Fast and Accurate High-Sigma Failure Rate Estimation through Extended Bayesian Optimized Importance Sampling

Abstract

Due to the aggressive technology downscaling, process variations are becoming pre-dominent, causing performance fluctuations and impacting the chip yield. Therefore, individual circuit components have to be designed with very small failure rates to guarantee functional correctness and robust operation. The assessment of high-sigma failure rates however cannot be achieved with conventional Monte Carlo (MC) methods due to the huge amount of required time-consuming circuit simulations. To this end, Importance Sampling (IS) methods were proposed to solve the otherwise intractable failure rate estimation problem by focusing on high-probable failure regions. However, the failure rate could largely be underestimated while the computational effort for deriving them is high. In this paper, we propose an eXtended Bayesian Optimized IS (XBOIS) method, which addresses the aforementioned shortcomings by deployment of an accurate surrogate model (e.g. delay) of the circuit around the failure region. The number of costly circuit simulations is therefore minimized and estimation accuracy is substantially improved by efficient exploration of the variation space. As especially memory elements occupy a large amount of on-chip resources, we evaluate our approach on SRAM cell failure rate estimation. Results show a speedup of about 16x as well as a two orders of magnitude higher failure rate estimation accuracy compared to the best state-of-the-art techniques.