Adaptive Segmentation Gaussian Mixtures Models for Approximating to Drastically Scaled-Various Sloped Long-Tail RTN Distributions

Abstract

Abstract-This paper proposes a fitting method to approximate the mixtures of various sloped-tail Gamma distribution characterizing the random telegraph noises (RTN) by an adaptive segmentation 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. This allows the fitting model to apply various bounded tail distribution even with multiple convex and concave folding curves. 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.Index Terms-Mixtures of Gaussian, random telegraph noise, em algorithm, heavy-tail distribution, long-tail distribution, fail-bit analysis, static random access memory, guard band design.