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
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 Notes on the Implementation of the Monte Carlo method for GaAs
- Assignment 4 – Scattering Table Construction - Due March 18th
- Assignment 5 – Bulk
Solving the Poisson and the Maxwell’s equations
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 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,
- 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 (
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
- 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
- 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)
Assignments:
- Non-equilibrium PN diode simulator (equilibrium simulator provided) /10
- Scattering rates derivation /5
- Rode’s Iterative Method for GaAs /15
- Scattering Table Construction /5
- EMC for Bulk GaAs /15
- Equilibrium Poisson Solver for GaN MESFET/10
- Modeling of GaAs MESFETs /20
- EPM method implementation for Si, Ge and GaAs /10
- Recursive Green’s function implementation/10
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