Quasi-neutral limit to the drift–diffusion models for semiconductors with physical contact-insulating boundary conditions and the general sign-changing doping profile

The quasi-neutral limit in a bipolar drift–diffusion model for semiconductors with physical contact-insulating boundary conditions, the general sign-changing doping profile and general initial data which allow the presence of the left and right boundary layers and the initial layers is studied in the one-dimensional case. The dynamic structure stability of the solution with respect to the scaled Debye length is proven by the asymptotic analysis of singular perturbation and the entropy-energy method. The key point of the proof is to use sufficiently the fact that the ‘length’ of the boundary layer is very small in a short time period.