Non-gaussian statistical parameter modeling for SSTA with confidence interval analysis

Authors:
Lizheng Zhang;Jun Shao;Charlie Chung-Ping Chen
Affiliations:
Cadence Design Systems, San Jose, CA;University of Wisconsin, Madison, WI;University of Wisconsin, Madison, WI
Venue:
Proceedings of the 2006 international symposium on Physical design
Year:
2006

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Abstract

Most of the existing statistical static timing analysis (SSTA) algorithms assume that the process parameters of have been given with 100% confidence level or zero errors and are preferable Gaussian distributions. These assumptions are actually quite questionable and require careful attention.In this paper, we aim at providing solid statistical analysis methods to analyze the measurement data on testing chips and extract the statistical distribution, either Gaussian or non-Gaussian which could be used in advanced SSTA algorithms for confidence interval or error bound information.Two contributions are achieved by this paper. First, we develop a moment matching based quadratic function modeling method to fit the first three moments of given measurement data in plain form which may not follow Gaussian distributions. Second, we provide a systematic way to analyze the confident intervals on our modeling strategies. The confidence intervals analysis gives the solid guidelines for testing chip data collections. Extensive experimental results demonstrate the accuracy of our algorithm.