Optimisation of the scintillation light collection and uniformity for the SoLid experiment

This paper presents a comprehensive optimisation study to maximise the light collection efficiency of scintillating cube elements used in the SoLid detector. Very short baseline reactor experiments, like SoLid, look for active to sterile neutrino oscillation signatures in the anti-neutrino energy spectrum as a function of the distance to the core and energy. Performing a precise search requires high light yield of the scintillating elements and uniformity of the response in the detector volume. The SoLid experiment uses an innovative hybrid technology with two different scintillators: polyvinyltoluene scintillator cubes and $^6$LiF:ZnS(Ag) screens. A precision test bench based on a $^{207}$Bi calibration source has been developed to study improvements on the energy resolution and uniformity of the prompt scintillation signal of antineutrino interactions. A trigger system selecting the 1~MeV conversion electrons provides a Gaussian energy peak and allows for precise comparisons of the different detector configurations that were considered to improve the SoLid detector light collection. The light collection efficiency is influenced by the choice of wrapping material, the position of the $^6$LiF:ZnS(Ag) screen, the type of fibre, the number of optical fibres and the type of mirror at the end of the fibre. This study shows that large gains in light collection efficiency are possible compared to the SoLid SM1 prototype. The light yield for the SoLid detector is expected to be at least 52$\pm$2 photo-avalanches per MeV per cube, with a relative non-uniformity of 6 %, demonstrating that the required energy resolution of at least 14 % at 1 MeV can be achieved.


Introduction
SoLid very short baseline reactor antineutrino experiment [1] will search for active to sterile antineutrinos oscillations between 6 and 9 m of the BR2 research reactor at the SCK · CEN in Mol, Belgium. It consists of a novel fine segmented hybrid scintillator detector technology made of optically isolated polyvinyltoluene (PVT) plastic scintillator cubes, each coupled to neutron sensitive inorganic scintillator 6 LiF:ZnS(Ag) screens as illustrated in figure 1. These two different scintillators are used to detect both the positron and the neutron produced by the inverse beta decay (IBD) interaction of an antineutrino. The scintillation signals from the two scintillators are collected via the same wavelength shifting fibres connected with silicon Multi-Pixel Photon Counter from Hamamatsu (MPPCs ™ ). Interactions in each scintillator can easily be distinguished because of the different decay time structure of the two signals. The high level of segmentation given by the 5×5×5 cm 3 detector elements provides an unprecedented granularity for reconstructing the antineutrino energy with a limited energy contamination of the 511 keV γ-rays coming from the IBD positron annihilation. Combined together, the robust neutron capture identification, signal localization and event reconstruction should allow the SoLid experiment to perform a precise very short baseline reactor based antineutrino oscillation search. This fine segmented plastic scintillator and optical fibre readout technology is also considered for other neutrino experiments, like the T2K near detector for example [2]. A real scale prototype of 288 kg, called SM1, was built and deployed at BR2 in 2014-2015 to demonstrate the antineutrino detection capabilities and background rejection [3]. The module consisted of 9 planes of 16×16 cubes. A cost-effective cube readout scheme was chosen with two single-clad optical fibres with one MPPC per fibre and a mirror at the other end of the fibre. First measurements of the light yield were performed resulting in 12 photo-avalanches (PA) per fibre corresponding to an energy resolution of 20 %/ E(MeV) per cube. This first deployment validated the hybrid scintillator technology and the effect of the fine segmentation to discriminate and reduce the main experimental backgrounds.
The next phase of the SoLid experiment, called Phase 1, consists of a 1.6 t detector which has been constructed in 2017 and is now taking data. For a precise and timely antineutrino oscillation search, the aim of Phase 1 is to reach a non stochastic term of the energy resolution σ E /E of at least 14 % at 1 MeV. This would require to collect at least 50 PA/MeV/cube summing the light yield from all the fibres in a cube and after correcting for effects such as cross-talk in the MPPCs. This paper will present the studies and improvements in terms of light yield compared to the SM1 prototype in order to achieve these performances.

