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arXiv:2307.01505

Kinetic inductance and voltage response dependence on temperature: Asymmetric dc SQUID case study

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

Published Jul 4, 2023• 0 citations
arXivHTMLPDF

Abstract

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, $ΔT \sim 30 K$, while wider tracks operate in a smaller temperature range, $ΔT \sim 10 K$, but are more sensitive to temperature changes; and (iv) the device performance versus temperature strongly depends on the bias current used.

DOI
10.48550/arxiv.2307.01505

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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.
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.
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.
The authors are developing a bolometer with a temperature sensor based on the temperature dependence of the inductance of a superconducting microstrip line. As a first step in exploring this idea experimentally, they have designed experiments to test only the temperature sensor. The experimental devices are all-niobium inductance thermometers fabricated on silicon substrates which have been deeply etched to provide areas of relative thermal isolation. The ground plane superconductor is thin enough so that its kinetic inductance dominates the audio frequency impedance of the stripline near its critical temperature, at 0.9 T/sub c/. This differential thermometer uses a commercial SQUID (superconducting quantum interference device) as the preamplifier. Preliminary results demonstrate a proof-of-principle for the thermometer design. An important quality factor for this type of measurement system is the depth of the null. The authors achieved a high value of 0.4*10/sup -6/, which is satisfying for a first try.>
Extremely sensitive far-infrared detectors suitable for both direct detection and heterodyne applications, based on mu m-sized thin films with thickness less than a superconducting penetration depth are possible. The penetration depth of such a film, and therefore its inductance, varies with temperature and with quasiparticle population (described by an effective temperature T*), resulting in both bolometric and nonequilibrium photoinductive responses. Incident radiation is coupled into the small-area kinetic inductor by a lithographic antenna, and the resulting inductance changes are amplified and converted to a voltage signal by an integrated microstrip DC SQUID. The device is sensitive because, unlike junction-based devices with large capacitive reactances, the kinetic inductor is naturally well matched to the antenna impedance at the far-IR frequency ( nu >2 Delta /h) and to the preamplifier (SQUID) impedance at microwave or video frequencies ( nu <<2 Delta /h). The best kinetic inductor materials are those with low electronic mean free path, large penetration depth, and high critical current density. Thus, common magnet alloys such as NbTi are the natural choice for liquid-He temperature operation. A detailed analysis predicts a (phonon-limited) NEP of 4*10/sup -17/ W/ square root Hz for a bolometer with an iridium kinetic inductor operated at 0.1 K. A heterodyne noise temperature of 2250 K (single-sideband) at 3 THz, with a 200-MHz bandwidth, is predicted for a Nb-Ti mixer operated at 4 K.
It has been shown that the voltage versus flux (V-Φ) relation of dc superconducting quantum interference devices (SQUIDs) operating at T=77 K is degraded considerably by thermal noise. Since degradation of modulation voltage in the V-Φ relation becomes more significant when inductance increases, a very restricted range of inductance exists which can be used at T=77 K. In order to reduce the degradation due to thermal noise and to enable the use of large inductances, a new SQUID using three Josephson junctions (3J-SQUID) is proposed. Numerical simulation shows that inductance of 3J-SQUID can be increased to twice as large as that of the conventional case without degrading modulation voltage. It is also shown that modulation voltage is highly improved by damping resistance parallel to inductance. As a result, we can expect to use inductances as large as L<500 pH if 3J-SQUID with damping resistance is employed. Large inductances available in 3J-SQUID will be useful in realizing efficient coupling of external magnetic field to the SQUID inductance.