An algorithm to improve accuracy of criticality in statistical static timing analysis

Statistical design approaches have been studied intensively in the last decade so as to deal with the process variability, and statistical delay fault testing is one of key techniques for the statistical design. In order to represent the distributions of timing information such as a gate delay, a signal arrival time, and a slack, various techniques have been proposed. Among them, Gaussian mixture model is distinguished from the others in that it can handle any correlation, non-Gaussian distributions, and slew distributions easily. However, the previous method of computing the statistical maximum for Gaussian mixture models has a defect such that it produces a distribution similar to Gaussian in a certain case, although the correct distribution is far from Gaussian. In this paper, we propose a novel method for statistical maximum (minimum) operation for Gaussian mixture models. It takes cumulative distribution function curve into consideration so as to compute accurate criticalities (probabilities of timing violation), which is important for detecting delay faults and circuit optimization. The proposed method reduces the error of criticality almost 80% from the previous method.