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Statistical analysis of SRAM has emerged as a challenging issue because the failure rate of SRAM cells is extremely small. In this paper, we develop an efficient importance sampling algorithm to capture the rare failure event of SRAM cells. In particular, we adapt the Gibbs sampling technique from the statistics community to find the optimal probability distribution for importance sampling with a low computational cost (i.e., a small number of transistor-level simulations). The proposed Gibbs sampling method applies an integrated optimization engine to adaptively explore the failure region in a Cartesian or spherical coordinate system by sampling a sequence of 1-D probability distributions. Several implementation issues such as 1-D random sampling and starting point selection are carefully studied to make the Gibbs sampling method efficient and accurate for SRAM failure rate prediction. Our experimental results of a 90 nm SRAM cell demonstrate that the proposed Gibbs sampling method achieves 1.4-4.9× runtime speedup over other state-of-the-art techniques when a high prediction accuracy is required (e.g., the relative error defined by the 99% confidence interval reaches 5%). In addition, we further demonstrate an important example for which the proposed Gibbs sampling algorithm accurately estimates the correct failure probability, while the traditional techniques fail to work.
Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on (Volume:31 , Issue: 12 )
Date of Publication: Dec. 2012