Test bench setup
The setup presented here has been inspired by the trigger system of an electron spectrometer [4] used for the NEMO-3 and SuperNEMO experiments to qualify the plastic scintillators [5,6] and the regular deployment of 207 Bi sources in those detectors to produce the absolute energy calibrations. The principle of this setup is to use a 207 Bi calibration source and a trigger system to produce mono-energetic conversion electrons (see section 2.1) in order to compare different detector element configurations. The setup is also capable of giving the absolute light yield to determine the energy scale and energy resolution of the PVT detection elements. It has been designed to be as flexible as possible in order to test various configurations for the SoLid scintillator cubes: wrapping, position and type of fibres, effect of the 6 LiF:ZnS(Ag) screen, machining and cleaning of the cubes, MPPCs and fibre reflectors. The test bench has been installed in a polyethylene black box (120×120×20 cm 3 ) sufficiently large to accommodate the full length of the SoLid fibres in both X and Y directions. The setup is installed in an air-conditioned room at a temperature of around 19 • C.
Since the 207 Bi radioactive source is mainly emitting γ particles, it is necessary to use a triggering system to select only the conversion electrons entering the cubes (see section 2.1). Otherwise, the signal will be dominated by Compton-scattering of γ-rays and the energy spectrum would give a lower precision on the light yield measurements than the peak from conversion electrons. The triggering system is described in section 2.2. The energy spectrum and losses in the materials have been studied with Monte-Carlo simulations and are presented in section 2.4.
In order to make comparisons between the different measurements and to simplify the operations a standard configuration has been defined for the main tests. This configuration is presented in figure 2. It consists of a single SoLid scintillator cube (almost always the same for this publication) with its Tyvek wrapping of thickness 270 µm and read out by a single fibre and one MPPC at each end. The MPPCs are supplied with an over-voltage of 1.5 V, which is the bias voltage applied to operate the MPPC. This setting balances gain and cross-talk for this generation of photo-detectors (see section 3.3). The uncertainties on the measurements are discussed in section 3.5.
The scintillator cubes and the triggering system are both mounted on a rail and can be moved with a light tight manual jack from outside the black box. This design allows for moving the full system along the fibre to be able to measure the light attenuation for different cube positions along the fibre (see section 4.3). In the case of the SM1 prototype the thickness of the Tyvek wrapping allowed for scintillation light to pass through the wrapping. However, the wrapping of neighbouring  Figure 2. Schematic description of the scintillator test setup in the standard configuration used for most of the measurements (a single wrapped cube along one optical fibre with double end MPPC readout). The calibration source, the PMTs and the scintillator cube are mounted on a rail in order to allow moving the system along the fibre. cubes allowed to recover a fraction of the light otherwise lost to the neighbouring environment. The rail allows then to perform measurements with a series of 16 cubes connected to a single fibre, which is closer to a realistic detector configuration (see section 6).

The 207 Bi radioactive source
The 207 Bi isotope is well suited to test the SoLid scintillator performance in term of the energy scale and resolution since it produces mono-energetic electrons around 1 MeV. This is the same order of magnitude as the antineutrino energy determined from the positron energy deposit, which is between the IBD threshold of 1.806 MeV and 8 MeV. As already mentioned the detected 1 MeV Gaussian peak allows accurate comparisons between different detector configurations.
The 207 Bi isotope decays through electron capture almost exclusively to excited states of 207 Pb [10]. The 207 Pb de-excitations occur through 3 main γ-ray emissions (570, 1064 and 1770 keV) as illustrated in figure 3. These γ-ray emissions could be replaced by atomic K, L or M shell conversion electrons as presented in table 1. The conversion electrons associated to the 1770 keV de-excitation are negligible and those associated to the 570 keV occur only in 1.5 % of the decays over an important γ background. Most of the useful conversion electrons are associated to the 1064 keV de-excitation and have an energy between 976 and 1060 keV with a total probability of 9.5 %. Given the finite energy resolution of the SoLid detector (14-20 %), only one main peak at an average energy of 995 keV is expected (see section 2.4).
The 207 Bi source used in the setup has an activity of 37 kBq. The active material has been deposited between 2 mylar foils of 0.9 mg cm −2 . The energy losses in these mylar foils is negligible compared to our detector energy resolution. The active area of the radioactive source represents a 5 mm diameter disk, which is small compared to the 5×5 cm 2 surface of the scintillator cube.

