An Introduction to the Physics and Electrochemistry of Semiconductors

Foreword xv Preface xvii 1 Our Universe and the Sun 1 1.1 Formation of the Universe 1 1.2 Formation of Stars 2 1.2.1 Formation of Energy in the Sun 3 1.2.2 Description of the Sun 6 1.2.3 Transfer of Solar Rays through the Ozone Layer 6 1.2.4 Transfer of Solar Layers through Other Layers 7 1.2.5 Effect of Position of the Sun vis-à-vis the Earth 8 1.2.6 Distribution of Solar Energy 8 1.2.7 Solar Intensity Calculation 8 1.3 Summary 12 Reference 12 2 Solar Energy and Its Applications 13 2.1 Introduction to a Semiconductor 14 2.2 Formation of a Compound 14 2.2.1 A Classical Approach 14 2.2.2 Why Call It a Band and Not a Level? 15 2.2.3 Quantum Chemistry Approach 17 2.2.3.1 Wave Nature of an Electron in a Fixed Potential 17 2.2.3.2 Wave Nature of an Electron under a Periodically Changing Potential 19 2.2.3.3 Bloch’s Solution to the Wave Function of Electrons under Variable Potentials 20 2.2.3.3 Concept of a Forbidden Gap in a Material 22 2.2.4 Band Model to Explain Conductivity in Solids 25 2.2.4.1 Which of the Total Electrons Will Accept the External Energy for Their Excitation? 26 2.2.4.2 Density of States 28 2.2.4.3 How Do We Find the Numbers of Electrons in These Bands? 29 2.2.5 Useful Deductions 31 2.2.5.1 Extrinsic Semiconductor 33 2.2.5.2 Role of Dopants in the Semiconductor 36 2.3 Quantum Theory Approach to Explain the Effect of Doping 37 2.3.1 A Mathematical Approach to Understanding This Problem 39 2.3.2 Representation of Various Energy Levels in a Semiconductor 40 2.4 Types of Carriers in a Semiconductor 42 2.4.1 Majority and Minority Carriers 42 2.4.2 Direction of Movement of Carriers in a Semiconductor 42 2.5 Nature of Band Gaps in Semiconductors 44 2.6 Can the Band Gap of a Semiconductor Be Changed? 45 2.7 Summary 47 Further Reading 47 3 Theory of Junction Formation 49 3.1 Flow of Carriers across the Junction 49 3.1.1 Why Do Carriers Flow across an Interface When n- and p-Type Semiconductors Are Joined Together with No Air Gap? 49 3.1.2 Does the Vacuum Level Remain Unaltered, and What Is the Significance of Showing a Bend in the Diagram? 52 3.1.3 Why Do We Draw a Horizontal or Exponential Line to Represent the Energy Level in the Semiconductor with a Long Line? 52 3.1.4 What Are the Impacts of Migration of Carriers toward the Interface? 52 3.2 Representing Energy Levels Graphically 54 3.3 Depth of Charge Separation at the Interface of n- and p-Type Semiconductors 56 3.4 Nature of Potential at the Interface 56 3.4.1 Does Any Current Flow through the Interface? 56 3.4.2 Effect of Application of External Potential to the p:n Junction Formed by the Two Semiconductors 58 3.4.2.1 Flow of Carriers from n-Type to p-Type 59 3.4.2.2 Flow of Carriers from p-Type to n-Type 60 3.4.2.3 Flow of Current due to Holes 60 3.4.2.4 Flow of Current due to Electrons 61 3.4.3 What Would Happen If Negative Potential Were Applied to a p-Type Semiconductor? 62 3.4.3.1 Flow of Majority Carriers from p- to n-Type Semiconductors 63 3.4.3.2 Flow of Majority Carriers from n- to p-Type 63 3.4.3.3 Flow of Minority Carrier from p- to n-Type Semiconductors 64 3.4.3.3 Flow of Minority Carriers from n- to p-Type Semiconductors 64 3.5 Expression for Saturation (or Exchange) Current I0 67 3.5.1 Factors on Which Diffusion Length Depends 70 3.6 Contact Potential θ 71 3.7 Width of the Space Charge Region 75 3.8 Metal–Schottky Junction 81 3.8.1 Current–Voltage Characteristics for Metal–Schottky Junctions 84 3.8.2 Saturation Current for Metal–Schottky Junctions 87 3.9 Effect of Light on p:n Junctions 90 3.10 Factors to Be Considered in Illuminating the p:n Junction 94 3.10.1 Grids for Collecting the Charges 95 3.10.2 Ohmic Contact on the Back Side of the Junction 96 3.11 Types of p:n Junctions 97 3.12 A Photoelectrochemical Cell 97 3.13 Summary 100 Further Reading 100 4 Effect of Illumination of a PEC Cell 101 4.1 Effect of Light on the Depletion Layer of the Semiconductor—Electrolyte Junction 101 4.1.1 Origin of Photopotential 102 4.1.2 Origin of Photocurrent 104 4.2 The Fate of Photogenerated Carriers 105 4.3 Magnitude