A threshold voltage model is presented which is valid for short- and long-channel MOSFET's with a nonuniform substrate doping profile. The model is based upon an approximate two-dimensional analytical solution of Poisson's equation for a MOSFET of arbitrary substrate doping profile which takes into account the effect of curved junctions of finite depth. The analytical model is compared to MINIMOS simulations showing that it can accurately predict short-channel threshold voltage falloff and threshold voltages in this vicinity without the use of fitting parameters.
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Kendall et al. (1986) studied this question.
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