Splitter-Aware Multiterminal Routing With Length-Matching Constraint for RSFQ Circuits

Abstract

Aided by the advancement of super-conductive materials, rapid single flux quantum (RSFQ) digital circuits are emerging as a promising complement or even replacement of the traditional CMOS digital integrated circuits. RSFQ digital circuits typically work at a low temperature of around 4.2 K, i.e., around −268.95 °C. Nevertheless, the operating frequency of RSFQ digital circuits reaches up to 770 GHz, which is orders of magnitudes faster than contemporary CMOS digital circuits. The high operating frequency causes critical design challenges especially for the clock networks and data path signals, where relative skew on wires need to be observed for achieving the correct functionality. Therefore, for designing a timing-variability-aware SFQ layout, it is necessary to match the PTL delays that are proportional to their respective lengths. And the matching of PTL delays should be carried out by extensions in PTL lengths. To meet the above-mentioned critical timing requirements, it is necessary to incorporate length-matching constraints into a routing problem, which is transformed from the timing requirements of matching the PTL delays during the logical synthesis stage. However, existing routing algorithms are inherently limited by preallocated splitters (SPLs), which complicates the subsequent routing stage under length-matching constraints. In this article, in order to effectively address the length-matching constraints, we reallocate SPLs to fully utilize routing resources. We propose the first multiterminal routing algorithm for RSFQ circuits, which integrates SPL reallocation into the routing stage and achieves 100% routing completion in the tested benchmarks. Compared with the state-of-the-art method, the proposed multiterminal routing algorithm reduces the required area by 17% and the runtime by 7%.