Introduction to the Physics and Electrochemistry of Semiconductors

Maheshwar Sharon, (Retd. Professor IIT Bombay) Ph.D. from Leicester University UK, Post-Doctoral Research from Bolton Institute of Technology U.K., is Director of NSN Research Centre for Nanotechnology & Bionanotechnology and Technical Director of Monad Nanotech also Adjunct-Professor University of Mumbai. His specializations are Electrochemistry (Photoelectrochemistry & Battery), Solid State Chemistry (Diffusion & Electrical Properties), Superconductivity, Carbon (fullerenes, nanocarbon, low band gap semiconductor etc) and Energy: Photovoltaic wet & dry Solar Cells. For his contribution to carbon he was awarded "Bangur Award". He has five patents, five books and 173 publications to his credit. He has research collaboration with Chubu University of Japan.

• Foreword xvPreface xvii1 Our Universe and the Sun 11.1 Formation of the Universe 11.2 Formation of Stars 21.2.1 Formation of Energy in the Sun 31.2.2 Description of the Sun 61.2.3 Transfer of Solar Rays through the Ozone Layer 61.2.4 Transfer of Solar Layers through Other Layers 71.2.5 Effect of Position of the Sun vis-à-vis the Earth 81.2.6 Distribution of Solar Energy 81.2.7 Solar Intensity Calculation 81.3 Summary 12Reference 122 Solar Energy and Its Applications 132.1 Introduction to a Semiconductor 142.2 Formation of a Compound 142.2.1 A Classical Approach 142.2.2 Why Call It a Band and Not a Level? 152.2.3 Quantum Chemistry Approach 172.2.3.1 Wave Nature of an Electron in a Fixed Potential 172.2.3.2 Wave Nature of an Electron under a Periodically Changing Potential 192.2.3.3 Bloch’s Solution to the Wave Function of Electrons under Variable Potentials 202.2.3.3 Concept of a Forbidden Gap in a Material 222.2.4 Band Model to Explain Conductivity in Solids 252.2.4.1 Which of the Total Electrons Will Accept the External Energy for Their Excitation? 262.2.4.2 Density of States 282.2.4.3 How Do We Find the Numbers of Electrons in These Bands? 292.2.5 Useful Deductions 312.2.5.1 Extrinsic Semiconductor 332.2.5.2 Role of Dopants in the Semiconductor 362.3 Quantum Theory Approach to Explain the Effect of Doping 372.3.1 A Mathematical Approach to Understanding This Problem 392.3.2 Representation of Various Energy Levels in a Semiconductor 402.4 Types of Carriers in a Semiconductor 422.4.1 Majority and Minority Carriers 422.4.2 Direction of Movement of Carriers in a Semiconductor 422.5 Nature of Band Gaps in Semiconductors 442.6 Can the Band Gap of a Semiconductor Be Changed? 452.7 Summary 47Further Reading 473 Theory of Junction Formation 493.1 Flow of Carriers across the Junction 493.1.1 Why Do Carriers Flow across an Interface When n- and p-Type Semiconductors Are Joined Together with No Air Gap? 493.1.2 Does the Vacuum Level Remain Unaltered, and What Is the Significance of Showing a Bend in the Diagram? 523.1.3 Why Do We Draw a Horizontal or Exponential Line to Represent the Energy Level in the Semiconductor with a Long Line? 523.1.4 What Are the Impacts of Migration of Carriers toward the Interface? 523.2 Representing Energy Levels Graphically 543.3 Depth of Charge Separation at the Interface of n- and p-Type Semiconductors 563.4 Nature of Potential at the Interface 563.4.1 Does Any Current Flow through the Interface? 563.4.2 Effect of Application of External Potential to the p:n Junction Formed by the Two Semiconductors 583.4.2.1 Flow of Carriers from n-Type to p-Type 593.4.2.2 Flow of Carriers from p-Type to n-Type 603.4.2.3 Flow of Current due to Holes 603.4.2.4 Flow of Current due to Electrons 613.4.3 What Would Happen If Negative Potential Were Applied to a p-Type Semiconductor? 623.4.3.1 Flow of Majority Carriers from p- to n-Type Semiconductors 633.4.3.2 Flow of Majority Carriers from n- to p-Type 633.4.3.3 Flow of Minority Carrier from p- to n-Type Semiconductors 643.4.3.3 Flow of Minority Carriers from n- to p-Type Semiconductors 643.5 Expression for Saturation (or Exchange) Current I0 673.5.1 Factors on Which Diffusion Length Depends 703.6 Contact Potential θ 713.7 Width of the Space Charge Region 753.8 Metal–Schottky Junction 813.8.1 Current–Voltage Characteristics for Metal–Schottky Junctions 843.8.2 Saturation Current for Metal–Schottky Junctions 873.9 Effect of Light on p:n Junctions 903.10 Factors to Be Considered in Illuminating the p:n Junction 943.10.1 Grids for Collecting the Charges 953.10.2 Ohmic