In-situ study of light production and transport in phonon/light detector modules for dark matter search

The CRESST experiment (Cryogenic Rare Event Search with Superconducting Thermometers) searches for dark matter via the phonon and light signals of elastic scattering processes in scintillating crystals. The discrimination between a possible dark matter signal and background is based on the light yield. We present a new method for evaluating the two characteristics of a phonon/light detector module that determine how much of the deposited energy is converted to scintillation light and how efficiently a module detects the produced light. In contrast to former approaches with dedicated setups, we developed a method which allows us to use data taken with the cryogenic setup, during a dark matter search phase. In this way, we accounted for the entire process that occurs in a detector module, and obtained information on the light emission of the crystal as well as information on the performance of the module (light transport and detection). We found that with the detectors operated in CRESST-II phase 1, about 20% of the produced scintillation light is detected. A part of the light is likely absorbed by creating meta-stable excitations in the scintillating crystals. The light not detected is not absorbed entirely, as an additional light detector can help to increase the fraction of detected light.

In this article, we present a method for understanding the light yield measured with entire detector modules in terms of the efficiencies of light production and detection. Based on data taken during a dark matter search phase, it considers the entire process of conversion of deposited energy into scintillation light as well as transport and collection of the light that occur in a detector module. We can confirm the results by using a cross-check method with different systematic uncertainties.
We found that with the detectors operated in CRESST-II phase 1, about 20 % of the produced scintillation light is detected. A part of the light loss is likely caused by light absorption creating meta-stable excitations in the scintillating crystals. We also found that, consistent with the relatively low detection efficiency, an additional light detector increases the amount of detected light within an otherwise unmodified detector module.

General Context
The CRESST (Cryogenic Rare Event Search with Superconducting Thermometers) dark matter experiment aims at detecting WIMP-nucleus scattering [1]. With modular detectors, it simultaneously measures phonon and scintillation signals associated with energy depositions in inorganic scintillating crystals. These crystals are usually cylinders made of calcium tungstate, of 40 mm height and diameter. The phonon signal is measured by a transition-edge sensor (TES) on one flat surface of the scintillating crystal. The scintillation light is detected by a separate light detector consisting of a silicon-on-sapphire wafer of 40 mm diameter with a TES [2]. In order to prevent light from leaving the detector module without contributing to the signal, the absorber crystal and the light detector are surrounded by a housing made of a scintillating and reflective foil.
The signal of the phonon channel is a measure of the deposited energy. The fraction of deposited energy that is converted to scintillation light depends on the nature of the interacting particle and on the quality of the crystal. Hence, the ratio of scintillation light to deposited energy can be used to distinguish different interacting particle types.
Only a fraction of the produced light is actually detected. The limited transparency of the crystal, the geometry of the reflector as well as size and absorptivity of the absorber of the light detector determine this fraction. Increasing the arXiv:1503.07806v1 [astro-ph.IM] 26 Mar 2015 amount of detected scintillation light per deposited energy is crucial for maximizing the background suppression and hence the overall sensitivity of the experiment. Therefore, methods for determining individually the quality of the crystals and the efficiency of transport and detection of scintillation light are important elements for deciding on future detector design strategies.

Method for determining the quality of entire modules
We developed a new method of measurement that provides information on the light emission of the crystal as well as on the light transport and detection of the module. It relies on precisely determining the distribution of energy between phonon and light channel using data acquired with the CRESST setup during dark matter data taking. Starting from the deposition of a well-defined amount of energy in a detector module, energy not seen in the phonon detector is considered emitted as scintillation light. Only a fraction of the emitted light is actually seen in the light detector. The rest is considered lost.
For cross-checking the results, we use light produced by α-particles interacting with the scintillating and reflective foil of the detector modules in the fashion of a reference light source. It provides an independent way of obtaining the same information as the main method.

Experimental Setup, Data and Analysis
In order to obtain more detailed information about possible optimizations, we evaluated two detector designs in terms of light production and light detection. This section describes the designs investigated and the analysis method.

Detector Designs
All data analyzed here have been acquired in CRESST-II phase 1 [3]. The detector modules of the standard design (cf. Fig. 1, left) consist of a target crystal in which the energy deposition takes place. The target crystal is equipped with a TES which detects the phonons. The crystal face opposite to the TES is roughened in order to facilitate light propagation towards the light detector, a separate crystal wafer equipped with another TES.
The double light detector module depicted on the right in Fig. 1 allows to assess the light propagation inside the module and the reflective housing. The light detector called Q is located adjacent to the roughened surface of the scintillating crystal. The light detector named Burkhard faces the crystal at the opposite side, near the phonon TES. If the reflectivity of the housing, the absorptivity of the light detector and the transparency of the crystal were perfect, a single light detector should already gather all the available light. The sum of light detected by two detectors then should not exceed the amount detected with a single detector. If such a setup yielded more light in total, the light detection could possibly be improved by changing the light detectors and/or the path of the light within a module.

