Comparison of measurements and simulations of series-parallel incommensurate area superconducting quantum interference device arrays fabricated from YBa2Cu3O7− δ ion damage Josephson junctions

Abstract

We have fabricated series-parallel (two-dimensional) arrays of incommensurate superconducting quantum interference devices (SQUIDs) using YBa2Cu3O7−δ thin film ion damage Josephson junctions. The arrays initially consisted of a grid of Josephson junctions with 28 junctions in parallel and 565 junctions in series, for a total of 15 255 SQUIDs. The 28 junctions in the parallel direction were sequentially decreased by removing them with photolithography and ion milling to allow comparisons of voltage–magnetic field (V–B) characteristics for different parallel dimensions and area distributions. Comparisons of measurements for these different configurations reveal that the maximum voltage modulation with magnetic field is significantly reduced by both the self inductances of the SQUIDs and the mutual inductances between them. Based on these results, we develop a computer simulation model from first principles which simultaneously solves the differential equations of the junctions in the array while considering the effects of self inductance, mutual inductance, and non-uniformity of junction critical currents. We find that our model can accurately predict V–B for all of the array geometries studied. A second experiment is performed where we use photolithography and ion milling to split another 28 × 565 junction array into 6 decoupled arrays to further investigate mutual interactions between adjacent SQUIDs. This work conclusively shows that the magnetic fields generated by self currents in an incommensurate array severely reduce its performance by reducing the maximum obtainable modulation voltage.

From single SQUID to superconducting quantum arrays

“…One should note also that the expected progress in Josephson junction fabrication technology, e.g., with a further increase in critical current density of the niobium process or with advancement in high-temperature superconductor technology [37][38][39], will allow improving characteristics of the quantum cells and hence the SQA-based devices.…”

High-Tc Step-Edge Josephson Junction Arrays: Comparison of Simulated and Experimental Voltage Responses

“…Models to simulate parallel arrays have been developed based on circuit theory as a summation of the single SQUID equations [15] over multiple junctions and wires [3]. Similar models have been expanded to cover 2D arrays, summing over junctions in series and parallel [6]. These models have been incorporated into Wavenology's SPICE environment to simulate the response of SQUIDs and SQUID arrays.…”

“…K To date, most models have been developed for Low Temperature Superconducting (LTS) arrays, using models based on circuit theory [5]. Some models have been developed for HTS arrays [6], [7], again using a circuit theory approach.…”

Modelling the transfer function of two-dimensional SQUID and SQIF arrays with thermal noise

“…Two-dimensional SQUID arrays models without considering thermal noise have been previously investigated by Cybart et al 25 , Dalichaouch et al 26 and Taylor et al 24 , but these models become inaccurate at 77 K where the thermal noise strength is large.…”