Fast Monte Carlo Estimation of Timing Yield: Importance Sampling with Stochastic Logical Effort (ISLE)

In the nano era in integrated circuit fabrication technologies, the performance variability due to statistical process and circuit parameter variations is becoming more and more significant. Considerable effort has been expended in the EDA community during the past several years in trying to cope with the so-called statistical timing problem. Most of this effort has been aimed at generalizing the static timing analyzers to the statistical case. In this paper, we take a pragmatic approach in pursuit of making the Monte Carlo method for timing yield estimation practically feasible. The Monte Carlo method is widely used as a golden reference in assessing the accuracy of other timing yield estimation techniques. However, it is generally believed that it can not be used in practice for estimating timing yield as it requires too many costly full circuit simulations for acceptable accuracy. In this paper, we present a novel approach to constructing an improved Monte Carlo estimator for timing yield which provides the same accuracy as the standard Monte Carlo estimator, but at a cost of much fewer full circuit simulations. This improved estimator is based on a novel combination of a variance reduction technique, importance sampling, and a stochastic generalization of the logical effort formalism for cheap but approximate delay estimation. The results we present demonstrate that our improved yield estimator achieves the same accuracy as the standard Monte Carlo estimator at a cost reduction reaching several orders of magnitude. Keywords— logical effort, statistical variations, timing yield estimation and optimization, statistical timing analysis, Monte Carlo methods, variance reduction techniques, importance sampling.