Efficient SRAM failure rate prediction via Gibbs sampling

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 minimum 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 by sampling a sequence of one-dimensional probability distributions. Several implementation issues such as one-dimensional 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 commercial 65nm SRAM cell demonstrate that the proposed Gibbs sampling method achieves 3-10× runtime speed-up over other state-of-the-art techniques without surrendering any accuracy.