Calibration Sources
Energy depositions in the phonon and the light detectors result in voltage pulses delivered by the read-out system [4]. Their height is a measure of the deposited energy. By using radioactive sources, we calibrate pulse heights to actual energies.
-We calibrated the phonon detector against the α-decay of 147 Sm at 2310.5 keV 1 [5]. Linearity of the energy scale to lower energies was confirmed by using γ-lines at 338, 583, 911, 1588, and 2614 keV; all γ-lines originate from either 208 Tl or 228 Ac from an external 232 Thsource [6]. -The light detectors are directly exposed to low-energy X-rays from an external 55 Fe-source, setting the absolute energy scale. In this case, we used electrical pulses injected into heaters connected to the TESs to confirm linearity of the detector response. The calibration source emits single photons of 5.9 and 6.5 keV, while scintillation light of the same energy consists of many photons in the eV-range. Since the emission of scintillation light does not happen instantaneously, the signals of the Symbol Name

Q dep
Physical energy deposited in the crystal Q S Physical energy converted to scintillation light Q P/L Physical energy deposited in the phonon/light detector E P/L Calibrated energy reading of the phonon/light detector C P/L Calibration factor for the phonon/light channel F φ Fraction of energy, deposited by particle φ , converted to light R φ Relative light yield of particle φ (compared to γs) ε s Scintillation efficiency (fraction of energy deposited by a γ, converted to light) ε d Detection efficiency (fraction of created light that is registered in the light detector) Table 1 Symbols introduced calibration source and of the scintillation events have a slightly different pulse shape. We took this difference into account via the integral/pulse height ratio for the different event classes.

Analysis Method
We consider, conceptually similar to [7], the energy flow in the detector module as illustrated schematically in Fig. 2: The fraction of deposited energy that is converted into scintillation light depends on the nature of the particle and the quality of the crystal. The fraction of the produced light that is finally detected depends on the limited transparency of the crystal, the geometry and efficiency of the reflector as well as size and absorptivity of the absorber of the light detector. At the beginning of the process, a particle of type φ deposits an energy Q dep in the scintillating crystal 2 . This energy divides up into a relatively small fraction leaving the crystal as scintillation light Q S = F φ Q dep and the part remaining in the crystal as phonons Q P = 1 − F φ Q dep . The fraction F φ depends on the particle type and on the characteristics of the crystal. It is defined as The term ε s describes the scintillation efficiency of the crystal. It is the fraction of energy which a crystal converts to scintillation light when it is excited by a γ-quantum. The particle-dependent part can be described [8] by a relative light yield R φ which for e.g. α-particles or nuclei contains the effect of light quenching [9] relative to γ-quanta.
We define the relative light yield of a generic particle φ as the fraction of the measured light energy E L over the deposited energy Q dep of the particle φ compared to the values obtained when measuring a γ-quantum 2 For an overview of the symbols used in this section, cf. Tab. 1 We neglect effects like e.g. energy dependences [10,11,12], the scintillator non-proportionality [13] or the different behavior of electrons and γ-events [13] as they are only relevant at energies which are at least one order of magnitude below the ones considered here.
Thus, the amount of energy converted into phonons is The energy in the light channel divides up further. The detection efficiency ε d describes how much of the light escaping the crystal is absorbed by the light detector. The fraction (1 − ε d ) is lost e.g. because the housing is not a perfect reflector. It is also possible that the crystal re-absorbs part of the propagating light and converts it back into phonons. This re-absorbed energy is seen in the phonon channel and not considered emitted as scintillation light.
The energy finally absorbed in the light detector is thus If the phonon energies Q P were exactly known, it would be possible to directly determine the scintillation efficiency ε s of the crystals from a γ-measurement using equation (3). However, the fact that the detectors are calibrated with particles that produce scintillation light requires further consideration: In general, a calibration is done by exposing the detector to particles of a well-known energy and setting the detector reading to that energy. The energy which escapes as scintillation light is neglected in the calibration as the detector reading is set to indicate the entire amount of deposited energy.
We model this calibration effect with the factors C P,L , for the phonon and the light channel respectively. The physical energy depositions Q P,L in the detectors thus result in energy readings E P , E L : As the energy of the aforementioned 55 Fe source is directly absorbed in the light detector, we assume a calibration factor of C L = 1 for the light channel. In case of the phonon channel, we have to consider the energy that escapes as scintillation light. Since the phonon channel read-out shows the total energy deposited by α-particles in the crystal, the calibration factor for the phonon detector must be such that it compensates for the energy escaping as light in case of an α-deposition. This means that The scintillation efficiency ε s can be extracted by exploiting the fact that the compensation is only exact for αparticles. For γ-quanta, the relative light yield is higher. This  Figure 2 Partitioning of the deposited energy in the detector module (see text for details). The deposited energy Q dep is shared between phonons (Q P ) and scintillation light (Q L ). The interpretation of the sensor readings E P,L depend on the calibration factors C P,L , taking into account the fraction F φ and the light detection efficiency ε d . means more energy turns into scintillation light. Therefore, less energy remains as phonons and thus the phonon channel reading is slightly lower than the energy actually deposited. Hence ε s can be extracted from the phonon detector reading of a γ-line which was calibrated with an α-source (resolving equations (5) (with R γ = 1, per definition) and (7)): Afterwards, the detection efficiency ε d can be determined from the light detector reading of the γ-event:

