Phonon-mediated crystal detectors with metallic film coating capable of rejecting α and β events induced by surface radioactivity

Phonon-mediated particle detectors¹ (often defined “bolometers”) have nowadays important applications in neutrino physics,^2,3 dark-matter searches,⁴ and rare nuclear decay investigations.⁵ They also provide outstanding α, β, γ, x-ray, and neutron spectroscopy.^1,4–6

Neutrinoless double-beta (⁠$0ν2β$⁠) decay⁷ is a hypothetical rare nuclear transition of an even–even nucleus to an isobar with two more protons, with the emission of just two electrons. Its observation would provide a unique insight into neutrino physics.⁸ Bolometers based on Li₂MoO₄ crystals are promising detectors for a next-generation $0ν2β$ decay experiment.^6,9,10 They embed the favorable candidate ¹⁰⁰Mo, maximizing the detection efficiency. The $0ν2β$ decay signature is a peak in the sum energy spectrum of the two emitted electrons, expected at 3.034 MeV for ¹⁰⁰Mo. In a bolometer, the energy deposited by a particle in the crystal is converted into phonons, which are then detected by a suitable sensor.

The highest challenge in $0ν2β$ decay search is the control of the radioactive background, due to the long-expected lifetime of the process (⁠$>1025−1026$ y).^11–13 The experiments are located underground under heavy shielding. To reduce the current background level of bolometric experiments, it is mandatory to reject α or β events—defined “surface α's or β's” in the following for brevity—induced by radioactive impurities located either close to the surface of the crystal itself or to that of the surrounding structure.^14,15 Surface α's can be rejected in scintillating materials—such as Li₂MoO₄—by detecting simultaneously scintillation and phonons for the same event^14,16,17 and exploiting the generally lower light yield (LY) of α's with respect to β's,¹⁸ but the rejection of surface β's requires dedicated techniques capable of tagging surface events in bolometers.^19–23 

In this Letter, we report an effective method to identify both surface α's and β's in Li₂MoO₄ bolometers. The discrimination is achieved by coating a Li₂MoO₄ crystal side with a metallic film acting as a pulse-shape modifier for events that release energy close to the coated face. When an ionizing event occurs in a dielectric crystal kept at mK temperature, the deposited energy is readily converted to athermal phonons with typical energies of the order of tens of meV, to be compared with the few μeV thermal-bath energy. The energy downconversion of these athermal phonons occurs mainly by anharmonic decay and is progressively slowing down, as the phonon lifetime scales as the fifth power of the energy.^24,25 If a sensor sensitive mainly to thermal phonons is used (as in this work), the rise time of the signal is in the $∼10$ ms range, which corresponds to the typical thermalization time of the deposited energy. However, thermalization can speed up via a metallic film covering a crystal side. If the particle is absorbed close to the film, a significant fraction of its energy is trapped in the metal in the form of hot electrons, excited by the absorption of the particle-generated athermal phonons. The energy is quickly thermalized in the electron system, so that phonons of much lower energies are re-injected in the crystal from the film. Signals from events occurring close to the film will present, therefore, a shorter rise time and a modified time evolution. We show here that surface events can be tagged according to this approach.

All the detectors in this work share a common basic structure, which is similar to that used in the $0ν2β$ experiments CUORE,¹³ LUMINEU,⁹ CUPID-Mo,^10,26 and CUPID-0,²⁷ and in the dark-matter experiment EDELWEISS²⁸ as far as the phonon readout is concerned. The surface sensitivity was studied above ground with prototypes of reduced size with respect to the final $0ν2β$ bolometers. The energy absorber of the bolometers described here is a single Li₂MoO₄ crystal²⁹ with a size of $20×20×10$ mm³ and a mass of $∼12$ g. All the tests involve just a single 20 × 20 mm² coated side.

The phonon sensor is a neutron transmutation-doped Ge thermistor³⁰ (NTD) with a size of $3×3×1$ mm³. Its resistivity increases exponentially as the temperature decreases.³¹ The NTD is glued on the crystal by means a two-component epoxy. The glue provides a slow transmission interface, making the NTD sensitive mainly to thermal phonons.

We used uranium radioactive sources to test the detector surface sensitivity. They were obtained by drying up a drop of uranium acid solution on a copper foil. These sources provide two main α lines at $∼4.2$ and $∼4.7$ MeV from ²³⁸U and ²³⁴U, respectively, affected by a significant straggling due to partial α absorption in the source residues and/or in the copper substrate. ²³⁸U disintegration is followed by two consecutive β emissions, from ²³⁴Th (with a half-life of 24.1 d and an end point of 0.27 MeV) and from $234m$ Pa (with a half-life of 1.2 min and an end point of 2.27 MeV). The ²³⁸U α rate and the $234m$ Pa β rate are extremely close.

