Hypersphere Sampling for Accelerating High-Dimension and Low-Failure Probability Circuit-Yield Analysis

This paper proposes a novel and an efficient method termed hypersphere sampling to estimate the circuit yield of low-failure probability with a large number of variable sources. Importance sampling using a mean-shift Gaussian mixture distribution as an alternative distribution is used for yield estimation. Further, the proposed method is used to determine the shift locations of the Gaussian distributions. This method involves the bisection of cones whose bases are part of the hyperspheres, in order to locate probabilistically important regions of failure; the determination of these regions accelerates the convergence speed of importance sampling. Clustering of the failure samples determines the required number of Gaussian distributions. Successful static random access memory (SRAM) yield estimations of 6to 24-dimensional problems are presented. The number of Monte Carlo trials has been reduced by 2–5 orders of magnitude as compared to conventional Monte Carlo simulation methods. key words: design for manufacturing, Monte Carlo method, importance sampling, SRAM, process variation, yield, norm minimization, Gaussian mixture models, clustering, hypersphere sampling