band Unpinning.......................................................................... 176</p><p>9.8 Inversion and Accumulation Layer............................................................................................ 180</p><p>9.9 Heterojunctions.......................................................................................................................... 181</p><p>9.10 Effect of Voltage on Highly Doped Nanocrystalline Semiconductors...................................... 183</p><p>9.11 Homogeneous Carrier Accumulation in Low-Doped Nanocrystalline Semiconductors........... 188</p><p>General References............................................................................................................................. 192</p><p>References........................................................................................................................................... 192</p><p>PART II Foundations of Carrier Transport</p><p>Chapter 10 Carrier Injection and Drift Transport.................................................................................................. 197</p><p>10.1 Transport by Drift in the Electrical Field.................................................................................. 197</p><p>10.2 Injection at Contacts.................................................................................................................. 198</p><p>10.3 The Metal-Insulator-Metal Model.............................................................................................202</p><p>10.4 The Time-of-Flight Method......................................................................................................205</p><p>General References.............................................................................................................................206</p><p>References...........................................................................................................................................206</p><p>Chapter 11 Diffusion Transport.............................................................................................................................209</p><p>11.1 Diffusion in the Random Walk Model......................................................................................209</p><p>11.2 Macroscopic Diffusion Equation............................................................................................... 211</p><p>11.3 The Diffusion Length................................................................................................................ 212</p><p>11.4 Chemical Diffusion Coefficient and the Thermodynamic Factor............................................. 213</p><p>General References............................................................................................................................. 215</p><p>References........................................................................................................................................... 215</p><p>Chapter 12 Drift-Diffusion Transport.................................................................................................................... 217</p><p>12.1 General Transport Equation in Terms of Electrochemical Potential......................................... 217</p><p>12.2 The Transport Resistance.......................................................................................................... 217</p><p>12.3 The Einstein Relation................................................................................................................ 219</p><p>12.4 Drift-Diffusion Equations..........................................................................................................220</p><p>12.5 Ambipolar Diffusion Transport................................................................................................221</p><p>12.6 Relaxation of Injected Charge..................................................................................................222</p><p>12.7 Transient Current in Insulator Layers.......................................................................................223</p><p>12.8 Modeling Transport Problems..................................................................................................224</p><p>General References.............................................................................................................................227</p><p>References...........................................................................................................................................227</p><p>Chapter 13 Transport in Disordered Media...........................................................................................................229</p><p>13.1 Multiple Trapping and Hopping Transport...............................................................................229</p><p>13.2 Transport by Hopping in a Single Level...................................................................................231</p><p>13.3 Trapping Factors in the Kinetic Constants...............................................................................233</p><p>13.4 Two-Level (Single-Trap) Model................................................................................................235</p><p>13.5 Multiple Trapping in Exponential DOS....................................................................................237</p><p>13.6 Activated Transport in a Gaussian DOS...................................................................................237</p><p>13.7 Multiple Trapping in the Time Domain....................................................................................239</p><p>13.8 Hopping Conductivity...............................................................................................................241</p><p>13.9 The Transport Energy...............................................................................................................242</p><p>13.10 Variable Range Hopping...........................................................................................................243</p><p>General References.............................................................................................................................245</p><p>References...........................................................................................................................................245</p><p>Chapter 14 Thin Film Transistors..........................................................................................................................249</p><p>14.1 Organic Thin Film Transistors.................................................................................................249</p><p>14.2 Carrier Density in the Channel.................................................................................................250</p><p>14.3 Determination of the DOS in Thin Film Transistor Configuration..........................................252</p><p>14.4 Current-Voltage Characteristics................................................................................................255</p><p>14.5 The Mobility in Disordered Semiconductors............................................................................257</p><p>14.6 Electrochemical Transistor.......................................................................................................258</p><p>General References.............................................................................................................................259</p><p>References...........................................................................................................................................259</p><p>Chapter 15 Space-Charge-Limited Transport........................................................................................................263</p><p>15.1 Space-Charge-Limited Current................................................................................................263</p><p>15.2 Injected Carrier Capacitance in SCLC.....................................................................................265</p><p>15.3 Space Charge in Double Injection............................................................................................267</p><p>General References.............................................................................................................................269</p><p>References...........................................................................................................................................269</p><p>Chapter 16 Impedance and Capacitance Spectroscopies....................................................................................... 