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We present a detailed analysis of the fundamental noise sources in superconducting transition-edge sensors (TESs), ac voltage biased at MHz frequencies and treated as superconducting weak links. We have studied the noise in the resistive transition as a function of bath temperature of several detectors with different normal resistances and geometries. We show that the excess noise, typically observed in the TES electrical bandwidth, can be explained by the equilibrium Johnson noise of the quasiparticles generated within the weak link. The fluctuations at the Josephson frequency and higher harmonics contribute significantly to the measured voltage noise at the detector bandwidth through the nonlinear response of the weak link with a sinusoidal current-phase relation., Comment: 9 pages, 7 figures

Controlling thermal transport is important for a range of devices and technologies, from phase change memories to next-generation electronics. This is especially true in nano-scale devices where thermal transport is altered by the influence of surfaces and changes in dimensionality. In superconducting nanowire single-photon detectors, the thermal boundary conductance (TBC) between the nanowire and the substrate it is fabricated on influences most of the performance metrics that make these detectors attractive for applications. This includes the maximum count rate, latency, jitter, and quantum efficiency. Despite its importance, the study of TBC in superconducting nanowire devices has not been done systematically, primarily due to the lack of a straightforward characterization method. Here, we show that simple electrical measurements can be used to estimate the TBC between nanowires and substrates and that these measurements match acoustic mismatch theory across a variety of substrates. Numerical simulations allow us to refine our understanding, however, open questions remain. This work should enable thermal engineering in superconducting nanowire electronics and cryogenic detectors for improved device performance.

We estimate the depairing current of superconducting nanowire single photon detectors (SNSPDs) by studying the dependence of the nanowires kinetic inductance on their bias current. The kinetic inductance is determined by measuring the resonance frequency of resonator style nanowire coplanar waveguides both in transmission and reflection configurations. Bias current dependent shifts in the measured resonant frequency correspond to the change in the kinetic inductance, which can be compared with theoretical predictions. We demonstrate that the fast relaxation model described in the literature accurately matches our experimental data and provides a valuable tool for direct determination of the depairing current. Accurate and direct measurement of the depairing current is critical for nanowire quality analysis, as well as modeling efforts aimed at understanding the detection mechanism in SNSPDs.

A number of current approaches to quantum and neuromorphic computing use superconductors as the basis of their platform or as a measurement component, and will need to operate at cryogenic temperatures. Semiconductor systems are typically proposed as a top-level control in these architectures, with low-temperature passive components and intermediary superconducting electronics acting as the direct interface to the lowest-temperature stages. The architectures, therefore, require a low-power superconductor-semiconductor interface, which is not currently available. Here we report a superconducting switch that is capable of translating low-voltage superconducting inputs directly into semiconductor-compatible (above 1,000 mV) outputs at kelvin-scale temperatures (1 K or 4 K). To illustrate the capabilities in interfacing superconductors and semiconductors, we use it to drive a light-emitting diode (LED) in a photonic integrated circuit, generating photons at 1 K from a low-voltage input and detecting them with an on-chip superconducting single-photon detector. We also characterize our device's timing response (less than 300 ps turn-on, 15 ns turn-off), output impedance (greater than 1 M{\Omega}), and energy requirements (0.18 fJ/um^2, 3.24 mV/nW).

We analyze the origin of the intrinsic timing jitter in superconducting nanowire single photon detectors (SNSPDs) in terms of fluctuations in the latency of the detector response, which is determined by the microscopic physics of the photon detection process. We demonstrate that fluctuations in the physical parameters which determine the latency give rise to the intrinsic timing jitter. We develop a general description of latency by introducing the explicit time dependence of the internal detection efficiency. By considering the dynamic Fano fluctuations together with static spatial inhomogeneities, we study the details of the connection between latency and timing jitter. We develop both a simple phenomenological model and a more general microscopic model of detector latency and timing jitter based on the solution of the generalized time-dependent Ginzburg-Landau equations for the 1D hotbelt geometry. While the analytical model is sufficient for qualitative interpretation of recent data, the general approach establishes the framework for a quantitative analysis of detector latency and the fundamental limits of intrinsic timing jitter. These theoretical advances can be used to interpret the results of recent experiments measuring the dependence of detection latency and timing jitter on photon energy to the few-picosecond level.

