Exploring the performance of thin-film superconducting multilayers as kinetic inductance detectors for low-frequency detection

We have solved numerically the diffusive Usadel equations that describe the spatially varying superconducting proximity effect in Ti-Al thin-film bi- and trilayers with thickness values that are suitable for kinetic inductance detectors (KIDs) to operate as photon detectors with detection thresholds in the frequency range of 50-90 GHz. Using Nam's extension of the Mattis-Bardeen calculation of the superconductor complex conductivity, we show how to calculate the surface impedance for the spatially varying case, and hence the surface impedance quality factor. In addition, we calculate energy-and spatially-averaged quasiparticle lifetimes at temperatures well-below the transition temperature and compare to calculation in Al. Our results for the pair-breaking threshold demonstrate differences between bilayers and trilayers with the same total film thicknesses. We also predict high quality factors and long multilayer-averaged quasiparticle recombination times compared to thin-film Al. Our calculations give a route for designing KIDs to operate in this scientifically-important frequency regime

Nonlinear effects in superconducting thin film microwave resonators

We discuss how reactive and dissipative non-linearities affect the intrinsic response of superconducting thin-film resonators. We explain how most, if not all, of the complex phenomena commonly seen can be described by a model in which the underlying resonance is a single-pole Lorentzian, but whose centre frequency and quality factor change as external parameters, such as readout power and frequency, are varied. What is seen during a vector-network-analyser measurement is series of samples taken from an ideal Lorentzian that is shifting and spreading as the readout frequency is changed. According to this model, it is perfectly proper to refer to, and measure, the resonant frequency and quality factor of the underlying resonance, even though the swept-frequency curves appear highly distorted and hysteretic. In those cases where the resonance curve is highly distorted, the specific shape of the trajectory in the Argand plane gives valuable insights into the second-order physical processes present. We discuss the formulation and consequences of this approach in the case of non-linear kinetic inductance, two-level-system loss, quasiparticle generation, and a generic model based on a power-law form. The generic model captures the key features of specific dissipative non-linearities, but additionally leads to insights into how general dissipative processes create characteristic forms in the Argand plane. We provide detailed formulations in each case, and indicate how they lead to the wide variety of phenomena commonly seen in experimental data. We also explain how the properties of the underlying resonance can be extracted from this data. Overall, our paper provides a self-contained compendium of behaviour that will help practitioners interpret and determine important parameters from distorted swept-frequency measurements

Modelling proximity effects in transition edge sensors to investigate the influence of lateral metal structures

The bilayers of transition edge sensors (TESs) are often modified with additional normal-metal features such as bars or dots. Previous device measurements suggest that these features improve performance, reducing electrical noise and altering response times. However, there is currently no numerical model to predict and quantify these effects. Here we extend existing techniques based on Usadel's equations to describe TESs with normal-metal features. We show their influence on the principal TES characteristics, such as the small-signal electrothermal parameters $\alpha$ and β and the superconducting transition temperature $T_c$. Additionally, we examine the effects of an applied magnetic field on the device performance. Our model predicts a decrease in $T_c$, $\alpha$ and β as the number of lateral metal structures is increased. We also obtain a relationship between the length $L$ of a TES and its critical temperature, $T_c$ $\propto$ $L^{-0.7}$ for a bilayer with normal-metal bars. We predict a periodic magnetic flux dependence of $\alpha$, β and $I_c$. Our results demonstrate good agreement with published experimental data, which also show the reduction of $\alpha$, β and $T_c$ with increasing number of bars. The observed Fraunhofer dependence of critical current on magnetic flux is also anticipated by our model. The success of this model in predicting the effects of additional structures suggests that in the future numerical methods can be used to better inform the design of TESs, prior to device processing

First characterization of a superconducting filter-bank spectrometer for hyper-spectral microwave atmospheric sounding with transition edge sensor readout

We describe the design, fabrication, integration and characterization of a prototype superconducting filter bank with transition edge sensor readout designed to explore millimetre-wave detection at frequencies in the range 40 to 65 GHz. Results indicate highly uniform filter channel placement in frequency and high overall detection efficiency. The route to a full atmospheric sounding instrument in this frequency range is discussed.Centre for Earth Observing Instrumentation UK (CEOI

Suppressed-gap millimetre wave kinetic inductance detectors using DC-bias current

Funder: CSC Cambridge ScholarshipIn this study, we evaluate the suitability of using DC-biased aluminium resonators as low-frequency kinetic inductance detectors operating in the frequency range of 50 - 120 GHz. Our analysis routine for supercurrent-biased resonators is based on the Usadel equations and gives outputs including density of states, complex conductivities, transmission line properties, and quasiparticle lifetimes. Results from our analysis confirm previous experimental observations on resonant frequency tuneability and retention of high quality factor. Crucially, our analysis suggests that DC-biased resonators demonstrate significantly suppressed superconducting density of states gap. Consequently these resonators have lower frequency detection threshold and are suitable materials for low-frequency kinetic inductance detectors

