Impact of embedded $^{163}$Ho on the performance of the transition-edge sensor microcalorimeters of the HOLMES experiment

TL;DR

The HOLMES study investigates how embedding $^{163}$Ho in TES microcalorimeters affects detector performance by adding an excess heat capacity from a Schottky anomaly near the operating temperature. The authors fabricate and characterize three arrays with varying Ho activities, calibrate with Mn K$eta$-line anchors, and use the ETF-based model to relate energy resolution to total heat capacity, extracting the Ho-specific heat capacity $oldsymbol{c_{Ho}}$ from both $oldsymbol{ riangle E_0(A_{Ho})}$ and decay-time measurements. They report $oldsymbol{c_{Ho} = (2.9 \\pm 0.4 ext{(stat)} \\pm 0.7 ext{(sys)})}$ J/K/mol at $oldsymbol{T \\approx 94}$ mK, in agreement with metallic holmium, and find no evidence for slow, weakly coupled thermodynamic systems; extrapolations indicate that keeping performance at higher Ho activities would require operating temperatures as low as $oldsymbol{T_0 < 40}$ mK for ~50 Bq per pixel. The results demonstrate TES robustness to implanted radionuclides and provide critical design guidance for next-generation neutrino-mass experiments aiming at sub-eV sensitivities, including how to balance activity, energy resolution, and operating temperature.

Abstract

We present a detailed investigation of the performance of transition-edge sensor (TES) microcalorimeters with $^{163}$Ho atoms embedded by ion implantation, as part of the HOLMES experiment aimed at neutrino mass determination. The inclusion of $^{163}$Ho atoms introduces an excess heat capacity due to a pronounced Schottky anomaly, which can affect the detector's energy resolution, signal height, and response time. We fabricated TES arrays with varying levels of $^{163}$Ho activity and characterized their performance in terms of energy resolution, decay time constants, and heat capacity. The intrinsic energy resolution was found to degrade with increasing $^{163}$Ho activity, consistent with the expected scaling of heat capacity. From the analysis, we determined the specific heat capacity of $^{163}$Ho to be $(2.9 \pm 0.4 \mathrm{(stat)} \pm 0.7 \mathrm{(sys)})$ J/K/mol at $(94 \pm 1)$\,mK, close to the literature values for metallic holmium. No additional long decay time constants correlated with $^{163}$Ho activity were observed, indicating that the excess heat capacity does not introduce weakly coupled thermodynamic systems. These results suggest that our present TES microcalorimeters can tolerate $^{163}$Ho activities up to approximately 5 Bq without significant performance degradation. For higher activities, reducing the TES transition temperature is necessary to maintain energy resolution. These findings provide critical insights for optimizing TES microcalorimeters for future neutrino mass experiments and other applications requiring embedded radioactive sources. The study also highlights the robustness of TES technology in handling implanted radionuclides while maintaining high-resolution performance.

Figures (8)

• Figure 1: Left: Layout of the TES microcalorimeter, showing the side-by-side Mo/Cu bilayer sensor and gold absorber, with a copper perimeter for enhanced thermal conductionhays-wehle_thermal_2016. Right: Schematic (not to scale) of the micromachined TES microcalorimeter with embedded $^{163}$Ho as used in this work.
• Figure 2: Top: Layout of one of the two $16\times4$ pixel arrays fabricated on $14\times19$ mm$^2$ chips. Each cell reproduces the layout shown in Fig. \ref{['fig:fab']} (Left). Bottom: Copper box used for characterizing Arrays 0 and 1. The TES arrays are mounted at the center. Only the upper half of the arrays (32 microcalorimeters) is instrumented with the bias network and microwave multiplexer chips. The multiplexers have their feedlines aligned with the SMA connectors and the central interconnecting feedline. The box is closed with a light-tight cover featuring two openings above the array, each shielded by a 6 $\mu$m aluminum foil, to allow irradiation with an external X-ray source. For Array 2, a new box accommodating a single array was used (see figure in alpert_most_2025).
• Figure 3: Averaged pulses from N1 capture events in pixels with about 0.02 Bq, 0.2 Bq, and 0.5 Bq of $^{163}$Ho activity from Array 2. The logarithmic scale in the inset highlights the absence of additional long decay time constants.
• Figure 4: Mn K$\alpha$ X-ray peak measured with the best pixel in Array 0. The FWHM energy resolution is $(4.2\pm0.1)$ eV, while the intrinsic resolution, calculated from Eq. (\ref{['eq:nep']}), is about 3.7 eV.
• Figure 5: The four panels from left to right show the Mn K$_\alpha$ peaks obtained summing spectra from a few pixels with increasing activity. The FWHM energy resolutions obtained fitting the Mn K$_\alpha$ peaks from left to right are $6.5\pm0.1$, $6.9\pm0.1$, $8.5\pm0.1$ and $13.1\pm0.1$ eV. Red curves show the fitted model with Gaussian peaks for all seven Mn K$\alpha$ components holzer_$kensuremathalpha_12$_1997; blue curves show the flat background; green curves represent the sum of all Gaussians.