of the Photocurrent 106 4.4 Gartner Model for Photocurrent 108 4.4.1 Photocurrent due to Photogenerated Carriers in the Space Charge Region 109 4.4.2 Photocurrent due to Photogenerated Carriers in the Diffusion Region 109 4.4.3 Application of the Gartner Model 111 4.4.4 When α Is Constant 112 4.4.5 When w Is Kept Constant 115 4.4.6 Lifetime of Carriers and Their Mobility 118 4.5 Carrier Recombination 118 4.5.1 Significance of the Lifetime of Carriers 119 4.5.2 Effect of Recombination Center on the Magnitude of Photocurrent 120 4.5.3 Origin of Recombination Centers 121 4.6 A Mathematical Treatment for the Lifetime of Carriers 122 4.7 Effect of Illumination on Fermi Level-Quasi Fermi Level 124 4.8 Solar Cell Performance 130 4.9 Current—Voltage Characteristics of a Solar Cell 135 4.10 The Equivalent Circuit of a Solar Cell 138 4.11 Solar Cell Efficiency 139 4.11.1 Absorption Efficiency αλ 141 4.11.2 Generation Efficiency gλ 141 4.11.3 Collection Efficiency Cλ 141 4.11.4 Current Efficiency Qλ 142 4.11.5 Voltage Factor and Fill Factor 142 4.11.6 Analytical Methods for J-V Characteristics of a Solar Cell 144 4.11.7 Back Wall Cell 145 4.12 Ohmic Contact 147 4.13 Defects in Solids 148 4.13.1 Bulk Defects 150 4.13.2 Surface Structure 150 4.14 Summary 153 Further Reading 153 References 154 5 Electrochemistry of the Metal–Electrolyte Interface 157 5.1 What Is a Metal? 158 5.2 What Is the Structure of Electrolyte and Water Molecules in an Aqueous Solution? 158 5.3 What Happens When a Metal Is Immersed in Solution? 160 5.4 Existence of a Double Layer Near the Metal–Electrolyte Interface 160 5.5 Influence of Concentration of Electrolyte on Helmholtz and Diffusion Potentials 166 5.6 Impact of Charge Accumulation at Various Regions 166 5.7 Electron Transfer and Its Impact on Potential Barrier 171 5.8 Butler–Volmer Approach to Electrochemical Reaction 181 5.9 Significance of Symmetry Factor β 191 5.10 Electrochemical Corrosion at the Metal–Electrolyte Interface 194 5.11 Summary 199 Further Reading 199 References 199 6 Electrochemistry of the Semiconductor–Electrolyte Interface 201 6.1 Difference between Metal and Semiconductor 201 6.1.1 Hydration of Electrolytes 202 6.1.2 Effect of Hydrogen Bond 203 6.2 Gaussian Distribution of the Potential Energy of Electrolytes 203 6.3 Capacitance at the Semiconductor–Electrolyte Interface 212 6.4 Stability of the Semiconductor 216 6.5 Modifying the Surface of Low Band Gap Materials 223 6.6 Summary 225 References 225 7 Impedance Studies 227 7.1 Types of AC Circuits 228 7.2 Significance of Vector Analysis 230 7.3 Impedance Measurement Techniques 234 7.3.1 Audio Frequency Bridges 234 7.3.2 Transformer Ratio Arms Bridge 236 7.3.3 Berberian–Cole Bridge Technique 237 7.3.4 Potentiostatic Measurement 238 7.3.5 Oscilloscope Technique 239 7.4 AC Impedance Plots and Data Analysis 242 7.4.1 Nyquist Plot 242 7.4.2 Bode Plot 243 7.4.3 Randles Plot 244 7.5 Equivalent Circuit Representation of a Simple System 245 7.6 Equivalent Circuit Representation for Electro-chemical Systems 246 7.7 Procedure for Running an Experiment 248 7.8 Semiconductor Interface 250 7.9 Summary 253 Further Reading 254 References 254 8 Photoelectrochemical Solar Cell 257 8.1 Classification of Photoelectrochemical Cells Based on the Energetics of the Reactions 263 8.2 Solar Chargeable Battery 264 8.3 Electrolyte-(Ohmic)-Semiconductor-Electrolyte (Schottky) Junction 273 8.3.1 On the Illuminated Side of Fe2O3 275 8.3.2 On the Dark Side of the Semiconductor—Compartment II 276 8.4 Synthesis of Value-Added Products 280 8.5 Summary 283 References 283 9 Photoeletrochromism 285 9.1 Photochromic Glasses 287 9.2 Electrochromism 291 9.2.1 Types of Chromogenic Materials 292 9.2.2 Electrolytes 294 9.2.3 Electrode Materials 294 9.2.4 Reservoir 294 9.3 Electrochromic Devices and Their Applications 295 9.4 Imaging Employing a Semiconductor Photo-electrode 301 9.4.1 Image-Forming Step 302 9.4.2 Image-Vanishing Step 302 9.5 Summary 303 References 303 10 Dye-Sensitized Solar Cells 305 10.1 The Dye-Sensitized Cell 306 10.2 Flexible Polymer Solar Cell 308 10.3 Summary 310 References 310 Index 313