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Chinese Physics B

Simulation of dielectric resonator for a high-Tcradio frequency superconducting quantum interference device

Ji Gao, Yang Tao, Ping Ma, Dai Yuan-Dong

Published Jun 1, 2010• 6 citations
Publisher

Abstract

Nowadays, the high-critical-temperature radio frequency superconducting quantum interference device (high- T c rf SQUID) is usually coupled to a dielectric resonator that is a standard 10 × 10 × 1 mm 3 SrTiO 3 (STO) substrate with a YBa 2 Cu 3 O 7−δ (YBCO) thin-film flux focuser deposited on it. Recently, we have simulated a dielectric resonator for the high- T c rf SQUID by using the ANSOFT High Frequency Structure Simulator (ANSOFT HFSS). We simulate the resonant frequency and the quality factor of our dielectric resonator when it is unloaded or matches a 50-Ω impedance. The simulation results are quite close to the practical measurements. Our study shows that ANSOFT HFSS is quite suitable for simulating the dielectric resonator used for the high- T c rf SQUID. Therefore, we think the ANSOFT HFSS can be very helpful for investigating the characteristics of dielectric resonators for high- T c rf SQUIDs.

DOI
10.1088/1674-1056/19/6/067402

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Nowadays, the high-critical-temperature radio frequency superconducting quantum interference device (high- T c rf SQUID) is usually coupled to a dielectric resonator that is a standard 10 × 10 × 1 mm 3 SrTiO 3 (STO) substrate with a YBa 2 Cu 3 O 7−δ (YBCO) thin-film flux focuser deposited on it. Recently, we have simulated a dielectric resonator for the high- T c rf SQUID by using the ANSOFT High Frequency Structure Simulator (ANSOFT HFSS). We simulate the resonant frequency and the quality factor of our dielectric resonator when it is unloaded or matches a 50-Ω impedance. The simulation results are quite close to the practical measurements. Our study shows that ANSOFT HFSS is quite suitable for simulating the dielectric resonator used for the high- T c rf SQUID. Therefore, we think the ANSOFT HFSS can be very helpful for investigating the characteristics of dielectric resonators for high- T c rf SQUIDs.
At present, the high-transition-temperature radio frequency superconducting quantum interference device (High- T c RF SQUID) is usually coupled to a dielectric resonator which is a standard 10 mm×10 mm× 1 mm SrTiO3 (STO) substrate with a YBa2Cu3O7-δ (YBCO) thin-film flux focuser deposited on it. The dielectric resonator for the High- Tc RF SQUID has a high quality factor and a resonant frequency in the microwave range. In order to find out the effect of the flux focuser’s geometry on the dielectric resonator’s resonant frequency, we used ANSOFT high frequency structure simulator (ANSOFT HFSS) to simulate the resonance characteristics of some dielectric resonators with different flux focuser geometries. Our simulation results show that when the width of the flux focuser’s slit increases or the radius of the flux focuser’s inner hole decreases, the dielectric resonator’s resonant frequency increases. To estimate the reliability of our simulation results, we selectively prepared a few dielectric resonators and measured their resonance characteristics. The experimental results are virtually consistent with the simulation results. Our study shows that changing the flux focuser geometry is an effective way to adjust the dielectric resonator’s resonant frequency.
We simulate the dielectric SrTiO3 (STO) resonator for radio frequency superconducting quantum interference devices (rf SQUIDs) using electromagnetic analysis software. The simulated values of the resonant frequencies, the unloaded quality factor, the loaded quality factor under 50Ω matching, and the coupling with the SQUID are in good agreement with the experimental results. The simulation also shows that the strength of the electromagnetic field outside the resonator decreases exponentially with the distance from the resonator, which proves that the field is confined to a small volume near the resonator. Due to the strong temperature dependence of the permittivity of STO, the resonant frequency changes with the temperature fluctuations of liquid nitrogen, which may cause the low frequency noise of rf SQUIDs with dielectric resonators.
