Elementary scattering theory of the Si MOSFET

A simple one-flux scattering theory of the silicon MOSFET is introduced. Current-voltage (I-V) characteristics are expressed in terms of scattering parameters rather than a mobility. For long-channel transistors, the results reduce to conventional drift-diffusion theory, but they also apply to devices in which the channel length is comparable to or even shorter than the mean-free-path. The results indicate that for very short channels the transconductance is limited by carrier injection from the source. The theory also indicates that evaluation of the drain current in short-channel MOSFETs is a near-equilibrium transport problem, even though the channel electric field is large in magnitude and varies rapidly in space.