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IEEE Transactions on Applied Superconductivity

Unraveling Current-Bias-Induced Transition Discrepancy in Transition-Edge Sensors in R-T Tests and Establishing a Reliable Characterizing Method

Qing Yu, Yongping Li, Guanhua Gao, Yu Xu, Kaiyong He, Mingjun Cheng, Zhengwei Li, S. Shu, Guodong Chen, Wei Chen

Published Feb 16, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1109/tasc.2026.3664997

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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.
In contemporary cosmic microwave background experiments, bolometric detectors are often background limited, and in this case the sensitivity of instruments can only be improved by increasing the number of background-limited detectors, and so contemporary TES receivers contain as many pixels as possible. Frequency-domain multiplexing (fMUX) is one strategy for reading out many detectors with one SQUID. For any readout system, it is important to carefully evaluate the thermal design of detector, in conjunction with the readout bandwidth, in order to ensure stable electro-thermal feedback (ETF). We demonstrate a novel technique for characterizing the thermal circuit of our detectors, using am AC-bias and the fMUX electronics. This technique is used to study the internal thermal coupling of a TES bolometer. We illustrate how the insights gathered by this technique have been instrumental in improving the stability of our multiplexed detectors for the south pole telescope (SPT).
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 theoretical analysis and experimental evaluation of a transition-edge superconducting bolometer for detecting infrared and millimeter waves. The superconducting film is voltage biased and the current is read by a superconducting quantum interference device ammeter. Strong electrothermal feedback maintains the sensor temperature within the transition, gives a current responsivity that is simply the inverse of the bias voltage, and reduces the response time by several orders of magnitude below the intrinsic time constant C/G. We evaluated a voltage-biased bolometer that operates on the Tc∼95 mK transition of a tungsten film with a thermal conductance of G∼1.2×10−9 W/K. As expected, the electrical noise equivalent power of 3.3×10−17/W√Hz is close to the thermal fluctuation noise limit and is lower than that of other technologies for these values of G and temperature. The measured time constant of 10 μs is ∼100 times faster than the intrinsic time constant.
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.
A number of groups have produced TES bolometers and other devices using dielectric membranes for thermal isolation in which excess heat capacity is reported. We have fabricated a series of TES devices using large area membranes and narrow legs for thermal isolation to study the scaling of intrinsic parameters like the heat capacity of the membrane. The devices are arranged on a single chip to ensure similarity of devices parameters (i.e., film thicknesses) and processing history. Measurements (non-multiplexed) of the current-voltage characteristic and complex impedance are made using a well-characterized, highly uniform, multichannel SQUID setup. We have developed model for non-ideal transition edge sensor performance that enables extraction of heat capacities and thermal conductances identified in the models. We report on the magnitude of excess heat capacity in the dielectric membrane and thermal conductance of the metal-to-dielectric interface in each of the designs.
SQUIDs can be used as amplifiers for superconducting Transition Edge Sensor (TES) photon counting detectors. According to the physical process of photon counting, a TES signal simulator was developed to evaluate the performance of SQUID amplifier for TES detectors. A triangle simulation signal was determined to be a close match to that from a real TES photon counter. The dynamic range for the output voltage versus bias current was first characterized and then the current signals were incrementally coupled to circuit to determine the highest sensitivity of a series-array SQUID amplifier. The sensitivities are obtained by changing the triangle signal amplitude added to the TES signal simulator. The impedance changes can be deduced and further obtain the temperature changes of TES devices. When knowing the photon energy, TES design parameters can be known according to the thermal characteristics. In conclusion, the TES simulator can be well applied to guide the device design for effective readout.