Physics of Solar Energy Conversion

Juan Bisquert is a professor ofapplied physics at the UniversitatJaume I de Castello and the fundingdirector of the Institute of AdvancedMaterials at UJI. He earned anMSc in physics in 1985 and a PhDfrom the Universitat de Valenciain 1992. The research work is inperovskite solar cells, semiconductoroptoelectronics, mixed ionicelectronicconductors, and solar fuel converters based onvisible light and semiconductors for water splitting andCO2 reduction. His most well-known work is about themechanisms governing the operation of nanostructuredand solution-processed thin film solar cells. He hasdeveloped insights in the electronic processes in hybridorganic–inorganic solar cells, combining the noveltheory of semiconductor nanostructures, photoelectrochemistry,and systematic experimental demonstration.His contributions produced a broad range of conceptsand characterization methods to analyze the operationof photovoltaic and optoelectronic devices. He is a senioreditor of the Journal of Physical Chemistry Letters. Hehas been distinguished several times in the list of ISIHighly Cited Researchers. Bisquert created nanoGeConferences and is the president of the Fundacio Scito.He wrote a novel of speculative fiction, The CanamelConjecture.

• ContentsPreface........................................................................................................................................................................xvAcknowledgments....................................................................................................................................................xviiAuthor.......................................................................................................................................................................xixChapter 1 Introduction to Energy Devices...............................................................................................................1References...............................................................................................................................................9PART I Equilibrium Concepts and KineticsChapter 2 Electrostatic and Thermodynamic Potentials of Electrons in Materials...............................................132.1 Electrostatic Potential..................................................................................................................132.2 Energies of Free Electrons and Holes.......................................................................................... 142.3 Potential Energy of the Electrons in the Semiconductor............................................................. 172.4 The Vacuum Level....................................................................................................................... 172.5 The Fermi Level and the Work Function....................................................................................202.6 The Chemical Potential of Electrons........................................................................................... 212.7 Potential Step of a Dipole Layer or a Double Layer....................................................................232.8 Origin of Surface Dipoles............................................................................................................242.9 The Volta Potential......................................................................................................................252.10 Equalization of Fermi Levels of Two Electronic Conductors in Contact....................................272.11 Equilibration of Metal Junctions and the Contact Potential Difference......................................282.12 Equilibrium across the Semiconductor Junction.........................................................................29General References............................................................................................................................... 31References............................................................................................................................................. 31Chapter 3 Voltage, Capacitors, and Batteries.........................................................................................................333.1 The Voltage in the Device...........................................................................................................333.2 Anode and Cathode.....................................................................................................................343.3 Applied Voltage and Potential Difference...................................................................................353.4 The Capacitor..............................................................................................................................373.5 Measurement of the Capacitance.................................................................................................383.6 Energy Storage in the Capacitor..................................................................................................403.7 Electrochemical Systems: Structure of the Metal/Solution Interface..........................................403.8 Electrode Potential and Reference Electrodes.............................................................................423.9 Redox Potential in Electrochemical Cells...................................................................................443.10 Electrochemical and Physical Scales of Electron Energy in Material Systems..........................453.11 Changes of Electrolyte Levels with pH.......................................................................................463.12 Principles of Electrochemical Batteries.......................................................................................473.13 Capacity and Energy Content......................................................................................................503.14 Practical Electrochemical Batteries............................................................................................. 513.14.1 Zinc-Silver Battery.......................................................................................................... 513.14.2 Sodium-Sulfur Battery....................................................................................................523.15 Li-Ion Battery.............................................................................................................................. 53General References...............................................................................................................................57References.............................................................................................................................................57Chapter 4 Work Functions and Injection Barriers.................................................................................................594.1 Injection to Vacuum in Thermionic Emission.............................................................................594.2 Richardson–Dushman Equation..................................................................................................604.3 Kelvin Probe Method.................................................................................................................. 614.4 Photoelectron Emission Spectroscopy.........................................................................................634.5 Injection Barriers.........................................................................................................................664.6 Pinning of the Fermi Level and Charge-Neutrality Level...........................................................69General References...............................................................................................................................73References.............................................................................................................................................73Chapter 5 Thermal Distribution of Electrons, Holes, and Ions in Solids............................................................... 755.1 Equilibration of the Electrochemical Potential of Electrons....................................................... 755.2 Configurational Entropy of Weakly Interacting Particles...........................................................765.3 Equilibrium Occupancy of Conduction Band and Valence Band States.....................................765.4 Equilibrium Fermi Level and the Carrier Number in Semiconductors.......................................795.5 Transparent Conducting Oxides.................................................................................................. 815.6 Hot Electrons...............................................................................................................................825.7 Screening.....................................................................................................................................845.8 The Rectifier at Forward and Reverse Voltage............................................................................855.9 Semiconductor Devices as Thermal Machines that Realize Useful Work..................................885.10 Cell Potential in the Lithium Ion Battery....................................................................................905.11 Insertion of Ions: The Lattice Gas Model....................................................................................94General References...............................................................................................................................98References.............................................................................................................................................98Chapter 6 Interfacial Kinetics and Hopping Transitions...................................................................................... 