Contact on the Back Side of the Junction 963.11 Types of p:n Junctions 973.12 A Photoelectrochemical Cell 973.13 Summary 100Further Reading 1004 Effect of Illumination of a PEC Cell 1014.1 Effect of Light on the Depletion Layer of the Semiconductor—Electrolyte Junction 1014.1.1 Origin of Photopotential 1024.1.2 Origin of Photocurrent 1044.2 The Fate of Photogenerated Carriers 1054.3 Magnitude of the Photocurrent 1064.4 Gartner Model for Photocurrent 1084.4.1 Photocurrent due to Photogenerated Carriers in the Space Charge Region 1094.4.2 Photocurrent due to Photogenerated Carriers in the Diffusion Region 1094.4.3 Application of the Gartner Model 1114.4.4 When α Is Constant 1124.4.5 When w Is Kept Constant 1154.4.6 Lifetime of Carriers and Their Mobility 1184.5 Carrier Recombination 1184.5.1 Significance of the Lifetime of Carriers 1194.5.2 Effect of Recombination Center on the Magnitude of Photocurrent 1204.5.3 Origin of Recombination Centers 1214.6 A Mathematical Treatment for the Lifetime of Carriers 1224.7 Effect of Illumination on Fermi Level-Quasi Fermi Level 1244.8 Solar Cell Performance 1304.9 Current—Voltage Characteristics of a Solar Cell 1354.10 The Equivalent Circuit of a Solar Cell 1384.11 Solar Cell Efficiency 1394.11.1 Absorption Efficiency αλ 1414.11.2 Generation Efficiency gλ 1414.11.3 Collection Efficiency Cλ 1414.11.4 Current Efficiency Qλ 1424.11.5 Voltage Factor and Fill Factor 1424.11.6 Analytical Methods for J-V Characteristics of a Solar Cell 1444.11.7 Back Wall Cell 1454.12 Ohmic Contact 1474.13 Defects in Solids 1484.13.1 Bulk Defects 1504.13.2 Surface Structure 1504.14 Summary 153Further Reading 153References 1545 Electrochemistry of the Metal–Electrolyte Interface 1575.1 What Is a Metal? 1585.2 What Is the Structure of Electrolyte and Water Molecules in an Aqueous Solution? 1585.3 What Happens When a Metal Is Immersed in Solution? 1605.4 Existence of a Double Layer Near the Metal–Electrolyte Interface 1605.5 Influence of Concentration of Electrolyte on Helmholtz and Diffusion Potentials 1665.6 Impact of Charge Accumulation at Various Regions 1665.7 Electron Transfer and Its Impact on Potential Barrier 1715.8 Butler–Volmer Approach to Electrochemical Reaction 1815.9 Significance of Symmetry Factor β 1915.10 Electrochemical Corrosion at the Metal–Electrolyte Interface 1945.11 Summary 199Further Reading 199References 1996 Electrochemistry of the Semiconductor–Electrolyte Interface 2016.1 Difference between Metal and Semiconductor 2016.1.1 Hydration of Electrolytes 2026.1.2 Effect of Hydrogen Bond 2036.2 Gaussian Distribution of the Potential Energy of Electrolytes 2036.3 Capacitance at the Semiconductor–Electrolyte Interface 2126.4 Stability of the Semiconductor 2166.5 Modifying the Surface of Low Band Gap Materials 2236.6 Summary 225References 2257 Impedance Studies 2277.1 Types of AC Circuits 2287.2 Significance of Vector Analysis 2307.3 Impedance Measurement Techniques 2347.3.1 Audio Frequency Bridges 2347.3.2 Transformer Ratio Arms Bridge 2367.3.3 Berberian–Cole Bridge Technique 2377.3.4 Potentiostatic Measurement 2387.3.5 Oscilloscope Technique 2397.4 AC Impedance Plots and Data Analysis 2427.4.1 Nyquist Plot 2427.4.2 Bode Plot 2437.4.3 Randles Plot 2447.5 Equivalent Circuit Representation of a Simple System 2457.6 Equivalent Circuit Representation for Electro-chemical Systems 2467.7 Procedure for Running an Experiment 2487.8 Semiconductor Interface 2507.9 Summary 253Further Reading 254References 2548 Photoelectrochemical Solar Cell 2578.1 Classification of Photoelectrochemical CellsBased on the Energetics of the Reactions 2638.2 Solar Chargeable Battery 2648.3 Electrolyte-(Ohmic)-Semiconductor-Electrolyte (Schottky) Junction 2738.3.1 On the Illuminated Side of Fe2O3 2758.3.2 On the Dark Side of the Semiconductor—Compartment II 2768.4 Synthesis of Value-Added Products 2808.5 Summary 283References 2839 Photoeletrochromism 2859.1 Photochromic Glasses 2879.2 Electrochromism 2919.2.1 Types of Chromogenic Materials 2929.2.2 Electrolytes 2949.2.3 Electrode Materials 2949.2.4 Reservoir 2949.3 Electrochromic Devices and Their Applications 2959.4 Imaging Employing a Semiconductor Photo-electrode 3019.4.1 Image-Forming Step 3029.4.2 Image-Vanishing Step 3029.5 Summary 303References 30310 Dye-Sensitized Solar Cells 30510.1 The Dye-Sensitized Cell 30610.2 Flexible Polymer Solar Cell 30810.3 Summary 310References 310Index 313