Quantifying robustness metrics in parameterized static timing analysis

Process and environmental variations continue to present significant challenges to designers of high-performance integrated circuits. In the past few years, while much research has been aimed at handling parameter variations as part of timing analysis, few proposals have actually included ways to interpret the results of this parameterized static timing analysis (PSTA) step. In this paper, we propose a new post-variational analysis metric that can be used to quantify the (timing) robustness of designs to parameter variations. In addition to helping designers diagnose if and when different nodes can fail, this metric can guide optimization and can give insights on what to fix, by identifying nodes with small robustness values and proceeding to fix those nodes first. Inspired by the rich literature on design centering, tolerancing, and tuning (DCTT), we use distance as a measure for robustness. Our analysis thus determines the minimum distance from the nominal point in the parameter space to any timing violation, and works under the assumption that parameters are specified as ranges rather than statistical distributions. We demonstrate the usefulness of this distance-based robustness metric on circuit blocks extracted from a commercial 45 nm microprocessor.