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Superconductor Science and Technology

Performance of DC SQUIDs with parasitic elements

J Schambach, L Warzemann, Peter B. Weber, H.‐G. Meyer, K. Blüthner, G. Daalmans, Franz Bömmel, D. Uhl

Published May 1, 1994• 3 citations
Publisher

Abstract

The influence on the I-V curves and on the noise properties of parasitic capacitances caused by a covered slit of a Ketchen-type SQUID has been studied. The experimental results are compared with numerical simulations based on a lumped-circuit-element model. In the I-V characteristics we found two operating points, with minimum white noise, that were independent of the parasitic capacitance.

DOI
10.1088/0953-2048/7/5/027

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IEEE Transactions on Electron Devices•Oct 1, 1980•88 citations
The influence on the I-V curves and on the noise properties of parasitic capacitances caused by a covered slit of a Ketchen-type SQUID has been studied. The experimental results are compared with numerical simulations based on a lumped-circuit-element model. In the I-V characteristics we found two operating points, with minimum white noise, that were independent of the parasitic capacitance.
The effect of parasitic capacitance C/sub p/ on DC SQUID characteristics and noise performance has been studied using a test structure consisting of 11 identical SQUID washers with Nb films of various widths covering the slit. The measured I-V characteristics are in good agreement with simulations based on a simple lumped circuit model. The energy resolution in seems to scale roughly according to in approximately= gamma /sub k/B/sup T/ square root L(C=2C/sub p/), where gamma is a dimensionless constant, k/sub B/ is the Boltzmann constant, T is the temperature, C is the junction capacitance, and L is the inductance.
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.
The dynamics of the dc-SQUID in the presence of a signal coil was studied. The signal coil creates an additive parasitic capacitance between the junctions and its self-resonance imports new features to the SQUID dynamics. Our results suggest that if a SQUID with smooth characteristics and low noise properties is desired, all the resonances present in the SQUID ring or in the flux coupling circuit should be damped properly. Low attenuation yields a system with high gain but with higher excess noise. On the other hand, heavy damping of the device yields low gain and a high noise level and thus a compromise is necessary.
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 experimental results obtained with low noise dc superconducting quantum interference devices (dc-SQUIDs) are sometimes not well understood. In particular, when the critical current is high, very irregular voltage versus flux characteristics can be measured. On the other hand, when the critical current is low, the characteristics follow perfectly the resistively shunted junction model. We have studied the dynamics of a dc-SQUID in the presence of stray capacitance and shunting resistors imbalance. The equations describing a circuit model for this physical system are integrated numerically and the results are compared with voltage versus flux characteristics obtained from fabricated devices. We find that the theoretical analysis accounts very well for previously misunderstood experimental features of the dc-SQUID. This model can give more physical sense to the various regimes of behavior of the dc-SQUID giving more insight into the experimental results.
The operation and noise limitations of de and RF SQUID's are outlined, and recent advances in their sensitivity are discussed. A model of the dc SQUID predicts an energy noise level per hertz referred to the SQUID of approximately8 k_{B}TL/R \approx 8 k_{B}T(\piLC)^{1/2}, whereL, R,andCare the SQUID inductance and the shunt resistance and capacitance of each Josephson junction. Some examples of dc SQUID's are described to show that their performance is generally in reasonable agreement with the model. The noise energy has improved from about 2 × 10-30J. Hz-1for a device withL = 1nH and a tunnel junction area of 104µm2to about 2 × 10-33J . Hz-1for a device withL = 0.1nH and a microbridge resistance of 40 Ω. Further improvements axe expected in the near future. The model of the RF SQUID predicts a noise energy per hertz referred to the SQUID of[(\pi\alpha^{2}\phi\min{0}\max{2}/2L) + 2 \pi \alpha k_{B}T\min{a}\max{(eff)}]/\omega_{RF}, where α is the intrinsic width of the distribution of flux transitions,T\min{a}\max{(eff)}is an effective amplifier noise temperature, and ωRFis the pump frequency. With one exception, the performance of the seven types of RF SQUID listed is in reasonable agreement with the model. The noise energy ranges from about 1.5 × 10-29J . Hz-1for a 20-MHz toroidal SQUID to 3.5 × 10-31J . Hz-1for 9-GHz reentrant toroidal SQUID; a somewhat better sensitivity has been reported for a 430-MHz device, apparently in conflict with the theory. In both dc and RF SQUID's, 1/fnoise (fis frequency) is likely to extend to higher frequencies as the white-noise level is decreased.