Development of MMC-based lithium molybdate cryogenic calorimeters for AMoRE-II

Low-temperature detectors that are used for thermal calorimetric detection typically operate at temperatures of a few tens of millikelvin. At these temperatures, the heat capacity of the crystal absorber with a mass of a few hundred grams is low enough ($\sim$1 nJ/K) to support high resolution measurements of energy depositions of a few MeV. When a particle deposits energy in a dielectric crystal, highly energetic phonons close to Debye frequencies are generated. These phonons quickly decay via anharmonic processes to lower-energy phonons at a rate proportional to the fifth power of their energy. Once they reach a state where they travel ballistically with a mean free path longer than the dimension of the typical crystal absorber (a few centimeters), these phonons, usually called athermal phonons, travel around the crystal on a timescale of a few milliseconds before thermalization probst ; sust_review . The phonon thermalization process, which results in a thermal phonon distribution at a specific temperature, includes isotope and defect scattering in the bulk and inelastic surface scatterings. By introducing a small metal film evaporated on the crystal surface, athermal phonons and their thermalization can be detected via the film, thereby serving as a phonon collector. In the AMoRE setups, an MMC that is thermally connected to the phonon collector detects the corresponding temperature change, which is reflected as the change in magnetization of the paramagnetic sensor. The athermal and thermal processes of heat flow among the detector components are described in detail in references epjplus_2023 ; jltp_thermal_model_2024 . The MMC is equipped with a superconducting current loop with persistent current. The change in magnetization introduces a screening current in the superconducting current loop that is measured by a SQUID, leading to a voltage signal that can be recorded as the heat channel signal amore_det_principle .

In the case of a scintillating crystal, a small fraction (a few percent) of the absorbed energy generates scintillation photons, while most of the energy converts into phonons in the crystal lattice. An addtional detector setup with a wafer of Si or Ge and an MMC sensor is used to detect the scintillation photons in the AMoRE crystals (light channel) hjlee_LD2015 ; mbkim_ieee2023 . The early detector development of the heat and light detection is described in previous reports gbkim_2017 ; amore_det_principle ; wtkim_jinst2022 ; wtkim_jltp2022 .

We report about the characterization of four detector setups as AMoRE-II R&D detector modules that were built based on the details discussed in subsection 2.2.1. The specifications of each setup are described in Table 1. In the AMoRE-I experiment, MMCs with two meander-shaped pickup coils, each covered by Ag:Er layers to form a gradiometric flux transformer, were utilized mmc_meander ; mmc_meander_kriss . In the R&D experiments, we tested MMCs where only one pickup coil is covered by the Ag:Er layer to investigate the temperature-dependent baseline change to establish the magnetization as a function of temperature. Although MMCs with two Ag:Er areas (“double side MMC”) are considered better for cancelling noises common to both areas, we found that MMCs with one Ag:Er area (“one side MMC”) provide a viable solution. The DC baseline in the one side MMCs allows for correction of gain changes due to temperature drift and does not suffer from serious noise issue. In the detector setups discussed in this report, except for one light detector, which was paired in DET2, one side MMCs were used. We previously reported the reduced noise level and improved energy resolution using MMCs with no thermal link and followed this approach for one detector (DET3) as specified in Table 1 wtkim_jinst2022 . There were attempts to improve the performance of the light channel, including optimization of the phonon collector (annealing and increased area) and thermal conductance between the phonon collector and the MMC mbkim_ieee2023 . These efforts were reflected in some detector modules such as DET3 and DET4. For the R&D setups, normal copper frames were also used in addition to NOSV copper frames. A strict protocol for the cleanliness of materials was not applied since the test was conducted at an above-ground cryostat with high environmental radioactive background and the primary focus was on the detector performance test.

We used the above-ground cryogen-free dilution refrigerator, which is located in CUP, IBS headquarter in Daejeon, South Korea. It is a large cryostat that accommodates a 10 cm thick lead layer, which shields radiation from the top direction, and a vibration damping structure vibration_damper under which the detector tower of multiple detectors is installed at the mixing chamber stage. The cryostat is enveloped by 10 cm thick layers of lead bricks along the sides and underneath the bottom to substantially reduce environmental radiation background. The base temperature is below 10 mK and the cooling power is a few $\mu$W at 10 mK. We tested the performance of the detectors at temperatures of 10, 20 and 30 mK at the mixing chamber stage. To avoid crystal damage caused by exposure to ambient moisture, the cryostat is located in the low-humidity facility, which provides a humidity level below 10 % RH at room temperature when we install the detectors. Figure 2 shows the low-humidity facility with the cryostat and a detector tower installed at the mixing chamber stage of the cryostat with the vibration damper.