The external triggering system
The principle of the triggering system is to select only the 1 MeV mono-energetic conversion electrons by detecting them in the thin (110 µm) plastic scintillator (BC 400 -2×1 cm 2    Good optical coupling is ensured by optical grease (BC 630) between the thin scintillator and the light-guides and by an optical epoxy silicone rubber compound (RTV 615) between the light-guides and the PMTs. The light collection of this setup is not sufficient to reconstruct precisely the energy deposited by the crossing electrons but detailed G 4 based simulations, described in section 2.4, show that it represents negligible energy loss. This thin scintillator provides a triggering signal to tag the charged particle entering the cube. The triggering system has been designed to minimize the distance between the source and the scintillator cube in order to reduce the solid angle and the energy loss of the electrons before they enter the cube. Figure 4 illustrates the impact of the triggering system for selecting the 1 MeV conversion electrons. The three spectra represented are obtained when triggering in coincidence on the 2 MPPCs only (gammas + electrons in blue), when triggering in coincidence with the small scintillator (electrons in magenta), and when using the small scintillator as an electron veto to select only the gammas (in cyan). The reconstruction of the energy deposited in the cube is explained in section 3.1. The shape of the energy spectrum of the gammas is less sensitive to light collection improvement tests but still gives valuable information on the detector response to antineutrino interactions. Indeed the gammas are interacting in the whole volume of the scintillator while the conversion electrons will only interact in a small portion of the scintillator (<1 cm 3 ) in front of the source. The detector response to gammas is closer to the prompt signal from antineutrino interactions that will also occur in the whole volume of the scintillator. Less than 2 % difference between the energy scale determination from the Compton edge fit and the 1 MeV peak is observed1. This is within the systematics uncertainties (section 3.5) and shows that the average response through the scintillator volume is the same as the centre of the cube surface.  In blue is the spectrum in coincidence with the two MPPCs only, in magenta the spectrum in coincidence with the 110 µm triggering scintillator and in cyan using this scintillator as an electron veto.

Electronics and acquisition
The photo-detectors selected for SoLid are the Hamamatsu MPPCs S12572-050P 3×3 mm 2 . These devices were not specifically studied in our setup. The measurements performed only concerned the cross-talk probability of the MPPCs (section 3.3) that needs to be accounted for light yield determination. The MPPCs were soldered on custom made PCBs installed in 3D printed supports also used to hold the optical fibre, as in the SM1 prototype. The optical contact between the MPPC and the fibre is made by optical grease (BC 630).
To supply voltage, amplify, shape and extract the MPPC signals, a custom made three channels prototype board is used. This board has been developed to validate the analog electronic boards of the SM1 prototype. The voltage is provided by two external power supplies (EA-PSI 6150-01): one at 65 V for the MPPC supply and one at 5 V for the amplifiers. These power supplies have a very good resolution of 10 mV and a stability of better than 5 mV. With this setup the same voltage is provided to all the channels. The two MPPCs have been selected to have close operating voltages (V OP = 67.40 and 67.46 V respectively). The two trigger PMTs are powered by an Ortec 556 power supply at -1400 V.
An eight channel waveform digitizer developed at LAL based on the WaveCatcher ASIC is capturing the signals from all photon detectors ( [11,12]). This module is directly controlled by 1The energy of the Compton edge for the 1064 keV γ is 858 keV and because of energy losses and resolution the "1 MeV" peak is expected at 910 keV. The respective fitted values were 39.0 and 40.8 photo-avalanches. USB and a CVI software allowing to define the acquisition settings, perform analysis and store the digitized pulses. The trigger is set as a coincidence of the two negative PMT signals at -5 mV and the positive MPPC signals at 2 mV. The sampling is made over 1024 points at 1.6 GS/s to properly sample the waveforms over their whole pulse length. This corresponds to a 640 ns time window. More details on the reconstruction of the MPPC pulses and the energy are presented in section 3.

