Three-dimensional multi-terminal superconductive integrated circuit inductanceextraction

Abstract

Accurate inductance calculations are critical for the design of both digital and analoguesuperconductive integrated circuits, and three-dimensional calculations are gainingimportance with the advent of inductive biasing, inductive coupling and sky plane shieldingfor RSFQ cells. InductEx, an extraction programme based on the three-dimensionalcalculation software FastHenry, was proposed earlier. InductEx uses segmentationtechniques designed to accurately model the geometries of superconductive integratedcircuit structures. Inductance extraction for complex multi-terminal three-dimensionalstructures from current distributions calculated by FastHenry is discussed. Results forboth a reflection plane modelling an infinite ground plane and a finite segmentedground plane that allows inductive elements to extend over holes in the groundplane are shown. Several SQUIDs were designed for and fabricated with IPHT’s1 kA cm − 2 RSFQ1D niobium process. These SQUIDs implement a number of loop structures thatspan different layers, include vias, inductively coupled control lines and ground planeholes. We measured the loop inductance of these SQUIDs and show how theresults are used to calibrate the layer parameters in InductEx and verify theextraction accuracy. We also show that, with proper modelling, FastHenry canbe fast enough to be used for the extraction of typical RSFQ cell inductances.