Models and algorithms for statistical timing and power analysis of digital integrated circuits



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The increased variability of process and environmental parameters is having a significant impact on timing and power performance metrics of digital integrated circuits. Traditionally formulated deterministic timing and power analysis algorithms based on worst-case values of parameters often lead to over-pessimistic predictions, and may miss actual worst-case performance corners. As a result, there is an increasing need for statistical algorithms that can take into account the probabilistic nature of parameters. The practical applications of statistical approaches, however, are restricted by the limited availability of parameter distributions, and the idealized modeling of parameters adopted in the statistical frameworks. In some cases, only partial probabilistic descriptions of parameters are available, such as the mean and variance. Thus, designers are in an urgent need for statistical approaches that can handle partially-specified uncertainty. The objective of this dissertation is to provide robust and accurate timing and power estimates for designers to assess the impact of variability on circuit performance. This dissertation proposes a set of statistical analysis algorithms to estimate circuit timing and leakage power dissipation based on robust probabilistic approaches and rigorous mathematical modeling of parameter uncertainty. Full and partial probabilistic descriptions of parameters can be incorporated into the developed statistical frameworks. Specifically, the proposed approaches include: 1) a path-based statistical timing analysis algorithm handling path delay correlations; 2) a statistical timing analysis algorithm based on partial probabilistic descriptions of parameters; 3) analytical techniques for assessing the impact of threshold voltage variation on leakage power of dual-threshold voltage designs, and selecting optimal values of the threshold voltages for leakage power reduction; and 4) a robust estimation algorithm for parametric yield and leakage dissipation based on realistic descriptions of parameter uncertainty. The developed algorithms along with the new modeling strategy effectively improve the overconservatism of the corner-based deterministic algorithms, and also permit assessing the impact of variability on circuit performance in the early design phase, which facilitates fast power and timing verifications in the design process. As the magnitude of variability continues to increase, the developed statistical algorithms and modeling strategy will become increasingly important for the future technology generations.