Gradient importance sampling: An efficient statistical extraction methodology of high-sigma SRAM dynamic characteristics

Gradient importance sampling: An efficient statistical extraction methodology of high-sigma SRAM dynamic characteristics

The impact of within-die transistor variability has increased with CMOS technology scaling up to the point where it has emerged as a systematic problem for the designer. Estimating extremely low failure rate, i.e. “high-sigma” probabilities, by the conventional Monte Carlo (MC) approach requires millions of simulation runs, making it an impractical approach for circuit designers. To overcome this problem, alternative failure estimation methodologies, which require a smaller number of runs have been proposed. In this paper, we propose a novel methodology called “gradient importance sampling” (GIS) for fast statistical extraction of high-sigma circuit characteristics. It is based on conventional Importance Sampling combined with a gradient-based approach to find the most probable failure point (MPFP). By applying GIS to extract SRAM dynamic characteristics in 28nm FDSOI CMOS, we show that the proposed methodology is straightfor-ward, computationally efficient and the results are in line with those obtained via standard MC. To the best of our knowledge, the GIS results are the best in their class for low failure rate estimation.

随着CMOS技术的不断缩小，芯片内晶体管的可变性影响日益增大，以至于对设计人员来说已成为一个系统性问题。通过传统的蒙特卡洛（MC）方法估算极低的故障率，即“高西格玛”概率，需要进行数百万次模拟运行，这对电路设计人员来说是一种不切实际的方法。为了克服这个问题，人们提出了一些只需较少运行次数的替代故障估算方法。在本文中，我们提出了一种名为“梯度重要性抽样”（GIS）的新方法，用于快速统计提取高西格玛电路特性。它基于传统的重要性抽样，并结合一种基于梯度的方法来找到最可能的故障点（MPFP）。通过将GIS应用于28nm全耗尽绝缘体上硅（FDSOI）CMOS中的静态随机存取存储器（SRAM）动态特性提取，我们表明所提出的方法简单直接、计算高效，且结果与通过标准蒙特卡洛方法获得的结果一致。据我们所知，GIS在低故障率估算方面的结果在同类方法中是最佳的。