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 power 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 topographies. 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 using InductEx, which is a pre- and post-processor for the magnetoquasistatic field solver FastHenry, is used to calculate the inductances of a set of SQUIDs (superconducting quantum interference devices) with ground plane holes of different sizes. The results are compared to measurements of physical structures fabricated with the IPHT Jena 1 kA cm−2 RSFQ niobium process to verify accuracy. We then do a parameter study and derive empirical equations for fast and useful estimation of the inductance of wires surrounded by ground plane holes. We also investigate practical circuits and show excellent accuracy.