Singular Initial Data In Semiconductor Models

Existence and comparison theorems are given for a time-dependent semiconductor model with singular initial data; in the adopted model, the carrier mobilities are allowed to depend on the electronic field. It is shown that coupled circuit-device analysis requires only the approximation of certain moments of the carrier current densities, provided that sufficiently small time steps are used. Computations are reported for an IGFET model at fixed terminal voltages, with singular initial data corresponding to excess carrier parts from an energetic ion. These results suggest that the electric field dependence of the carrier mobilities is critical in such computations, but that Auger recombination and the precise treatment of the initial data may be significantly less important. Our computations also suggest that such computations in three space dimensions may be much more difficult than those with only two.