Fast Statistical Analysis of Rare Circuit Failure Events via Scaled- Sigma Sampling for High-Dimensional Variation Space

Accurately estimating the rare failure rates for nanoscale circuit blocks (e.g., SRAM, DFF, etc.) is a challenging task, especially when the variation space is high-dimensional. In this paper, we propose a novel scaled-sigma sampling (SSS) method to address this technical challenge. The key idea of SSS is to generate random samples from a distorted distribution for which the standard deviation (i.e., sigma) is scaled up. Next, the failure rate is accurately estimated from these scaled random samples by using an analytical model derived from the theorem of “soft maximum”. Several circuit examples designed in nanoscale technologies demonstrate that the proposed SSS method achieves superior accuracy over the traditional importance sampling technique when the dimensionality of the variation space is more than a few hundred. 1