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 Nb 50 Ti 50 superconducting resonators. S-shaped split ring resonators (S-SRRs), approximately 20 nm to 150 nm thick, are designed to be electromagnetically coupled with standard Cu coplanar waveguides (CPWs) and their microwave properties are characterised at temperatures below 10 K . The combined contributions of the kinetic inductance L K ( T ) increase and the decreasing loaded quality factor Q L , for thinner films, induce an optimum condition on the temperature sensitivity and resolution of the resonators. A noise equivalent temperature as low as ( 0.53 ± 0.09 ) μ K 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- μ K resolution. Thus, the application of superconducting S-SRRs, eventually benefiting from an even higher
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 Nb 50 Ti 50 superconducting resonators. S-shaped split ring resonators (S-SRRs), approximately 20 nm to 150 nm thick, are designed to be electromagnetically coupled with standard Cu coplanar waveguides (CPWs) and their microwave properties are characterised at temperatures below 10 K . The combined contributions of the kinetic inductance L K ( T ) increase and the decreasing loaded quality factor Q L , for thinner films, induce an optimum condition on the temperature sensitivity and resolution of the resonators. A noise equivalent temperature as low as ( 0.53 ± 0.09 ) μ K 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- μ K resolution. Thus, the application of superconducting S-SRRs, eventually benefiting from an even higher
Cryogenic systems are essential to many modern scientific and technological applications, including MRI superconducting magnets, particle accelerators, astrophysical detectors and quantum computing platforms, all of which operate at temperatures well below 120 K. In this framework, accurate temperature monitoring is, therefore, critical. However, conventional Resistance Temperature Detectors (RTDs) suffer from significant limitations in cryogenic environments, such as wiring complexity, power dissipation, limited low-temperature operation and large footprint, which restrict their integration in increasingly complex cryogenic infrastructures. Superconducting devices offer a promising alternative due to their high sensitivity at low temperatures, low power dissipation and compatibility with integrated quantum technologies. Inspired by Microwave Kinetic Inductance Detectors (MKIDs), this work investigates superconducting microwave resonators as minimally invasive, frequency-multiplexed cryogenic thermometers operating below 12 K. In particular, strategies to tune and enhance temperature sensitivity are explored by studying the effects of the superconducting thin-film thickness and surface nanostructuring. The first part of the study examines NbTi(N) planar resonators with thicknesses ranging from 20 nm to 150 nm, where temperature sensing is based on the temperature dependence of the kinetic inductance. S-shaped split-ring resonators resonating near 1.1 GHz are inductively coupled to a coplanar transmission line and characterized under cryogenic conditions. A clear trade-off between temperature sensitivity and quality factor is observed: thinner films achieve higher sensitivity, up to approximately 19 MHz/K for 20 nm thick devices, while the quality factor, typically exceeding 10^4, is found to degrade when the thickness is reduced. This trade-off leads to an optimal temperature resolution, with sub-microkelvin noise-equivalent temperature (NET) values. In particular, a minimum NET of (0.53±0.09) µK/Hz^(1/2) at 4.2 K is achieved for a 100 nm thick resonator, which is also exploited to study low-frequency temperature fluctuations in liquid helium. In the second part, a possible approach to enhance the temperature sensitivity, through surface nanostructuring, is investigated. Arrays of nanogaps are patterned in high-current regions of a 1.3 GHz resonator, in order to locally suppress superconductivity, reduce the critical temperature of the film and, therefore, accentuate the slope of the temperature-sensitive curve. These weak-links are realized by partially etching a 100 nm NbTi film, to leave 20-30 nm thick remaining nanogaps. Measurements reveal a significant increase in temperature sensitivity, reaching values as high as up to (62±1) MHz/K, which correspond to one order-of-magnitude improvement over non-nanostructured devices. Although this enhancement comes with increased noise-equivalent temperature, the results demonstrate the feasibility of engineering superconducting weak links to improve RF cryogenic thermometry and provide a solid foundation for future optimization. In reason of the achieved results, such an approach could find successful applications for a sub-µK high-resolution cryogenic temperature monitoring, specifically for integrated quantum architectures, further benefiting from the frequency-multiplexing that naturally arises from the multiple allocation of different superconducting microwave resonators.
Abstract The rising complexity of cutting-edge cryogenic systems is currently imposing challenging technical constraints to the monitoring of ultra-cold temperatures through standard commercially available sensors. Among different alternative technologies, superconducting microwave resonators have been recently investigated as ideal candidates for performing on-chip cryogenic thermometry, in reason of their intrinsically low power dissipation, typically large temperature sensitivities and excellent sub- μ K resolution below 10 K. In such a framework, through this study we aim at demonstrating the possibility to enhance the temperature performance of superconducting microwave resonators by means of surface nanostructuring. More specifically, different arrays of nanotrenches are strategically patterned on the inductive line of a 1.3 GHz planar resonator, by partially etching a Nb 50 Ti 50 thin-film, in order to tune the critical transition of the material and, therefore, increase the curvature of the f res ( T ) response. Although the presence of such thinned superconducting regions introduces larger microwave losses, a 1.5 K decrease of T C is recorded, which directly translates into an enhancement of the temperature sensitivity by a factor 10, with respect to a reference non-nanostructured sensor. In particular, a maximum value of d f res / d T ≃ 62 MHz/K , at 4.2 K, is achieved for the device showing the largest nanotrench width of about 350 nm. These results demonstrate that such a surface nanostructuring approach can be exploited as an effective design strategy to tune the response of superconducting microwave resonators and enhance their temperature sensitivity around a target operating condition. Although this technique is found to introduce additional RF losses into the superconducting device, thereby limiting the achievable temperature resolution to the few- μ K/Hz 1 / 2 range (at 1 Hz and 4.2 K), we believe that similar approaches could be further investigated for the development of future cryogenic sensors.
