In the first part the small Debye length limit in a self-consistent bipolar drift-diffusion model is considered. The limiting problems on the two significant time scales are analyzed. One scaling gives an initial time layer problem and the other one a quasi-neutral limit. In the second part the small Debye length limit is studied in a bipolar hydrodynamic model. This limit is combined with a relaxation limit. In the quasi-neutral scaling the limiting problem consist of a nonlinear diffusion equation, whereas in the other scaling a pure drift type model is obtained.

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