Low-field limit for a nonlinear discrete drift-diffusion model arising in semiconductor superlattices theory

Charge transport in semiconductor superlattices can be described through a discrete drift-diffusion model. In this model, we identify some small parameter h > 0, related to the ratio between the length of a superlattice period and the observation length scale. Specifically, we investigate a regime where the length of the superlattice period is small while the doping pro. le is low. In the limit h --> 0, we are led to a nonlinear drift-diffusion model, coupled to the Poisson equation.