Abstract: The paper analyzes an one dimensional current coupled hybrid model for
semiconductors consisting of a drift-diffusion model
and a quantum transmitting Schroedinger-Poisson
system. The model is discretized which leads to a dissipative hybrid
model consisting of a drift-diffusion model and a dissipative
Schroedinger-Poisson system. It is shown that the dissipative hybrid
model admits always a solution with constant current densities.
All solutions are uniformly
bounded where the bound depends only on the data of the
hybrid model. The current densities are different from
zero iff the boundary values of the electro-chemical
potentials are different. The model can be used to describe resonant
tunneling diodes. Numerical results are in good agreement with
experimental data. In particular, the phenomena of negative resistance
is present.