Discontinuous Galerkin methods for the Boltzmann-Poisson systems in semiconductor device simulations

We are interested in the deterministic computation of the transients for the Boltzmann-Poisson system describing electron transport in semiconductor devices. The main difficulty of such computation arises from the very high dimensions of the model, making it necessary to use relatively coarse meshes and hence requiring the numerical solver to be stable and to have good resolution under coarse meshes. In this paper we consider the discontinuous Galerkin (DG) method, which is a finite element method using discontinuous piecewise polynomials as basis functions and numerical fluxes based on upwinding for stability, for solving the Boltzmann-Poisson system. In many situations, the deterministic DG solver can produce accurate solutions with equal or less CPU time than the traditional DSMC (Direct Simulation Monte Carlo) solvers. Numerical simulation results on a diode and a 2D double-gate MOSFET are given.