A generalized Scharfetter-Gummel method to eliminate crosswind effects [semiconduction device modeling]

A generalized Scharfetter-Gummel discretization method is proposed for semiconductor device modeling. Motivated by the classical Scharfetter-Gummel approach and the SUPG (streamline upwind/Petrov-Galerkin) method, an optimal nonlinear artificial diffusion term is added to the standard Galerkin finite element formula within a weighted residual form to construct the generalized Scharfetter-Gummel method, which exhibits better properties in precluding numerical oscillation and crosswind effects than the classical Scharfetter-Gummel method and the SUPG method. The generalized Scharfetter-Gummel method is more general and applicable to complicated problems