Impact of embedded ¹⁶³Ho on the performance of the transition-edge sensor microcalorimeters of the HOLMES experiment

We present a detailed investigation of the performance of transition-edge sensor (TES) microcalorimeters with ¹⁶³ 163 Ho atoms embedded by ion implantation, as part of the HOLMES experiment aimed at neutrino mass determination. The inclusion of ¹⁶³ 163 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 ¹⁶³ 163 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 ¹⁶³ 163 Ho activity, consistent with the expected scaling of heat capacity. From the analysis, we determined the specific heat capacity of ¹⁶³ 163 Ho to be (2.9 ± 0.4 (stat) ± 0.7 (sys)) ( 2.9 ± 0.4 ( stat ) ± 0.7 ( sys ) ) J/K/mol at (94 ± 1) ( 94 ± 1 ) mK, close to the literature values for metallic holmium. No additional long decay time constants correlated with ¹⁶³ 163 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 ¹⁶³ 163 Ho activities up to approximately 5 Bq, with only about a factor of three degradation in performance compared to detectors without ¹⁶³ 163 Ho. For higher activities, reducing the TES transition temperature is necessary to maintain or improve the 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 limited amounts of implanted radionuclides while maintaining high-resolution performance.