Fast Monte Carlo Estimation of Timing Yield With Importance Sampling and Transistor-Level Circuit Simulation

Considerable effort has been expended in the electronic design automation community in trying to cope with the statistical timing problem. Most of this effort has been aimed at generalizing the static timing analyzers to the statistical case. On the other hand, detailed transistor-level simulations of the critical paths in a circuit are usually performed at the final stage of performance verification. We describe a transistor-level Monte Carlo (MC) technique which makes final transistor-level timing verification practically feasible. The MC method is 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 as it requires too many costly transistor-level simulations. We present a novel approach to constructing an improved MC estimator for timing yield which provides the same accuracy as standard MC but at a cost of much fewer transistor-level simulations. This improved estimator is based on a unique combination of a variance reduction technique, importance sampling, and a cheap but approximate gate delay model. The results we present demonstrate that our improved yield estimator achieves the same accuracy as standard MC at a cost reduction reaching several orders of magnitude.