An existence theorem for weak solutions of the basic stationary semiconductor equations

Abstract

The paper concerns the existence of weak solutions to a system of nonlinear PDE's which governs the stationary distribution of carriers in a semiconductor device (drift–diffusion model). The conditions on the mobilities allow to take into account the effect of saturation of drift velocities. Our method of proof relies on approximation by bounding the lower order nonlinearities. In addition, we establish positive bounds from below on the densities of electrons and holes.

Keywords:

• Drift-diffusion model of semi-conductor theory
• weak solutions

AMS:

• 35J60
• 82A70