Data used for the Analysis
To study the scintillation light of γ-absorptions, we measured a double peak of 228 Ac and 212 Bi γ-lines at 726 and 727 keV. It originates from the 232 Th source already used for confirming the linearity of the detector response. With this choice, we avoid low energies (E ≤ 60 keV) where the fraction of energy converted to scintillation light may become energy-dependent as mentioned above. We used 180 W (Q = 2516 keV [14]) to determine the relative light yield of α-particles. This isotope is distributed uniformly through the volume of all tungstate crystals. Thus, the situation is similar to the γ-events from the 232 Th-source. By contrast, α-emitters associated with surface impurities would only probe a thin skin region due to the short range of α-particles.  Table 2 The scintillation efficiency ε s and the detection efficiency ε d . The values are given with their 1-σ -errors ∆ .

Results and Discussion
The values of ε s indicate that depending on the modules, between 7.4 and 9.2 % of the deposited energy is emitted as scintillation light (cf. Tab. 2 and Fig. 3). In case of single light detectors, a fraction between ε d = 18 and 28 % of the produced light is detected (cf. Tab. 2 and Fig. 4) 3 .
The upper values in the table are from the double light detector module, with its individual light detectors treated separately as well as in combination. When considering Q and Burkhard individually, they are the two light detectors with the lowest detection efficiencies. When one adds up their energies, the module Q/Verena/Burkhard has the highest detection efficiency ε d of nearly 34 %. The average for single light detector modules is ≈ 23 %.

Self-Consistency
The double light detector module provides a check for the self-consistency of the method. The readings of Burkhard and Q are different (e.g. for the 727 keV-γ-line: E L = 9.9 keV and E L = 8.4 keV, respectively), which can be attributed to one of the light detectors facing the roughened and the other the polished surface of the crystal.  Table 3 The fraction (ε s · ε d ) of the energy deposited by a γ that is detected as scintillation light in different detector modules. The third column represents the values obtained with the method introduced in this work, the fifth column (PMT) contains the light output of the roomtemperature measurement relative to the reference crystal. Light output (% of reference crystal) Figure 5 The fraction (ε s · ε d ) of the deposited energy seen by the light detectors, obtained with the newly-introduced method (black) and with the PMT method (red).
Nonetheless, the method yields the same value for the scintillation efficiency ε s for both light detectors while the detection efficiency ε d differs. Therefore, characteristics related to the production of light can be distinguished from other effects in the detector modules.

Comparison with PMT Measurements of the Crystal Scintillation
A simple approach to compare the relative amount of scintillation light of different crystals is to irradiate the crystals at room temperature with a source of known energy and measure the scintillation with a photo-multiplier tube (PMT). A reference crystal is used to compare the results.
The product of scintillation and detection efficiency (see Tab. 3, 3rd and 4th columns / black horizontal axis and data points in Fig. 5) is the fraction of the deposited energy that is detected in the light detector. For all modules with a single light detector 4 , the values of the PMT measurements (Tab. 3, 5th column / red horizontal axis and data points in Fig. 5) and the products of scintillation and detection efficiency agree within errors. Although being performed at room temperature, the PMT measurements are therefore a good indicator for the quality of the detector modules.

