Adaptive sampling for efficient failure probability analysis of SRAM cells

In this paper, an adaptive sampling method is proposed for the statistical SRAM cell analysis. The method is composed of two components. One part is the adaptive sampler that manipulates an alternative sampling distribution iteratively to minimize the estimated yield error. The drifts of the sampling distribution are re-configured in each iteration toward further minimization of the estimation variance by using the data obtained from the previous circuit simulations and applying a high-order Householder's method. Secondly, an analytical framework is developed and integrated with the adaptive sampler to further boost the efficiency of the method. This is achieved by the optimal initialization of the alternative multi-variate Gaussian distribution via setting its drift vector and covariance matrix. The required number of simulation iterations to obtain the yield with a certain accuracy is several orders of magnitude lower than that of the crude-Monte Carlo method with the same confidence interval.