The operation of YBa2Cu3O7 rf superconducting quantum interference devices (SQUIDs) using a dielectric SrTiO3 resonator as tank circuit was tested. At 77 K, we attained for such resonators unloaded quality factors Q0 up to 7000 at resonant frequencies near 1 GHz, when measuring without electromagnetic shielding. For a washer SQUID with an area of 4×4 mm2 and an inductance of ≂100 pH, which was properly coupled to the resonator, we measured an approximately 60 μV peak-to-peak SQUID signal and a white flux noise spectral density of SΦ1/2=1×10−5Φ0/√Hz, corresponding to a field sensitivity of BN=105 fT/√Hz. With an additional single-layer flux transformer with a diameter of the pickup loop of 22 mm in flip-chip arrangement, the field sensitivity was improved to 30 fT/√Hz.
Characteristics of a lumped element L-C tank circuit resonator of high-Tc rf-SQUIDs, which plays an important role in the device operation, have been experimentally investigated, according to the corresponding simulations obtained by COMSOL Multiphysics. We experimentally investigated the characteristics of the resonators by measuring their scattering parameters, as well as evaluating the rf-SQUID signal. Our SQUIDs are made of sputtered YBCO thin films with 3-mm-diameter washer areas. Different configurations of the resonator are investigated, and it is observed that, by increasing the thickness of the dielectric in a specific range, the reflection coefficient (S11) increases. For the experimental verifications, we constructed resonators with different dielectric thicknesses and different configurations. The resonators are made of a dielectric board with a hole in its middle to hold the inductors for close coupling to the SQUID mounted on the backside. An increase in the thickness of the dielectric board confines the RF field distribution close to the SQUID, while also making further distance between the contact pads and the SQUID reducing their parasitic effects on the device signal. This is observed to improve the stability of the operating point of the SQUIDs, while also reducing the noise for measured frequency range of 0.1 to 100 Hz.
This article describes three planar layouts of superconducting multiturn flux transformers integrated with a coplanar resonator for radio frequency (rf) superconducting quantum interference device (SQUID) magnetometers. The best magnetic field noise values of 22 and 11.5 fT/Hz1/2 in the white noise regime were obtained for the layout with two input coils and the layout with the labyrinth resonator, respectively. Excess low-frequency noise (about 200 fT/Hz1/2 at 10 Hz) was present. Computer simulation showed that the loss in this trilayer system was dominated by the high loss tangent of the dielectric film used for the separation of the upper and lower superconducting films. The rf coupling coefficient krf between the resonator and the flip-chip-coupled SQUID was also estimated. The values krf2≈14×10−3 obtained for the layout with two input coils, and krf2≈45×10−3 for the layout with the labyrinth resonator were considerably higher than the typical value of krf2≈7×10−3 for the single-layer coplanar resonator. These high coupling coefficients have compensated the somewhat degraded unloaded quality factor of the resonator, thus securing the optimum operation of the rf SQUID.
We developed a novel magnetic coupling module, formed of a monolayer superconducting flux concentrator that is integrated with a coplanar resonator, strongly coupled to high-temperature superconducting radio frequency superconducting quantum interference device (SQUID). Three types of resonators, including a long stripline resonator between the input loop and the pick-up loop of the flux concentrator, a complementary split ring resonator, and a spiral shape inside the input loop, are explored. The resonance quality factor of different patterns of these three types of the resonators, as well as their coupling to the SQUID, is evaluated using finite-element-method simulations. Several readout methods are tested to couple the electronic system to the resonators by inductive (coil) or capacitive (transmission line) methods, and the optimum readout is reported for each of the resonators. Among the evaluated resonator types, a spiral shape with an optimal behavior at the resonance frequency of 836 MHz, showing the highest quality factor together with the strongest coupling to the SQUID, compared to other types of the resonators, is fabricated using a 200-nm-thick YBCO film on a 1-mm-thick crystalline LaAlO3substrate. The flux concentrator of the module is optimized by the variation of the linewidth of its different parts and also its input loop radius to obtain the maximum flux transformation efficiency.