WIAS Preprint No. 946, (2004)

Current coupling of drift-diffusion models and dissipative Schrödinger--Poisson systems: Dissipative hybrid models


  • Baro, Michael
  • Neidhardt, Hagen
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 47B44 47E05 35J05

2008 Physics and Astronomy Classification Scheme

  • 73.23.-b, 73.23.Ad, 73.63.-b, 73.63.Nm


  • semi-conductors, quantum-classical coupling, hybrid models, drift-diffusion models, dissipative Schrödinger systems, Poisson equation, current coupling




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.

Appeared in

  • SIAM J. Math. Anal., Vol. 37, No. 3, pp. 941-981, 2005

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