1016.1 Principle of Detailed Balance.................................................................................................... 1016.2 Form of the Transition Rates.....................................................................................................1046.3 Kinetics of Localized States: Shockley-Read-Hall Recombination Model...............................1066.4 Reorganization Effects in Charge Transfer: The Marcus Model............................................... 1076.5 Polaron Hopping........................................................................................................................ 1126.6 Rate of Electrode Reaction: Butler-Volmer Equation................................................................ 1156.6.1 Availability of Electronic Species................................................................................. 1166.6.2 Availability of Redox Species........................................................................................ 1166.6.3 The Kinetic Constant for Charge Transfer.................................................................... 1176.7 Electron Transfer at Metal-Semiconductor Contact..................................................................1206.8 Electron Transfer at the Semiconductor/Electrolyte Interface.................................................. 121General References.............................................................................................................................126References...........................................................................................................................................127Chapter 7 The Chemical Capacitance.................................................................................................................. 1317.1 Carrier Accumulation and Energy Storage in the Chemical Capacitance................................. 1317.2 Localized Electronic States in Disordered Materials and Surface States................................. 1337.3 Chemical Capacitance of a Single State.................................................................................... 1357.4 Chemical Capacitance of a Broad DOS.................................................................................... 1367.5 Filling a DOS with Carriers: The Voltage and the Conductivity.............................................. 1387.6 Chemical Capacitance of Li Intercalation Materials................................................................. 1397.7 Chemical Capacitance of Graphene.......................................................................................... 140General References............................................................................................................................. 142References........................................................................................................................................... 143Chapter 8 The Density of States in Disordered Inorganic and Organic Conductors........................................... 1458.1 Capacitive and Reactive Current in Cyclic Voltammetry.......................................................... 1458.2 Kinetic Effects in CV Response................................................................................................ 1498.3 The Exponential DOS in Amorphous Semiconductors.............................................................1508.4 The Exponential DOS in Nanocrystalline Metal Oxides.......................................................... 1528.5 Basic Properties of Organic Layers........................................................................................... 1568.6 The Gaussian DOS.................................................................................................................... 160General References............................................................................................................................. 162References........................................................................................................................................... 163Chapter 9 Planar and Nanostructured Semiconductor Junctions......................................................................... 1679.1 Structure of the Schottky Barrier at a Metal/Semiconductor Contacts..................................... 1679.2 Changes of the Schottky Barrier by the Applied Voltage.......................................................... 1689.3 Properties of the Planar Depletion Layer.................................................................................. 1709.4 Mott–Schottky Plots.................................................................................................................. 1719.5 Capacitance Response of Defect Levels and Surface States..................................................... 1729.6 Semiconductor Electrodes and the Flatband Potential.............................................................. 1739.7 Changes of Redox Level and Band Unpinning.......................................................................... 1769.8 Inversion and Accumulation Layer............................................................................................ 1809.9 Heterojunctions.......................................................................................................................... 1819.10 Effect of Voltage on Highly Doped Nanocrystalline Semiconductors...................................... 1839.11 Homogeneous Carrier Accumulation in Low-Doped Nanocrystalline Semiconductors........... 188General References............................................................................................................................. 192References........................................................................................................................................... 192PART II Foundations of Carrier TransportChapter 10 Carrier Injection and Drift Transport.................................................................................................. 19710.1 Transport by Drift in the Electrical Field.................................................................................. 19710.2 Injection at Contacts.................................................................................................................. 19810.3 The Metal-Insulator-Metal Model.............................................................................................20210.4 The Time-of-Flight Method......................................................................................................205General References.............................................................................................................................206References...........................................................................................................................................206Chapter 11 Diffusion Transport.............................................................................................................................20911.1 Diffusion in the Random Walk Model......................................................................................20911.2 Macroscopic Diffusion Equation............................................................................................... 21111.3 The Diffusion Length................................................................................................................ 21211.4 Chemical Diffusion Coefficient and the Thermodynamic Factor............................................. 213General References............................................................................................................................. 215References........................................................................................................................................... 215Chapter 12 Drift-Diffusion Transport.................................................................................................................... 21712.1 General Transport Equation in Terms of Electrochemical Potential......................................... 21712.2 The Transport Resistance.......................................................................................................... 21712.3 The Einstein Relation................................................................................................................ 