Analytical modeling of the subthreshold current in short-channel MOSFET's

In this paper an analytical model for subthreshold current for both long-channel and short-channel MOSFET's is presented. The analytical electrostatic potential derived from the explicit solution of a two-dimensional Poisson's equation in the depletion region under the gate for uniform doping is used. The case for nonuniform doping can easily be incorporated and will be published later. The results are compared to a numerical solution obtained by using MINIMOS, for similar device structures. An analytical expression for the channel current is obtained as a function of drain, gate, substrate voltages, and device parameters for devices in the subthreshold region. The short-channel current equation reduces to the classical long-channel equation as the channel length increases.