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

Abstract

SUMMARYWe 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.

Recent Progress on Reversible Quantum-Flux-Parametron for Superconductor Reversible Computing

“…The RQFP cell is placed between AQFP BUF chains to confirm its compatibility with current AQFP cells. The layout of the RQFP cell was designed using an inductance extraction tool, InductEx [33], [34]. The dimension of the RQFP cell is 180 μm × 145 μm, which is only 36% of that of the original design (270 μm × 270 μm) [10].…”

Adiabatic quantum-flux-parametron cell library designed using a 10 kA cm−2niobium fabrication process

“…The layout was designed symmetrically to avoid unwanted couplings inside the cell [16]. The circuit parameters of the cell, which were extracted using InductEx [25,26], are shown in the caption. L q and L out were designed asymmetrically to increase the output current, I out , [16], so that L out /L q is approximately 3.7.…”

Flux transfer circuits breaking conventional limit in transfer coefficient based on a negative inductance of a π-junction

“…The estimated parameters are described in the figure caption of figure 3. InductEX was used to extract the geometrical inductances and the coupling coefficients from the actual layout [30,31].…”