Drift‐Diffusion Models with Schottky Contacts at Metal–Semiconductor Interfaces

ABSTRACT

The paper deals with a drift‐diffusion model for semiconductor devices with Schottky contacts at all metal–semiconductor interfaces. The presented analytical investigations permit Boltzmann as well as Fermi–Dirac statistics for the charge‐carrier densities. We report on energy estimates as well as the existence and boundedness of weak solutions of the instationary van Roosbroeck system for this type of boundary conditions. Under additional assumptions, higher regularity of the solutions is obtained. Here, higher regularity results for scalar quasilinear parabolic PDEs are used. Exploiting the higher regularity of the solutions, the uniqueness of the solution is demonstrated.