The detector signals were saved continuously using a multi-channel ADC digitizer. In digitization, the sampling rate was set as 100k samples/s with 18-bit resolution and a dynamic range of 10 V. The ADC was optically connected to a trigger condition board (TCB), which controls the global clock and transfers data to a data storage computer, to minimize noise interference in the signals. The event triggering was conducted offline with bandpass filtering.

Fig. 3 (a) shows the measured heat channel pulses for 2.615 MeV gamma rays (²⁰⁸Tl) produced from a ²³²Th calibration source with DET2 at 10, 20, and 30 mK. The characteristic features of the pulses for overall detectors are summarized in Table 2. The pulse shape for different detectors may depend on various factors, including the interface between the phonon collector and the crystal surface, crystal conditions with different degrees of surface roughness, MMC response, the amount of MMC field current, and actual conductance of gold wires which realize the thermal connections at MMC for the phonon collector and heat bath. All the detectors showed reasonable signal responses up to 30 mK. The signal amplitude increase at lower temperatures, as expected, due to the lower heat capacities of the detector components and the temperature dependence of the sensor responsivity mmc . The rise times (the time elapsed between 10 and 90 % of the pulse maximum on the rising edge) of the heat channel signals range from 3.82 and 5.92 ms at 10 mK and become shorter as 1.22 – 2.26 ms at 30 mK. Generally, a faster time response is beneficial for minimizing backgrounds in the ROI from unresolved pile-up events. Considering the signal and noise traces measured in the heat channel at 10 mK, we estimated the rate of unresolved pile-ups from 2$\nu$DBD events to be less than $3\times 10^{-5}$ counts/keV/kg/year in the ROI ymoh_neutrino2024 . The rate is tolerable within the AMoRE-II background budget, which aims for a level of less than $10^{-4}$ counts/keV/kg/year in the ROI. Futhermore, with the aid of fast light signals, the timing resolution can be improved, and the rate of unresolved pile-ups can be suppressed. Alternatively, this rate can be further reduced at higher operational temperatures, albeit with a trade-off in energy resolution due to smaller signal amplitudes. Regarding the decay time (the time between 90 and 10 % of the height on the falling edge), it is generally in the range of 10 – 40 ms except for the signal of DET2 at 10 mK, which exhibits a decay time of about 111 ms, requiring further understanding.

In previous experiments for crystals with polished surfaces, a two-band structure was clearly visible in a plot of energy versus rise time due to the muon passage at the edge of the crystals wtkim_jinst2022 ; wtkim_jltp2023 . We reported that crystals with diffusive surfaces showed longer rise times of the signals and mitigation of position-dependent behavior wtkim_jltp2023 . This effect resulted in a smaller spread in the rise time distribution and, therefore, stronger pulse shape discrimination (PSD). In the present setups prepared with diffusive crystal surfaces, this phenomena was confirmed even in a large crystal with dimensions of 6 cm (H) $\times$ 6 cm (D). As shown in Fig. 4 (a) and (b), the split structure is not apparent, allowing clear discrimination of alpha events using pulse shape parameters such as rise time. The discrimination power (DP) is defined as:

where $m_{\beta/\gamma/\mu}$, $m_{\alpha}$ are the mean values of the parameters for non-alpha signals (beta, gamma, and muon signals) and alpha signals respectively, $\sigma_{\beta/\gamma/\mu},\sigma_{\alpha}$ are the corresponding standard deviations. DP based on PSD between alpha particles and muons at the energy region around ⁶Li$(n,\alpha)^{3}$H (Q-value = 4.785 MeV) are summarized in Table LABEL:tab:performance. The energy scales in Fig. 4 are calibrated with distinct gamma lines, and the energy of the alpha events is slightly overestimated due to different pulse shapes. At 10 mK, these detectors showed DP values larger than 3. The R&D test was not conducted long enough to collect a large amount of the degraded alpha (or surface alpha) events around the ROI, but the DP around 5 MeV, where we can find a good population of alpha events, can be a good indicator for the DP at the ROI. DET1 and DET4, which we built with the exact same crystal, still showed a wide spread of rise times, as shown in Fig. 4 (c) and (d). We believe either its surface treatment was not optimal or the crystal might have a non-uniformity issue. A more detailed discussion about the position-dependent behavior of events with some detectors was presented in our earlier report wtkim_jltp2023 .

