Principles of Semiconductor Devices

Short table of contents

Introduction

0.1. The semiconductor industry

0.2. Purpose and goal of the Text

0.3. The primary focus: CMOS integrated circuits

0.4. Applications illustrated with computer-generated animations

Chapter 1: Review of Modern Physics

1.1. Introduction

1.2. Quantum mechanics

1.2.1. Particle-wave duality

1.2.2. The photo-electric effect

1.2.3. Blackbody radiation

1.2.4. The Bohr model

1.2.5. Schrödinger's equation

1.2.6. Pauli exclusion principle

1.2.7. Electronic configuration of the elements

1.3. Electromagnetic theory

1.3.1. Gauss's law

1.3.2. Poisson's equation

1.4. Statistical thermodynamics

1.4.1. Thermal equilibrium

1.4.2. Laws of thermodynamics

1.4.3. The thermodynamic identity

1.4.4. The Fermi energy

1.4.5. Some useful thermodynamics results

Chapter 2: Semiconductor fundamentals

2.1. Introduction

2.2. Crystals and crystal structures

2.2.1. Bravais lattices

2.2.2. Miller indices, crystal planes and directions

2.2.3. Common semiconductor crystal structures

2.2.4. Growth of semiconductor crystals

2.3. Energy bands

2.3.1. Free electron model

2.3.2. Periodic potentials

2.3.3. Energy bands of semiconductors

2.3.4. Metals, insulators and semiconductors

2.3.5. Electrons and holes in semiconductors

2.3.6. The effective mass concept

2.3.7. Detailed description of the effective mass

2.4. Density of states

2.4.1. Calculation of the density of states

2.4.2. Density of states in 1, 2 and 3 dimensions

2.5. Carrier distribution functions

2.5.1. The Fermi-Dirac distribution function

2.5.2. Example

2.5.3. Impurity distribution functions

2.5.4. Other distribution functions and comparison

2.5.5. Derivation of the Fermi-Dirac distribution function

2.6. Carrier densities

2.6.1. General discussion

2.6.2. Calculation of the Fermi integral

2.6.3. Intrinsic semiconductors

2.6.4. Doped semiconductors

2.6.5. Non-equilibrium carrier densities

2.7. Carrier transport

2.7.1. Carrier drift

2.7.2. Carrier mobility

2.7.3. Velocity saturation

2.7.4. Carrier diffusion

2.7.5. The Hall effect

2.8. Carrier recombination and generation

2.8.1. Simple recombination-generation model

2.8.2. Band-to-band recombination

2.8.3. Trap-assisted recombination

2.8.4. Surface recombination

2.8.5. Auger recombination

2.8.6. Generation due to light

2.9. Continuity equation

2.9.1. Derivation

2.9.2. The diffusion equation

2.9.3. Steady state solution to the diffusion equation

2.10. The drift-diffusion model

2.11 Semiconductor thermodynamics

2.11.1. Thermal equilibrium

2.11.2. Thermodynamic identity

2.11.3. The Fermi energy

2.11.4. Example: an ideal electron gas

2.11.5. Quasi-Fermi energies

2.11.6. Energy loss in recombination processes

2.11.7. Thermo-electric effects in semiconductors

2.11.8. The thermoelectric cooler

2.11.9. The "hot-probe" experiment

Chapter 3: Metal-Semiconductor Junctions

3.1. Introduction

3.2. Structure and principle of operation

3.2.1. Structure

3.2.2. Flatband diagram and built-in potential

3.2.3. Thermal equilibrium

3.2.4. Forward and reverse bias

3.3. Electrostatic analysis

3.3.1. General discussion - Poisson's equation

3.3.2. Full depletion approximation

3.3.3. Full depletion analysis

3.3.4. Junction capacitance

3.3.5. Schottky barrier lowering

3.3.6. Derivation of Schottky barrier lowering

3.3.7. Solution to Poisson's equation

3.4. Schottky diode current

3.4.1. Diffusion current

3.4.2. Thermionic emission current

3.4.3. Tunneling

3.4.4. Derivation of the Metal-Semiconductor junction current

3.5 Metal-Semiconductor contacts

3.5.1. Ohmic contacts

3.5.2. Tunnel contacts

3.5.3. Annealed and alloyed contacts

3.5.4. Contact resistance to a thin semiconductor layer

3.6 Metal-Semiconductor Field Effect Transistors (MESFETs)

3.7 Schottky diode with an interfacial layer

3.8 Other unipolar junctions

3.8.1. The n-n⁺ homojunction

3.8.2. The n-n⁺ heterojunction

3.8.3. Currents across a n-n⁺ heterojunction

3.9 Currents through insulators

3.9.1. Fowler-Nordheim tunneling

3.9.2. Poole-Frenkel emission

3.9.3. Space charge limited current

3.9.4. Ballistic transport in insulators

Chapter 4: p-n Junctions

4.1. Introduction

4.2. Structure and principle of operation

4.2.1. Flatband diagram

4.2.2. Thermal equilibrium

4.2.3. The built-in potential

4.2.4. Forward and reverse bias

4.3. Electrostatic analysis of a p-n diode

4.3.1. General discussion - Poisson's equation

4.3.2. The full-depletion approximation

4.3.3. Full depletion analysis

4.3.4. Junction capacitance

4.3.5. The linearly graded p-n diode

4.3.6. The abrupt p-i-n diode

4.3.7. Solution to Poisson's equation

4.3.8. The heterojunction p-n diode

4.4. The p-n diode current

4.4.1. General discussion

