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

TL;DR

This paper introduces a novel Monte Carlo estimator for timing yield that significantly reduces computational cost by combining importance sampling with a stochastic logical effort model, enabling practical and accurate yield estimation in advanced IC design.

Contribution

It presents a new variance reduction technique that combines importance sampling with stochastic logical effort to make Monte Carlo timing yield estimation feasible and efficient.

Findings

Achieves same accuracy as standard Monte Carlo with fewer simulations

Reduces computational cost by several orders of magnitude

Demonstrates effectiveness on practical circuit examples

Abstract

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 improvedMonte 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.