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arXiv:2212.06443 · Physical Review Applied

Weak-Link Physics in the Dynamical Response of Transition-Edge Sensors

Marios Kounalakis, Luciano G. Gottardi, Martin de Wit, Yaroslav M. Blanter

Published Aug 7, 2023• 3 citations
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Abstract

We theoretically predict and experimentally observe the onset of weak-link physics in the dynamical response of transition-edge sensors (TESs). We develop a theoretical framework based on a Fokker-Planck description that incorporates both the TESs electrical response, stemming from Josephson phenomena, and the electrothermal effects due to coupling to a thermal bath. Our measurements of a varying dynamic resistance are in excellent agreement with our theory, thereby establishing weak-link phenomena as the main mechanism underlying the operation of TESs. Furthermore, our description enables the calculation of power spectral densities, paving the way for a more thorough investigation of the unexplained ``excess noise'' in long diffusive junctions and TESs reported in recent experiments.

DOI
10.1103/physrevapplied.20.024017

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We theoretically predict and experimentally observe the onset of weak-link physics in the dynamical response of transition-edge sensors (TESs). We develop a theoretical framework based on a Fokker-Planck description that incorporates both the TESs electrical response, stemming from Josephson phenomena, and the electrothermal effects due to coupling to a thermal bath. Our measurements of a varying dynamic resistance are in excellent agreement with our theory, thereby establishing weak-link phenomena as the main mechanism underlying the operation of TESs. Furthermore, our description enables the calculation of power spectral densities, paving the way for a more thorough investigation of the unexplained ``excess noise'' in long diffusive junctions and TESs reported in recent experiments.
Transition-edge sensors (TESs) are two-dimensional superconducting films utilized as highly sensitive detectors of energy or power. These detectors are voltage biased in the superconducting-normal transition where the film resistance is both finite and a strong function of temperature. Unfortunately, the amount of electrical noise observed in TESs exceeds the predictions of existing noise theories. We describe a possible mechanism for the unexplained excess noise, which we term "mixed-down noise." The source is Johnson noise, which is mixed down to low frequencies by Josephson oscillations in devices with a nonlinear current-voltage relationship. We derive an expression for the power spectral density of this noise and show that its predictions agree with measured data.
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.
It has been recently demonstrated that superconducting transition edge-sensors 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 transition-edge sensors (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 of 3.2 \\times 10 -19 W/\\sqrt{Hz} developed for the short wavelength band for the instrument SAFARI on the SPICA telescope.
The noise in superconducting transition-edge sensors (TESs) commonly exceeds simple theoretical predictions. The reason for this discrepancy is presently unexplained. We have measured the amplitude and frequency dependence of the noise in TES sensors with eight different geometries. In addition, we have measured the dependence of the noise on operating resistance, perpendicular magnetic field, and bath temperature. We find that the unexplained noise contribution is inversely correlated with the temperature width of the superconducting-to-normal transition and is reduced by a perpendicular field and in certain geometries. These results suggest paths to improved sensor performance.
Understanding the weak thermal links in supporting legs of transition edge sensors (TES) is crucial for developing highly sensitive bolometers used in cosmic microwave background (CMB) detection. Conventional current-biased differential resistance measurements under varying temperature (R-T) used to characterizeRand critical temperature (Tc) of TES often encounter a phenomenon: the bias current will affect the transition temperature obtained duringTbdrop testing, as well as affect the obtained shape of the transition region. This behavior stems from the weak thermal links of TES under current bias, limitingR-Tmeasurements to only rough information about the TES transition regime sometimes. The detailed and accurate performance parameters typically relying on voltage-biased current-voltageI-Vmeasurements using using superconducting quantum interference devices (SQUIDs). In fact, the positive electro-thermal feedback induced by current bias contains valuable insights into the device's intrinsic properties. This work focuses on elaborating this underlying mechanism: by analyzing the current-induced suppression of measured transition temperature inR-Tmeasurements, we extract key parameters including thermal conductance (G), thermal exponent (n),Tc, and saturation power (Psat). This study provides intuitive calculations and visualizations of the electro-thermal behaviors induced by current bias in TES devices, and offers a simple and rapid complementary tool for electro-thermal parameter extraction. In batch TES fabrication, it can serve as a pre-screening tool to improve the efficiency of subsequent high-precision SQUID-basedI-Vcharacterization.
Impedance measurements of superconducting transition-edge sensors (TESs) are a powerful tool to obtain information about the TES thermal and electrical properties. We apply this technique to a 20 µm × 20 µm Ti/Au TES, suitable for application in the optical and near-infrared range, and extend the measurements up to 250 kHz in order to obtain a complete frequency response in the complex plane. From these measurements we obtain important thermal and electrical device parameters such as heat capacity C , thermal conductance G and effective thermal time constant τ eff that will be compared with the corresponding values obtained from noise measurements.