Reachability-Based Robustness Verification and Optimization of SRAM Dynamic Stability Under Process Variations

The dynamic stability margin of SRAM is largely suppressed at nanoscale due to not only dynamic noise but also process variation. This paper introduces an analog verification for SRAM dynamic stability under threshold-voltage variations. A zonotope-based reachability analysis by the backward Euler method is deployed for SRAM dynamic stability in state space with consideration of SRAM nonlinear dynamics. It can simultaneously consider multiple SRAM variation sources without multiple repeated computations. What is more, sensitivity analysis is developed for zonotope to optimize SRAM designs departing from unsafe regions by simultaneously tuning multiple SRAM device parameters. In addition, compared to the SRAM optimization by single-parameter small-signal sensitivity, the proposed method can converge faster with higher accuracy. As shown by numerical experiments, the proposed optimization method can achieve 600× speedup on average when compared to the repeated Monte Carlo simulations under the similar accuracy.