The Role of Light Transport for the Light Signal
We found that the light output is mainly influenced by the light transport which happens within the crystal. In terms of light production (Tab. 2 (left), Fig. 3), there is no significant difference between the modules. However, the light detection efficiency varies by nearly 50 % (Tab. 2 (right), Fig. 4).
The housing of the detector modules is similar in all detector modules, hence it is not plausible that its reflectivity determines the detection efficiency. The missing light has to be absorbed in the crystal itself. This is consistent with results of the PMT measurements which also suggest that light absorption is the dominant effect. It measures the crystals in a different type of housing and still reproduces the behavior of the combined efficiencies ε d and ε s .
In the common assumption, light absorbed in the crystal is converted to phonons. However, this seems not to be true in this case as an increased amount of phonons would lead to a lower scintillation efficiency ε s instead of a lower detection efficiency ε d . The outcome can be explained if the reabsorbed light excites meta-stable states in the crystal whose relaxation time is longer than the phonon integration time of the measurements.

The Role of the Light Detectors for the Light Signal
With two light detectors combined, the double light detector module has a higher detection efficiency ε d than any module with only a single light detector.
This indicates that the single light detectors in the setup presented are not capable of detecting all of the light which is available to two light detectors in a similar housing. Hence it is possible to increase the detected light of a module by e.g. increasing the size or absorptivity of the light detectors, or by changing the geometry to favor propagation of light outside the crystal.

Concept
Data from a second, independent method with different systematic uncertainties for determining the scintillation and detection efficiency to have the same proportionality as in case of a module with a single light detector. the detection efficiency can be used as a cross-check which confirms the results. The core element of the cross-check method is a light source which is considered to emit the same amount of light, independent of the scintillating crystal used in the modules.
If individual modules detect different amounts of light from this reference light source, that must be due to different light detection efficiencies. Hence, we consider the amount of light detected from the reference light source E L ref to be proportional to the detection efficiency ε d .
The amount of light which is detected due to a scintillation process in the crystal depends on the deposited energy, the scintillation efficiency of the crystal and the detection efficiency of the module. We measure the energy of the light signal E L γ associated with a well-defined γ-line and divide it by the light signal of the reference light source: For both measurements E L γ , E L ref , the deposited energy is fixed. We assume that both measurements are done with the same light detection efficiency ε d . Therefore, fraction ρ is proportional to the scintillation efficiency ε s .

Data
As in case of the main method, the data for the crystal scintillation were obtained from the 228 Ac and 212 Bi lines. The reference light source used in the method is scintillation light created in the foil which encloses the module. Apart from serving as a reflector keeping the light inside the detector module, the foil is a scintillator which helps to veto events caused by surface contaminations of the detector. A certain set of events which make the foil scintillate is caused by α-particles from the decay of 210 Po on the surfaces of either the crystal or the housing (cf. [3]). The α-particles are emitted with a well-defined energy and produce scintillation light in the foil 5 . As the foil is the same for all modules, this special class of events is a reference light source whose light detector reading E L ref can serve as reference for every detector module.

Results
The absolute values ρ (cf. (10)) and scaled with a constant factor determined with a least squares fit over all detector modules investigated.

Conclusion and Outlook
The present work introduces a method for determining the energy distribution in a CRESST detector module. It uses data obtained at low temperatures, during the actual running for the experiment. It determines the scintillation and detection efficiencies from the phonon and light signals of an α-line and a γ-line of known energies. We could show that the method can successfully distinguish between the efficiencies of light production and detection in a module. The results are consistent with a second method which provides an independent cross-check with different systematics. We found that for γ-events, the crystals convert slightly below 10 % of the energy into scintillation light, and that 20 % to 30 % of this light is detected in the modules we investigated. Concerning the light production, the difference between the individual detector modules is in the range of 10 %. In contrast, the detection efficiencies of the different detector modules vary by nearly 50 %. We found that low detection efficiencies are consistent with the assumption of light being absorbed by exciting meta-stable states in the crystal.
Apart from producing crystals which absorb less light, detecting more of the available light seems a promising way of further optimizing the detector modules. The results obtained with the double light detector module indicate that the single light detector of a standard module does not absorb the entire amount of collectible light. In the current setup [15], we operate two new designs which feature a light output that is increased with respect to comparable modules with the geometry as described above. One is a cuboid target crystal with roughened sides (further details in [16]), the other module has a beaker-shaped light detector which covers a larger solid angle around the target crystal.