Introduction to Semiconductor Physics and Devices

✍ Scribed by Mykhaylo Evstigneev

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 325
• Category: Library

✦ Synopsis

This classroom-tested textbook provides a self-contained one-semester course in semiconductor physics and devices that is ideal preparation for students to enter burgeoning quantum industries. Unlike other textbooks on semiconductor device physics, it provides a brief but comprehensive introduction to quantum physics and statistical physics, with derivations and explanations of the key facts that are suitable for second-year undergraduates, rather than simply postulating the main results. The book is structured into three parts, each of which can be covered in around ten lectures. The first part covers fundamental background material such as quantum and statistical physics, and elements of crystallography and band theory of solids. Since this provides a vital foundation for the rest of the text, concepts are explained and derived in more detail than in comparable texts. For example, the concepts of measurement and collapse of the wave function, which are typically omitted, are presented in this text in language accessible to second-year students. The second part covers semiconductors in and out of equilibrium, and gives details which are not commonly presented, such as a derivation of the density of states using dimensional analysis, and calculation of the concentration of ionized impurities from the grand canonical distribution. Special attention is paid to the solution of Poisson’s equation, a topic that is feared by many undergraduates but is brought back down to earth by techniques and analogies from first-year physics. Finally, in the third part, the material in parts 2 and 3 is applied to describe simple semiconductor devices, including the MOSFET, the Schottky and PN-junction diodes, and optoelectronic devices. With a wide range of exercises, this textbook is readily adoptable for an undergraduate course on semiconductor physics devices, and with its emphasis on consolidating and applying knowledge of fundamental physics, it will leave students in engineering and the physical sciences well prepared for a future where quantum industries proliferate.

