Inductance and Current Distribution Extraction in Nb Multilayer Circuits with Superconductive and Resistive Components

We describe a calculation tool and modeling methods to find self and mutual inductance and current distribution in superconductive multilayer circuit layouts. Accuracy of the numerical solver is discussed and compared with experimental measurements. Effects of modeling parameter selection on calculation results are shown, and we make conclusions on the selection of modeling parameters for fast but sufficiently accurate calculations when calibration methods are used. Circuit theory for the calculation of branch impedances from the output of the numerical solver is discussed, and compensation for solution difficulties is shown through example. We elaborate on the construction of extraction models for superconductive integrated circuits, with and without resistive branches. We also propose a method to calculate current distribution in a multilayer circuit with multiple bias current feed points. Finally, detailed examples are shown where the effects of stacked vias, bias pillars, coupling, ground connection stacks and ground return currents in circuit layouts for the AIST advanced process (ADP2) and standard process (STP2) are analyzed. We show that multilayer inductance and current distribution extraction in such circuits provides much more information than merely branch inductance, and can be used to improve layouts; for example through reduced coupling between conductors. key words: ground plane return currents, inductex, layout extraction, numerical inductance calculation, parasitic coupling