The experiments were conducted above ground with a ²³²Th source placed just outside the OVC of the cryostat to irradiate the detector tower. The total event rate for each detector was in the range of about 3 – 4 Hz. Due to frequent high-energy events, including those from cosmic muons, and the typical recovery time for event signals to return to baseline being longer than 100 ms, there is a good chance that signal events appear in the long tail of the preceding events. To determine the signal amplitudes, we applied a bandpass filter to the raw signals with passband frequencies chosen to minimize the influence of baseline fluctuations and other high-frequency noises wtkim_nmo_2022 . For the heat channel signal, a first-order Butterworth bandpass filter was employed with typical lower bound frequencies ranging from 15 to 30 Hz and upper bound frequencies from 40 to 200 Hz.

The DC voltage signal from an MMC is proportional to the detector temperature, which reflects the transient temperature change due to the particle interaction in addition to tiny fluctuation of the baseline temperature. Therefore, it is possible to correct for temperature-dependent signal gain by analyzing the dependence of the height of pulses corresponding to a well defined energy with the average value of the DC pre-trigger samples (baseline) of the event pulses. The relation between the signal height and the baseline was investigated with the 2.615 MeV gamma line, as shown in Fig. 5, and was used for the correction. The improvement in energy resolution across overall energy range is clearly shown in Fig. 5. Although the R&D setups do not have stabilization heaters for drift correction, the baseline correction effectively recovers the energy resolution from temperature drift. Previously, the spectral shape of the peaks in the measured energy spectrum were typically approximated as Gaussian shapes. However, there are non-Gaussian components, although subtle, arising from various factors such as event position. For example, if events occur near the phonon collectors, their energy tends to be overestimated. Additionally, we sometimes observe a left-hand shoulder on the peak spectrum due to imperfect energy collection. For this reason, we adopted a Crystal Ball function crystalball to describe the shape of the energy peaks:

where

Here, $N$ is a normalization factor, and $\alpha$, $n$, $\bar{x}$ and $\sigma$ are fitting parameters. In this report, we use the energy resolutions defined as FWHM of the Crystal Ball functions, even though the values are very close to the FWHM with the Gaussian approximation with differences within a few percent. An illustration of a peak from 2.615 MeV gamma events fitted with a crystal ball function is shown in Fig. 5 (c). Energy resolutions of various calibration peaks at 10 – 30 mK temperatures are summarized in Table LABEL:tab:performance. At the 2.615 MeV gamma line, the calibration peak close to the ROI, the detectors showed FWHM of 7.55 – 8.82 keV at 10 mK, 8.48 – 12.34 keV at 20 mK and 10.74 – 12.84 keV at 30 mK. The AMoRE-I detectors showed 10 – 20 keV FWHM at the same calibration peak with the detector operation at 12 mK. The overall energy resolution performance is significantly improved compared to AMoRE-I experiments even though we used larger crystals than those in AMoRE-I and included operation at higher temperatures. In setting the target discovery sensitivity for AMoRE-II, we assumed energy resolution of 10 keV FWHM at the ROI. The results show that the energy resolutions sufficiently meet the design value of AMoRE-II at 10 mK and remain acceptable even up to 30 mK operation. This demonstrates that the detectors developed for AMoRE-II are not extremely sensitive to the operation temperature and allows for the operation of detectors at the higher temperature ($\sim$ 30 mK), where the pulse response is much faster implying better pile-up rejections with moderate sacrifice of the energy resolution. When operating AMoRE-II, the operating temperature can be tuned to optimize energy resolution and DP, which are better at lower temperatures, as well as timing resolution for pile-up rejections, which is better at higher temperatures.

The MMC-based light detectors were developed to be integrated in the AMoRE modules hjlee_LD2015 ; mbkim_ieee2023 . Although these light detectors themselves demonstrated high sensitivities, the light channels in previous AMoRE and R&D setups were found to be more vulnerable to vibrations from the operation of a pulse tube refrigerator (PTR). The energy input from the absorption of scintillation light is small and easily swamped by the low-frequency noise (a few Hz) associated with cryostat vibration. In the pulse-height estimation for the light channels, bandpass filters were applied similarly to the heat channel wtkim_jinst2022 ; wtkim_nmo_2022 . We set the passband frequencies as 400 – 900 Hz for the light channel signals. Figure 6 (a) shows an example plot of the rise times of the signals versus their energies, indicating two distinct groups in the rise time distribution. The signals from the measurement of scintillation light show greater rise time values centered near 450 $\mu$s, while other non-scintillation events, such as X-rays and muons, referred to as direct hit events in this report, indicate shorter rise times. This difference originates from the scintillation decay time, on the order of 100 $\mu$s, appearing in LMO crystals bagrat_ieee2023 ; bijaya_jltp2023 . The energy of the scintillation signals can be calibrated with the direct hit X-ray signals. As demonstrated in Fig. 6 (b) and (c), this detector obtained 198 eV FWHM for 5.9 keV X-ray signals from an ⁵⁵Fe source covered by aluminum foils with a total thickness of a few hundreds of micrometers, irradiating a large area of the wafer surfaces, and 481 eV FWHM for 17.5 keV X-rays from Mo in the crystal. We assumed a Gaussian shape for the energy peaks in the light channel signals. The energy resolutions at baseline and the 17.5 keV X-ray peak for the overall R&D detectors are summarized in Table LABEL:tab:performance. The baseline energy resolutions were measured as 83 – 383 eV at 10 mK, 101 – 640 eV at 20 mK and 159 – 775 eV at 30 mK. At the 17.5 keV peak, the estimated energy resolution was 481 - 850 eV at 10 mK, 573 – 1190 eV at 20 mK and 750 – 1290 eV at 30 mK. Overall, the R&D detectors showed a modest decline of the energy resolution as the operation temperature increased, yet maintained good performance up to 30 mK. The energy resolution of the light detectors at other X-ray peaks is fully discussed in other report bijaya_jltp2023 .

