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arXiv:2303.05609 · Superconductor Science and Technology

The effect of bias current configuration on the performance of SQUID arrays

M. A. Galí Labarias, K.‐H. Müller, E.E. Mitchell

Published Sep 17, 2023• 6 citations
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Abstract

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.

DOI
10.1088/1361-6668/acfa7a

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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.
We present a theoretical model for two-dimensional (2D) superconducting quantum interference device (SQUID) and superconducting quantum interference filter (SQIF) arrays with overdamped Josephson junctions for uniform bias-current injection at 77 K. Our simulations demonstrate the importance of including Johnson thermal noise and reveal that only the SQUID-loops self-inductance contributions are of importance. Our numerical results establish the validity of a scaling behavior between the voltages of one-dimensional (1D) and 2D SQUID arrays and show that the same scaling behavior applies to the maximum transfer functions. The maximum transfer function of a 2D SQUID array can be further optimized by applying the optimal bias current, which depends on the SQUID-loop self-inductance and the junction critical current. Our investigation further reveals that a scaling behavior exists between the maximum transfer function of a 2D SQUID array and that of a single dc SQUID. Finally, we investigate the voltage response of 1D and 2D SQIF arrays and illustrate the effects of adding spreads in the heights and widths of SQUID loops.
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.
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.
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.
We experimentally studied two important parameters of helium-cooled superconducting quantum interference devices (SQUIDs) in the voltage bias mode: the dynamic resistance Rd and the flux-to-current transfer coefficient ∂i/∂Φ, with different junction shunt resistors RJ. We investigated a voltage-biased SQUID using the direct readout current-to-voltage converter scheme involving an operational amplifier. At higher RJ, the flux-to-voltage conversion coefficient ∂V/∂Φ becomes sufficiently large to effectively suppress the room-temperature amplifier's noise without any need for additional feedback circuits. The McCumber parameter limits the rise of ∂V/∂Φ. We discuss the performance of voltage-biased SQUIDs at different effective McCumber parameters.
Arrays of dc-superconducting quantum interference devices (dc-SQUIDs) were investigated, in which each dc-SQUID element has a multiturn input coil. The dependence of flux noise on the number of turns of the input coil was studied for current amplifiers. SQUID arrays were fabricated by a Nb/AlO x /Nb Josephson tunnel junction fabrication process. Results show that the flux noise of the SQUID array amplifier does not depend on the turn number of the input coil. A SQUID array amplifier consisting of 128 dc-SQUID elements was fabricated, in which each element had a 7-turn input coil and a mutual inductance between the input coil and the SQUID loop of 460 pH. This amplifier showed an ultrahigh current resolution of 1 pA/Hz0.5 and a maximum input current of 11 µA for signals of 50 kHz, which is sufficient bandwidth for X-ray detection applications. These values correspond to a large dynamic range of 87 dB. The flux-voltage characteristics of this SQUID array, however, showed asymmetric behavior, which originated from electronic resonance in stray capacitance and the mutual inductance between the SQUID loop and the multiturn input coil.