The detector assembly is shown in Fig. 1. A first test was conducted with a Li₂MoO₄ crystal without coating to establish the bare detector performance. All subsequent tests have adopted the configuration shown in Fig. 1, where the metal-coated side, which is optically polished before the film deposition, faces the radioactive source. A bolometric light detector based on a Ge wafer^9,10 is used to separate α from β/γ/muon events by detecting the scintillation light.^14,16,17

The detectors were cooled down in a dilution refrigerator located in IJCLab, Orsay, France.³² All the data discussed here have been collected with the detector thermalized to a copper plate at $∼22$ mK (Fig. 1). A current of the order of $∼5$ nA is injected in the NTD, rising the detector temperature to about $∼25$ mK, at which the NTD resistance is about 0.5 MΩ. The voltage signal amplitude across the NTD is $∼60$ μV/MeV for the bare crystal, corresponding to an NTD temperature change of $∼0.5$ mK/MeV. The pulse rise time (from 10% to 90% of maximum amplitude) is typically in the 3–10 ms range, and the pulse decay time (from 90% to 30% of maximum amplitude) is tens of ms. The signals are readout by a DC-coupled low-noise voltage-sensitive amplifier.³³ In all the tests, the Li₂MoO₄ detector is energy-calibrated using γ peaks of the environmental background, and the light detector using the cosmic muons crossing the Ge wafer.³⁴ In the Li₂MoO₄ heat channel, we obtained routinely good energy resolutions of 5–10 keV FWHM for environmental γ peaks in the 0.2–1 MeV region.

The first test to attain surface sensitivity was performed with a 10-μm-thick Al-film coating. The details of the achieved results are reported elsewhere.^35,36 We remind here that an excellent separation of surface α particles was demonstrated, thanks to pulse-shape discrimination.

The best separation between surface α's and any type of interior events was obtained via a particularly developed pulse-shape parameter—extensively used here—that we will designate as $m/Sm$⁠.³⁵ To construct it, the signals are passed through a digital optimal filter,³⁷ whose transfer function is built using the noise power spectrum and the pulse shape of an interior event. This filter provides the best estimator of the signal amplitude S_m (i.e., energy). An individual pulse S(t) is plotted point by point against an average pulse A(t)—formed from a large sample of interior events and normalized to 1—obtaining approximately a straight line. The related slope parameter m is an estimator of the pulse amplitude as well. The ratio $m/Sm$ turns out to be very sensitive to the pulse shape. Interior events have $m/Sm∼1$⁠, as expected. On the contrary, $m/Sm$ deviates from 1 for surface α events.

For the Al-coated Li₂MoO₄ crystal, the separation between the interior and the surface α events from a uranium source is better than $10σ$ in terms of $m/Sm$ distributions.³⁵ Unfortunately, only a slight hint of separation of the surface β events emitted by the same source was observed,^35,38 ruling out Al coating as a viable method for a complete surface-event tagging.

Aluminum was chosen as it is superconductive at the bolometer operation temperature, with a critical temperature $TC(Al)∼1.2$ K.³⁹ This leads to a negligible contribution to the heat capacity of the full bolometer, as the electron specific heat of superconductors vanishes exponentially with the temperature. We remark that the heat capacity of a bolometer must be as low as possible to achieve high signal amplitudes. In fact, no deterioration of the detector sensitivity was observed with respect to the bare Li₂MoO₄ crystal. However, the behavior of superconductors can spoil surface particle tagging. The prompt absorption of athermal phonons by the film breaks Cooper pairs and forms quasi-particles. Theoretically, quasi-particle lifetime diverges as the temperature of the superconductor decreases,^40,41 although it is often experimentally found to saturate at low temperatures.^42,43 In aluminum, at very low temperatures such as ours (⁠$T/TC<0.02$⁠), we expect the quasi-particle lifetime to be as large as several ms,^42–45 similar to the thermalization time of interior events. This mechanism competes with the faster thermalization that should be provided by the film.

Driven by these considerations, we tested a Li₂MoO₄ bolometer with a normal-metal coating. At low temperatures, the electron specific heat of normal metals is proportional to the temperature and tends to dominate over the crystal heat capacity, which scales as T³ according to the Debye law. The thickness of normal-metal films must be substantially smaller than the aluminum ones. We chose palladium as a coating material as it can provide continuous thin films down to 2 nm thickness, and no challenging radioactive isotopes are present in its natural composition. A thickness of 10 nm was chosen as a good compromise between heat capacity reduction and phonon absorption probability. The particle-identification results are encouraging, as shown in Fig. 2: both surface α's and β's are well separated from the interior events.