We performed a convolution fit to estimate the energy of scintillation light actually detected, assuming two-component exponential decay for the scintillation of the LMO crystals bijaya_jltp2023 . At 10 mK, the fraction of deposited energy observed as scintillation light was obtained as 0.79 - 0.96 keV/MeV using the events of 2.615 MeV gamma rays as the reference signal (Tab. LABEL:tab:performance). This scintillation detection remains almost the same up to 30 mK. The quenching of the scintillation light for alpha particles is essential because it allows the discrimination of alpha particles based on the light/heat signal ratios. We compared the averaged pulses for 2.615 MeV gamma rays and 4.785 MeV alpha particles with tritium from the neutron capture on ⁶Li, which can be considered as alpha events, and estimated the ratio of these pulse heights after normalizing each pulse by its own energy. We found that the quenching for alpha signals is around 0.25 for every detector in the tested temperature range, as shown in Table LABEL:tab:performance. It means that the amount of scintillation energy collected from alpha particles is about 25% as much as that collected for full-energy deposition of gamma rays with the same energy as the alpha particles.

Figure 7 shows the light/heat signal ratio versus the energy of the signals measured with DET2 at 10 mK. Two groups of events are notable. A band of events with greater light/heat ratios originates from beta, gamma rays and muons. The light/heat ratio of ⁶Li neutron capture events is, indeed, approximately 25% of that observed in the band with beta, gamma, and muon events. This plot indicates that degraded alphas, which release only a fraction of its energy in the crystal due to their occurrences at the surface, can also be well discriminated. We estimated DP between the muon and the alpha signals around the signals from the ⁶Li neutron capture to be 12.37 – 19.50 at 10 mK as shown in Table  LABEL:tab:performance. Interestingly, the DP based on the light/heat ratio at 30 mK is as high as 7.04 - 15.78, which still can allow excellent alpha signal rejections. We tried to project the DP value at the ROI (E = 3.034 MeV) based on the measured scintillation detection (number of photons for a given energy). We introduced an additional energy-independent spread in the scintillation detection to account for the measured DP around E = 4.785 MeV. The projected values (L/H (ROI)) are also presented in Table 3. The projected DP ranges from 8.1 to 13.1 at 10 mK, reaching 4.5 – 10.6 at 30 mK. The improved DP values compared to the AMoRE-I experiment are mainly attributed to the detector design. The AMoRE-II setup features a small gap between the light absorber and the crystal, along with more efficient coverage by the reflector film, increasing light collection efficiency cupid_detectors_epjc2021 . Additionally, the setup introduced a tightened grip on the light absorber in the detector holder, reducing low-frequency noise caused by cryostat vibration.

To illustrate the time response of the scintillation light signals, the averaged signal for 2.615 MeV gamma rays with DET2 is shown in Fig. 3 (b). The characteristics of the scintillation signal for all four detectors are summarized in Table. 2. The rise time of the scintillation signals is 461 – 873 $\mu$s at 10 mK, 403 – 721 $\mu$s at 20 mK and 373 – 582 $\mu$s at 30 mK. The faster time responses, in comparison to the heat channel signals, can be exploited to enhance the pile-up rejection capability and may allow for bigger crystal absorbers, such as crystals of 7 cm (D) $\times$ 7 cm (H) dimensions, which are already grown by NIIC to be tested for the target absorber. Except for detector DET4, the decay time of the scintillation signals are in the range of 10 – 30 ms, with faster response at the higher temperatures. DET4 shows a very slow decay compared to other detectors. We suspect that the thermal link on the MMC was somehow damaged.