Simulation of the setup
Simulation studies were performed to determine the mean energy of the ∼1 MeV conversion electron peak from the 207 Bi source and to compute the energy losses in the thin triggering scintillator and the wrapping around the cubes. These simulations are using the Bayeux suite [7] developed for the simulation of the SuperNEMO experiment, in conjunction with G 4 [8]. The result of this simulation indicates that on average only ∼25 keV is lost by the electrons in the triggering scintillator as can be seen in figure 5. This is negligible compared to the conversion electron energy in the main peak (figure 5 right) and the energy resolution of the SoLid scintillator cubes. Applying the detector energy resolution to the simulation, one can see in figure 6 that the double-peak structure around 1 MeV disappears. Also the conversion peak around 500 keV is no longer visible over the Compton background of the 1064 keV γ-rays. It is therefore not possible to observe both conversion electron energy peaks distinctly. For this reason, the light yields will be determined by fitting the electron energy peak around 1 MeV by a gaussian function. Different cube wrappings have been tested to improve the light reflectivity in the SoLid cubes. Tyvek ® is the most suitable material to wrap the scintillator cubes for the SoLid experiment, as will be explained in section 4.2. In the simulation of this setup the Tyvek has been added as a uniform material of a given thickness and density around the cubes. This is an approximation since Tyvek, consisting of HDPE fibres, is non-uniform in thickness. In table 2 the properties of the Tyvek sheets used for the SM1 and SoLid Phase 1 detectors are presented. The respective average thicknesses are 205 and 270 µm. The ranges are estimates given by the producer DuPont ™ based on the measurement of individual specimens. These values have been used to simulate different samples for estimating the electron energy loss before entering the cubes and to obtain the reference peak position to be compared to the measured values.  Figure 7 left shows that the energy loss in the Tyvek wrapping is also of the order of a few tens of keV. The non-uniformity of the Tyvek wrapping should not influence the measurements since the average energy peak position is changing only ∼2 % over the whole thickness range simulated. The difference in the fitted peak value as a function of energy resolution is due to the averaging over a different fraction of lower energy events seen before the electron conversion peak. For SM1 cube wrapping and a 20 % energy resolution a calibration peak around 900 keV is obtained. For the SoLid Phase 1 cube wrapping and a 15 % energy resolution a calibration peak of around 910 keV is obtained. The function fitted in figure 7 right, for the 270 µm SoLid Phase 1 Tyvek wrapping, will be used at each measurement to determine the energy peak position and the energy light yield in PA/MeV. The input energy resolution is first determined by the number of PA measured in the peak, as presented in section 3

Pulse reconstruction
When comparing the light yield performance for different configurations, the amplitude, the integral and the pedestal of the pulses are the main parameters to compute. This reconstruction is done off-line from the samplings registered by the acquisition. Figure 8 shows a cumulated view of all the pulses registered during one 207 Bi run. The individual photo-avalanches peaks cannot be distinguished well from the amplitude. In contrast, the integral spectrum of the photo-avalanche peaks shows a good resolution. This will be presented in figures 9 and 10. To calculate the pedestal, the pulse position in the 640 ns acquisition window is set to buffer samples in a period of 100 ns before the rise of the pulse. This method has been compared to a pedestal measurement with random triggers over the full sampling window and the results are similar. The pedestal value is typically around 0.1 V ns (integration of amplitude pulses in V over time in ns) while the 207 Bi peak is around 2.5 V ns in a single channel. After determining the pedestal, the MPPC pulses are identified by the maximal amplitude value. The integral is obtained by integrating the voltage amplitudes from 50 ns before the maximum value to around 190 ns after the maximum value. This integral is expressed in V ns as for the pedestal. The integration end value of the range is not exactly at the end of the pulse for high amplitude pulses but it avoids fluctuations due to the noise. Variable integration windows as a function of the pulse amplitude have also been tested but no improvements were observed. Therefore, a fixed integration window was used.

Temperature effects
As previously mentioned the setup is installed in an air-conditioned room. The temperature inside the black box is sampled every minute by a Lascar probe (EL-USB-TP-LCD). The maximal temperature variation was of the order of 2 • C over 24 h. Given the activity of the radioactive source a measurement takes only few minutes. Since a set of measurements for a given comparison is taking place within a few hours the temperature variation is assumed to be negligible.
The gain of MPPCs is quite temperature dependent. The applied voltage has to be corrected from room temperature using the formula given by the data sheets [13] and confirmed by laboratory measurements [14,15]: where V OP is the operating voltage given by Hamamatsu for a gain at 1.25×10 6 at 25 • C, V BR the breakdown voltage, V OV the selected over-voltage (1.5 V for SoLid2) and T the temperature in • C. At a nominal room temperature of 19±1 • C, the voltage correction is around 0.3-0.4 V.

