Impedance measurements and modeling of a transition-edge-sensor calorimeter

Abstract

We describe a method for measuring the complex impedance of transition-edge-sensor ͑TES͒ calorimeters. Using this technique, we measured the impedance of a Mo/Au superconducting transition-edge-sensor calorimeter. The impedance data are in good agreement with our linear calorimeter model. From these measurements, we obtained measurements of unprecedented accuracy of the heat capacity and the gradient of resistance with respect to temperature and current of a TES calorimeter throughout the phase transition. The measurements probe the internal state of the superconductor in the phase transition and are useful for characterizing the calorimeter.

Normal metal-superconductor decoupling as a source of thermal fluctuation noise in transition-edge sensors

“…We have performed impedance measurements between 4 Hz and 100 kHz both by the white noise method 12 , where a white noise excitation is used and the broadband response is measured, and by the lock-in method where a sinusoidal excitation is used at certain frequency points 30 . Both methods can in general be used, however, we have seen that the sine-wave method is more reliable, as the total heating power generated by the excitation is typically less in the sine-wave method.…”

“…Importantly, within the transition this impedance depends not only on the electrical, but also on the thermal circuit of the device, through the electrothermal feedback effect 1,2 . With the help of this technique, a more accurate picture of the electrical and thermal properties of TES sensors has emerged: First of all, it was realized that the dependence of the detector resistance on current, and not only on temperature, is critical for the detector response, as well 2,12 . This was later shown to influence the Johnson noise directly 13 , and some of the excess noise could then be explained as non-equilibrium Johnson noise.…”

“…A useful tool in characterizing TES detectors is the measurement of their frequency-dependent complex electrical impedance 12 . Importantly, within the transition this impedance depends not only on the electrical, but also on the thermal circuit of the device, through the electrothermal feedback effect 1,2 .…”

Development of Cryogenic X-Ray Detectors Based on Mo/Au Transition Edge Sensors

“…The logarithmic sensitivities to temperature ( I ) and current ( I ), and the effective time constant  eff can be determined at different operating points and bath temperatures. The heat capacity C of the TES can also be deduced from these data with the use of the G extracted from the IV measurements [22]- [25]. Z() measurements were performed by carrying out frequency sweeps at different bath temperatures and operating points along the superconducting transition.…”

Complex impedance, responsivity and noise of transition-edge sensors: Analytical solutions for two- and three-block thermal models

“…We take advantage of the fact that we also derive the analytical equation for the complex impedance of the a Electronic mail: maasilta@jyu.fi detector [17][18][19] of each model. Measurement of the complex impedance of a TES detector has been shown in recent years 5,[19][20][21] to be a very valuable tool for characterising TES detectors; in particular for the discussion here, it gives information about the thermal model. There is some previously published 4,10,12,15 and unpublished 13 analytical work on certain two-and three-block models of bolometers.…”