In this work, we investigated how different under- and capping layers on patterned Nb films impacted the RF losses of flexible thin-film superconducting microstrip transmission line resonators measured in a frequency range from 2 to 20 GHz. We studied how different thicknesses of Ti(10 and 50 nm) under-layer, used for adhesion, impacts conductor losses. We also studied Cu(20, 50, 100, and 200 nm) capping layers and how they affect conductor loss. These studies were carried out on 20-μm-thick spin-on polyimide (PI-2611) thin films and characterized at various cryogenic temperatures between 1.2 and 4.2 K. The results indicate normal-superconductor (Ti/Nb) and superconductor-normal (Nb/Cu) bilayer structures have increased surface resistance, which leads to an increase in microwave loss when compared to Nb-only signal traces. We quantified this additional loss by extracting resonator quality factors for weakly coupled resonators with various conductor stack-ups. Our experimental results can help inform decisions regarding material stack-ups when designing multiconductor multilayer superconducting flexible cables intended for use with ultralow-temperature electronic systems.
In this thesis I describe work on developing theoretical and numerical models of supercon- ducting thin-film microwave resonators. Superconducting resonators are used in a variety of applications, one of which is as kinetic inductance detectors (KIDs). KIDs are ultra-low noise, highly sensitive, multiplexable detectors, with uses in a wide variety of fields including astrophysics, medical imaging, and particle physics. Resonators are also crucial for supercon- ducting qubit readout, superconducting mixers and parametric amplifiers, and as multiplexers for other devices. The results described in this thesis apply to all thin film resonators, but are primarily described in the context of KIDs. I develop models of how constant absorbed power affects superconducting thin films, driving them out of thermal equilibrium with the bath. Using the Chang & Scalapino equations, I calculate numerically the steady-state quasiparticle and phonon distributions for various sources of power (sub-gap and above-gap photons and phonons, single frequency and broadband). Many new results emerge, a few of which are: the quasiparticle heating effects of microwave power, explaining the experimentally measured saturation of resonator performance; the frequency dependence of the quasiparticle generation efficiency in the sub-mm wavelength range; and the importance of phonon trapping in thin films at low temperatures. I then use these nonequilibrium results in higher-level device models. Starting from a generic framework for resonators, I present and implement a model of a KID with variable thermal isolation. I calculate the effects of quasiparticle heating on both the large-signal and small-signal behaviour, highlighting the effects of electrothermal feedback caused by readout power. Electrothermal feedback is shown to be able to increase or decrease the magnitude and bandwidth of the responsivity and noise, depending on the operating point. Finally, I propose an experimental measurement of quasiparticle heating effects in a new device – a four-port ring resonator. In such a device, unlike in the standard two-port resonator, the device can be heated and read out independently. I develop detailed models for the thermal and electrical behaviour of these devices, and suggest a scheme by which the quasiparticle heating effects of microwave power, predicted in this thesis, can be measured.
The high critical magnetic field and relatively high critical temperature of niobium nitride (NbN) make it a promising material for applications in superconducting quantum technology. However, NbN-based superconducting circuits are sensitive to decoherence sources such as two-level system (TLS) defects. Here, we numerically and experimentally investigate NbN superconducting microwave coplanar waveguide resonator arrays with a 100 nm thickness, capacitively coupled to a common coplanar waveguide on a silicon chip. We observe that the resonators' internal quality factor (Qi) decreases fromQi∼1.07×106in a high power regime toQi∼1.36×105in the single photon regime. Data from this study is consistent with the TLS theory, which describes the TLS interactions in resonator substrates and interfaces. Moreover, we study the temperature (T) dependence ofQiand resonance frequencyfrof coplanar waveguide resonators to characterize the quasiparticle density. We observe that the increase in kinetic inductance at higher temperatures is the main reason for the frequency shift. Finally, we measurefrandQiin response to in-plane magnetic fields (B∣∣). We verify thatQistays well above104up toB∣∣= 240 mT in the photon number<nph>= 1.8 atT= 100 mK. Our results could enable the development of robust microwave superconducting circuits for circuit quantum electrodynamics at high magnetic fields required for hybrid superconducting-semiconducting quantum circuits.
Superconducting resonators are widely used in fields spanning from quantum computing to electron spin resonance (ESR) spectroscopy. With the goal of realizing superconducting resonators, a broad variety and combination of superconducting materials, substrates and fabrication processes have been used and thoroughly reported in the literature. High temperature superconductors such as YBCO and low temperature superconductors such as Nb, NbN, NbTiN and Al are the major actors in the domain. In this work, we investigate the possibility to extend the family of suitable low temperature superconductors for the realization of planar superconducting microwave resonators for future ESR applications. In particular, this study focuses on NbTi, a widely used material to realize superconducting cables but not investigated for planar resonating structures at GHz frequencies. A 150 nm thick film of NbTi is sputtered and patterned on top of an Al2O3 substrate. For devices resonating around 6.8 GHz quality factors greater than 10,000 are observed at 3 K and in magnetic fields up to 250 mT.