A new statistical timing analyzer propagating delay and slew distributions simultaneously

Due to the progress of nanometer process technologies, variability of circuit parameters is increasing and the statistical static timing analysis (S-STA) has been studied intensively. The existing block-based S-STA algorithms assume that the distribution of delay of each circuit element does not change through the analysis. However, such a delay depends on the input-slew, and the slew to be considered in S-STA is also a random variable associated with a propagated signal for computing the distribution of arrival time (delay) of the signal. Therefore, in order to increase the accuracy of S-STA, the distribution of slew must be propagated together with delay distribution, and the delay of a circuit element must be calculated dynamically by using the propagated slew. In this paper, we propose an algorithm for such a novel S-STA by using Gaussian mixture model to represent the delay and slew distributions. Moreover, with the use of propagated slew, we propose an estimation method of the probability for two inputs to switch at the same time (Multiple Input Switching).