On a Petrov–Galerkin method for the electrical and thermal behaviour of semiconductor devices in two dimensions

We consider the equations governing the electrical and thermal behaviour of a semiconductor device in two dimensions. A non-standard Petrov-Galerkin method is used to obtain a discretisation of the equations for stationary problems. The resulting scheme is a generalization to the two-dimensional case and to the full set of equations of the well-known Scharfetter-Gummel scheme, which is the most successful discretisation for one-dimensional problems. The dependent variables used are the carrier densities, the electrostatic potential and the absolute temperature.