Non-gaussian statistical timing analysis using second-order polynomial fitting

In the nanometer manufacturing region, process variation causes significant uncertainty for circuit performance verification. Statistical static timing analysis (SSTA) is thus developed to estimate timing distribution under process variation. However, most of the existing SSTA techniques have difficulty in handling the non-Gaussian variation distribution and non-linear dependency of delay on variation sources. To solve such a problem, in this paper, we first propose a new method to approximate the max operation of two non-Gaussian random variables through second-order polynomial fitting. We then present new non-Gaussian SSTA algorithms under two types of variational delay models: quadratic model and semi-quadratic model (i.e., quadratic model without crossing terms). All atomic operations (such as max and sum) of our algorithms are performed by closed-form formulas, hence they scale well for large designs. Experimental results show that compared to the Monte-Carlo simulation, our approach predicts the mean, standard deviation, and skewness within 1%, 1%, and 5% error, respectively. Our approach is more accurate and also 20x faster than the most recent method for non-Gaussian and nonlinear SSTA.