Current lines and accurate contact current evaluation in 2-D numerical simulation of semiconductor devices

The conservation of the total current density in semiconductor devices implies that the current derives from a vector potential. The calculation of this current potential is a dual problem of the original device simulation problem. A simple and elegant discrete method is proposed for the 2-D case, which yields the current potential for a given, numerically calculated current density. The approach is based upon a least squares principle and is consistent with the assumptions leading to the discrete formulation of the semiconductor transport equations. Accurate values of the contact currents are obtained and a simple way to generate representations of current lines becomes available. The method has the advantage that it does not require any definition of paths for the integration of current files.