Unfortunately, the heat capacity of the Pd film⁴⁶ competes with that of the Li₂MoO₄ crystal⁴⁷ affecting seriously the sensitivity of the detector, which was only $∼23$ μV/MeV, about one-third of that achieved with the bare crystal. Therefore, this option is not viable for a full coating of the crystal.

To overcome the heat-capacity problem, we developed a detector coated with an Al–Pd bi-layer (100 nm and 10 nm thick, respectively, with Al on the top), which is superconducting by proximity effect below T_C(Al–Pd) $=0.65$ K. The superconductive gap induced in Pd by the Al film reduces substantially the Pd specific heat with respect to the normal state. This gap is, however, low enough to ensure the fast thermalization of the energy deposited by surface events. In fact, the surface-event discrimination capability was fully maintained (see Fig. 3, left). The detector sensitivity was measured to be 43 μV/MeV, almost doubled with respect to the pure Pd film.

We performed two runs with the bi-layer detector. In the first, a uranium source was present, while the second was a background measurement in the same configuration. The trigger rate was $∼0.2$ Hz with the source. The contribution of the source is at the level of $∼0.03$ Hz. First, we developed a method to separate the surface β component. The events below the black curve in the left panel of Fig. 3—collected in a source run—are selected as surface events, while those above represent more than 99% of the interior event population. The same analysis was performed for the background run. By means of Geant4-based⁴⁸ Monte Carlo simulations (using the G4RadioactiveDecay and Decay0⁴⁹ event generators), we were then able to confirm that the surface β events isolated at low energies come actually from the radioactive source. We built a model to predict the β spectrum shape considering the observed α straggling (Fig. 4) and the β interactions in the detector. We fitted then the experimental β spectrum using the predicted shape and taking the background into account (right panel in Fig. 3). The total number of $234m$ Pa decay events returned by the fit—the only free parameter—is 3526(81). To build the source model, we set a uranium-source depth profile capable of reproducing the observed α spectrum and the related straggling, as shown in Fig. 4. From the model and the experimental number of α counts, it was possible to predict independently the expected total number of $234m$ Pa events, which resulted to be 3455(273), in excellent agreement with that deduced from the selection of the source β events. The efficiency in selecting surface β events can be estimated as 102(8)%.

The β-particle range in Li₂MoO₄ is in the order of 2 mm at 1 MeV and 4 mm at 2 MeV. Therefore, we can separate events that deposit a significant amount of energy up to $∼4$ mm from the film, well beyond its thickness. We performed then a last test by replacing the continuous Al–Pd film with an Al–Pd grid. The width of the grid lines was 70 μm, and the spacing between each line was 700 μm (see inset in Fig. 5). The purpose of using a grid is manifold: (1) further reduction of the heat capacity of the coating; (2) possibility to extract scintillation light through the coating; (3) availability of geometrical parameters to possibly tune the discrimination depth. The grid was tested with another uranium source, prepared with the same method as the first one, but about twice less intense. The detector with grid coating can separate surface β events (see Fig. 5). The β selection efficiency resulted to be 93(10)%, in good agreement with the continuous-film results. In addition, we measured a discrimination power of about 4.5σ for surface α events using the $m/Sm$ parameter. In terms of detector performance, we observed an almost full recovering of the detector sensitivity, that was $∼51$ μV/MeV for β/γ events. Therefore, the grid method is currently our protocol for surface event discrimination.

In conclusion, we have shown that both α and β particles absorbed close to a metal-coated surface of a Li₂MoO₄ bolometer can be rejected with high efficiency by pulse-shape discrimination. The prospects of this approach for $0ν2β$ searches are promising. In fact, the current background model of the future $0ν2β$ experiment CUPID⁵⁰ predicts a background level of 0.1 counts/(tonne y keV). Next-to-next generation experiments aim to a reduction of an additional factor 10. Since surface β events contribute significantly to the current background level, a necessary condition to achieve the desired reduction is to reject them with an efficiency up to 90%. This is achievable with the technique here described.

This work is supported by the European Commission (Project CROSS, Grant No. ERC-2016-ADG, ID 742345). The ITEP group was supported by the Russian Scientific Foundation (Grant No. 18-12-00003). F.A.D., V.I.T., and M.M.Z. were supported in part by the National Research Foundation of Ukraine (Grant No. 2020.02/0011). The Ph.D. fellowship of H.K. has been partially funded by the P2IO LabEx (No. ANR-10-LABX-0038) managed by the Agence Nationale de la Recherche (France). The dilution refrigerator used for the tests and installed at IJCLab (Orsay, France) was donated by the Dipartimento di Scienza e Alta Tecnologia of the Insubria University (Como, Italy).