Semiconductor Transport

Lecture Notes on

EEE534: Semiconductor Transport

These lecture notes have been prepared by Dragica Vasileska during the course of teaching the EEE534 Class at Arizona State University.

Class Syllabys

Handwritten Lecture Notes that have been prepared during the course of teaching this class:

Review of Statistical Mechanics

Quantum Theory of Electrons in Periodic Lattices

Lattice Dynamics

Time-Dependent Perturbation Theory; Side Notes on Variable Matrix Elements

Scattering Rates Calculation for Bulk Carriers:

1. Deformation Potential Scattering

2. Non-Polar Optical Phonon Scattering

3. Polar Optical Phonon Scattering

4. Piezoelectric Scattering

5. Intervalley Scattering

6. Carrier-Carrier Scattering: Binary Collisions and Plasma Excitations

Confined Carriers - Some Introductory Comments

1. Scattering Rates Calculation – Acoustic Phonons
2. Surface/Interface-Roughness
3. Coulomb Scattering of Confined Carriers

Boltzmann Transport Equation (BTE)

1. Introductory Concepts

2. Relaxation-Time Approximation

3. Conductivity Calculation

4. Rode’s Iterative Method

5. Orthogonal Polynomials, Conductivity Calculation

6. Transport in a Weak and Strong Magnetic Field

7. Thermoelectric Effects

8. Limitations of the BTE

9. High-Field Transport – General Considerations: Velocity Saturation and Velocity Overshoot

Monte Carlo Method for Solving BTE at High Fields

1. Monte Carlo and Path Integral Formulation

2. Single Particle and Ensemble Monte Carlo Method

3. Many-body and Degeneracy Effects

4. Jacoboni Paper on Monte Carlo Method

Hydrodynamic Modeling: Derivation of the Hydrodynamic Equations

Powerpoint slides on the subject

· Introductory Concepts:

1. Class syllabus. Computational Electronics. Diffusive vs. ballistic transport

2. Semiconductor statistics and Density Of States (DOS) function

3. Semiconductor Statistics

4. Time-dependent perturbation theory. Fermi’s Golden Rule

5. Lattice Dynamics

6. Assignments

v Semiconductor Statistics and DOS (100 pts)

v Electronic Band Structure (100 pts)

v Lattice Dynamics (100 pts)

· Scattering Theory

1. General derivation of scattering rate out of state k

2. Elastic scattering processes – Coulomb Scattering

3. Inelastic scattering processes – Phonon Scattering

4. Assignments

v Scattering Theory – Assignment 1

v Scattering Theory – Assignment 2

· Boltzmann Transport Equation – General Low-field Transport

1. Relaxation Time Approximation

2. Conductivity Calculation

3. Rode’s Iterative Method, Implementation details

4. Project 1

v Implementation of Rode’s Iterative Technique

for GaAs mobility calculation

· Boltzmann Transport Equation – Thermoelectric and Thermomagnetic Effects

1. Thermoelectric Effects

2. Thermomagnetic Effects

· Boltzmann Transport Equation – High Field Transport

1. Device Scaling and Some General Ideas on High-Field Transport

2. Monte Carlo and Path Integral Formulation of the BTE

3. Langevin Equations

4. Single Particle and Ensemble Monte Carlo Method

5. Reading Material for Bulk MC for GaAs

6. Device Simulations, FD-Poisson, Device Simulator Description

7. Assignments

v Ensemble Bulk Monte Carlo Homework

v Ensemble Device Simulator for Modeling MESFETs

· Hydrodynamic Equations

· Confined Carriers

1. General Comments on Confined Carriers (Mark Lundstrom’s Lecture)

2. Scattering Rates for Confined Carriers

a. Acoustic Phonon Scattering and

b. Interface Roughness Scattering