MPPC cross-talk correction
Optical cross-talk occurs in MPPCs when during the primary avalanche multiplication some photons are emitted and start secondary avalanches in one or more neighbouring cells. Since a few tens of photons are emitted by a single avalanche, the cross-talk probability is high when no optical barrier (metallic trench) is implemented. This is the case for the generation of MPPCs used in the SoLid experiment, resulting in cross-talk probability of 10 to 30 % depending on the over-voltage. The optical cross-talk can be measured using dark count rate (DCR) pulses when the MPPCs are not connected to the fibre. Acquiring random trigger events only 1 PA signal peak should be observed from DCR. However, because of the optical cross-talk also peaks higher than the 1 PA peak are observed as shown in figure 9. The cross-talk probability is measured as the ratio of the number of DCR events above the 1.5 and 0.5 PA thresholds, noted N 1.5P A and N 0.5P A , as explained by the following equation: These numbers of DCR events above each threshold are obtained by integrating the number of events in the peaks as illustrated on the figure 9 by the two coloured regions. At 1.5 V over-voltage we find on average 17.7 ± 1.0 (stat) % for the two MPPCs. . Determination of the optical cross-talk probability of an MPPC from the integral of dark count pulses. The first peak from left corresponds to the pedestal and the following peaks correspond to 1, 2, 3 or more PA.

Procedure to calculate the light yield
Between 30000 and 50000 events are registered for a scintillator configuration measurement in a few minutes run. After the reconstruction of the pulses parameters several steps are still needed to obtain the light yield in PA for the 1 MeV source peak. The first step consists of calibrating the MPPC integral response to a number of PA. To achieve this, the low energy part of the integral spectrum is considered after pedestal subtraction. Using ROOT [9] about 10 individual PA peaks are identified and fitted with a Gaussian function (figure 10 left). The first PA peak is truncated by the threshold trigger so only the following ones are used. Each integral peak corresponds to a number of PA and the relation between the integral and the number of PA is fitted by linear function (figure 10 right). This provides the conversion between the integral of the MPPC pulses and the number of PAs. The quality of this procedure is tested by looking at the higher PA peaks. A very good linearity is observed up to ∼20 PA where the peaks start to be less visible. Fitting the peaks in this region gives a difference in peak position of less than 0.2 %. Figure 11 shows the calibrated integral spectra expressed in PAs of the two MPPCs, their sum and the correlation between the signals. The integral spectra for the individual MPPCs give a similar peak position (here 19.1 and 20.0 PAs) and the linear correlation is over 60 %. The summed integral spectrum is used to give the final result of the measurement with the 1 MeV peak fitted by a Gaussian function. In this example N P A = 40.5 PA has been measured without taking into account the cross-talk. At an over-voltage of 1.5 V the optical cross-talk is expected to be 17.7 % (section 3.3). Subtracting it results in a light yield of N P A = 33.3 PA at ∼910 keV (section 2.4) corresponding to 36.6 PA/MeV. The stochastic term of the detector energy resolution could then be estimated by 1/ √ N P A , which corresponds to 16.5 % at 1 MeV ( √ 0.91 energy losses correction to the resolution) for this cube with only 1 fibre and a double MPPC readout.
This example illustrates the procedure to get the light yield for a given configuration. After the calibration the optical cross-talk is subtracted from the fitted peak of the summed integral spectrum. Afterwards the electron energy is corrected for the energy loss and the expected peak position for the energy resolution.

Measurement uncertainties
The statistical uncertainty of the measurements is negligible since between 30000 and 50000 events are acquired. Indeed the fit of the Gaussian peak is returning a statistical uncertainty of around 0.2 % on the mean of the function ( figure 11). Therefore the statistical uncertainties in the following will not be mentioned for each measurement.
The systematic uncertainties can have two origins: the measurement set-up and the fitting procedure. For the latter, the Gaussian fit has been tested in different ranges and binning on a reference measurement. The variation of the start and end value of the fit range gives a variation of less than 2 % in the fitted mean position. The fit quality in these ranges is always very good with χ 2 /N DF ≈ 1. Also the number of bins for the histogram has been varied and shows even smaller variations of the fitted mean value (∼1 %).
For the uncertainty related to setting up a measurement, we have identified several sources of systematic uncertainties that could come from the handling or the positioning of the scintillator  cubes and fibres, temperature variations and voltage setting variations. Some of these issues have been addressed separately and will be presented in the next sections. In addition, most of the time this setup is used for comparison between different configurations in order to minimize the systematic uncertainties. This also means that for each test a reference measurement is performed and is in most cases the same (same cube, wrapping and fibre). These measurements have been made over several weeks by different operators at different temperature and voltage settings. Comparing these results leads to an estimation of the total systematic uncertainty. Figure 12 shows the relative variation in PA for 32 of these reference measurements. On average 40.3 PA for the 1 MeV peak with a standard deviation of 2.3 PA is observed, which corresponds to about 5 %. This value of 5 % is considered as the systematic uncertainty of the light yield measurements.

