Weak-link phenomena in AC-biased transition edge sensors
Luciano G. Gottardi, Hiroki Akamatsu, M. P. Bruijn, J. R. Gao, R. den Hartog, R. A. Hijmering, Henk F. C. Hoevers, P. Khosropanah, Alexander G. Kozorezov, Jan van der Kuur, Van Der Linden, A., M. Ridder
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.
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.
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.
SRON is developing the Frequency Domain Multiplexing (FDM) read-out and the ultra low NEP TES bolometers array for the infra-red spectrometer SAFARI on board of the Japanese space mission SPICA. The FDM prototype of the instrument requires critical and complex optimizations. For single pixel characterization under AC bias we are developing a simple FDM system working in the frequency range from 1 to 5 MHz, based on the open loop read-out of a linearized two-stage SQUID amplifier and high Q lithographic LC resonators. We describe the details of the experimental set-up required to achieve low power loading (<1 fW) and low noise ( NEP∼10−19W/Hz ) in the TES bolometers. We conclude the paper by comparing the performance of a 4×10−19W/Hz TES bolometer measured under DC and AC bias.
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.
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.
It has long been recognized that weak-link effects play an important role in transition edge sensors (Sadleir et al., 2010 and Sadleir et al., 2011), especially when the intrinsic transition temperature of the leads is much higher than that of the device itself. The weak-link physics has also been identified as an important complication if the TES is read-out under MHz-range AC bias for multiplexing purposes (Gottardi et al., 2014). More recently, it has been proposed that the commonly observed “excess” Johnson noise could also be explained as a white Johnson noise component that is mixed down into the signal band from higher frequencies via Josephson oscillations on a non-linear I-V relation (Gottardi et al., 2021 and Wessels et al., 2021). In recent experiments with small scale Mo/Au (50μm length, 15μm wide) TES devices with Nb leads (fabricated at GSFC) with a small DC bias applied, we have been able to directly observe Josephson oscillations over a kHz to MHz frequency range. The spectrum of the oscillations is well described by a simple damped oscillator model, with its center frequency scaling in direct proportion to the voltage across the TES. The second harmonic is also observed at small bias. If nothing else, we show that the Josephson oscillations provide a straightforward way to determine the value of the shunt-resistor with accuracy of10−4or better, as well as the offset voltage of the bias circuit. This is complementary to our previous work demonstrating that Shapiro steps in the IV curve induced by AC magnetic fields can be used for shunt resistor calibration (Zhou et al., 2018). Further work will be needed to determine if this effect can be observed in larger TES or those with relatively low-Tccontacts, where Shapiro steps are too weak to observe. It remains to be seen whether additional insights on the mixed-down Johnson noise can be obtained from a physics-based model of the weak-link.
The frequency domain multiplexing (FDM) readout of arrays of transition edges sensors for the X-IFU/Athena and SAFARI/SPICA instruments requires SQUID amplifiers with low input inductance, low flux noise, high-dynamic range and low power consumption. We report the performance of two-stage SQUID amplifiers developed at VTT coupled to multiple high-Q LC resonators of the SRON FDM readout operating in the frequency range from 2 to 5 MHz. The SQUIDs have been tested in the following configurations: 1) the two SQUIDs at base temperature with open input; 2) the amplifier SQUID at 1K temperature and the front-end SQUID at base temperature in the FDM readout of low-G TES bolometers; and 3) and in the FDM readout of X-ray microcalorimeter arrays with both SQUIDS at base temperature. We measured an input flux noise equal to 0.18 μΦ0/Hz1/2at 20 mK, equivalent to an energy resolution of 9 b. The measured current noise at the SQUID input is ~1 pA/Hz1/2at 20 mK, which corresponds to a coupled energy resolution of about 15 b.