Low-Field Limit for a Nonlinear Discrete Drift-Diffusion Model Arising in Semiconductor Superlattices Theory

Abstract

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 profile is low. In the limit h → 0, we are led to a nonlinear drift-diffusion model, coupled to the Poisson equation.

Existence of Solutions of a Partial Integrodifferential Equation with Thermostat and Time Delay

“…Research perspectives include the possibility of performing an asymptotic analysis by parabolic (low-field) and hyperbolic (high-field) scalings (see [24][25][26][27][28][29][30][31][32][33][34]) with the aim of obtaining the dynamics of the system at the macroscopic scale. This is a work in progress and results will be presented in due course.…”