04-214 M.Baro, H.Neidhardt, J.Rehberg

Current Coupling of Drift-Diffusion Models and Dissipative Schr dinger-Poisson Systems: Dissipative Hybrid Models (804K, pdf) Jul 15, 04

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Abstract. A 1D coupled drift-diffusion dissipative Schr dinger model (hybrid model), which is capable to describe the transport of electrons and holes in semi-conductor devices in a non-equilibrium situation, is mathematically analyzed. The device domain is split into a part where the transport is well-described by the drift-diffusion equations (classical zone) and a part where a quantum description via a dissipative Schr dinger system (quantum zone) is used. Both system are coupled such that the continuity of the current densities is guaranteed. The electrostatic potential is self-consistently determined by Poisson's equation on the whole device. We show that the hybrid model is well-posed, prove existence of solutions and show their uniform boundedness provided the distribution function satisfy a so-called balance condition. The current densities are different from zero in the non-equilibrium case and uniformly bounded.

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