New IGFET short-channel threshold voltage model

A simple closed form expression for the threshold voltage V
T
of non-uniformly doped short-channel IGFET's is derived by solving two-dimensional Poisson equation over the depletion region under the gate using a step doping profile approximation. An exponential dependence on channel-length L and a linear dependence on drain-to-source voltage V
DS
and substrate bias V
BS
are predicted for
\Delta V_{T}
, the reduction in short-channel threshold voltage. These predictions are in close agreement with measured V
T
charactersistics of submicron IGFET's.