Fast and Accurate Statistical Static Timing Analysis with Skewed Process Parameter Variation

Lin Xie and Azadeh Davoodi
University of Wisconsin at Madison


This paper presents a fast and accurate statistical static timing analysis method that supports skewed non-Gaussian process parameter variations. First, we propose modeling of non-Gaussian sources of variation using a Skew-Normal random variable which can represent a large class of non-Gaussian distributions such as Log-Normal and Poisson. Second, we present a linear gate delay model in terms of this Skew-Normal as well as Gaussian parameters. Third, we approximate arrival times as skewed random variables in an effort to simply capture the shape of the arrival times without loss of accuracy. A proposed linear encoding of skewed arrival times enables computing the exact analytical expression for the MAX of arrival times as well as for their first three moments which can be evaluated in an efficient manner. Overall, calculation of the MAX operation is done efficiently (i.e., comparable to the fastest-known Gaussian linear approximation of Clark) with high accuracy and restriction-free for a realistic representation of non-Gaussian process parameters.