Low and high field scaling limits for the Vlasov- and Wigner-Poisson-Fokker-Planck systems

This paper is concerned with scaling limits in kinetic semiconductor models . For the classical Vlasov-Poisson-Fokker-Planck equation and its quantum m echanical counterpart, the Wigner-Poisson-Fokker-Planck equation, three dis tinguished scaling regimes are presented. Using Hilbert and Chapman-Enskog expansions, we derive two drift-diffusion type approximations. The test cas e of a n(+) - n - n(+) diode reveals that different scaling regimes may be present at the same time in different subregions of a semiconductor device. Numerical simulations of the stationary solution illustrate the good appro ximation of the kinetic solution by a drift-diffusion model and by a hybrid (adaptive domain decomposition) model.