Numerical solutions for hydrodynamical models of semiconductors

Numerical solutions of recent hydrodynamical models of semiconductors are computed in one-space dimension. Such models describe charge transport in semiconductor devices. Two models are taken into consideration. The first one has been developed by Blotekjaer, Baccarani et al., and the second one by Anile et al. In both cases the system of equations can be written as a convection-diffusion type system, with a right-hand side describing relaxation effects and interaction with a self-consistent electric field. The numerical scheme is a splitting scheme based on the Nessyahu-Tadmor scheme for the hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results are compared to detailed Monte-Carlo simulation.