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

Abstract

For nanometer manufacturing, process variation causes significant uncertainty for circuit performance verification. Statistical static timing analysis (SSTA) is thus developed to estimate timing distribution under process variation. Most existing SSTA techniques have difficulty in handling the non-Gaussian variation distribution and nonlinear dependence of delay on variation sources. To address this problem, we first propose a new method to approximate the max operation of two non-Gaussian random variables through second-order polynomial fitting. With such approximation, we then present new non-Gaussian SSTA algorithms for three delay models: quadratic model, quadratic model without crossing terms (semiquadratic model), and linear model. All the atomic operations (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, skewness, and 95% percentile point within 1%, 1%, 6%, and 1% error, respectively. © 2009 IEEE.