Quasineutral Limit of a Nonlinear Drift Diffusion Model for Semiconductors: The Fast Diffusion Case

The limit of vanishing Debye length (charge neutral limit) in a nonlinear bipolar drift-diffusion model for semiconductors without pn-junction (i.e. with a unipolar background charge) is studied. The quasineutral limit (zero-Debye-length limit) for the fast diffusion case is performed rigorously by using the compactness argument and the so-called entropy functional which yields appropriate uniform estimates.