Scintillator light collection studies
This section presents the studies of the light collection for a single SoLid cube. The influence of the scintillator material, the cube wrapping, the optical fibres and the 6 LiF:ZnS(Ag) screen on the light collection is studied.

Plastic scintillator material, production and cleaning
Plastic scintillator cubes in the SoLid experiment primarily serve as the antineutrino target since they contain a large number of free protons in the form of hydrogen nuclei. At the same time, it allows the measurement of the positron energy deposition, which in turn is related to the neutrino energy. The SoLid experiment uses ELJEN Technology EJ-200 PVT scintillator, one of the most efficient plastic scintillators with a light yield of around 10,000 photons per MeV. Light around 425 nm wavelength is produced with a decay time of 2.1 ns. Its refractive index is 1.58.
For the SoLid Phase 1 detector, the scintillator cube machining has been improved to obtain a better cube surface quality. Polishing the 12800 cubes needed for the experiment would improve the light yield further, but this was not cost effective. Therefore we focussed on optimizing surface quality after machining. In order to estimate the quality of the machining we measured with a roughness meter the surface roughness average (R a ). For SM1 cubes it was around 0.45 µm compared to 0.04 µm for the new cubes. This increased the light yield by 10 %.
In order to prevent the scintillator from heating, a lubricant is used during the machining. This leaves a grease film on the surface of all the cubes. As a reference measurement, the light yield of a cube was measured directly after machining, hence before cleaning. This gave a light yield of 35 PA/MeV. The cubes were then cleaned by hand in a soap solution at room temperature, rinsed with demineralised water and left to dry in the air or with tissues. Two other cleaning methods were tested: cold ultra-sonic bath and the same cleaning method as before but using a nylon brush to better clean the grooves. The cold ultrasonic bath was not efficient, increasing the light yield by only 5 %. All other cleaning methods were equivalent increasing the light yield by 25 % as long as enough soap was used and the cubes were well rinsed.

Cube wrapping material
The primary role of the cube wrapping is to optically isolate each scintillator cube in order to be able to locate the position of the IBD interaction. Additionally, the wrapping also acts as a reflector, increasing the light collected by the fibres.
Teflon (or PTFE) is known to be one of the best reflective materials for scintillation light. A SoLid cube was wrapped with 0.2 mm thick Teflon tape (80 g m −2 ) and tested. The result of the measurement with Teflon leads to the best light yield measured in this configuration, giving 44 PA/MeV. However, the wrapping of cubes with Teflon tape, leaving a hole for the fibre and avoiding extra layers for electron energy loss is time consuming and error prone. Since the SoLid Phase 1 contains 12800 cubes, Teflon tape was excluded for practical reasons. Nevertheless, this test provides a good reference to select appropriate wrapping material.
Tyvek is another very good candidate for reflecting scintillation light. It is also much more convenient to use as wrapping for the cubes since it is possible to cut and pre-fold a pattern using press techniques. This is shown in figure 13 where the Tyvek wrapping is unfolded around a cube. This material was already used for the SM1 detector but, as discussed in section 2.4, the Tyvek used at that time was not the thickest possible. Indeed for cubes assembled in the detector plane, the surrounding Tyvek layers from other cubes contributed to an increase of the light yield compared to a single cube. To quantify this effect, up to four layers of Tyvek wrapping have been added successively around a PVT cube. The second layer improved the light yield by about 20 %, the third one gave an extra 10 % with respect to two layers while the fourth one had no additional effect. For the construction of the SoLid Phase 1 detector it is not convenient to use several layers of wrapping around each cube so we have selected the thickest Tyvek from DuPont ™ (1082D as presented in section 2.4). A light yield of 36.7 PA/MeV was measured for this Tyvek compared to 33.6 PA/MeV for the Tyvek used in the SM1 detector. This is an improvement of 10 % for a single cube. Although this is a 15 % lower light yield than Teflon, it was the best material found taking into account construction constraints.

