A quasistationary limit and convergence to equilibrium in the drift diffusion system for semiconductors coupled with Maxwell's equations

Abstract

The transient drift-diffusion model describing the charge transport in semiconductors is investigated in the case that the currents are prescribed. It is shown that the solutions of the drift-diffusion system coupled with Maxwell's equations converge to the solution of the drift-diffusion system coupled with Poisson's equation if the magnetic susceptibility tends to zero. Furthermore it is shown that the densities converge to the thermal equilibrium state for $t\rightarrow\infty$ provided that the boundary conditions are compatible with the thermal equilibrium.