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

Superconducting single-flux-quantum (SFQ) technology is a beyond-complementary metal;oxide;semiconductor (CMOS) technology, promising ultrahigh processing speed and low power consumption. A timing analysis tool for SFQ circuits should check circuit timing behavior, including working frequencies and hold time violations to determine the circuit performance. Unlike CMOS gates, generic SFQ gates are clocked gates, which produce their output pulses in response to a clock pulse and have a fan-out capability of one. An SFQ splitter, a special clockless gate that has a fan-out capability of two, is used to address the fan-out limitation. This gate is also utilized in the clock tree, which distributes clock pulses to various SFQ gates. The delay of a clock path in a clock tree is determined by the wire delays of connection nets and gate delays of splitters. However, the splitter delays in a clock path are significantly affected by process variations, resulting in a challenging skew problem. Furthermore, existing timing analysis tools of SFQ circuits are developed based on the timing definitions, rules, and constraints from CMOS technology with very few modifications. This article demonstrates the incompleteness of the existing SFQ technology timing definitions. Precisely, it presents a novel static timing analysis (STA) tool, qSTA, which checks the timing behavior of SFQ circuits based on revised definitions of the setup time and hold times. qSTA encompasses the common path pessimism removal technique, which removes the delays of the shared path segments between two clock paths to achieve a better approximation of real skew values. qSTA takes only 5.33 s to check the timing behavior of a 16-bit integer divider with 36;732 gates and 55;939 nets.