Elementary scattering theory of the Si MOSFET

TLDR

The paper introduces a simple one‑flux scattering theory for silicon MOSFETs. The theory models I‑V characteristics using one‑flux scattering parameters instead of mobility. It shows that long‑channel devices follow drift‑diffusion, while in very short channels transconductance is limited by source injection and drain current remains a near‑equilibrium transport problem despite large, rapidly varying fields.

Abstract

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.