Because of their universal nature, Fano fluctuations are expected to influence the response of superconducting nanowire single-photon detectors (SNSPDs). We predict that photon counting rate ($PCR$) as a function of bias current ($I_B$) in SNSPDs is described by an integral over a transverse coordinate-dependent complementary error function. The latter describes smearing of local responses due to Fano fluctuations of the amount of energy deposited into electronic system. The finite width, $\sigma$, of the $PCR$ vs $I_B$ arises from fluctuations in the energy partition between quasiparticles and phonons during the energy down-conversion cascade. In narrow-nanowire SNSPDs the local responses are uniform, and the effect of Fano-fluctuations on $\sigma$ is dominant. In wide-nanowire SNSPDs with strong coordinate dependence of local responses due to vortex-antivortex unbinding and vortex entry from edges, Fano-fluctuations smear singularities imprinted by vorticity on the transition part of $PCR$ curve. We demonstrate good agreement between theory and experiments for a series of bath temperatures and photon energies in narrow-wire WSi SNSPDs. The time-resolved hotspot relaxation curves predicted by Fano fluctuations match the Lorentzian shapes observed in experiments over the whole range of bias currents investigated except for their tails., Comment: 12 pages, 8 figures

We developed the model of the internal phonon bottleneck to describe the energy exchange between the acoustically soft ultrathin metal film and acoustically rigid substrate. Discriminating phonons in the film into two groups, escaping and nonescaping, we show that electrons and nonescaping phonons may form a unified subsystem, which is cooled down only due to interactions with escaping phonons, either due to direct phonon conversion or indirect sequential interaction with an electronic system. Using an amplitude-modulated absorption of the sub-THz radiation technique, we studied electron-phonon relaxation in ultrathin disordered films of tungsten silicide. We found an experimental proof of the internal phonon bottleneck. The experiment and simulation based on the proposed model agree well, resulting in tau_{e-ph} = 140-190 ps at T_C = 3.4 K, supporting the results of earlier measurements by independent techniques., Comment: 13 pages, 9 figures, 2 table

It has been recently demonstrated that superconducting transition edge sensors (TESs) behave as weak-links due to longitudinally induced superconductivity from the leads with higher Tc. In this work we study the implication of this behaviour for TES-based bolometers and microcalorimeter under ac bias. The TESs are read-out at frequencies between 1 and 5 MHz by a Frequency Domain Multiplexer based on a linearised two-stage SQUID amplifier and high- Q lithographically made superconducting LC resonators. In particular, we focus on SRON TiAu TES bolometers with a measured dark Noise Equivalent Power (NEP) of $3.2 \cdot 10^{-19} W/Hz^{1/2}$ developed for the short wavelength band for the instrument SAFARI on the SPICA telescope., Comment: 6 pages, 5 figure

We report the experimental evidence of the ac Josephson effect in a transition edge sensor (TES) operating in a frequency domain multiplexer and biased by ac voltage at MHz frequencies. The effect is observed by measuring the non-linear impedance of the sensor. The TES is treated as a weakly linked superconducting system and within the resistively shunted junction model framework. We provide a full theoretical explanation of the results by finding the analytic solution of the non-inertial Langevian equation of the system and calculating the non-linear response of the detector to a large ac bias current in the presence of noise., Comment: 4 pages, 4 figures

We experimentally studied the dynamics of optically excited hotspots in current carrying WSi superconducting nanowires as a function of bias current, bath temperature and excitation wavelength. We discovered that: (1) the hotspot relaxation is a factor of ~ 4 slower in WSi than in NbN; (2) the hotspot relaxation time depends on bias current, and (3) the current dependence of the hotspot relaxation time changes with temperature and wavelength. We explained all of these effects with a model based on quasi particle recombination.

We have developed a model describing the non-proportional response in scintillators based on non-thermalised carrier and phonon transport. We show that the thermalization of e-h distributions produced in scintillators immediately after photon absorption may take longer than the period over which the non-proportional signal forms. The carrier and LO-phonon distributions during this period remain non-degenerate at quasi-equilibrium temperatures far exceeding room temperature. We solve balance equations describing the energy exchange in a hot bipolar plasma of electrons/holes and phonons. Taking into account dynamic screening we calculate the ambipolar diffusion coefficient at all temperatures. The non-proportional light yields calculated for NaI are shown to be consistent with experimental data. We discuss the implications of a non-equilibrium model, comparing its predictions with a model based on the transport of thermalised carriers. Finally, evidence for non-equilibrium effects is suggested by the shape of non-proportionality curve and wide dispersion in data observed in K-dip spectroscopy near the threshold. A comparison of the predicted curves shows good agreement for deformation potential value in the range 7-8 eV.

We report preliminary results from a synchrotron radiation study of Te inclusions in a large volume single crystal CdZnTe (CZT) coplanar-grid detector. The experiment was carried out by probing individual inclusions with highly collimated monochromatic X-and gamma-ray beams. It was found that for shallow X-ray interaction depths, the effect of an inclusion on measured energy loss spectra is to introduce a ~10% shift in the peak centroid energy towards lower channel numbers. The total efficiency is however not affected, showing that the net result of inclusions is a reduction in the Charge Collection Efficiency (CCE). For deeper interaction depths, the energy-loss spectra shows the emergence of two distinct peaks, both downshifted in channel number. We note that the observed spectral behavior shows strong similarities with that reported in semiconductors which exhibit polarization effects, suggesting that the underlying mechanism is common., Comment: 6 pages, 6 figures, submitted to Nuclear Instruments and Methods in Physics A

In a superconductor with magnetic impurities, Kondo scattering results in the formation of localized states inside the superconducting gap. We show that inelastic electronic transitions involving quasiparticle scattering into and out of the localized states may result in significant changes in the non equilibrium properties of the superconductor. Using the model of Muller-Hartmann and Zittartz for the extreme dilute limit, and including both deformation potential and spin-lattice coupling we have calculated the rates of such inelastic transitions between continuum and discrete states, and shown that they may greatly modify quasiparticle interactions. The individual processes are: quasiparticle trapping into discrete states, enhanced recombination with localized quasiparticles, and pair breaking and detrapping of localized quasiparticles by sub-gap phonons. We find that all these processes give rise to clearly distinguishable temperature dependences of the kinetic parameters.

