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 (V
D
), and an inverse dependence on oxide capacitance (ε
ox
/t
ox
). 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 (t
ox
, V
D
, L, substrate bias, and substrate doping concentration) without making premature approximations. Also, this expression reduces to the corresponding expression for long-channel devices.