Introduction to Simulations of Semiconductor Lasers

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