Thermal fluctuation noise in Mo/Au superconducting transition-edge sensor microcalorimeters

Abstract

In many superconducting transition-edge sensor (TES) microcalorimeters, the measured electrical noise exceeds theoretical estimates based on a thermal model of a single body thermally connected to a heat bath. Here, we report on noise and complex impedance measurements of a range of designs of TESs made with a Mo/Au bilayer. We have fitted the measured data using a two-body model, where the x-ray absorber and the TES are connected by an internal thermal conductance G ae . We find that the so-called excess noise measured in these devices is consistent with the noise generated from the internal thermal fluctuations between the x-ray absorber and the TES. Our fitted parameters are consistent with the origin of G ae being from the finite thermal conductance of the TES itself. These results suggest that even in these relatively low resistance Mo/Au TESs, the internal thermal conductance of the TES may add significant additional noise and could account for all the measured excess noise. Furthermore, we find that around regions of the superconducting transition with rapidly changing derivative of resistance with respect to temperature, an additional noise mechanism may dominate. These observations may lead to a greater understanding of TES devices and allow the design of TES microcalorimeters with improved performance.

A Review of X-ray Microcalorimeters Based on Superconducting Transition Edge Sensors for Astrophysics and Particle Physics

“…As suggested and observed in many experiments [50][51][52][53][54], a single-body thermal model for a TES calorimeter is rarely sufficient to explain the detector response. This is due to the presence of dangling heat capacitance and parasitic thermal conductance in the TES-absorber structures or to a not sufficiently high thermal conductance between TES and absorber.…”

“…It can be shown that a two-body model [49,50,53], as drawn in Figure 1b, is sufficiently general to account for parasitic thermal effects in TES-based detectors. A more detailed analysis for even more complex thermal structures can be found in [51][52][53][54]. However, one has to keep in mind that the model is unconstrained when too many thermal bodies are added into the system of equations.…”

High aspect ratio transition edge sensors for x-ray spectrometry

“…Here k B is Boltzmann's constant and M 2 is the excess noise, given by the difference between the measured and predicted noise. This excess noise is typically explained by other noise sources, such as the weak-link effect described by the resistively shunted junction (RSJ) model 20,45 , the presence of phase-slip lines 46 , or ITFN 11,15,[47][48][49] . In this paper, we will not go into a detailed analysis of the origin of the excess noise, but instead use it as a guideline to find the optimal TES design.…”

“…Traditionally, TESs used for X-ray calorimetry have been pushed to low resistance values (R n 10 mΩ). This type of device is very suitable for the DC-biased TDM readout since they typically have very sharp superconducting transitions and low internal thermal fluctuation noise between different parts of the calorimeter 15 , leading to very good energy resolution 8 . However, these low-Ohmic devices are generally unsuited for AC-biased readout.…”

“…For this reason we are developing TESs with high normal resistances (R n 100 mΩ). This has to be done carefully though: Fabricating high normal resistance devices by changing the resistivity of the bilayer is not a viable approach, as it was shown by Wakeham et al that this would increase the internal thermal fluctuation noise (ITFN) 15 . Therefore, we are keeping a constant sheet resistance, and instead develop TESs with high aspect ratios (width:length up to 1:6) with values for the normal resistance of ∼ 50-150 mΩ.…”