Effects of the thin-film thickness on superconducting NbTi microwave resonators for on-chip cryogenic thermometry

TL;DR

This work demonstrates that superconducting Nb50Ti50 thin-film S-SRRs used as on-chip thermometers exhibit a thickness-dependent trade-off between enhanced kinetic inductance and degraded quality factor. The authors show an optimum film thickness around $t\approx100$ nm, achieving a NET as low as $0.5$ μK/√Hz at 1 Hz and 4.2 K, and they establish a multiplexed readout approach to track temperatures from multiple sensors along a single CPW. By combining DC, lock-in, and FM techniques, the study achieves sub-µK resolution and reveals that low-frequency fluctuations originate from environmental effects rather than intrinsic TLS noise. The results highlight the potential for integrated, distributed cryogenic thermometry with on-chip back-end integration for quantum devices and cryogenic systems.

Abstract

Superconducting microwave resonators have recently gained a primary importance in the development of cryogenic applications, such as circuit quantum electrodynamics, electron spin resonance spectroscopy and particles detection for high-energy physics and astrophysics. In this work, we investigate the influence of the film thickness on the temperature response of microfabricated Nb50Ti50 superconducting resonators. S-shaped split ring resonators (S-SRRs), 20 nm to 150 nm thick, are designed to be electromagnetically coupled with standard Cu coplanar waveguides (CPWs) and their microwave properties are characterized at temperatures below 10 K. The combined contributions of the kinetic inductance LK(T) increase and the decreasing loaded quality factor QL, for thinner films, induce an optimum condition on the temperature sensitivity and resolution of the resonators. A noise equivalent temperature (NET) as low as 0.5 uK/Hz^(1/2), at 1 Hz, is reported for 100 nm thick resonators at 4.2 K. We also asses the possibility of implementing a multiplexed frequency readout, allowing for the simultaneous temperature tracking of several sensors along a single CPW. Such results demonstrate the possibility to perform a distributed cryogenic temperature monitoring, with a sub-mK resolution. Thus, the application of superconducting S-SRRs, eventually benefiting from an even higher LK(T), for a further miniaturization, as well as a back-end integration directly on-chip, can be envisioned for the accurate monitoring of localized temperature of devices operating in cryogenic conditions.

Figures (7)

• Figure 1: Description of the S-SRR chip and excitation PCB. a) Optical microscope picture of the $\text{1.1GHz}$ resonator under test. The coloured arrow represents the direction of the antisymmetric B-field of a GCPW underneath. b) PCB exploited for the characterization of the resonators in cryogenic environments. The separation distance between the chip and the Cu GCPW is set by the black PLA support; a plastic lid (bottom-left) and Kapton-tape are exploited to keep the suspended chip in position. The presence of two resonators, showing a similar geometry but a significant difference in overall sizes (and, thus, in resonance frequency), has to be attributed to our initial intention to perform a simultaneous frequency-multiplexed readout in different regions of the microwave spectrum. A chip containing 4-wires structures, for the Nb50Ti50 films cryogenic DC characterization, is wire-bonded at the bottom-right of the PCB.
• Figure 2: Experimental search for an optimal resonator-to-GCPW coupling distance. a) Renormalized real and imaginary parts of the $S_{21}$ parameter, for the $d_{cpl} = \text{2.5mm}$ case. The complex data (blue dots) are fitted to a notch-type circular model (yellow line). b) Magnitude and phase of the $S_{21}$$S_{21}$ parameter, for the $d_{cpl} = \text{2.5mm}$ case. c) Evolution of the loaded $Q_L$ (dashed blue line), coupling $Q_c$ (dashed orange line) and internal $Q_i$ (dashed yellow line) quality factors with respect to the coupling distance. The single pentagram points represent the critical coupling condition (i.e.$Q_i = Q_c \longrightarrow Q_L = Q_i/2$ ). d) Evolution of the loaded Q-factor (dashed blue line) and the resonance peak depth (dashed orange line), for an increasing coupling distance.
• Figure 3: Temperature response of the S-SRRs for different film thicknesses. a) Temperature-induced resonance frequency shifts for the $\text{147nm}$ thick sample. The two insets show the $|S_{21}|$ resonances at $\text{4.2K}$ ($f_{res} = \text{1.1442GHz}$, $Q_{L} = \text{1.61$\times$104}$) and $\text{7.6K}$ ($f_{res} = \text{1.1133GHz}$, $Q_{L} = \text{1.08$\times$103}$): the yellow curves stand for the notch-type complex plane circular fit. b) Resonance frequency shifts for the different film thicknesses: the solid line represents the $f_{res}(T)$ model, fitted to the data points. c) Temperature evolution of the loaded Q-factor. d) Temperature evolution of the S-SRRs sensitivity, estimated as the derivative of the $f_{res}(T)$ fitting model. The single points refer to the value at $\text{4.2K}$. e) Temperature sensitivity of the different S-SRRs, evaluated at $\text{4.2K}$.
• Figure 4: Frequency response of the S-SRRs for different film thicknesses. a) Experimental setup used to characterize the devices in liquid He at $\text{4.2K}$ b) DC component of the resonance signal: the single points represent the maximum slope condition. c) Maximum slope of the DC component versus film thickness. d) X component of the lock-in output signal: the single points represent the maximum slope condition, in this case located at the resonance frequency. The color legend is the same as the one reported for the DC signal graph. e) Maximum slope of the X component versus film thickness.
• Figure 5: Noise characterization of the different S-SRRs at $\text{4.2K}$. a) Frequency spectra of the $NET$ for the $\text{147nm}$ thick resonator. b) Noise equivalent temperatures of the different S-SRRs, evaluated in DC, both at $\text{10kHz}$ (blue-square points) and $\text{1Hz}$ (orange-diamond points), and in AC, at $\text{1Hz}$ (yellow-triangle points). c) Typical $\text{2h}$ time evolution of an S-SRR temperature monitoring through the X signal (in this case, related to the $\text{147nm}$ thick resonator).