The Design Chronicles Blogs

Every year, the industry’s brightest minds in static timing analysis (STA) and EDA gather to discuss the latest challenges and solutions at the Tau Workshop. Earlier this spring, Cadence’s Praveen Ghanta, sr. principal software engineer, and Igor Keller, distinguished engineer, had the honor of addressing the “Importance of Modeling Non-Gaussianities in STA in Sub-16nm Nodes” at the conference.

On-chip variation (OCV) has become a larger problem at advanced nodes (16nm and below) with respect to its impact on timing. There are various methodologies to address variation; some have stuck and some have not.

Statistical STA (SSTA) emerged in the early 2000s, providing a promising approach to address OCV. It’s very accurate, delivering a complete statistical distribution. But it also requires a lot of memory, long runtimes, and high associated costs. And timing signoff tools at that time were not equipped to support the amount of data delivered. So, SSTA is not widely adopted

Advanced OCV (AOCV) addresses path-length dependency to reduce timing pessimism, but compared to SSTA, can be either very optimistic or very pessimistic. Statistical OCV (SOCV) accounts for factors like pin-to-related pin dependency, input slew, and output load, thus modeling a more complete statistical representation. So you get the accuracy near that of SSTA, but without its cost. SOCV uses standardized variation data tables in timing libraries known as Liberty Variation Format (LVF) extensions. This additional data models the delay variation of a cell in terms of standard deviation (sigma) of delay per timing arc per slew and load combination. Additional data is included for variation of slew and timing constraints.

Accurately Modeling Quantiles

At sub-16nm nodes (and even at 28nm at under 0.6V), the delay distributions are mostly non-Gaussian and there’s low voltage headroom. Therefore, LVF with sigma tables aren’t accurate enough to model quantiles. That is why, according to Ghanta and Keller, there is a need to model delay, slew, and constraints with non-Gaussian distributions. The distributions should be propagated through timing graphs or paths with minimal runtime impact. The engineers proposed user-defined extensions to LVF to include the first three moments: mean-shift, standard deviation, and skewness. Their approach would accurately model arrival/slack distribution of STA paths and also keep the runtime impact low versus running with only sigma tables.

After presenting their calculations, the engineers shared their conclusions:

• At ultra-low V_DD, mean-shift and skewness modeling are essential
• Characterization tools are available to characterize mean-shift, standard deviation, and skewness accurately at no extra cost
• Good accuracy is possible in modeling non-Gaussian effects on delay quantiles
• The runtime impact of skewness modeling is small (5-10%)

Ghanta’s and Keller’s STA presentation is available from the Tau Workshop website. And, in case you didn’t already know, Cadence’s Tempus Timing Signoff Solution now features non-Gaussian LVF extension support.

Christine Young