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IEEE Transactions on Applied Superconductivity

High-T$_\text{c}$ SQUID Optimization: Exploring Competing Design and Operating Parameters

M. A. Galí Labarias, Oscar A. Nieves, Shane Keenan, E.E. Mitchell

Published May 2, 2024• 2 citations
Publisher

Abstract

Improving the design of superconducting quantum interference devices (SQUIDs) for quantum sensing applications can involve a compromise between competing device parameters. For SQUIDs made from high-temperature superconductors (HTS), accurate modelling for optimization should include the device geometry, material properties and their temperature dependences, as well as thermal noise. We outline here a lumped element model that calculates the voltage response to magnetic flux of a hairpin SQUID and use it to explore the effect of these parameters on optimizing the SQUID voltage output. We first validate our model by showing close agreement with current-voltage and voltage-flux measurements performed on Yttrium Barium Copper Oxide hairpin SQUIDs with different geometries by including structures such as the bias leads. We show the effect of track width on the kinetic to geometric inductance ratios ($\kappa$) for a range of film thicknesses and temperatures, to aid researchers how to optimize SQUID designs. Then, through numerical simulations, we show on how (i) the voltage modulation depth decreases exponentially with the total inductance, independent of the asymmetry ratio; (ii) narrower superconducting tracks lead to a broader temperature operation range,$\Delta T \sim 30$K, while wider tracks operate in a narrower temperature range,$\Delta T \sim 10$K, but are more sensitive to temperature changes; and (iv) the optimal bias current, which maximises the device performance, depends on the operating temperature.

