SRAM memory margin probability failure estimation using Gaussian Process regression

Abstract

Estimating the failure probabilities of SRAM memory cells using Monte Carlo or Importance Sampling techniques is expensive in the number of SPICE simulations needed. This paper presents a methodology for estimating the dynamic margin failure probabilities by building a surrogate model of the dynamic margin using Gaussian Process regression. Additive kernel functions that can extrapolate the margin values from the simulated samples are presented. These proposed kernel functions decrease the out-of-sample error of the surrogate model for a 6T cell by 32% compared with a six-dimensional universal kernel such as a Radial-Basis-Function kernel (RBF). Finally, the failure probability values predicted by a surrogate model built using 1250 SPICE simulations are reported and compared with Monte Carlo analysis with 106 samples. The results show a relative error of 30% at 0.4V (predicted value of 4×10-6 for the Monte Carlo estimate of 3×10-6) and a relative error of 172% at 0.3V (predicted value of 3×10-5 for the Monte Carlo estimate of 1.1×10-5) for the dynamic read margin. These accuracy numbers are similar to those reported in previous proposals while the reduction in SPICE simulations is between 4× and 23× relative to these proposals and 800× compared to Monte Carlo method.