Drift-diffusion models with nonlinear boundary conditions modeling Schottky contacts at metal-semiconductor interfaces

Abstract

The paper deals with drift-diffusion models for semiconductor heterostructures with Schottky contacts at all metal-semiconductor interfaces. Our analytical investigations allow for Boltzmann as well as Fermi--Dirac statistics for the charge-carrier densities. We verify the existence and boundedness of weak solutions of the instationary van Roosbroeck system in this context. Moreover, under additional assumptions the uniqueness and the higher regularity of the solution are demonstrated. Here, higher regularity results for scalar quasilinear parabolic PDEs are used.