Experimentally verified inductance extraction and parameter study for superconductive integrated circuit wires crossing ground plane holes

As the complexity of Rapid Single Flux Quantum (RSFQ) circuits increases, both current and energy consumption of the circuits become important design criteria. Various new concepts such as inductive biasing for energy efficient RSFQ circuits and inductively coupled RSFQ cells for current recycling have been proposed to overcome increasingly severe design problems. Both of these techniques use ground plane holes to increase the inductance or coupling factor of superconducting integrated circuit wires. New design tools are consequently required to handle the new topologies. One important issue in such circuit design is the accurate calculation of networks of inductances even in the presence of finite holes in the ground plane. We show how a fast network extraction method with InductEx and FastHenry is used to extract the inductances of a set of SQUIDs with ground plane holes of different sizes. The results are compared to measurements of physical structures fabricated with IPHT’s 1kA cm-2 RSFQ1D niobium process. Based on this parameter study, an empirical equation is derived that provides a rough but useful estimation for the inductance of a wire surrounded by a ground plane hole. We also investigate practical circuits and show excellent accuracy.