Progress in modeling of semiconductor structures with heterojunctions

In this paper we extend our previous work on a computational model for heterojunctions in semiconductors which can be used, e.g., for modeling higher efficiency solar cells. The problem of charge transport in a semiconductor structure with a heterojunction is described by a multiscale model consisting of the drift-diffusion equations posed on subdomains corresponding to distinct semiconductor materials connected by transmission conditions across the heterojunction interface. The interface conditions arise from approximating the heterojunction region by a lower-dimensional manifold and consist of a non-homogeneous jump in the electrostatic potential and Robin-like interface conditions for carrier transport. The data for the interface conditions are calculated by a Density Functional Theory model over a few atomic layers in the heterojunction region. The model lends itself naturally to domain decomposition, and we extend our previous algorithms as well as provide new analysis. We also provide a study of the propagation of uncertainty in heterojunction data through the continuum model, and present work on the transient model. The paper is illustrated with numerical simulations of several heterojunction structures.