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A method for incorporating impact ionization into a general control-volume formulation of semiconductor transport is described. The methods for electric-field and current-density vector evaluation and generated charge partitioning within a two-dimensional triangular element are given. The techniques employed allow device breakdown to be accurately determined independent of mesh orientation to current flow direction. The avalanche breakdown of a 1-µm n-MOSFET illustrates the approach. Regions where the drain current is a multivalued function of drain voltage are directly and self-consistently calculated for this device.