SSFB: A highly-efficient and scalable simulation reduction technique for SRAM yield analysis

Estimating extremely low SRAM failure-probabilities by conventional Monte Carlo (MC) approach requires hundreds-of-thousands simulations making it an impractical approach. To alleviate this problem, failure-probability estimation methods with a smaller number of simulations have recently been proposed, most notably variants of consecutive mean-shift based Importance Sampling (IS). In this method, a large amount of time is spent simulating data points that will eventually be discarded in favor of other data-points with minimum norm. This can potentially increase the simulation time by orders of magnitude. To solve this very important limitation, in this paper, we introduce SSFB: a novel SRAM failure-probability estimation method that has much better cognizance of the data points compared to conventional approaches. The proposed method starts with radial simulation of a single point and reduces discarded simulations by: a) random sampling-only-when it reaches a failure boundary and after that continues again with radial simulation of a chosen point, and b) random sampling is performed-only-within a specific failure-range which decreases in each iteration. The proposed method is also scalable to higher dimensions (more input variables) as sampling is done on the surface of the hyper-sphere, rather than within-the-hypersphere as other techniques do. Our results show that using our method we can achieve an overall 40x reduction in simulations compared to consecutive mean-shift IS methods while remaining within the 0.01-Sigma accuracy.