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 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 (50
μm length, 15
μm 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 of
10−4or 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.
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 propose to operate a superconducting transition edge sensor (TES) using a different type of biasing, in which the resistance of the TES is kept constant by means of feedback on the bias voltage and is independent of the incoming signal power. By combining a large negative electrothermal feedback with a load independent resistance, this approach can significantly linearise the response of the detector in the large signal limit. The electrothermal feedback is enhanced in comparison with the commonly applied voltage biasing, which further increases the speed of the detector. Furthermore, in frequency domain multiplexed readout, the sinusoidal bias voltages for each TES can be generated cryogenically with the readout SQUIDs.
We have developed a model for the resistive transition in a transition edge sensor (TES) based on the model of a resistively and capacitively shunted junction, taking into account phase-slips of a superconducting system across the barriers of the tilted washing board potential. We obtained analytical expressions for the resistance of the TES, R(T, I), and its partial logarithmic derivatives αI and βI as functions of temperature and current. We have shown that all the major parameters describing the resistive state of the TES are determined by the dependence on temperature of the Josephson critical current, rather than by intrinsic properties of the S-N transition. The complex impedance of a pristine TES exhibits two-pole behaviour due to its own intrinsic reactance.
We systematically study the analysis and simulation of ac-biased superconductor transition-edge sensor (TES) circuits. In these ac-biased circuits, the current and voltage of the TES experience large swings in both directions, and small-signal analysis around a dc steady state does not apply. To understand their electrical and thermal behavior, we rely on concepts and techniques from radio-frequency circuit simulation and introduce the periodic steady state and perform periodic ac analysis. We also construct TES device models based on a comprehensive two-fluid physical model and investigate the behavior of ac-biased TES circuits using advanced circuit simulators. By relating our findings to results for the analysis of dc-biased TES circuits, we give appropriate definitions for the current and temperature sensitivity of the TES in ac-biased circuits. Our work not only builds a rigorous foundation for theoretical analysis of ac-biased TES circuits but also introduces powerful simulation techniques valuable for their design and research.