qSSTA: A Statistical Static Timing Analysis Tool for Superconducting Single-Flux-Quantum Circuits

Superconducting single flux quantum (SFQ) technology is an ultra-high performance and low power technology. The technology, however, lacks many of the design automation tools and capabilities that are commonplace in CMOS technology. This article describes methods to efficiently find the conditional probability density function (PDF) of the minimum workable clock period of SFQ circuits in view of manufacturing-induced process variations and presents qSSTA, a statistical static timing analysis tool targeting SFQ circuits. Following a grid-based correlation model, qSSTA represents spatial correlation of SFQ gates at different positions with respect to process parameters. By approximating timing characteristics of SFQ gates in a linear model, qSSTA is able to estimate the clock period as a normal random variable. Furthermore, process variations that generally result in extra delays in CMOS circuits can result in functional errors in SFQ circuits. qSSTA derives the closed form of the conditional PDF of the clock period under the scenario where all SFQ gates in the circuit work correctly. Compared to Monte Carlo simulations on look-up tables, experimental results show that the average percentage errors are 0.89% for the mean values, 8.04% for the standard deviation, and 0.61% for the 98-percentile point, whereas the runtime of qSSTA is 83% faster on average.