ENEE 704 Summary Final Exam Topics

Drift-Diffusion 5 Equations, Five Unknowns. – n, p, Jn, Jp,  Solve Self-Consistently Analytical Method: – Equilibrium: Reduces to One Exact Poison Equation – Non Equilibrium: Make many approximations so you can solve the equations. – Equations solved approximately in 1-dimension to obtain:

Drift-Diffusion Analytical Method, continued: – Equations solved approximately in 1-dimension to obtain: Approximate Internal device operations and state variables in specific regions. (n, p, Jn, Jp,  From variables obtain characteristic device equations. – Know how to derive from DD model: Diode equation, BJT equations, MOSFET equations in Linear and Sat, and Vth

Drift-Diffusion Numerical Method: Know – Deriving Central Difference formulas – Scharfetter Gummel Discretization – Newtons Method of System – Matrix structure for 1, 2 and 3D. – Boundary Conditions Implementation.

Electron Transport Fundamental Points of Semi-classical Transport. – Band Structure and what you get from it Gap and intrinsic carrier concentration, velocity, effective mass, density of states – Effect of Electric Field on mobile electrons: dK = -qE*dt/hbar – Scattering 1/tau:   E’E g(E)

Electron Transport Fundamental Points of Semi-classical Transport, continued. – Schrodinger Equation: 3 Main potential Terms Periodic: Bands and Bloch Functions Macro Field: dK = -qE*dt/hbar Scattering: perturbations in perfect periodic potential – Know transform Schrodinger equation into matrix equation Use to Calculate bands, Perturbation theory Scattering Rates

Electron Transport Monte Carlo Simulation – Know MC algorithm – Be able to write MC flow chart – Know how to write MC – Be able to explain how MC is an implementation of the theory of electron transport (describe above) on a computer