21912.4 Drift-Diffusion Equations..........................................................................................................22012.5 Ambipolar Diffusion Transport................................................................................................22112.6 Relaxation of Injected Charge..................................................................................................22212.7 Transient Current in Insulator Layers.......................................................................................22312.8 Modeling Transport Problems..................................................................................................224General References.............................................................................................................................227References...........................................................................................................................................227Chapter 13 Transport in Disordered Media...........................................................................................................22913.1 Multiple Trapping and Hopping Transport...............................................................................22913.2 Transport by Hopping in a Single Level...................................................................................23113.3 Trapping Factors in the Kinetic Constants...............................................................................23313.4 Two-Level (Single-Trap) Model................................................................................................23513.5 Multiple Trapping in Exponential DOS....................................................................................23713.6 Activated Transport in a Gaussian DOS...................................................................................23713.7 Multiple Trapping in the Time Domain....................................................................................23913.8 Hopping Conductivity...............................................................................................................24113.9 The Transport Energy...............................................................................................................24213.10 Variable Range Hopping...........................................................................................................243General References.............................................................................................................................245References...........................................................................................................................................245Chapter 14 Thin Film Transistors..........................................................................................................................24914.1 Organic Thin Film Transistors.................................................................................................24914.2 Carrier Density in the Channel.................................................................................................25014.3 Determination of the DOS in Thin Film Transistor Configuration..........................................25214.4 Current-Voltage Characteristics................................................................................................25514.5 The Mobility in Disordered Semiconductors............................................................................25714.6 Electrochemical Transistor.......................................................................................................258General References.............................................................................................................................259References...........................................................................................................................................259Chapter 15 Space-Charge-Limited Transport........................................................................................................26315.1 Space-Charge-Limited Current................................................................................................26315.2 Injected Carrier Capacitance in SCLC.....................................................................................26515.3 Space Charge in Double Injection............................................................................................267General References.............................................................................................................................269References...........................................................................................................................................269Chapter 16 Impedance and Capacitance Spectroscopies....................................................................................... 27116.1 Frequency Domain Measurements...........................................................................................27116.2 Dielectric Relaxation Functions................................................................................................27216.3 Resistance and Capacitance in Equivalent Circuit Models.......................................................27416.4 Relaxation in Time Domain......................................................................................................27916.5 Universal Properties of the Frequency-Dependent Conductivity..............................................28116.6 Electrode Polarization...............................................................................................................283General References.............................................................................................................................284References...........................................................................................................................................284PART III Radiation, Light, and SemiconductorsChapter 17 Blackbody Radiation and Light...........................................................................................................28917.1 Photons and Light......................................................................................................................28917.2 Spread and Direction of Radiation............................................................................................28917.3 Color and Photometry................................................................................................................ 29117.4 Blackbody Radiation.................................................................................................................29317.5 The Planck Spectrum................................................................................................................29417.6 The Energy Density of The Distribution of Photons in Blackbody Radiation..........................29517.7 The Photon and Energy Fluxes in Blackbody Radiation...........................................................29717.8 The Solar Spectrum...................................................................................................................299General References.............................................................................................................................302References...........................................................................................................................................302Chapter 18 Light Absorption, Carrier Recombination, and Luminescence...........................................................30518.1 Absorption of Incident Radiation..............................................................................................30518.2 Luminescence and Energy Transfer..........................................................................................30718.3 The Quantum Efficiency........................................................................................................... 31018.4 The Recombination of Carriers in Semiconductors.................................................................. 31118.5 Recombination Lifetime............................................................................................................ 314General References............................................................................................................................. 316References........................................................................................................................................... 316Chapter 19 Optical Transitions in Organic and Inorganic Semiconductors.......................................................... 31919.1 Light Absorption in Inorganic Solids........................................................................................ 31919.2 Free Carrier Phenomena............................................................................................................32319.3 Excitons.....................................................................................................................................32519.4 Quantum Dots...........................................................................................................................32819.5 Organic Molecules and Materials..............................................................................................33019.6 The CT Band in Organic Blends and Heterojunctions.............................................................. 333General References............................................................................................................................. 336References........................................................................................................................................... 