Asymptotic Methods for Metal Oxide Semiconductor Field Effect Transistor Modeling

Abstract

The behavior of metal oxide semiconductor field effect transistors (MOSFETs) with small aspect ratio and large doping levels is analyzed using formal perturbation techniques. Specifically, the influence of interface layers in the potential on the averaged channel conductivity is closely examined. The interface and internal layers that occur in the potential are resolved in the limit of large doping using the method of matched asymptotic expansions. This approach, together with other asymptotic techniques, provides both a pointwise description of the state variables as well as lumped current-voltage relations that vary uniformly across the various bias regimes. These current-voltage relations are derived for a variable doping model respresenting a particular class of devices.