4.4.2. The ideal diode current

4.4.3. Recombination-generation current

4.4.4. I-V characteristics of real p-n diodes

4.4.5. The diffusion capacitance

4.4.6. High injection effects

4.4.7. p-n heterojunction current

4.5. Reverse bias breakdown

4.5.1. General breakdown characteristics

4.5.2. Edge effects

4.5.3. Avalanche breakdown

4.5.4. Zener breakdown

4.5.5. Derivations

4.6. Optoelectronic devices

4.7.1. p-i-n photodiodes

4.7.2. Photoconductors

4.7.3. Metal-Semiconductor-Metal (MSM) photodetectors

4.8. Solar cells

4.8.1. The solar spectrum

4.8.2. Calculation of maximum power

4.8.3. Conversion efficiency for monochromatic illumination

4.8.4. Effect of diffusion and recombination in a solar cell

4.8.5. Spectral response

4.8.6. Influence of the series resistance

4.9. Light Emitting Diodes (LEDs)

4.9.1. Rate equations

4.9.2. DC solution to the rate equations

4.9.3. AC solution to the rate equations

4.9.3. Equivalent circuit of an LED

4.10. Laser diodes

4.10.1. Emission absorption and modal gain

4.10.2. Principle of operation of a laser diode

4.10.3. Longitudinal modes in the laser cavity

4.10.4. Waveguide modes

4.10.5. The confinement factor

4.10.6. The rate equations for a laser diode

4.10.7. Threshold current of multi quantum well laser

4.10.8. Large signal switching of a laser diode

Chapter 5: Bipolar Junction Transistors

5.1. Introduction

5.2. Structure and principle of operation

5.3. Ideal transistor model

5.3.1. Forward active mode of operation

5.3.2. General bias modes of a bipolar transistor

5.3.3. The Ebers-Moll model

5.3.4. Saturation.

5.4. Non-ideal effects

5.4.1. Base-width modulation

5.4.2. Recombination in the depletion region

5.4.3. High injection effects

5.4.4. Base spreading resistance and emitter current crowding

5.4.5. Temperature dependent effects in bipolar transistors

5.4.6. Breakdown mechanisms in BJTs

5.5 Base and Collector transit time effects

5.5.1. Collector transit time through the base-collector depletion region

5.5.2. Base transit time in the presence of a built-in field

5.5.3. Base transit time under high injection

5.5.4. Kirk effect

5.6 BJT circuit models

5.6.1. Small signal model (hybrid pi model)

5.6.2. Large signal model (Charge control model)

5.6.3. SPICE model

5.7. Heterojunction bipolar transistors

5.8. BJT technology

5.8.1. First Germanium BJT

5.8.2. First silicon IC technology

5.9. BJT power devices

5.9.1. Power BJTs

5.9.2. Darlington Transistors

5.9.3. Silicon Controlled Rectifier (SCR) or Thyristor

5.9.4. DIode and TRiode AC switch (DIAC and TRIAC)

Chapter 6: Metal-Oxide-Silicon Capacitors

6.1. Introduction

6.2. Structure and principle of operation

6.2.1. Flatband diagram

6.3.1. Flatband voltage calculation

6.3.2. Inversion layer charge

6.3.3. Full depletion analysis

6.3.4. MOS Capacitance

6.4. MOS capacitor technology

6.5. Solution to Poisson's equation

6.5.1. Introduction

6.5.2. Electric field versus surface potential

6.5.3. Charge in the inversion layer

6.5.4. Low frequency capacitance

6.5.5. Derivation

6.6. p-MOS equations

6.6.1. p-MOS equations

6.6.2. General equations

Chapter 7: MOS Field Effect Transistors

7.1. Introduction

7.2. Structure and principle of operation

7.3. MOSFET analysis

7.3.1. The linear model

7.3.2. The quadratic model

7.3.3. The variable depletion layer model

7.4. Threshold voltage

7.4.1. Threshold voltage calculation

7.4.2. The substrate bias effect

7.5. MOSFET SPICE MODEL

7.6. MOSFET Circuits and Technology

7.6.1. Poly-silicon gate technology

7.6.2. CMOS

7.6.3. MOSFET Memory

7.7. Advanced MOSFET issues

7.7.1. Channel length modulation

7.7.2. Drain induced barrier lowering

7.7.3. Punch through

7.7.4. Sub-threshold current

7.7.5. Field dependent mobility

7.7.6. Avalanche breakdown and parasitic bipolar action

7.7.7. Velocity saturation

7.7.8. Oxide Breakdown

7.7.9. Scaling

7.8. Power MOSFETs

7.7.1. LDMOS

7.8.2. VMOS transistors and UMOS

7.8.3. Insulated Gate Bipolar Transistor (IGBT)

Appendices

A.1 List of Symbols

List of symbols by name

Extended list of symbols

A.2 Physical constants

A.3 Material parameters

A.4 Prefixes

A.5 Units

A.6 The greek alphabet

A.7 Periodic table

A.8 Numeric answers to selected problems

A.9 Electromagnetic spectrum

A.10 Maxwell's equations

A.11 Chemistry related issues

A.12 Vector calculus

A.13 Hyperbolic functions

A.14 Stirling approximation

Principles of Semiconductor Devices

Table of Contents

Introduction

Chapter 1: Review of Modern Physics

Chapter 2: Semiconductor fundamentals

Chapter 3: Metal-Semiconductor Junctions

Chapter 4: p-n Junctions

Chapter 5: Bipolar Junction Transistors

Chapter 6: Metal-Oxide-Silicon Capacitors

Chapter 7: MOS Field Effect Transistors

Appendices