Energy calibration of bulk events in the BULLKID detector

TL;DR

This work validates the optical surface-based energy calibration of the BULLKID silicon KID detector by using bulk interactions from a $^{241}$Am source at $E=59.5$ keV, which probe the entire crystal volume. It reveals depth-dependent phonon leakage from the main die to neighboring dice and demonstrates a calorimetric approach that sums main and neighbor signals to recover the deposited energy with substantially improved resolution, from about $5\%$ to $2\%$ (σ). The optical calibration is shown to have a systematic deficit of up to $\sim10\%$, which is acceptable within current goals, and the bulk calibration confirms the detector’s readiness for DM and CE$\nu$NS experiments. The study also highlights systematic aspects, such as Poisson phonon statistics, that will guide future refinements of the calibration model.

Abstract

BULLKID is a cryogenic, solid-state detector designed for direct searches of particle Dark Matter candidates, with mass $\lesssim 1$ GeV/c$^2$, and coherent neutrino-nucleus scattering. It is based on an array of dice carved in 5 mm thick silicon crystal, sensed by phonon-mediated Kinetic Inductance Detectors. In previous works, the array was calibrated with bursts of optical photons, which are absorbed in the first hundreds nanometers of the dice and give rise to surface events. In this work, we present the reconstruction of bulk events through the 59.5 keV $γ$-ray generated by an $^{241}$Am source, which emulates more closely the interaction of Dark Matter and neutrinos. The peak resolution is $5\%~(σ)$ and its position is shifted by less than $10\%$ with respect to the optical calibration. We observe that the resolution is further improved by a factor $2$ combining the signal from neighboring dice. These results confirm the performance of the detector in view of the physics goals of the BULLKID-DM experiment for dark matter search.

Figures (5)

• Figure 1: Top: silicon wafer of BULLKID. It is made of 60 silicon dice of $5.4 \times 5.4 \times 5~\text{mm}^3$ and $0.34~\text{g}$ each. It is installed in a copper holder for the mechanical stacking and the thermalization at cryogenic temperatures; Center: picture of the wafer (from the side of the lithography) and map of its working KIDs. The resonators inside the orange continuous line represent the acquired KIDs when the main resonators $46,47,49$, in the green boxes, trigger. The empty cells represent missing KIDs while the colorscale is representative of the total quality factor of each resonator. Bottom: scheme (not in scale) of the aluminum pot (light grey) that hosts the BULLKID detector (dark grey) and of the screw with the Americium source on its head. On the top of the aluminum pot, a sketch of the optical fibers used for the illumination of the main KIDs.
• Figure 2: Schematic representation of a $59.5$ keV $\gamma$-ray emitted from a radioactive $^{241}$Am source interacting within BULLKID. The plot on the right shows the interaction probability, evaluated through a GEANT4 GEANT4:2002zbu simulation, of such $\gamma$-rays as a function of the depth in the silicon crystal. The depth origin is referenced from the top of the common disk of the structure, as the radioactive source is positioned on the lithography side. Athermal phonons (red dots) generated by the $\gamma$-ray interaction are predominantly collected by the KID located on the corresponding die. A fraction of these phonons leaks through the common disk into adjacent dice, inducing signals in their respective KIDs. For reference, the light bulb represents the optical fiber, used for the optical calibration, that shines the side of the die opposite to the lithography.
• Figure 3: Top: dependence of the reconstructed amplitude $A_{\text{reco}}$ to the number of triggers $N_{\text{trig}}$ for the main KID $49$ and fit, orange curve, with the model described in Eq. \ref{['eq:parabolic-relation']}. The blue line corresponds to the response function after the correction for the non-linearity by mean of Eq. \ref{['eq:linearization']}. The black and green dots are the reconstructed amplitudes of the control LED and of the Americium peak; Bottom: energy spectrum of the same KID in the range $\left[45,70\right]$ keV calibrated with optical photons. The Americium peak is identified and fitted with a Gaussian model superimposed on the graph. The red-dashed vertical line represents the $59.5$ keV true energy.
• Figure 4: Top: energy ratio $R_n$, as defined in Eq. \ref{['eq:ratio']}, for the neighbor dice of the KID $49$ as a function of the LED calibrated energy in the main die. The position of the single plots corresponds to the die to which the ratio is evaluated. In the center of the plot, the energy spectrum of KID $49$. The insets in each cell is a close up on the region of Americium events ($\left[45,70\right]$ keV) in order to point out the anti-correlation that we measure for each neighbour; Bottom: energy ratio $R_n$ between three couples of neighbors of KID $49$: left/right, top/bottom and diagonal corners. Only events in the energy range $\left[45,70\right]$ keV in the main die are considered. We observe a positive correlation in all the three cases and the same is for all the possible neighbors pairs and for all the main KIDs.
• Figure 5: Left: linear relation between the calorimetric and the LED calibrated energy for the main KID $49$ in the energy range $\left[10,80\right]$ keV. The black fit superimposed gives the calibration parameter to convert the former amplitude in keV; Center: energy spectrum of KID $49$ in the range $\left[45,70\right]$ keV with the calorimetric amplitude defined in Eq. \ref{['eq:bol_ampl']}. The Americium peak is identified and fitted with a Gaussian model superimposed on the graph. The red-dashed vertical line represents the $59.5$ keV nominal energy; Right: energy spectrum of KID $49$ in the range $\left[45,70\right]$ keV with the calorimetric amplitude defined in Eq. \ref{['eq:bol_ampl']} during an optical calibration. The LED peak is identified and fitted with a Gaussian model superimposed on the graph. The red-dashed vertical line represents the $59.5$ keV nominal energy of Americium.