The complex conductivity of a superconducting thin film is related to the quasiparticle density, which depends on the physical temperature and can also be modified by external pair breaking with photons and phonons. This relationship forms the underlying operating principle of Kinetic Inductance Detectors (KIDs), where the detection threshold is governed by the superconducting energy gap. We investigate the electromagnetic properties of thin-film aluminum that is proximitized with either a normal metal layer of copper or a superconducting layer with a lower$T_{C}$, such as iridium, in order to extend the operating range of KIDs. Using the Usadel equations along with the Nam expressions for complex conductivity, we calculate the density of states and the complex conductivity of the resulting bilayers to understand the dependence of the pair breaking threshold, surface impedance, and intrinsic quality factor of superconducting bilayers on the relative film thicknesses. The calculations and analyses provide theoretical insights in designing aluminum-based bilayer kinetic inductance detectors for detection of microwave photons and athermal phonons at the frequencies well below the pair breaking threshold of a pure aluminum film.
The complex conductivity of a superconducting thin film is related to the quasiparticle density, which depends on the physical temperature and can also be modified by external pair breaking with photons and phonons. This relationship forms the underlying operating principle of Kinetic Inductance Detectors (KIDs), where the detection threshold is governed by the superconducting energy gap. We investigate the electromagnetic properties of thin-film aluminum that is proximitized with either a normal metal layer of copper or a superconducting layer with a lowerTC, such as iridium, in order to extend the operating range of KIDs. Using the Usadel equations along with the Nam expressions for complex conductivity, we calculate the density of states and the complex conductivity of the resulting bilayers to understand the dependence of the pair breaking threshold, surface impedance, and intrinsic quality factor of superconducting bilayers on the relative film thicknesses. The calculations and analyses provide theoretical insights in designing aluminum-based bilayer kinetic inductance detectors for detection of microwave photons and athermal phonons at the frequencies well below the pair breaking threshold of a pure aluminum film.
The response of superconducting pair-breaking detectors is dependent on the details of the quasiparticle distribution. In Kinetic Inductance Detectors (KIDs), where both pair breaking and non-pair breaking photons are absorbed simultaneously, calculating the detector response therefore requires knowledge of the often nonequilibrium distributions. The quasiparticle effective temperature provides a good approximation to these nonequilibrium distributions. We compare an analytical expression relating absorbed power and the quasiparticle effective temperature in superconducting thin films to full solutions for the nonequilibrium distributions, and find good agreement for a range of materials, absorbed powers, photon frequencies and temperatures typical of KIDs. This analytical expression allows inclusion of nonequilibrium effects in device models without solving for the detailed distributions. We also show our calculations of the frequency dependence of the detector response are in agreement with recent experimental measurements of the response of Ta KIDs at THz frequencies.
We describe measurements of the properties, at dc, gigahertz, and terahertz frequencies, of thin (10 nm) aluminum films with 10 Omega/square normal state sheet resistance. Such films can be applied to construct microwave kinetic inductance detector arrays for submillimeter and far-infrared astronomical applications in which incident power excites quasiparticles directly in a superconducting resonator that is configured to present a matched-impedance to the high frequency radiation being detected. For films 10 nm thick, we report normal state sheet resistance, resistance-temperature curves for the superconducting transition, quality factor and kinetic inductance fraction for microwave resonators made from patterned films, and terahertz measurements of sheet impedance measured with a Fourier Transform Spectrometer. We compare properties with similar resonators made from niobium 600 nm thick.
As superconducting kinetic inductance detectors (KIDs) continue to grow in popularity for sensitive submillimeter detection and other applications, there is a drive to advance toward lower-loss devices. We present measurements of diagnostic thin-film aluminum coplanar waveguide (CPW) resonators designed to inform ongoing KID development at NASA Goddard Space Flight Center. The resonance frequencies span f0 = 3.5-4 GHz and include quarter-wave and half-wave resonators with varying coupling capacitor designs. We present measurements of the device film properties and an analysis of the dominant mechanisms of loss in the resonators measured in a dark environment, demonstrating quality factors of Qi−1≈3.64−8.57×10−8. We observe an enhanced level of suppression in the loss contributions from two-level systems (TLS) at intermediate-to-high read powers, and a regime at these powers and low temperatures where contributions from intrinsic processes Qi−1,other dominate the total loss. We also observe deviations from the standard TLS loss model at low powers and temperatures below 60 mK, and use a modified model to describe this behavior.
Due to their multiplexing capability and their good sensitivity to radiation from submillimeter to X-ray wavelengths, microwave kinetic inductance detectors (MKIDs) are increasingly used in the field of astrophysics. The Advanced Technology Center of the National Astronomical Observatory of Japan is developing MKIDs for astronomical observations such as CMB B-mode search with LiteBIRD. MKIDs are made of superconductors whose energy gap determines the detector frequency range. The energy gap depends on Tc, the critical temperature of the superconductor. It is thus important to be able to adjust Tc in order to choose the suitable frequency range. When using a single-layer MKID, the Tc is fixed by the superconducting gap energy of the unique component and cannot be changed. One possibility is to make a bilayer MKID using the proximity effect to adjust its critical temperature. This paper presents our new study on MKIDs made of superconductor/metal bilayers. We investigated niobium and copper bilayers (Nb/Cu) and fabricated different bilayers in our clean room. The critical temperature of each of them has been measured. We show that the Tc depends on the ratio between Nb and Cu thicknesses and that we are able to control it. Then, we characterized one of these Nb/Cu bilayers (Nb = 8 nm and Cu = 22 nm) once integrated in a MKID. We measured the temperature dependence of the resonant frequency, and we achieved quality factors as high as 2 × 104. The measurement of the noise spectrum provided a lower limit equal to -85 dBc/Hz, and the calculation of the noise equivalent power has shown that the sensitivity of the Nb/Cu bilayer MKID is not very far from that of an Al monolayer MKID.
Understanding the detailed behaviour of superconducting pair breaking photon detectors such as Kinetic Inductance Detectors (KIDs) requires knowledge of the nonequilibrium quasiparticle energy distributions. We have previously calculated the steady state distributions resulting from uniform absorption of monochromatic sub gap and above gap frequency radiation by thin films. In this work, we use the same methods to calculate the effect of illumination by broadband sources, such as thermal radiation from astrophysical phenomena or from the readout system. Absorption of photons at multiple above gap frequencies is shown to leave unchanged the structure of the quasiparticle energy distribution close to the superconducting gap. Hence for typical absorbed powers, we find the effects of absorption of broadband pair breaking radiation can simply be considered as the sum of the effects of absorption of many monochromatic sources. Distribution averaged quantities, like quasiparticle generation efficiency η, match exactly a weighted average over the bandwidth of the source of calculations assuming a monochromatic source. For sub gap frequencies, however, distributing the absorbed power across multiple frequencies does change the low energy quasiparticle distribution. For moderate and high absorbed powers, this results in a significantly larger η–a higher number of excess quasiparticles for a broadband source compared to a monochromatic source of equal total absorbed power. Typically in KIDs the microwave power absorbed has a very narrow bandwidth, but in devices with broad resonance characteristics (low quality factors), this increase in η may be measurable.
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.