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A new short-channel threshold voltage model based on an analytic solution of the two-dimensional Poisson equation in the depletion region under the gate of an MOS transistor (MOSTs) is presented. A simple closed-form expression for the variation of threshold voltage as a function of drain voltage, substrate bias, channel length, oxide thickness, and channel doping is derived. An exponential dependence on channel length and a linear dependence on drain and substrate biases is prediced for the reduction in the short-channel threshold voltage. These results are in qualitative and quantitative agreement with simulated and experimental results reported in literature. The predictions for the threshold voltage and subthreshold drain current are in close agreement with measured characteristics of MOS transistors down to submicron dimensions. The closed-form expressions for the threshold voltage and subthreshold drain current are well suited for circuit simulation and for determining performance limits of MOSTs.
Date of Publication: Oct 1982