Access time optimization of SRAM memory with statistical yield constraint

A product may fail when design parameters are subject to large deviations. To guarantee yield one likes to determine bounds on the parameter range such that the fail probability P_fail is small. For Static Random Access Memory (SRAM) characteristics like Static Noise Margin and Read Current, obtained from simulation output, are important in the failure criteria. They also have non-Gaussian distributions. With regular Monte Carlo (MC) sampling we can simply determine the fraction of failures when varying parameters. We are interested to efficiently sample for a tiny fail probability P_fail ≤ 10^-10. For a normal distribution this corresponds with parameter variations up to 6.4 times the standard deviation σ. Importance Sampling (IS) allows to tune Monte Carlo sampling to areas of particular interest while correcting the counting of failure events with a correction factor. To estimate the number of samples needed we apply Large Deviations Theory, first to sharply estimate the amount of samples needed for regular MC, and next for IS. With a suitably chosen distribution IS can be orders more efficient than regular MC to determine the fail probability P_fail. We apply this to determine the fail probabilities the SRAM characteristics Static Noise Margin and Read Current. Next we accurately and efficiently minimize the access time of an SRAM block, consisting of SRAM cells and a (selecting) Sense Amplifier, while guaranteeing a statistical constraint on the yield target.