Assessment of a high resolution centered scheme for the solution of hydrodynamical semiconductor equations

Hydrodynamical models are suitable to describe carrier transport in submicr on semiconductor devices. These models have the form of nonlinear systems o f hyperbolic conservation laws with source terms, coupled with Poissons equ ation. In this article we examine the suitability of a high resolution cent ered numerical scheme for the solution of the hyperbolic part of these exte nded models, in one space dimension. Because of the lack of physically sign ificant exact analytical solutions, the method is assessed against a benchm ark for the system of compressible, unsteady Euler equations with source te rms, which has an exact solution; the latter is shown to be nearly identica l to the numerical one. The method is then used to solve the extended hydro dynamical model (EM) based on the maximum entropy closure recently introduc ed by Anile, Romano, and Russo, simulating a ballistic diode n(+-)n-n(+), w hich models a metal oxide semiconductor field effect transistor ( MOSFET) c hannel. Results are presented for the reduced- and full-equation EM formula tion at steady state, for an initially discontinuous electron density at th e junctions. Transient results show the evolution of highly nonlinear waves emanating from the neighborhood of the junctions.