ANALYSIS OF A DISCRETIZATION ALGORITHM FOR TIME‐DEPENDENT SEMICONDUCTOR MODELS

A new algorithm is presented for the discretization of semiconductor models in one space dimension plus time. A complete error analysis is given, showing that the discretization errors do not depend on any derivatives of ill‐behaved quantities such as carrier densities. In this algorithm, the electrostatic potential is updated from a discretization of the equation of total current continuity, and parabolic equations for the current densities are discretized, rather than those for the carrier densities. Projection methods, e.g. simple finite‐element methods, are used for the space discretization. The equations for the current densities are similar to the familiar Scharfetter‐Gummel expressions in the stationary limit. However, the discrete time‐dependent current densities are required here to be H1 functions of x, obtained in a space with at least second order approximation property in L2. This method is fully compatible with recently developed methods for uncoupling the discrete systems to be solved at each time step, for an individual device or when a given problem involves multiple, coupled devices.