Fast and accurate statistical static timing analysis with skewed process parameter variation

Abstract

A fast and accurate statistical static timing analysis approach is presented, which supports skewed non-Gaussian process parameter variations. First, the authors propose modelling of non-Gaussian sources of variation using a skew-normal random variable that can represent a large class of non-Gaussian distributions such as log-normal and Poisson. Secondly, the authors present a linear gate delay model in terms of skew-normal as well as Gaussian parameters. The high accuracy of the linear model is discussed and verified using Spice simulations. Thirdly, the authors approximate arrival time expressions as skewed (and not skew-normal) random variables in an effort to quickly capture their shapes without loss of accuracy. A proposed linear representation 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, the calculation of the MAX operation is done efficiently (i.e. comparable to the solely linear-Gaussian case) with high accuracy and restriction-free for a realistic representation of non-Gaussian process parameters.