Electrothermal feedback in kinetic inductance detectors

In kinetic inductance detectors (KIDs) and other similar applications of superconducting microresonators, both the large and small-signal behaviour of the device may be affected by electrothermal feedback. Microwave power applied to read out the device is absorbed by and heats the superconductor quasiparticles, changing the superconductor conductivity and hence the readout power absorbed in a positive or negative feedback loop. In this work, we explore numerically the implications of an extensible theoretical model of a generic superconducting microresonator device for a typical KID, incorporating recent work on the power flow between superconductor quasiparticles and phonons. This model calculates the large-signal (changes in operating point) and small-signal behaviour of a device, allowing us to determine the effect of electrothermal feedback on device responsivity and noise characteristics under various operating conditions. We also investigate how thermally isolating the device from the bath, for example by designing the device on a membrane only connected to the bulk substrate by thin legs, affects device performance. We find that at a typical device operating point, positive electrothermal feedback reduces the effective thermal conductance from the superconductor quasiparticles to the bath, and so increases responsivity to signal (pair-breaking) power, increases noise from temperature fluctuations, and decreases the noise equivalent power (NEP). Similarly, increasing the thermal isolation of the device while keeping the quasiparticle temperature constant decreases the NEP, but also decreases the device response bandwidth

Performance of horn-coupled transition edge sensors for L- and S-band optical detection on the SAFARI instrument

We describe the geometry, architecture, dark- and optical performance of ultra-low-noise transition edge sensors as THz detectors for the SAFARI instrument. The TESs are fabricated from superconducting Mo/Au bilayers coupled to impedance-matched superconducting ß-phase Ta thin-film absorbers. The detectors have phonon-limited dark noise equivalent powers of order 0.5 - 1.0 aW/$\sqrt{Hz}$ and saturation powers of order 20 - 40 fW. The low temperature test configuration incorporating micro-machined backshorts is also described, and construction and typical performance characteristics for the optical load are shown. We report preliminary measurements of the optical performance of these TESs for two SAFARI bands; L-band at 110 - 210 µm and S-band 34 - 60 µm .European Space AgencyThis is the final version of the article. It first appeared from SPIE via http://dx.doi.org/10.1117/12.223274

Simulation method for investigating the use of transition-edge sensors as spectroscopic electron detectors

Transition-edge sensors (TESs) are capable of highly accurate single particle energy measurement. TESs have been used for a wide range of photon detection applications, particularly in astronomy, but very little consideration has been given to their capabilities as electron calorimeters. Existing electron spectrometers require electron filtering optics to achieve energy discrimination, but this step discards the vast majority of electrons entering the instrument. TESs require no such energy filtering, meaning they could provide orders of magnitude improvement in measurement rate. To investigate the capabilities of TESs in electron spectroscopy, a simulation pipeline has been devised. The pipeline allows the results of a simulated experiment to be compared with the actual spectrum of the incident beam, thereby allowing measurement accuracy and efficiency to be studied. Using Fisher information, the energy resolution of the simulated detectors was also calculated, allowing the intrinsic limitations of the detector to be separated from the specific data analysis method used. The simulation platform has been used to compare the performance of TESs with existing X-ray photoelectron spectroscopy (XPS) analysers. TESs cannot match the energy resolution of XPS analysers for high-precision measurements but have comparable or better resolutions for high count rate applications. The measurement rate of a typical XPS analyser can be matched by an array of 10 TESs with 120 microsecond response times and there is significant scope for improvement, without compromising energy resolution, by increasing array size

The development of a brief and objective method for evaluating moral sensitivity and reasoning in medical students

BACKGROUND: Most medical schools in Japan have incorporated mandatory courses on medical ethics. To this date, however, there is no established means of evaluating medical ethics education in Japan. This study looks 1) To develop a brief, objective method of evaluation for moral sensitivity and reasoning; 2) To conduct a test battery for the PIT and the DIT on medical students who are either currently in school or who have recently graduated (residents); 3) To investigate changes in moral sensitivity and reasoning between school years among medical students and residents. METHODS: Questionnaire survey: Two questionnaires were employed, the Problem Identification Test (PIT) for evaluation of moral sensitivity and a portion of the Defining Issues Test (DIT) for moral reasoning. Subjects consisted of 559 medical school students and 272 residents who recently graduated from the same medical school located in an urban area of Japan. RESULTS: PIT results showed an increase in moral sensitivity in 4(th )and 5(th )year students followed by a decrease in 6(th )year students and in residents. No change in moral development stage was observed. However, DIT results described a gradual rising shift in moral decision-making concerning euthanasia between school years. No valid correlation was observed between PIT and DIT questionnaires. CONCLUSION: This study's questionnaire survey, which incorporates both PIT and DIT, could be used as a brief and objective means of evaluating medical students' moral sensitivity and reasoning in Japan