336PART IV Photovoltaic Principles and Solar Energy ConversionChapter 20 Fundamental Model of a Solar Cell....................................................................................................34320.1 Majority Carrier Injection Mechanisms....................................................................................34320.2 Majority Carrier Devices...........................................................................................................34420.3 Minority Carrier Devices..........................................................................................................34520.4 Fundamental Properties of a Solar Cell.....................................................................................34620.5 Physical Properties of Selective Contacts in Solar Cells...........................................................348General References............................................................................................................................. 351References........................................................................................................................................... 351Chapter 21 Recombination Current in the Semiconductor Diode......................................................................... 35321.1 Dark Equilibrium of Absorption and Emission of Radiation.................................................... 35321.2 Recombination Current............................................................................................................. 35521.3 Dark Characteristics of Diode Equation.................................................................................... 35621.4 Light-Emitting Diodes............................................................................................................... 35721.5 Dye Sensitization and Molecular Diodes...................................................................................360General References.............................................................................................................................363References...........................................................................................................................................363Chapter 22 Radiative Equilibrium in a Semiconductor.........................................................................................36522.1 Utilization of Solar Photons......................................................................................................36522.2 Fundamental Radiative Carrier Lifetime..................................................................................36822.3 Radiative Emission of a Semiconductor Layer..........................................................................36922.4 Photons at Nonzero Chemical Potential.................................................................................... 370General References............................................................................................................................. 373References........................................................................................................................................... 373Chapter 23 Reciprocity Relations in Solar Cells and Fundamental Limits to the Photovoltage ........................... 37523.1 The Reciprocity between LED and Photovoltaic Performance Parameters.............................. 37523.2 Factors Determining the Photovoltage...................................................................................... 37823.3 External Radiative Efficiency....................................................................................................38223.4 Photon Recycling.......................................................................................................................38323.5 Radiative Cooling in EL and Photoluminescence.....................................................................38623.6 Reciprocity of Absorption and Emission in a CT Band............................................................387General References............................................................................................................................. 391References...........................................................................................................................................392Chapter 24 Charge Separation and Material Limits to the Photovoltage...............................................................39524.1 Light Absorption........................................................................................................................39524.2 Charge Separation.....................................................................................................................39524.3 Materials Limits to the Photovoltage.........................................................................................398General References.............................................................................................................................403References...........................................................................................................................................404Chapter 25 Operation of Solar Cells and Fundamental Limits to Their Performance..........................................40725.1 Current-Voltage Characteristics.................................................................................................40725.2 Power Conversion Efficiency.....................................................................................................40825.3 Analysis of FF........................................................................................................................... 41025.4 Shockley–Queisser Efficiency Limits........................................................................................ 41225.5 Practical Solar Cells Efficiency Limits...................................................................................... 413General References............................................................................................................................. 419References........................................................................................................................................... 419Chapter 26 Charge Collection in Solar Cells......................................................................................................... 42126.1 Introduction to Charge Collection Properties............................................................................ 42126.2 Charge Collection Distance.......................................................................................................42226.3 General Modeling Equations.....................................................................................................42426.4 The Boundary Conditions.........................................................................................................42526.4.1 Charge Extraction Boundary Condition........................................................................42626.4.2 Blocking Boundary Condition.......................................................................................42726.4.3 Generalized Boundary Conditions................................................................................42826.5 A Photovoltaic Model with Diffusion and Recombination........................................................42926.6 The Gärtner Model.................................................................................................................... 43326.7 Diffusion-Recombination and Collection in the Space-Charge Region.................................... 43526.8 Solar Cell Simulation................................................................................................................. 43626.9 Classification of Solar Cells....................................................................................................... 43726.10 Measuring and Reporting Solar Cell Efficiencies..................................................................... 439General References.............................................................................................................................442References...........................................................................................................................................442Chapter 27 Spectral Harvesting and Photoelectrochemical Conversion................................................................44527.1 Conversion of Photon Frequencies for Solar Energy Harvesting..............................................44527.2 Tandem Solar Cells....................................................................................................................44827.3 Solar Fuel Generation................................................................................................................450General References.............................................................................................................................456References...........................................................................................................................................456Appendix................................................................................................................................................................. 459Index........................................................................................................................................................................463