We recently predicted the formation of a highly non-equilibrium quasiparticle (qp) distribution in low TC multiple tunnelling superconducting tunnel junctions (STJs) [1]. The situation arises through qp energy gain in cycles of successive forward and back tunnelling events in the absence of relaxation via sub-gap phonon emission. The qps can acquire sufficient energy to emit phonons, which break more Cooper pairs and release additional qps. In this paper we report theoretical and experimental studies of the effect of this process on photon detection by such an STJ. We derived a set of energy-dependent balance equations [2], which describe the kinetics of the qps and phonons, including the qp multiplication process described above. Solution of the balance equations gives the non-equilibrium distribution of the qps as a function of time and energy, and hence the responsivity of the STJ as a function of bias voltage. We compared the theoretical results with experiments on high quality, multiple-tunnelling Al STJs cooled to 35mK in an adiabatic demagnetisation refrigerator, and illuminated with monochromatic photons with wavelengths between 250 and 1000 nm. It was found that in the larger junctions with the longest qp loss time, both responsivity and signal decay time increased rapidly with bias voltage. Excellent agreement was obtained between the observed effects and theoretical modelling., Comment: 8 pages, 6 figures

We describe a model for photon absorption by superconducting tunnel junctions in which the full energy dependence of all the quasiparticle dynamic processes is included. The model supersedes the well-known Rothwarf-Taylor approach, which becomes inadequate for a description of the small gap structures that are currently being developed for improved detector resolution and responsivity. In these junctions relaxation of excited quasiparticles is intrinsically slow so that the energy distribution remains very broad throughout the whole detection process. By solving the energy-dependent kinetic equations describing the distributions, we are able to model the temporal and spectral evolution of the distribution of quasiparticles initially generated in the photo-absorption process. Good agreement is obtained between the theory and experiment., Comment: 25 pages, 15 figures

A 6x6 array of symmetrical V/Al/AlOx/Al/V Superconducting Tunnel Junctions (STJs) was fabricated. The base electrode is a high quality epitaxial film with a residual resistance ratio (RRR) of ~30. The top film is polycrystalline with an RRR of ~10. The leakage currents of the 25x25 mm^2 junctions are of the order of 0.5 pA/mm^2 at a bias voltage of 100 mV, which corresponds to a dynamical resistance of ~ 3 10^5 ohms. When the array was illuminated by 6 keV X-ray photons from a 55Fe radioactive source the single photon charge output was found to be low and strongly dependent on the temperature of the devices. This temperature dependence at X-ray energies can be explained by the existence of a very large number of quasiparticle (QP) traps in the Vanadium. QPs are confined in these traps, having a lower energy gap than the surrounding material, and are therefore not available for tunneling. The number of traps can be derived from the energy dependence of the responsivity of the devices (charge output per electron volt of photon input energy)., Comment: 4 pages. presented at Low Temperature Detectors-9

Generic properties of elastic phonon transport at a disordered interface are studied. The results show that phonon transmittance is a strong function of frequency and the disorder correlation length. At frequencies lower than the van Hove singularity the transmittance at a given frequency increases as the correlation length decreases. At low frequencies, this is reflected by different power-laws for phonon conductance across correlated and uncorrelated disordered interfaces which are in approximate agreement with perturbation theory of an elastic continuum. These results can be understood in terms of simple mosaic and two-colour models of the interface., Comment: 17 pages, 5 figures, submitted to PRB

For an fcc crystal with central force interactions and separately for a scalar model on a square lattice, we compute exactly the phonon transmission coefficient $T(\omega)$ through a disordered planar interface between two identical semi - infinite leads. At high frequencies $T(\omega)$ exhibits a strong frequency dependence which is determined by the correlation length of the disorder., Comment: to appear in Physica B, proceedings of the 9th international conference on phonon scattering

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We present a simple experimental scheme for estimating the cryogenic thermal transport properties of thin films using superconducting nanowires. In a parallel array of nanowires, the heat from one nanowire in the normal state changes the local temperature around adjacent nanowires, reducing their switching current. Calibration of this change in switching current as a function of bath temperature provides an estimate of the temperature as a function of displacement from the heater. This provides a method of determining the contribution of substrate heat transport to the cooling time of superconducting nanowire single photon detectors. Understanding this process is necessary for successful electrothermal modeling of superconducting nanowire systems.