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Applied Physics Letters

Performance of dc SQUIDs with resistively shunted inductance

Vittorio Foglietti, W. J. Gallagher, M. B. Ketchen, Alan W. Kleinsasser, R. H. Koch, Robert L. Sandstrom

Published Oct 2, 1989• 45 citations
Publisher

Abstract

We have fabricated and characterized the noise performance of well-coupled Nb-Pb alloy edge junction dc superconducting quantum interference devices (SQUIDs) with a resistively shunted inductance. The extra damping resistor removes the resonances in the current-voltage characteristics resulting in a very low value of the extrinsic energy sensitivity in flux-locked-loop operation. Numerical simulations, with the junction capacitance included, indicate that the damping resistance does not degrade noise performance until it is significantly less than the junction-shunting resistance. We also tested different SQUID designs and demonstrated that a large SQUID inductance, proposed earlier to be desirable when resistively shunted, can seriously affect the low-frequency flux noise.

DOI
10.1063/1.101583

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Applied Physics Letters•Apr 26, 1993•24 citations
We have fabricated and characterized the noise performance of well-coupled Nb-Pb alloy edge junction dc superconducting quantum interference devices (SQUIDs) with a resistively shunted inductance. The extra damping resistor removes the resonances in the current-voltage characteristics resulting in a very low value of the extrinsic energy sensitivity in flux-locked-loop operation. Numerical simulations, with the junction capacitance included, indicate that the damping resistance does not degrade noise performance until it is significantly less than the junction-shunting resistance. We also tested different SQUID designs and demonstrated that a large SQUID inductance, proposed earlier to be desirable when resistively shunted, can seriously affect the low-frequency flux noise.
The design, fabrication, and noise properties of an ultra-low-noise tunnel junction dc SQUID (superconducting quantum interference device) are presented. The two resistively shunted Pb-alloy tunnel junctions are each 3.6 μm diam. The SQUID has an inductance L of ≈11 pH, a critical current per junction, I0 of ≈100 μA, and a resistance per shunt R of ≈2 Ω. At 2.3 K, eI0R≈kBT, and simple theory predicts that the minimum intrinsic energy sensitivity should be ≈2h. The actual minimum value of the measured high-frequency (70 kHz) flux noise at 4.2 K is φn=1.3×10−7φ0 Hz−1/2. This corresponds to an intrinsic energy sensitivity, φ2n/2L, of 3.2×10−33 J Hz−1 or 5h. Lowering the bath temperature to 1.8 K gave no improvement in performance.
Noise characteristics of a dc SQUID with an inductance shunted by a damping resistance are studied numerically. It is shown that the damping resistance improves considerably the resolution of the SQUID in the case of large β, where β=2LI0/Φ0, I0 is a critical current, L is a loop inductance and Φ0 is the flux quantum. The energy resolutions for β=4 and β=10 are only about 2 and 4 times larger than that for β=1, respectively. Furthermore, the ranges of both the bias current and the external flux, where good resolution is obtained, become very wide compared with the conventional SQUID. Therefore, the SQUID with the damping resistance can be used for large β (or L) without the significant degradation of the resolution, and will much improve the coupling properties between the SQUID and the input circuitry. The numerical simulation results are also compared with analytical ones, and a reasonable agreement is obtained.
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.
We have fabricated dc superconducting quantum interference devices (SQUIDs) incorporating Nb/Al-oxide/Nb Josephson junctions in both stripline and washer geometries. Low-frequency noise in excess of that predicted by the resistively-shunted junction model is present in both geometries and is demonstrated to be flux noise. This flux noise is not environmental. Improvements in fabrication processing over the past four years have reduced the level of this flux noise. SQUIDs are now fabricated with PdAu resistors, Nb wiring layers, and SiO/sub 2/ interlayer dielectric. In our best well-coupled SQUIDs, the white-noise energy sensitivity is 5/spl times/10/sup -31/ J/spl middot/s, with a 1/f knee below 0.1 Hz. We believe further reduction in the flux noise might be obtained with the use of on-chip flux shielding and/or trapping structures.
Noise characteristics of dc SQUIDs in large β regimes have been studied experimentally in the case when a SQUID inductance is resistively shunted. Here, β=2L I 0/Φ0 is the modulation parameter, L is the SQUID inductance, I 0 is the critical current of the Josephson junction and Φ0 is the flux quantum. It is shown experimentally that the performance of the SQUID does not degrade significantly even for large β values; for example, the minimum energy resolution of the SQUID is as small as ε=25h and the flux region where ε<50h is as wide as 0.1Φ0, even for the case β=12, where h is the Planck constant. The experimental results agree quantitatively with the theoretical ones.
We have fabricated Y1Ba2Cu3O7−x step-edge junction dc superconducting quantum interference devices (SQUIDs) and characterized their noise performance. The current-voltage characteristics of our SQUIDs are of resistively shunted junction type with critical current densities jc of about 104 A/cm2 and maximum flux to voltage transfer functions δV/δΦ of 20 μV/Φ0 at 77 K. We compare model predictions for 1/f noise in dc SQUIDs with experimental data and show that the frequency dependent noise in our devices results from critical current fluctuations of the Josephson junctions. A bias current reversing technique is effective in suppressing this noise contribution. A flux noise Φn of 80 μΦ0/Hz1/2 at 1 Hz and 77 K was measured on a dc SQUID with an inductance Ls of 60 pH.