Research Of Subset Adaptive Importance Sampling For Cell Circuit High-sigma Yiled Analysis

With the evolution of integrated circuit technology nodes and the increase in design complexity,circuit yield cannot be correctly predicted due to process variation.To ensure the entire chip system reaches a higher yield,the highly repeated cell circuit needs to achieve 1e^-6or even lower failure rate(high-sigma).The original Monte Carlo method requires billions of simulations under high-sigma scenario.Accuracy of min-norm importance sampling is sensitive to pre-sampling step and has poor stability.The sampling efficiency of adaptive imptance sampling based on Gaussian distribution declines quickly under high-sigma scenes.Therefore fast yield analysis under high-sigma scenes methods are urgently needed.In this thsis an adaptive clustering and sampling based on Weibull density(ACS-WBL)is proposed.ACS-WBL can be divided into two steps:initialization and adaptive iteration.In the initialization phase,hyperspherical pre-sampling method is used to obtain original failure samples.In the adaptive phase,the failure region are divided into disjoint subspace by clustering the failure samples.Then weibull sampling distribution is constructed in parallel to accelarate the convergence speed.The optimal parameters of the sampling distribution are obtained by solving relative entropy minimization.Finally,new samples are generated according to the sampling distribution and the importance weight of the samples is calculated to update the failure rate;The iterative framework can reduce the dependence on the pre-sampling step and improve the stability of the algorithm.SRAM bitcell,combinational logic circuits(NAND,buffers,XOR)and latch circuit are utilized as verification scenarios to compare the effectiveness of ACS-WBL,MNIS and AIS.In all experimental circuits,ACS-WBL obtains accurate failure rate within 6000 simulations under high yield scenarios;In addition,in latch circuit experiment,the algorithm was repeated ten times to verify its stability.The result proves that MNIS has poor stability and the fluctuation range of the estimated value exceeds±0.1?,while the ten estimated failure rate of ACS-WBL fluctuates within±0.1?.Compared with MNIS and AIS,ACS-WBL has2X?5X speedup under extremely high yield scenarios and has better stability.