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Journal of Physics Conference Series

Cooling fins to limit the hot-electron effect in dc SQUIDs

P. Falferi, R. Mezzena, Michael Mück, Andrea Vinante

Published Feb 1, 2008• 4 citations
Publisher

Abstract

The generally accepted noise theory of the dc SQUID predicts that the energy resolution scales as the electron temperature in the Josephson junction shunt resistors. As in metals at low temperature the electron-phonon coupling becomes very weak, the electron gas of the thin film shunt resistors undergoes a Joule heating due to the bias current and its temperature can be significantly higher than that of the thermal bath. This heating, the hot-electron effect, causes a deviation from the linear behaviour of noise versus temperature and a saturation of the SQUID noise, typically at temperatures of about 200 mK. This effect can be reduced considerably by increasing the effective volume available for the electron-phonon interaction by attaching "large" cooling fins to the shunt resistors. Our measurements have been performed on two thin film devices made with the same design of a dc SQUID but without the Josephson junctions: one device with standard shunt resistors, the other with shunt resistors with cooling fins. From these measurements one can expect for the SQUID with cooling fins an improvement of the noise saturation temperature of at most a factor 2, from 200 mK to about 100 mK.

DOI
10.1088/1742-6596/97/1/012092

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The generally accepted noise theory of the dc SQUID predicts that the energy resolution scales as the electron temperature in the Josephson junction shunt resistors. As in metals at low temperature the electron-phonon coupling becomes very weak, the electron gas of the thin film shunt resistors undergoes a Joule heating due to the bias current and its temperature can be significantly higher than that of the thermal bath. This heating, the hot-electron effect, causes a deviation from the linear behaviour of noise versus temperature and a saturation of the SQUID noise, typically at temperatures of about 200 mK. This effect can be reduced considerably by increasing the effective volume available for the electron-phonon interaction by attaching "large" cooling fins to the shunt resistors. Our measurements have been performed on two thin film devices made with the same design of a dc SQUID but without the Josephson junctions: one device with standard shunt resistors, the other with shunt resistors with cooling fins. From these measurements one can expect for the SQUID with cooling fins an improvement of the noise saturation temperature of at most a factor 2, from 200 mK to about 100 mK.
The dc Superconducting Quantum Interference Device (dc-SQUID) is one of the most sensitive magnetic field sensors available. In this thesis we concentrate on its application as an amplifier. In this configuration, an input circuit of interest can be connected by means of a coupling coil. The intended application of our developed low-Tc SQUID amplifiers is the readout of the first spherical gravitational wave antenna MiniGRAIL. Using small-signal analysis as well as numerical simulations, we study the achievable signal-to-noise ratio of such sensors in practical measurements. Published theories and studies could be extended. Some interesting points treated are the influence of the often used negative feedback (flux-locked loop), an altered input impedance of the SQUID amplifier and the influence of back-action noise, which directly affects the object of interest. The altered operation of the SQUID due to the presence of the input circuit is studied in numerical experiments. Another important issue, the influence of integrated input coils on the dynamics of SQUIDs, is investigated theoretically and experimentally. The performance of our developed sensors is compared to numerical simulations on detailed models. The results give insights into the behavior, design and usage of dc-SQUIDs with integrated coils. For a SQUID with input inductances of 1.5 μH we reached a good coupled energy sensitivity of about 170 ¯h in a dilution refrigerator. Furthermore, we investigated the hot-electron effect. This effect typically limits the sensitivity of superconducting electronics at sub-Kelvin bath temperatures due to a weakened electron-phonon coupling. We performed heating experiments on thin-film resistors which are similar to the shunt resistors of the Josephson junctions used in our sensors. The suppression of the hot-electron effect via electronic thermal transport to attached cooling fins is investigated both experimentally, theoretically and numerically. The numerical technique turns out to be a useful tool for the thermal design of superconducting electronics.
The energy sensitivity of a direct current (dc) superconducting quantum interference device (SQUID) can be improved if it is operated in a two-stage configuration. Employing this technique, a commercial dc SQUID system was modified and made competitive with other sensors especially designed for very low noise applications. We report the noise measurements performed in the temperature range 4.2 K–25 mK. At 4.2 K, the coupled energy sensitivity obtained with the two-stage dc SQUID was approximately ten times better than with a conventional readout electronics. The noise energy decreases linearly until approximately 300 mK, in good agreement with theoretical previsions. At lower temperature the hot-electron effect produces a saturation and the best energy sensitivity measured with open input coil is 35 ℏ.
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.
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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.
We have developed a set of SQUIDs optimized for readout of ac-biased transition edge sensors. Junction shunts are made of Pd and attached to cooling fins to facilitate low-noise operation at sub-kelvin temperatures. SQUID's have a low loop inductance in order to reach a large natural dynamic range even without negative feedback. The SQUIDs are intended to be used for frequency-domain multiplexing of X-ray calorimeter arrays. Both traditional dc-SQUIDs and novel un-SQUIDs are manufactured. The fabrication process and SQUID design criteria are reviewed.