# Upwind finite difference solution of Boltzmann equation applied to electron transport in semiconductor devices

## Abstract

We present a new numerical method for solving the Boltzmann-Poisson system which describes charge transport in semiconductor devices. The Boltzmann equation is reduced from three dimensions in velocity space to two by taking the electric field parallel to the z axis, which implies invariance of the probability density function under rotation around the z axis. We develop a finite difference discretization of the Boltzmann equation in one spatial dimension and two-dimensional velocity space, coupled to the Poisson equation. The system of equations obtained by taking the first five moments of the Boltzmann equation coupled to the Poisson equation is known as the hydrodynamic model in semiconductor modeling. A comparison of the numerical results from our method and the hydrodynamic model is given. Also a numerical investigation is done with respect to the heat conduction, viscosity, and momentum relaxation terms in the hydrodynamic model. © 1993 Academic Press, Inc.