Low and High Field Scaling Limits for the Vlasov- and Wigner-poisson-fokker-planck Systems
نویسندگان
چکیده
This paper is concerned with scaling limits in kinetic semiconductor models. For the classical Vlasov-Poisson-Fokker-Planck equation and its quantum mechanical counterpart, the Wigner-Poisson-Fokker-Planck equation, three distinguished scaling regimes are presented. Using Hilbert and Chapman-Enskog expansions, we derive two drift-diffusion type approximations. The test case 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 approximation of the kinetic solution by a drift-diffusion model and by a hybrid (adaptive domain decomposition) model. AMS 1991 Subject Classification: 35B25, 76P05, 82C70, 65M99
منابع مشابه
Low and High Field Scaling Limits Forthe
This paper is concerned with scaling limits in kinetic semiconductor models. For the classical Vlasov-Poisson-Fokker-Planck equation and its quantum mechanical counterpart, the Wigner-Poisson-Fokker-Planck equation, three distinguished scaling regimes are presented. Using Hilbert and Chapman-Enskog expansions, we derive two drift-diiusion type approximations. The test case of a n + ?n?n + diode...
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