Introduction to Simulations of Semiconductor Lasers

✍ Scribed by Marek Wartak

• Publisher: CRC Press
• Year: 2024
• Tongue: English
• Leaves: 364
• Edition: 1
• Category: Library

✦ Synopsis

Simulations play an increasingly important role not only in scientific research but also in engineering developments. Introduction to Simulations of Semiconductor Lasers introduces senior undergraduates to the design of semiconductor lasers and their simulations. The book begins with explaining the physics and fundamental characteristics behind semiconductor lasers and their applications. It presumes little prior knowledge, such that only a familiarity with the basics of electromagnetism and quantum mechanics is required. The book transitions from textbook explanations, equations, and formulas to ready-to-run numeric codes that enable the visualization of concepts and simulation studies. Multiple chapters are supported by MATLAB code which can be accessed by the students. These are ready-to-run, but they can be modified to simulate other structures if desired.

Providing a unified treatment of the fundamental principles and physics of semiconductors and semiconductor lasers, Introduction to Simulations of Semiconductor Lasers is an accessible, practical guide for advanced undergraduate students of Physics, particularly for courses in laser physics.

Key Features:

• A unified treatment of fundamental principles
• Explanations of the fundamental physics of semiconductor
• Explanations of the operation of semiconductor lasers
• An historical overview of the subject

