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If in the classic van Roosbroeck system (Bell Syst Tech J 29:560–607, 1950) the statistic function is modified, the equations can be derived by a variational formulation or just using a generalized Einstein relation. In both cases a dissipative generalization of the Scharfetter–Gummel scheme (IEEE Trans Electr Dev 16, 64–77, 1969), understood as a one-dimensional constant current approximation,...
The paper summarizes properties of Delaunay grids, Voronoi diagrams and presents a weak formulation of the Scharfetter-Gummel-scheme on d dimensional simplex grids. Other technical details, like the weak discrete maximum principle, are introduced, too. The advantage of the formalism is a direct 'reuse' of analytic results to obtain the discrete estimates. The results of (Zlamal, 1984) (restricted...
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