Optical fibres
SoLid optical fibres are 3×3 mm 2 squared fibres produced by Saint-Gobain under the reference BCF-91A. The shape and dimensions of these fibres are well adapted to the Hamamatsu MPPCs S12572-050P 3×3 mm 2 . They have a polystyrene core, an acrylic cladding and a fluor-acrylic cladding in the case of double clad fibres. The refractive indexes of these parts are respectively 1.60, 1.49 and 1.42. The BCF-91A optical fibres have been selected because they match both the PVT emission spectrum as well as the MPPC spectral response. These fibres shift blue light to green with absorption at 420 nm and emission peaking around 494 nm. The MPPC photon detection efficiency is maximal with 35 % at 450 nm but it is almost the same at 500 nm. The decay time constant of the emitted light of 12 ns is much shorter than the time difference between positron and neutron signals in the SoLid detector. This time difference is dominated by the thermalisation and capture of the IBD neutron, which takes several tens of micro seconds [1,3].
When the SM1 detector was constructed only single-clad fibres were available. However for the Phase 1 detector, Saint-Gobain was able to produce double-clad fibres. The test bench has been prepared with one single-clad fibre used in the SM1 detector and one double-clad fibre used for the Phase 1 detector going through the same cube at the same time to be able to compare both. The two MPPCs are each connected to one of the fibres and the other extremity is left free to avoid reflections. The assembly is mounted on the rail to allow cube translation along the fibres. The result of 12 measurements along the fibres at different cube positions is presented in figure 14. The exponential decay fit of the light yield as a function of the distance shows that about 15 % more light is trapped by the double-clad fibre ('Constant' parameter of the fit). The attenuation length for single and double-clad fibres are respectively measured to 106±11 and 112±11 cm. Thus we don't observe difference in the attenuation lengths for both fibres with this measurement method. Varying the fit range on the data shown in figure 14 gives a systematic uncertainty for this measurement, resulting in a change in light yield by 10 % and the attenuation length by 20 %.
These results show that double-clad fibres give an improvement in term of light yield compared to single-clad fibres. Therefore, the double-clad fibres are used for the SoLid Phase 1 experiment.

6 LiF:ZnS(Ag) neutron screens
The SoLid neutron screen (NS) is a 6 LiF:ZnS(Ag) scintillator from Scintacor. The neutron capture on 6 Li produces two nuclei 3 H and 4 He sharing a kinetic energy of 4.78 MeV. This energy is converted into scintillation light which enters in the PVT cube and is subsequently collected by the optical fibres. The 6 LiF:ZnS(Ag) scintillator emits light with a maximum emission at 450 nm, close to the PVT emission, so the collection will be similar as for the plastic scintillator. It is a slower scintillator with a decay time of about 80 µs. This time difference makes it easy to distinguish between light produced in the PVT and in the NS scintillators. The NS has a thickness of about 250 µm and a molecular LiF to ZnS ratio of 1:2. Three types of NS produced at different times are used for the construction of the SoLid Phase 1 detector. The first two generations were fragile so a third generation was produced with a less fragile substrate as backing. When neutrons interact in the NS the emitted light will have to go through the plastic scintillator before being trapped in the fibre. Since the sensitivity of the light yield to the wrapping material is large, an important impact of having a NS between the cube and its wrapping is expected. For the SM1 prototype only one NS per cube was used. For the SoLid Phase 1 detector, two NS will be used since simulation studies have shown that neutron detection efficiency could significantly increase, reducing at the same time the neutron capture time. One of the screens will be oriented perpendicular to the antineutrino direction to increase efficiency. The second NS will pass along a fibre between the PVT scintillator and the Tyvek (section 5.1).
To check this hypothesis, the light yield measurements were performed for a cube wrapped with SoLid Phase 1 Tyvek and either one fibre without NS, or with one NS sheet on a face without fibre, or with the same NS on a face where the fibre is going through the cube. For these three configurations respectively 33.6, 30.6 and 29.7 PA/MeV were measured. The first drop of about 9 % confirms that adding 6 LiF ZnS:Ag decreases the PVT light yield. The loss is then only ∼3 % when the surface of one NS is parallel to the fibre. This effect is close to our systematic error but is significant.
In conclusion for the SoLid Phase 1 detector, the plastic scintillator light loss due to the NS will be limited to about 12 % thanks to the fact that one of the two NS sheets will be placed along an optical fibre between the PVT scintillator and the Tyvek instead of covering a face of the cube where no fibre is going through.

Detector configuration studies
In this section the detector design and configuration will be studied for what concerns the light yield of individual scintillator cubes.