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
1. Introduction
1.1. Fundamentals of Lasers
1.1.1. Transitions in a TLS
1.1.2. Laser oscillations and resonant modes
1.2. Semiconductor Laser Diodes
1.2.1. Types of semiconductor lasers
1.2.2. Homogeneous p-n junction
1.2.3. Heterostructures
1.2.4. Basic characteristics
1.3. An Outline
Bibliography
2. Fundamentals of Semiconductors
2.1. Crystal structure of semiconductors
2.2. Simplified Band Structure of Semiconductors
2.3. Equilibrium Behavior in Semiconductors
2.3.1. Densities in semiconductors. Fermi-Dirac distribution function
2.3.2. Degenerate and nondegenerate semiconductors
2.4. Doped Semiconductors
2.4.1. Charge neutrality relations
2.5. Homostructures
2.5.1. Energy band diagrams for homostructures
2.6. Heterostructures
2.6.1. Energy bands in nonuniform semiconductors Nondegenerate case
2.6.2. Abrupt heterostructure
2.6.3. Interesting application
2.7. Double Heterostructure
2.8. Quantum well
Bibliography
3. Semiconductor Transport Equations and Contacts
3.1. Drift-Diffusion Model
3.2. Concentrations in Non-Equilibrium Situations
3.2.1. Boltzmann statistics
3.2.2. Fermi-Dirac statistics
3.3. Contacts
3.3.1. Schottky barriers
3.3.2. Ohmic contact
3.4. Currents across Heterointerface
3.4.1. Thermionic model
3.4.2. Gradient model
3.5. Appendix
Bibliography
4. p-n Junctions
4.1. Formation of p-n Homojunction
4.2. Simple Model of Homojunction: Debye Length
4.2.1. n-region
4.2.2. p-region
4.3. Homo Junction in the Depletion Approximation
4.3.1. Mathematical Details of the 1D Model
4.4. p-n Homojunction under Forward and Reverse Bias
4.5. Model of p-n Junction with Ohmic Contacts
4.6. p-i-n Diode
4.7. Hetero p-n Junction
4.7.1. Formation of heterojunctions
Bibliography
5. Electrical Processes
5.1. Basic Physical Constants
5.2. Band Structure Parameters
5.2.1. The effective densities of states
5.3. Doping
5.4. Carrier Mobilities
5.5. Recombination
5.5.1. Spontaneous recombination
5.5.2. Stimulated recombination
5.5.3. Shockley-Read-Hall (SRH) generation-recombination
5.5.4. Auger recombination
Bibliography
6. Poisson Equation
6.1. Simple Poisson Equation
6.2. p-n Diode in Equilibrium
6.3. Scaling of Poisson Equation
6.4. Boundary Conditions and Trial Values
6.4.1. Boundary conditions for electrostatic potential
6.4.2. Initial (trial) values for potential
6.5. Poisson Equation for Homojunction
6.5.1. Method on: Contacts outside
6.5.2. Method two: Contacts inside
6.6. Poisson Equation for Non-Uniform Systems
6.6.1. Linearization
6.6.2. Discretization
6.6.3. Boundary conditions for potential
6.6.4. Initial conditions for potential
6.7. Applications of Poisson Equation to Analyze p-n Diode
6.7.1. General
6.7.2. Analysis of convergence
6.7.3. Homo-junction with linear doping
Bibliography
7. Experiments Using Poisson Equation: Homo diode
7.1. Method One
7.1.1. Calculations of band edges
7.1.2. Comments about mesh
7.1.3. Description of functions
7.2. Method Two
7.3. Solution and Results
Bibliography
8. Hetero-Junction Using Poisson Equation
8.1. Heterostructure Diode with Step Doping
8.2. Summary of Implemented Equations
8.2.1. Nonuniform system (heterostructure)
8.2.2. Description of functions
8.2.3. Results for homo-structure
8.2.4. Data functions
8.2.5. Calculations
8.2.6. Test data
Bibliography
9. Homo-Diode Based on Drift-Diffusion
9.1. Electrical Equations
9.1.1. SRH recombination
9.1.2. Mobility models
9.1.3. Boundary conditions
9.1.4. Trial values
9.1.5. Choice of electrical variables
9.1.6. Summary of linearized Poisson equation
9.2. Integration of Current Continuity Equation
9.3. Approximations to Bernoulli Function
9.4. Steady State: Discretization
9.4.1. Discretization of electrons and holes
9.5. Scaling
9.5.1. Scaling at boundaries
9.5.2. Scaling of trial values of potential
9.5.3. Scaling of mobilities
9.5.4. Scaling of recombination
9.5.5. Scaling of continuity equations
9.6. Electric Current
9.7. Results
9.7.1. Results at equilibrium
9.7.2. Results for non-equilibrium
Bibliography
10. Matlab Code for p-n Homo-Diode
10.1. Summary of Implemented Equations: Homogeneous case
10.1.1. Main functions
10.1.2. Definitions of parameters
11. Hetero-Diode Based on Drift-Diffusion
11.1. Poisson Equation in Equilibrium
11.2. Poisson Equation in Non-Equilibrium
11.3. Electrons
11.4. Holes
11.5. SRH Recombination
11.6. Currents
11.7. Parameters
11.7.1. Mobilities
11.7.2. Dielectric constant
11.8. Code Summary
11.9. Simulated Structures
11.10. Results
11.10.1. Equilibrium case
11.10.2. Non-equilibrium case
11.10.3. Data files
11.10.4. Extra functions
11.10.5. Models
11.10.6. Main files
Bibliography
12. Multi-Layer Passive Slab Waveguides
12.1. Modes of the Arbitrary Three Layer Asymmetric Planar Waveguide in 1D
12.2. Multilayer Waveguide
12.2.1. Propagation matrix formulation
12.2.2. Propagation constant
12.2.3. Electric field
12.3. Testing
12.3.1. 6-layer lossy waveguide
12.3.2. p-i-n structure
12.4. List of Files
12.4.1. Data files
12.4.2. Extra files
12.4.3. Main files
Bibliography
13. Optical Parameters and Processes
13.1. Optical Parameters
13.1.1. Dielectric function and refractive index
13.1.2. Static permittivity
13.1.3. Optical gain
13.2. Absorption (losses) Coefficients
13.2.1. Free-carrier absorption
13.2.2. Intervalence band absorption
13.2.3. The mirror loss
13.2.4. Auger processes
13.3. Spontaneous emission factor
Bibliography
14. Semiconductor Laser
14.1. Summary of Electrical Equations
14.1.1. Poisson equation in equilibrium
14.1.2. Poisson equation in non-equilibrium
14.1.3. Electrons
14.1.4. Holes
14.2. Recombination Processes
14.2.1. Recombination coefficients
14.3. Optical Equations
14.3.1. Wave equation
14.3.2. Photon rate equation
14.3.3. Output power
14.3.4. Practical photon rate equation
14.4. Remaining Material Parameters
14.4.1. Static permittivity
14.4.2. Carrier mobilities
14.5. Description of the Program
14.5.1. Electrical part
14.5.2. Optical part
14.5.3. Full simulator
14.6. Results of Simulations
14.6.1. Data files
14.6.2. General
14.6.3. Models
14.6.4. Optical field
14.6.5. Semiconductors
Bibliography
15. Conclusions
Bibliography
A. Material Parameters
A.1. Some Properties of Important Materials
A.1.1. Bandgap energies
A.1.2. Mobilities
A.2. Practical Material: AlxGa1-xAs
A.2.1. Band structure parameters
A.2.2. Band discontinuity
A.2.3. Doping
A.2.4. Carrier mobilities
A.2.5. Optical parameters
A.2.6. Recombination parameters
A.2.7. Losses
A.3. In1-xGaxAsyP1-y Material System
A.3.1. Band discontinuity
A.3.2. Doping
A.3.3. Carrier mobilities
A.3.4. Optical parameters
A.3.5. Optical gain
A.3.6. Recombination coefficients
A.3.7. Absorption coefficients
A.3.8. Spontaneous emission factor
A.3.9. Summary of parameters for InP systems
Bibliography
B. Short History of Semiconductor Laser Simulations
B.1. Companies
B.2. More Recent Developments
Bibliography
Index