Numerical methods in the simulation of charge transport in solid dielectrics

This paper introduces some numerical methods pertaining to the simulation of charge transport in solid dielectrics that can be of interest to the electrical engineering community. These methods are generally scattered over numerical analysis and computing literature making difficult for the non-specialist to select the appropriate computing schemes. In the first part we consider an example of a set of physical parameters needed to describe charge transport and we introduce mathematical equations that must be solved. A series of numerical schemes are compared for one-dimensional convection problems in a second part. Numerical results show that a third order upwind scheme named QUICKEST, combined with a flux limiter (ULTIMATE) is competent for the resolution of the transport equation in solid dielectrics, avoiding numerical oscillations and numerical diffusion. The third part deals with numerical resolution of the Poisson's equation comparing two different methods.