Solution of semiconductor device problems using arbitrary quadrilateral grids

In recent years, several discretisation methods extending the classical Scharfetter-Gummel scheme to non-rectangular meshes have been described. Such methods can, for example, be found in Markovich ([6]), Polak et al. ([10], [11], [121]), Van Welij ([14]) and Zlamal ([15]). We have used Van Welij´s edge elements to design a box method which can cope with arbitrary quadrilateral grids, and have applied it to solve problems with non-rectangular geometries. Another area of application is (adaptive) meshing along characteristic lines or field lines. Thus, characteristics of the solution can be reflected in the mesh, which might be advantageous for the number of gridpoints needed to accurately represent the solution. In this paper we describe the method and present a number of examples of its application to practical problems.