Fitting Mixtures of Gaussians to Heavy-Tail Distributions to Analyze Fail-Bit Probability of Nano-Scaled Static Random Access Memory

Abstract

This paper proposes a fitting method to approximate a heavy-tailed Gamma distribution characterizing the random telegraph noises by simple Gaussian mixtures model (GMM). The concepts central to the proposed method are 1) adaptive segmentation of the long-heavy tailed distributions such that the log-likelihood of GMM in each partition is maximized and 2) copy and paste with an adequate weight into each partition. It is verified that the proposed method can reduce the error of the fail-bit predictions by 2-orders of magnitude while reducing the iterations for EM step convergence to 1/16 at the interest point of the fail probability of 10-12 which corresponds to the design point to realize a 99.9% yield of 1Gbit chips.