Since Stratton published his famous paper four decades ago, various transport models have been proposed which account for the average carrier energy or temperature in one way or another. The need for such transport models arose because the traditionally used drift-diffusion model cannot capture nonlocal effects which gained increasing importance in modern miniaturized semiconductor devices. In the derivation of these models from Boltzmann's transport equation, several assumptions have to be made in order to obtain a tractable equation set. Although these assumptions may differ significantly, the resulting final models show various similarities, which has frequently led to confusion. We give a detailed review on this subject, highlighting the differences and similarities between the models, and we shed some light on the critical issues associated with higher order transport models.

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.>