ABSTRACT
There are many approaches to computing the quantum transport properties of carriers in semiconductors. Nearly all of these start with the Schrodinger equation. The form of this equation is both reversible and dissipation free, while its use in actual devices is normally modified to incorporate the presence of dissipation. This chapter illustrates this with the recursive version of an approach to computing the transport with a technique based on the Schrodinger equation. The basic concepts of transport in mesoscopic quantum systems in the presence of localized scatterers can be traced to Landauer. The Landauer approach is quite fundamental as its extensions to the use of the distribution functions in the contact regions is all that is required. There have been many suggestions for different full quantum methods to model ultra-small semiconductor devices. However, the length and the depth are modeled rigorously, while the third dimension is usually included through the assumption that there is no interesting physics in this dimension.
