Loop flattening & spherical sampling: Highly efficient model reduction techniques for SRAM yield analysis

The impact of process variation in deep-submicron technologies is especially pronounced for SRAM architectures which must meet demands for higher density and higher performance at increased levels of integration. Due to the complex structure of SRAM, estimating the effect of process variation accurately has become very challenging. In this paper, we address this challenge in the context of estimating SRAM timing variation. Specifically, we introduce a method called loop flattening that demonstrates how the evaluation of the timing statistics in the complex, highly structured circuit can be reduced to that of a single chain of component circuits. To then very quickly evaluate the timing delay of a single chain, we employ a statistical method based on importance sampling augmented with targeted, high-dimensional, spherical sampling. Overall, our methodology provides an accurate estimation with 650X or greater speed-up over the nominal Monte Carlo approach.