Modeling statistical dopant fluctuations in MOS transistors

The impact of statistical dopant fluctuations on the threshold voltage V_T and device performance of silicon MOSFET's is investigated by means of analytical and numerical modeling. A new analytical model describing dopant fluctuations in the active device area enables the derivation of the standard deviation, σV_T , of the threshold voltage distribution for arbitrary channel doping profiles. Using the MINIMOS device simulator to extend the analytical approach, it is found that σV_T, can be properly derived from two-dimensional (2-D) or three-dimensional (3-D) simulations using a relatively coarse simulation grid. Evaluating the threshold voltage shift arising from dopant fluctuations, on the other hand, calls for full 3-D simulations with a numerical grid that is sufficiently refined to represent the discrete nature of the dopant distribution. The average V_T-shift is found to be positive for long, narrow devices, and negative for short, wide devices. The fast 2-D MINIMOS modeling of dopant fluctuations enables an extensive statistical analysis of the intrinsic spreading in a large set of compact model parameters for state-of-the-art CMOS technology. It is predicted that V_T-variations due to dopant fluctuations become unacceptably large in CMOS generations of 0.18 μm and beyond when the present scaling scenarios are pursued. Parameter variations can be drastically reduced by using alternative device designs with ground-plane channel profiles