Three-dimensional Statistical Modeling of the Effects of the Random Distribution of Dopants in Deep Sub-micron nMOSFETs

We have performed a three-dimensional statistical simulation of the threshold voltage distribution of deep submicron nMOSFETs, as a function of gate length, doping density, oxide thickness, based on a multigrid non-linear Poisson solver. We compare our results with statistical simulations presented in the literature, and show that essentially only the vertical distribution of dopants has an effect on the standard deviation of the threshold voltage.