271</p><p>16.1 Frequency Domain Measurements...........................................................................................271</p><p>16.2 Dielectric Relaxation Functions................................................................................................272</p><p>16.3 Resistance and Capacitance in Equivalent Circuit Models.......................................................274</p><p>16.4 Relaxation in Time Domain......................................................................................................279</p><p>16.5 Universal Properties of the Frequency-Dependent Conductivity..............................................281</p><p>16.6 Electrode Polarization...............................................................................................................283</p><p>General References.............................................................................................................................284</p><p>References...........................................................................................................................................284</p><p>PART III Radiation, Light, and Semiconductors</p><p>Chapter 17 Blackbody Radiation and Light...........................................................................................................289</p><p>17.1 Photons and Light......................................................................................................................289</p><p>17.2 Spread and Direction of Radiation............................................................................................289</p><p>17.3 Color and Photometry................................................................................................................ 291</p><p>17.4 Blackbody Radiation.................................................................................................................293</p><p>17.5 The Planck Spectrum................................................................................................................294</p><p>17.6 The Energy Density of The Distribution of Photons in Blackbody Radiation..........................295</p><p>17.7 The Photon and Energy Fluxes in Blackbody Radiation...........................................................297</p><p>17.8 The Solar Spectrum...................................................................................................................299</p><p>General References.............................................................................................................................302</p><p>References...........................................................................................................................................302</p><p>Chapter 18 Light Absorption, Carrier Recombination, and Luminescence...........................................................305</p><p>18.1 Absorption of Incident Radiation..............................................................................................305</p><p>18.2 Luminescence and Energy Transfer..........................................................................................307</p><p>18.3 The Quantum Efficiency........................................................................................................... 310</p><p>18.4 The Recombination of Carriers in Semiconductors.................................................................. 311</p><p>18.5 Recombination Lifetime............................................................................................................ 314</p><p>General References............................................................................................................................. 316</p><p>References........................................................................................................................................... 316</p><p>Chapter 19 Optical Transitions in Organic and Inorganic Semiconductors.......................................................... 319</p><p>19.1 Light Absorption in Inorganic Solids........................................................................................ 319</p><p>19.2 Free Carrier Phenomena............................................................................................................323</p><p>19.3 Excitons.....................................................................................................................................325</p><p>19.4 Quantum Dots...........................................................................................................................328</p><p>19.5 Organic Molecules and Materials..............................................................................................330</p><p>19.6 The CT Band in Organic Blends and Heterojunctions.............................................................. 333</p><p>General References............................................................................................................................. 336</p><p>References........................................................................................................................................... 336</p><p>PART IV Photovoltaic Principles and Solar Energy Conversion</p><p>Chapter 20 Fundamental Model of a Solar Cell....................................................................................................343</p><p>20.1 Majority Carrier Injection Mechanisms....................................................................................343</p><p>20.2 Majority Carrier Devices...........................................................................................................344</p><p>20.3 Minority Carrier Devices..........................................................................................................345</p><p>20.4 Fundamental Properties of a Solar Cell.....................................................................................346</p><p>20.5 Physical Properties of Selective Contacts in Solar Cells...........................................................348</p><p>General References............................................................................................................................. 351</p><p>References........................................................................................................................................... 351</p><p>Chapter 21 Recombination Current in the Semiconductor Diode......................................................................... 353</p><p>21.1 Dark Equilibrium of Absorption and Emission of Radiation.................................................... 353</p><p>21.2 Recombination Current............................................................................................................. 355</p><p>21.3 Dark Characteristics of Diode Equation.................................................................................... 356</p><p>21.4 Light-Emitting Diodes............................................................................................................... 