Advanced Device Simulation

EEE598: Advanced Device Simulation

Dragica Vasileska

Review of semiconductor physics and transport

o Semiconductor physics – basic concepts

o Review of drift-diffusion model

- Equilibrium Poisson Equation Solver

- Assignment 1

o Hydrodynamic model

The BTE and its solution

o Introduction of the BTE, Derivation of the Fermi’s Golden Rule, Scattering mechanisms description

- Assignment 2 – Scattering rates calculation for GaN

o Low-field transport: Relaxation Time Approximation and and Rode’s Iterative Method

- Assignment 3 – Implementation of the Rode’s Method for GaN

o High-field transport: Single particle Monte Carlo description, Ensemble Monte Carlo method, Simulation examples

o Notes on the Implementation of the Monte Carlo method for GaAs

- Assignment 4 – Scattering Table Construction - Due March 18th

- Assignment 5 – Bulk Monte Carlo Code for GaN – Due March 18th

Solving the Poisson and the Maxwell’s equations

o Computational Electromagnetics: Clasification of the Electromagnetic Problem and its Analytical and Numerical Solution

o Efficient Poisson Equation Solvers: Multigrid Method and the Conjugate Gradient Methods (article on conjugate gradient methods)

- Assignment 6 – Equilibrium Poisson Solver for GaN MESFET or HEMT

o Why Maxwell Solvers?, Complete Frank Schwierz presentation

o Solution of the Maxwell Equations using FDTD: part1, part2, part3 and part4; Transmission Lines and Waveguides, Basic FDTD

Particle-Based device simulator

o Particle-mesh coupling techniques, Stability criteria for time-step and mesh-size, Current calculation techniques

o Pauli Exclusion Principle, Carrier-Carrier Interactions and Molecular Dynamics

o Modeling of Coulomb effects in conjunction with particle-based device simulators

o Modeling of Thermal Effects with Particle-based device simulators

o Examples of particle-based device modeling:

- Quantum and Coulomb Effects in Nanoscale Devices (Shaikh Shahid Ahmed – Assistant Professor, Carbondale, IL)

- Modeling p-channel SiGe Devices – Full Band Simulations (Santhosh Krishnan – Micron)

- Xiaojiang He Thesis: Modeling 50 nm MOSFET devices

- Assignment 7 – Particle-based device simulator for modeling GaN MESFETs or HEMT

Quantum Corrections to Semiclassical Approaches

o Density Gradient Method (Ancona)

o Quantum Corrected Hydrodynamics (Ferry, Grubin)

o Effective potential approach used in conjunction with particle-based device simulators (Ferry, Ringhofer, Vasileska)

Quantum Simulation – Band Structure

o Schrodinger Equation, Quantum Mechanics Revisited

- Stationary States for a Free Particle

- Bulk dispersion, Periodic Potentials

o Realistic Semiconductor Bandstructure Models: Book Review by Dragica Vasileska on Semiempirical Band Structure Methods

- Empirical Pseudopotential Method, Salvador Gonzalez Thesis (Intel)

- k.p Method Description, MRS Presentation

- Tight Binding Description

- Assignment 8 - Implementation of the Empirical Pseudopotential Method

Quantum Transport in a single band – Non-interacting Systems

o Tunneling Theory – Continuum Semi-Analytical Method

- Current expression

- Landauer’s Approach

o Tunneling Theory – Discretized Numerical Method

- Transfer Matrix Approach

- QTBM method

- Usuki Method – guest lecturer Richard Akis

Non-Equilibrium Transport

o Green’s Functions Approach

- Second Quantization of Particles

- Single particle and two-particle operators

- Schrodinger, Heisenberg and Interaction representation

- Wicks Theorem

- Feynman Diagrams and the partial summation method for the self energy

- Dyson Equation

- Definition of the six Green’s functions

o Ballistic approaches for solving the Green’s Function problem in devices – guest Lecturer Denis Mamaluy

A. Recursive Green’s function Approach

B. Contact Block Reduction method

o Example: Simulation of FINFETs (Hasanur Rahman Khan PhD Thesis)