Root-Finding Methods for Assessing SRAM Stability in the Presence of Random Dopant Fluctuations

In this paper, we propose a closed-form method to evaluate the read stability of an SRAM cell via quartic root finding. By utilizing a simplified MOSFET device model, we model SRAM cell stability by a system of quartic equations. The algebraic nature of the equations along with simplified region boundaries provide the insight that only a few combinations of device operating regions correspond to the stability of the cell, instead of 729 combinations in the brute force approach. Such an insight not only makes it possible to have a quick ¿litmus test¿ to determine cell stability under variability but also significantly speeds up the analysis, compared to a traditional SPICE approach. Experimental results using industrial bulk CMOS models show that the results are in excellent agreement with SPICE results and 65× faster.