Research Of Generative Model Based Method For High-Dimensional SRAM Circuit Yield Analysis

As the device size decreases to the nanometer scale,process fluctuations have an increasing impact on the yield of static random access memory(SRAM).Typical importance sampling based methods use Gaussian distribution as the optimal sampling distribution,and there are problems such as weight degradation in high dimensional scenes.Generative model based Adaptive Importance Sampling(GMAIS)is proposed to estimate the yield of high dimensional circuits.GMAIS first analyzes the characteristics of samples in high dimensional standard normal space,and then chooses a non-Gaussian generative model based on the mixed von Mises-fisher distribution.Subsequently,the maximum likelihood estimation and expectation maximum algorithm are used to iteratively solve parameters of generative model.Finally,adaptive importance sampling is applied to find out the failure probability of SRAM circuit.In order to verify the accuracy and effectiveness of GMAIS,Monte Carlo is applied as the gold standard.Hyper spherical cluster sampling method,adaptive importance sampling method and high dimensional and multi-failure-region importance sampling method are used as benchmarks.The 18-dimensional SRAM bit cell and the 21-dimensional SRAM sensitive amplifier are used as a low dimensional verification scheme,and the high dimensional verification scheme uses a 576-dimensional SRAM array.In low dimensional scenarios,GMAIS and several other methods can have an accurate yield estimation;In terms of efficiency,GMAIS is at least 2227 times faster than Monte Carlo and 2-10 times faster than other three methods.In high dimensional scenarios,GMAIS has the smallest relative error of 4.5%,while neither the adaptive importance sampling method nor the hyper spherical cluster sampling method can converge to an accurate value;In terms of speed,GMAIS is 1796 times faster than Monte Carlo and 7.5 times faster than the high dimensional and multi-failure-region importance sampling method.