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IEEE Transactions on Electron Devices

Advances in SQUID magnetometers

John L. Clarke

Published Oct 1, 1980• 88 citations

Abstract

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.

DOI: 10.1109/t-ed.1980.20127

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IEEE Transactions on Magnetics•Jan 1, 1979•36 citations

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.

We have fabricated and characterized the noise performance of submicron edge junction dc superconducting quantum interference devices (SQUID’s) which exhibit excellent signal properties and extremely high flux sensitivity. At frequencies above about 3 MHz, the SQUID noise is white and is in reasonable agreement with computer simulations for a thermal noise-limited detector. In one device the measured flux energy resolution is 1.6±0.5ℏ at 1.5 K, within a factor of 2 of the quantum-limited value suggested by theoretical modeling.

A series of dc SQUIDs has been fabricated in an attempt to obtain quantum-limited sensitivity. Typically, the SQUID inductance, L, is 2 pH, the capacitance and critical current of each tunnel junction are 0.5 pF and 0.5 mA, and the shunt resistance for each junction is 1Ω. The measured spectral density of the voltage noise Sv contains a l/f component that extends typically to 100 kHz or higher. When the l/f component is subtracted out, the best energy sensitivity achieved to date is ε1Hz = Sv2L(θVθΦ)2 less than or approximately equal to 2h, where θV/θΦ PHI is the transfer coefficient.

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.

The authors have designed, fabricated and tested all-refractory DC SQUIDs in Nb-Al/sub 2/O/sub 3/-Nb trilayer technology that have noise performance comparable to the best previously reported for any technology. A variety of SQUID designs were incorporated as part of a trilayer process development test vehicle. SQUID inductance, junction area, and resistive shunt geometry were varied in matrix fashion to give SQUIDs with near-optimum parameter values for a factor of five range in Josephson current density and shunt sheet resistance. The devices were fabricated using a selective niobium anodization with a minimum feature size of 2 mu m. The base electrode and Nb wiring were patterned with dry etching, and the junction areas were defined by anodization: the Ti resistors were patterned with a lift-off process. Current density on different wafers was varied from 400 to 1000 A/cm/sup 2/ with typical junction V/sub m/'s of 60 mV. The shunt sheet resistance was varied in the 1-5- Omega / Square Operator range. The noise was measured with an RF SQUID direct small-signal readout scheme. A 50-pH SQUID with 3- mu m/sup 2/, 16- mu A junctions and 14- Omega shunt resistors was shown to have an ideally low white noise of 1*10/sup -13/ Phi /sub 0//sup 2//Hz, a white to 1/f crossover frequency at 7 Hz, and a noise level less than 6*10/sup -12/ Phi /sub 0//sup 2//Hz at 0.1 Hz.

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.

We have measured the characteristics of a novel SQUID magnetometer pumped at 9 GHz. The device comprises a niobium point-contact shunting a low impedance superconducting microwave transmission line which isolates the junction at high frequencies from a toroidal input transformer. The junction is matched to a 50 Ω coaxial transmission line and the SQUID is operated in a reflection mode. For low values of the weak link critical current we observe a modulation of the phase of the reflected microwave signal periodic in the applied flux. The modulation persists at high microwave power levels indicating that the junction response is maintained to at least 200 GHz. For large values of critical current, amplitude modulation is observed. We have obtained a differential sideband power of 230 pW/(\Phi_{0})^{2}which is close to the value predicted by a simple model. In flux-locked loop operation we have obtained an energy sensitivity referred to the input terminals of 7 × 10-31J/Hz, which is superior to that so far reported for any other SQUID.