✦ Table of Contents

Preface
Contents
Part I Fundamental Physics
1 Principles of Quantum Mechanics
1.1 Why Quantum Mechanics?
1.2 Wave–Particle Duality
1.3 Wavelength of a Free Particle in Terms of Its Energy
1.4 Energy Quantization
1.5 Radiation Spectrum of Hydrogen
1.6 The Wave Function
1.7 The Wave Function of a Free Particle
1.8 Schrödinger's Equation
1.8.1 Time-Dependent Schrödinger's Equation
1.8.2 Time-Independent Schrödinger's Equation
1.9 Probabilistic Interpretation and the Collapse of the Wave Function
1.10 Measurable and Unmeasurable in Quantum Mechanics
1.11 Electron States in a Hydrogen Atom
1.12 Spin
1.13 Degeneracy
1.14 Indistinguishability of Quantum Particles
1.15 Spin-Statistics Theorem
1.16 Pauli's Exclusion Principle
1.17 Problems
1.17.1 Solved Problems
1.17.2 Practice Problems
1.17.3 Solutions
2 Crystal Structure of Solids
2.1 Periodic Table of Elements
2.2 Chemical Bonding
2.3 Crystal Lattices
2.3.1 Atomic Order in Solids
2.3.2 Bravais Lattices
2.3.3 Unit Cell, Primitive Cell, and Crystal Basis
2.3.4 Volume Density and Atomic Packing Fraction
2.4 Basic Cubic Structures
2.5 Formation of Diamond Structure
2.6 Miller Indices
2.6.1 Determination of Miller Indices
2.6.2 Miller Indices for Cubic Structures
2.7 Imperfections and Impurities in Solids
2.8 Problems
2.8.1 Solved Problems
2.8.2 Practice Problems
2.8.3 Solutions
3 Equilibrium Statistical Mechanics
3.1 Microstates and Macrostates
3.2 Thermal Equilibrium
3.3 Postulate of Equal A Priori Probabilities
3.4 Grand Canonical Distribution
3.5 Fermi-Dirac Distribution
3.6 Boltzmann Approximation
3.7 Fermi Energy at Low Temperatures
3.8 Problems
3.8.1 Solved Problems
3.8.2 Practice Problems
3.8.3 Solutions
4 Band Theory of Solids
4.1 Bloch's Theorem
4.2 Energy Bands
4.2.1 Physical Origin of the Energy Bands
4.2.2 The First Brillouin Zone
Brillouin Zones
One-Dimensional Crystal
Band Gap
The Energy-Momentum Diagrams in Three Dimensions
Quasimomentum
4.2.3 Phase Velocity vs. Group Velocity
Phase Velocity
Group Velocity
4.2.4 Bloch Oscillations
4.3 Conduction Types of Solids
4.3.1 Band Filling and Electrical Conductivity
4.3.2 Metals and Semimetals
4.3.3 Dielectrics and Semiconductors
4.4 Conduction and Valence Bands
4.5 Holes
4.6 Effective Mass Tensor
4.7 Problems
4.7.1 Solved Problems
4.7.2 Practice Problems
4.7.3 Solutions
Part II Semiconductors in and out of Equilibrium
5 Semiconductors in Equilibrium
5.1 Density of States
5.2 Equilibrium Carrier Concentration
5.3 Energy Probability Distribution
5.4 Density of States Effective Mass vs. Conductivity Effective Mass
5.4.1 Density of States Effective Mass
5.4.2 Conductivity Effective Mass
Electrons
Holes
5.4.3 Thermal Velocity
5.5 Intrinsic Semiconductors
5.6 Doping and Extrinsic Semiconductors
5.7 Impurity Energy Levels
5.8 Statistics of Donors and Acceptors
5.9 Mass Action Law
5.10 Charge Neutrality Equation
5.11 Ionization Regimes
5.11.1 Complete Ionization
5.11.2 Intrinsic Regime
5.11.3 Carrier Concentration in a Semiconductor with One Type of Doping at Not Too High Temperatures
5.11.4 Electron Freeze-Out Regime
5.12 Numerical Determination of Fermi Energy and Carrier Concentrations
5.13 Problems
5.13.1 Solved Problems
5.13.2 Practice Problems
5.13.3 Solutions
6 Carrier Concentration and Electric Potential
6.1 Electron and Hole Concentrations in a Non-uniform Electric Potential
6.2 Poisson's Equation
6.3 Approximate Solution of Poisson's Equation
6.3.1 Problem Formulation
6.3.2 Debye Screening
6.3.3 Depletion Approximation
6.3.4 Validity Range of the Depletion Approximation
6.4 Band Diagrams and Band Bending
6.5 Electric Potential in a Semiconductor from Poisson's Equation
6.5.1 Exact Solution of Poisson's Equation
6.5.2 Numerical Results
6.6 Problems
6.6.1 Solved Problems
6.6.2 Practice Problems
6.6.3 Solutions
7 Generation–Recombination Processes
7.1 Recombination Mechanisms
7.2 Charge Carrier Dynamics
7.2.1 Generation and Recombination Rates
7.2.2 Recombination Time Approximation
7.3 Radiative Recombination
7.4 Auger Recombination
7.5 Shockley-Read-Hall (SRH) Recombination
7.5.1 Electron and Hole Capture and Emission by the Traps
7.5.2 The Principle of Detailed Balance
7.5.3 The Net SRH Recombination Rate
7.5.4 SRH Recombination Time
7.6 Surface Recombination
7.7 Quasi-Fermi Energies
7.8 Problems
7.8.1 Solved Problems
7.8.2 Practice Problems
7.8.3 Solutions
8 Carrier Transport
8.1 Flux and Electric Current Density
8.2 Diffusion Current
8.3 Drift Current
8.4 Conductivity and Resistivity
8.5 Current–Voltage Measurements
8.5.1 Photoconductivity
8.5.2 Hall Effect
8.6 Temperature and Doping Level Dependence of Mobility
8.7 Einstein's Relation
8.8 Continuity Equation
8.9 Problems
8.9.1 Solved Problems
8.9.2 Practice Problems
8.9.3 Solutions
Part III Semiconductor Devices
9 Metal–Semiconductor Contact
9.1 Reasons to Study
9.2 Energy Band Diagram
9.3 SCR Capacitance
9.4 Ohmic Contact
9.5 Rectification in a Metal–Semiconductor Contact
9.5.1 Metal/n-Type Semiconductor Junction
Qualitative Considerations
9.5.2 Reverse Saturation Current Density of a Schottky Diode
9.5.3 Metal/p-Type Semiconductor Junction
9.6 Non-ideality Effects
9.7 Problems
9.7.1 Solved Problems
9.7.2 Practice Problems
9.7.3 Solutions
10 Metal–Oxide–Semiconductor Field Effect Transistor (MOSFET)
10.1 MOSFET Schematics and Operation Principle
10.2 Qualitative Description of MOSFET I-V Curve
10.3 Quantitative Description of a MOSFET I-V Curve
10.4 Determination of the Threshold Voltage
10.4.1 Energy Band Diagram of a MOS Structure at Zero Gate Voltage
10.4.2 Energy Band Diagram of a MOS Structure for Non-zero Gate Voltage
10.4.3 Oxide Voltage
10.4.4 Flat-Band Voltage
10.4.5 Threshold Voltage
10.5 Capacitance–Voltage Measurements
10.6 Problems
10.6.1 Solved Problems
10.6.2 Practice Problems
10.6.3 Solutions
11 PN Junction Diode
11.1 The Structure of a pn Junction
11.2 The Energy Band Diagram of a pn Junction at Zero Bias
11.3 PN Junction Under an External Bias
11.4 SCR Capacitance
11.5 Current–Voltage Relation of a pn Junction Diode
11.5.1 Charge Carrier Concentrations Near the Boundaries of the SCR
11.5.2 Current–Voltage Relation of an Ideal pn Junction Diode
11.5.3 Current Densities in a pn Diode
11.5.4 SCR Recombination Current
11.6 Problems
11.6.1 Solved Problems
11.6.2 Practice Problems
11.6.3 Solutions
12 Optoelectronic Devices
12.1 Solar Cells (SCs)
12.1.1 SC Operation
12.1.2 Spectral Irradiance (Spectral Intensity)
12.1.3 Light Absorption
12.1.4 SC Current–Voltage Relation
12.2 Light-Emitting Diodes (LEDs)
12.2.1 LED Operation
12.2.2 LED Spectrum
12.2.3 LED Efficiency
12.2.4 Increasing the LED Efficiency
12.3 Semiconductor Lasers
12.3.1 Stimulated Emission and Einstein's Coefficients
12.3.2 Generation of Light
12.3.3 Semiconductor Laser Operation
The Structure of a Semiconductor Laser
Threshold Current
Laser Spectrum
12.4 Problems
12.4.1 Solved Problems
12.4.2 Practice Problems
12.4.3 Solutions
Appendices
A.1 A Crash Course in Complex Numbers
A.2 Proof of Bloch's Theorem
A.3 Properties of Si, Ge, and GaAs
A.4 Evaluation of Exponential Integrals
A.5 Planck's Radiation Law
Index