DOI
10.1109/tasc.2024.3396129

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High-Tc_\text{c}c​ SQUID Optimization: Exploring Competing Design and Operating Parameters
Improving the design of superconducting quantum interference devices (SQUIDs) for quantum sensing applications can involve a compromise between competing device parameters. For SQUIDs made from high-temperature superconductors (HTS), accurate modelling for optimization should include the device geometry, material properties and their temperature dependences, as well as thermal noise. We outline here a lumped element model that calculates the voltage response to magnetic flux of a hairpin SQUID and use it to explore the effect of these parameters on optimizing the SQUID voltage output. We first validate our model by showing close agreement with current-voltage and voltage-flux measurements performed on Yttrium Barium Copper Oxide hairpin SQUIDs with different geometries by including structures such as the bias leads. We show the effect of track width on the kinetic to geometric inductance ratios (κ\kappaκ) for a range of film thicknesses and temperatures, to aid researchers how to optimize SQUID designs. Then, through numerical simulations, we show on how (i) the voltage modulation depth decreases exponentially with the total inductance, independent of the asymmetry ratio; (ii) narrower superconducting tracks lead to a broader temperature operation range,ΔT∼30\Delta T \sim 30ΔT∼30K, while wider tracks operate in a narrower temperature range,ΔT∼10\Delta T \sim 10ΔT∼10K, but are more sensitive to temperature changes; and (iv) the optimal bias current, which maximises the device performance, depends on the operating temperature.
Inductance plays a crucial role in the design and optimization of superconducting quantum interference devices (SQUIDs) for quantum sensing applications, since it dictates the sensitivity and coupling ratio with other circuit elements. In high-temperature superconductors the kinetic inductance, which depends on both geometry and temperature, becomes a dominant part of the device's total self-inductance, since their London penetration depth is considerably larger compared to low-temperature superconductors. In this work, we use an asymmetric SQUID to investigate the kinetic self-inductance ratio and voltage modulation depth at different operating temperatures, device geometries and bias currents. We first validate our approach by comparing our modelled data with experimental measurements. Then, through numerical simulations, we show: (i) kinetic inductance dominates for thin superconducting films, while for thicker films the inductance is less sensitive to temperature changes; (ii) the voltage modulation depth decreases exponentially with the total inductance independent of the asymmetry ratio; (iii) narrower superconducting tracks lead to a broader temperature operation range, ΔT∼30KΔT \sim 30 KΔT∼30K, while wider tracks operate in a smaller temperature range, ΔT∼10KΔT \sim 10 KΔT∼10K, but are more sensitive to temperature changes; and (iv) the device performance versus temperature strongly depends on the bias current used.
Direct current-superconducting quantum interference devices (SQUIDs) characterized by asymmetric Josephson junctions have never been used for applications. In order to demonstrate their potential advantages, a throughout numerical analysis of different asymmetric configurations has been carried out. A damping resistance has been included in the SQUID circuit and the thermal noise associated with junction and damping resistances has been considered in the numerical model. Magnetic modulations and flux noise spectral densities have been computed as a function of many parameters (bias current, asymmetry, SQUID inductance, and damping resistance) and the performance of symmetric and asymmetric devices have been compared. The results show that, by properly optimizing the SQUID design, asymmetric SQUIDs are characterized by higher magnetic flux to voltage transfer coefficient and lower flux noise. As a result, asymmetric configurations can be very useful in all the applications where high sensitivity is required.
Abstract Designing superconducting electronic devices involves a careful study of all the elements in the circuit, including the superconducting bias leads. In this work, we introduce a theoretical model for two-dimensional (2D) superconducting quantum interference device (SQUID) arrays capable of simulating the voltage-to-magnetic flux response of devices with different bias current configurations. First, we compare uniformly biased and centre biased SQUID arrays by investigating the voltage versus magnetic flux response, maximum transfer function and voltage modulation depth. Then, we calculate the time-averaged fluxoid distributions for one-dimensional (1D) and 2D centre biased arrays. Finally, we study the performance of the two bias current configurations depending on array size, screening parameter, thermal noise strength and kinetic self-inductance fraction. Our calculations reveal: (i) centre biased 1D parallel SQUID arrays present an unusual voltage response caused by the asymmetric fluxoid distribution; (ii) the optimal transfer function of centre biased arrays strongly depends on the number of junctions in parallel; (iii) the performance of centre biased arrays approaches the uniform biased ones when the number of junctions in series exceeds those in parallel; (iv) while the screening parameter and the thermal noise strength clearly affect the device performance, the kinetic to self-inductance fraction seems to play only a secondary role.
Recently, we demonstrated and analysed the superconducting quantum interference device (SQUID) bootstrap circuit (SBC). It is a direct readout scheme for dc SQUID in the voltage bias mode, permitting one to suppress the preamplifier noise. The SBC enables us to control the two key parameters of a voltage-biased SQUID: the flux-to-current transfer coefficient and the dynamic resistance. The flux-to-current, I??, characteristics of SBC are made asymmetric by introducing the additional current feedback. Depending upon the choice of the working point, this feedback can be positive (working point W2 on the steeper I?? slope) or negative (W1 on the less steep slope). The dynamic resistance is controlled by the additional voltage feedback. In our publications to date we presented only the SBC operation at W2, while in this paper we demonstrate operation at W1 and show that also in this regime the preamplifier noise suppression is possible. We used a liquid-helium-cooled Nb SQUID with a loop inductance of 350 pH and attained white flux noise of 2.5? ??0?Hz ? 1/2 both at W2 and at W1. In the latter case, the linear flux range exceeded one half-flux quantum ?0. This large linear range should lead to a significantly improved stability and slew rate of the system and also make the tolerable spread in circuit parameters much wider than in all SQUID direct readout schemes known to date. Consequently, operation in this regime opens a new path to possible SBC optimization.
Practical thin-film dc superconducting quantum interference devices (SQUIDs) are often built with an integrated input coil which leads to the formation of various parasitic elements. We have designed and fabricated several square washer-shaped dc SQUID test devices with various amounts of parasitic capacitance formed by covering the washer slits with superconducting coverplates of various widths. In the simplest approximation, the parasitic capacitance Cp appears entirely across the Josephson junctions; in a better approximation, Cp divides the total inductance into two parts, an effective SQUID loop inductance L and a small parasitic inductance Lp. For both models, noise-free and noise-rounded current-voltage and voltage-flux characteristics are calculated for various values of the ratios L/Lp and Cp/C, where C is the Josephson junction capacitance. The SQUID dynamics are significantly affected by Cp and Lp. The energy resolution ε at first deteriorates with increasing Cp for Cp/C ≲ 2, but as Cp/C becomes large, ε improves to less than twice the value for Cp/C ≊ 0. The optimal points of operation for large Cp, however, are found at voltages above the low-frequency resonance determined by L and Cp where the flux-to-voltage transfer function is low. Furthermore, for devices with Cp/C ≫ 1 and Lp≠0, the double-loop geometry leads to an additional resonance determined by Lp and C that appears at high frequencies. The energy resolution inside this high-frequency resonance is nearly independent of Cp and comparable to the energy resolution of a device having the same total inductance but with Cp/C ≪ 1. Extensive noise mappings on several different test devices have been carried out using a computer-controlled measurement system. The measured characteristics and noise performance are shown to be in good agreement with the simulations.
Abstract Superconducting quantum interference devices (SQUIDs) with 3D nano-bridge junctions can be miniaturized into nano-SQUIDs that are able to sense a few spins in a large magnetic field. Among all device parameters, the inductance is key to the performance of SQUIDs with 3D nano-bridge junctions. Here, we measured the critical-current magnetic flux modulation curves of 12 devices with three design types using a current strip-line directly coupled to the SQUID loop. A best flux modulation depth of 71% was achieved for our 3D Nb SQUID. From the modulation curves, we extracted the inductance values of the current stripe-line in each design and compared them with the corresponding simulation results of InductEX. In this way, London penetration depths of 110 and 420 nm were determined for our Nb (niobium) and NbN (niobium nitride) films, respectively. Furthermore, we showed that inductances of 11 and 119 pH for Nb and NbN 3D nano-bridge junctions, respectively, dominated the total inductance of our SQUID loops which are 23 pH for Nb and 255 pH for NbN. A screening parameter being equal to one suggests optimal critical currents of 89.6 and 8.1 μ A for Nb and NbN SQUIDs, respectively. Additionally, intrinsic flux noise of 110 ± 40 n Φ 0 /(Hz) 1/2 is calculated for the Nb SQUIDs with 3D nano-bridge junctions by Langevin simulation.