On the Minimal Energy State of a Mixture of Charged Classical and Quantum Fluids

Abstract

The paper concerns the equilibrium state of ultra small semiconductor devices. Due to the quantum drift diffusion model, electrons and holes behave as a mixture of charged quantum fluids. Typically the involved scaled Planck's constants of holes, ξ, is significantly smaller than the scaled Planck's constant of electrons. By setting formally ξ = 0 a well-posed differential-algebraic system arises. Existence and uniqueness of an equilibrium solution is proved. A rigorous asymptotic analysis shows that this equilibrium solution is the limit (in a rather strong sense) of quantum systems as ξ → 0. In particular the ground state energies of the quantum systems converge to the ground state energy of the differential-algebraic system as ξ → 0.