Current Coupling of Drift-Diffusion Models and Dissipative Schroedinger-Poisson Systems: Dissipative Hybrid Models
Please always quote using this URN:urn:nbn:de:0296-matheon-1538
- A 1D coupled drift-diffusion dissipative Schroedinger 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 Schroedinger 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.
Author: | Michael Baro, Hagen Neidhardt, Joachim Rehberg |
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URN: | urn:nbn:de:0296-matheon-1538 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2004/07/20 |
Release Date: | 2004/07/20 |
Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
Preprint Number: | 142 |