Bayesian Optimized Mixture Importance Sampling for High-Sigma Failure Rate Estimation

Abstract

In many application domains, in particular automotives, guaranteeing a very low failure rate is crucial to meet functional and safety standards. Especially, reliable operation of memory components such as SRAM cells is of essential importance. Due to aggressive technology downscaling, process and runtime variations significantly impact manufacturing yield as well as functionality. For this reason, a thorough memory failure rate assessment is imperative for correct circuit operation and yield improvement. In this regard, Monte Carlo (MC) simulations have been used as the conventional method to estimate the variability induced failure rate of memory components. However, MC methods become infeasible when estimating rare events such as high-sigma failure rates. To this end, importance sampling (IS) methods have been proposed which reduce the number of required simulations substantially. However, existing methods still suffer from inaccuracies and high computational efforts, in particular for high-sigma problems. In this article, we fill this gap by presenting an efficient mixture IS approach based on Bayesian optimization, which deploys a surface model of the objective function to find the most probable failure points. Its advantages include constant complexity independent of the dimensions of design space, the potential to find the global extrema, and the higher trustworthiness of the estimated failure rate by accurately exploring the design space. The approach is evaluated on a 6T-SRAM cell as well as a master–slave latch based on a 28-nm FDSOI process. The results show an improvement in accuracy, resulting in up to $63\times $ better accuracy in estimating failure rates compared to the best state-of-the-art solutions on a 28-nm technology node.