ON THE STATIONARY QUANTUM DRIFT-DIFFUSION MODEL

A bipolar Quantum Drift Diffusion Model including generation-recombina tion terms is considered. Existence of solutions is proven for a gener al setting including the case of vanishing particle densities at some parts of the boundary. The proof is based on a Schauder fixed point it eration combined with a minimization procedure. It is proven that, con trary to the classical drift-diffusion model, vacuum can only appear a t the boundary. In the case of nonvanishing boundary data, the semicla ssical limit is carried out rigorously The variational structure of th e model allows to prove strong H-1 convergence of particle densities, Fermi levels and electrostatic potential.