Discretization of flux densities in device simulations using optimum artificial diffusivity

The discretization scheme for the current density and the energy flux density has been revisited from a numerical diffusion point of view. A general discretization scheme for both flux densities is provided using the optimum artificial diffusivity. This formulation is equivalent to that of Scharfetter and Gummel in most cases but is numerically more transparent. It has the advantage that one formula applies to all and is not dependent on a particular form of transport coefficient. Application of this scheme to a two-dimensional simulation of MOSFETs is included.>