2D semiconductor device simulations by WENO-Boltzmann schemes: Efficiency, boundary conditions and comparison to Monte Carlo methods

We develop and demonstrate the capability of a high order accurate finite difference weighted essentially non-oscillatory (WENO) solver for the direct numerical simulation of transients for a two space dimensional Boltzmann transport equation (BTE) coupled with the Poisson equation modeling semiconductor devices such as the MESFET and MOSFET. We compare the simulation results with those obtained by a direct simulation Monte Carlo (DSMC) solver for the same geometry. The main goal of this work is to benchmark and clarify the implementation of boundary conditions for both, deterministic and Monte Carlo numerical schemes modeling these devices, to explain the boundary singularities for both the electric field and mean velocities associated to the solution of the transport equation, and to demonstrate the overall excellent behavior of the deterministic code through the good agreement between the Monte Carlo results and the coarse grid results of the deterministic WENO-BTE scheme.