Numerical Solutions of the Boltzmann Equation

Abstract

Various concepts for the numerical solution of the semiclassical Boltzmann equation are discussed, including an illustration of the use of a linearized Boltzmann equation and its eigenfunction expansion for a 2D electron gas. The numerical results for the linearized Boltzmann equation are compared with those of an ensemble Monte Carlo simulation of the Master equation. Finally the Boltzmann equation together with the Poisson equation is solved self-consistently for a spatially inhomogeneous electron gas in the relaxation time approximation.