Gradient Importance Sampling: an Efficient Statistical Extraction Methodology of High‐Sigma SRAM Dynamic Characteristics
Thomas Haine1,a, Johan Segers2, Denis Flandre1 and David Bol1,b
1ICTEAM Institute
athomas.haine@uclouvain.be
bdavid.bol@uclouvain.be
2Institute of Statistics, Biostatistics and Actuarial Sciences Université catholique de Louvain, Louvain‐la‐Neuve, Belgium
ABSTRACT
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 straightforward, 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.
Keywords: Gradient, Importance sampling, Monte Carlo, Low failure rate probability, Variability, High‐sigma
