Two-dimensional analytical modeling of threshold voltages of short-channel MOSFET´s

We present an analytical model of the threshold voltage of a short-channel MOSFET based on an explicit solution of two-dimensional Poisson´s equation in the depletion region under the gate. This model predicts an exponential dependence on channel length (L), a linear dependence on drain voltage (VD), and an inverse dependence on oxide capacitance (εox/tox). An attractive feature of this model is that it provides an analytical closed-form expression for the threshold voltage as a function of material and device parameters (tox, VD, L, substrate bias, and substrate doping concentration) without making premature approximations. Also, this expression reduces to the corresponding expression for long-channel devices.