Device modeling of statistical dopant fluctuations in MOS transistors

This paper addresses the numerical requirements for device modeling of statistical dopant fluctuations in MOS transistors. It is found that the standard deviation of the threshold voltage V/sub T/ can be properly derived from 2D or 3D simulations using a relatively coarse simulation grid. Evaluating the threshold voltage shift arising from dopant fluctuations, on the other hand, calls for a full 3D approach with a numerical grid that is sufficiently refined to represent the discrete nature of the dopant distribution. The average V/sub T/-shift is found to be positive for long, narrow devices, and negative for short, wide devices.