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A method for discretizing the semiconductor transport equations using generalized mobility models is developed as an extension of the Scharfetter-Gummel finite difference approach. The method is sufficiently general to be applicable to nearly arbitrary empirical mobility models (including those for MOS surface effects) and may be used on a variety of mesh types in two or three dimensions. The impact of generalized mobility models on the sparsity of our resulting discrete equations is discussed. Convergence rate of a Newton's method linearization of the nonlinear system of equations is measured and interpreted. Some computational results from a study of short-channel MOSFETs are presented to illustrate the approach.
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