Current coupling of drift-diffusion models and dissipative Schrödinger--Poisson systems: Dissipative hybrid models
- Baro, Michael
- Neidhardt, Hagen
- Rehberg, Joachim
A 1D coupled drift-diffusion dissipative Schrödinger 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 Schrödinger 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.
- SIAM J. Math. Anal., Vol. 37, No. 3, pp. 941-981, 2005