357</p><p>21.5 Dye Sensitization and Molecular Diodes...................................................................................360</p><p>General References.............................................................................................................................363</p><p>References...........................................................................................................................................363</p><p>Chapter 22 Radiative Equilibrium in a Semiconductor.........................................................................................365</p><p>22.1 Utilization of Solar Photons......................................................................................................365</p><p>22.2 Fundamental Radiative Carrier Lifetime..................................................................................368</p><p>22.3 Radiative Emission of a Semiconductor Layer..........................................................................369</p><p>22.4 Photons at Nonzero Chemical Potential.................................................................................... 370</p><p>General References............................................................................................................................. 373</p><p>References........................................................................................................................................... 373</p><p>Chapter 23 Reciprocity Relations in Solar Cells and Fundamental Limits to the Photovoltage ........................... 375</p><p>23.1 The Reciprocity between LED and Photovoltaic Performance Parameters.............................. 375</p><p>23.2 Factors Determining the Photovoltage...................................................................................... 378</p><p>23.3 External Radiative Efficiency....................................................................................................382</p><p>23.4 Photon Recycling.......................................................................................................................383</p><p>23.5 Radiative Cooling in EL and Photoluminescence.....................................................................386</p><p>23.6 Reciprocity of Absorption and Emission in a CT Band............................................................387</p><p>General References............................................................................................................................. 391</p><p>References...........................................................................................................................................392</p><p>Chapter 24 Charge Separation and Material Limits to the Photovoltage...............................................................395</p><p>24.1 Light Absorption........................................................................................................................395</p><p>24.2 Charge Separation.....................................................................................................................395</p><p>24.3 Materials Limits to the Photovoltage.........................................................................................398</p><p>General References.............................................................................................................................403</p><p>References...........................................................................................................................................404</p><p>Chapter 25 Operation of Solar Cells and Fundamental Limits to Their Performance..........................................407</p><p>25.1 Current-Voltage Characteristics.................................................................................................407</p><p>25.2 Power Conversion Efficiency.....................................................................................................408</p><p>25.3 Analysis of FF........................................................................................................................... 410</p><p>25.4 Shockley–Queisser Efficiency Limits........................................................................................ 412</p><p>25.5 Practical Solar Cells Efficiency Limits...................................................................................... 413</p><p>General References............................................................................................................................. 419</p><p>References........................................................................................................................................... 419</p><p>Chapter 26 Charge Collection in Solar Cells......................................................................................................... 421</p><p>26.1 Introduction to Charge Collection Properties............................................................................ 421</p><p>26.2 Charge Collection Distance.......................................................................................................422</p><p>26.3 General Modeling Equations.....................................................................................................424</p><p>26.4 The Boundary Conditions.........................................................................................................425</p><p>26.4.1 Charge Extraction Boundary Condition........................................................................426</p><p>26.4.2 Blocking Boundary Condition.......................................................................................427</p><p>26.4.3 Generalized Boundary Conditions................................................................................428</p><p>26.5 A Photovoltaic Model with Diffusion and Recombination........................................................429</p><p>26.6 The Gärtner Model.................................................................................................................... 433</p><p>26.7 Diffusion-Recombination and Collection in the Space-Charge Region.................................... 435</p><p>26.8 Solar Cell Simulation................................................................................................................. 436</p><p>26.9 Classification of Solar Cells....................................................................................................... 437</p><p>26.10 Measuring and Reporting Solar Cell Efficiencies..................................................................... 439</p><p>General References.............................................................................................................................442</p><p>References...........................................................................................................................................442</p><p>Chapter 27 Spectral Harvesting and Photoelectrochemical Conversion................................................................445</p><p>27.1 Conversion of Photon Frequencies for Solar Energy Harvesting..............................................445</p><p>27.2 Tandem Solar Cells....................................................................................................................448</p><p>27.3 Solar Fuel Generation................................................................................................................450</p><p>General References.............................................................................................................................456</p><p>References...........................................................................................................................................456</p><p>Appendix................................................................................................................................................................. 459</p><p>Index........................................................................................................................................................................463</p>