Statistical circuit simulation exhibits increasing importance for circuit designs under process variations. In particular, high sigma analysis is needed to optimize highly-duplicated standard cells, where an extremely rare circuit failure event could lead to catastrophe of the entire chip. Conventional importance sampling (IS) approaches perform high sigma analysis efficiently at low dimensionality, but perform poorly either when there are a larger number of process variation variables, or when the failing samples are distributed in multiple regions.

In this dissertation, a series of high sigma analysis approaches have been proposed. First, a high dimensional importance sampling (HDIS) is presented to mitigate the dimensionality problem in traditional IS. A maximum entropy (MAXENT) based approaches is proposed to model the distribution of circuit performance under process variation. MAXENT models the distribution in overall, but does not specifically model the tail. To fix this issue, a piecewise distribution model (PDM) is proposed to consider the distribution as multiple segments and model each segment using MAXENT, hence improve high accuracy in the high sigma tail.

Moreover, two machine learning assisted approaches are proposed for high sigma analysis. The rare-event microscope (REscope) trains classifier(s) to filter out the majority of the unlikely-to-fail samples and surgically look into those likely-to-fail ones, whose distribution is analytically modeled as a generalized pareto distribution to estimate failure probability. Finally, hyperspherical clustering and sampling (HSCS) algorithm is proposed to cluster failing samples and to perform importance sampling around those clusters to cover all failure regions. Experiment results demonstrate that the proposed approaches are 2-3 orders faster than Monte Carlo, and more accurate than both academia solutions such as IS, Markov Chain Monte Carlo, and industrial solutions such as mixture IS used by ProPlus Design Automation, Inc.