Position of the fibres in the scintillator cube
For the SM1 cubes, squared 5×5 mm 2 grooves at the surface of the cube were holding the 3×3 mm 2 fibres ( figure 15 left). This design was relatively easy to machine and allowed for easy detector assembly. For the SoLid Phase 1 cubes a design was considered with the fibre going through the core of the cube to have more scintillating material surrounding the fibre. Cubes with circular holes drilled through the scintillator were tested and resulted in a 10 % increase in light yield. However, when considering the machining time, the cost and a possible heating damage to the scintillator during drilling, this design solution was not selected. Several positions for the surface grooves where then considered, but the actual position of the grooves turned out not to be important for the light yield. Hence the position of the grooves was driven by the detector mechanical design. The scintillator cube design has been optimized with four grooves on four faces with 2.5 mm spacing as shown in figure 15 right. The four fibres remain in the 16×16 cubes plane to allow the stacking of the detector planes along the neutrino direction. The SM1 detector was limited to two fibres per cube with a single readout. One potential optimization would be to have a double readout per fibre. Another option would be to have 4 fibres with a single readout. Both options result in a higher light yield. To decide which option is best a comparison was performed between single and double readout of a fibre. The test bench does not allow for reading out four fibres. Therefore, the measurement consisted of measuring the light yield of one fibre read out by one MPPC on one end and with or without a mirror at the other end of the fibre. The materials used were selected based on the studies in section 5. With mirror we measured 25.3 PA/MeV and without mirror 15.9 PA/MeV, which is an improvement of 60 %. For a double readout, the light yield of a fibre without mirror would be doubled. For two such fibres, we would therefore obtain 63.6 PA/MeV. For four fibres with single readout and a mirror, the light yield would become 101.2 PA/MeV. Based on this estimation, the latter configuration would be preferred. However, putting more fibres in the cube will reduce the amount of light collected per fibre. To quantify the reduction of the light yield due to the presence of other fibres an additional measurement is performed. A reference fibre is inserted in the cube with a double readout. Additional fibres are then inserted one by one into the cube and the light yield for the first fibre is measured. Since the cube is already machined with four grooves this measurement cannot take into account a possible light reduction produced by the grooves themselves. The result is presented in table 3. Each new fibre that is introduced takes on average ∼15 % of the light from the first one. The third row in the table 3 shows that ∼16 % less light is collected per fibre with the two fibres design and 40 % less light per fibre in the four fibres design. With this reduction, the estimated light yield for the two fibres with double readout is 53.4 PA/MeV compared to 60.7 PA/MeV for the four fibres with single readout and a mirror. Hence, the configuration with four fibres with single readout performs 15 % better in terms of light yield. The stochastic term of the energy resolution is also improved from 14 % to less than 13 % at 1 MeV. Moreover, the four fibres configuration with single readout and mirror also improves the detector uniformity, as discussed in section 6. Based on these studies, the four fibres configuration with single readout was adopted for the SoLid Phase 1 detector. Table 3. Impact of the number of double-clad optical fibres inserted in the plastic scintillator grooves on the light yield of the first fibre with double readout. Adding other fibres decrease the light-yield per fibre but increases the total light-yield. To verify whether the four fibres are collecting the same amount of light, we have measured the light yield four times, moving the same fibre each time in a different groove. These four measurements give a light yield that is consistent within 4 %, which is smaller than the systematic uncertainty. Hence the location of the fibre does not matter in terms of light yield. We also rotated the cube along the fibre direction to check different faces of the scintillator cube. We do not observe differences in all these measurements either. These tens of measurements indicate that the scintillation light is uniformly distributed in the scintillator volume, confirming the results in section 2.2 where the response for localized electron interactions and gamma interactions in the whole scintillator volume are compared.

Spatial freedom of the optical fibre
As already mentioned, the size of the grooves in the SoLid scintillator cubes is 5×5 mm 2 to hold the 3×3 mm 2 squared fibres. The relatively large grooves facilitate the insertion of the fibres once a detection plane is assembled. As consequence the fibre has the possibility to move in the grooves. We have measured the effect of the positions of the fibre with respect to the cube to quantify the reproducibility of the results. The maximal observed effect was the rotation of the fibre. The four measurements at different rotation angles vary less than 4 % as can be seen in table 4. This effect is within the systematics uncertainty, which implies that the position and orientation of the fibre in the groove have no effect on the light collected by the fibre. It is worth mentioning that these large rotation angles are not possible in the SoLid detector design since the fibres are held by 3D printed connectors at the two extremities to hold them in position in the planes.

Reflector at the end of the optical fibre
In section 5.1 the impact of using a mirror at one end of the fibres has been shown. Therefore we investigated the impact of the type of mirror. For the SM1 fibres, an aluminium sticker mirror was used. We have explored different other options and tested aluminised mylar film. The aluminium has a standard thickness of ∼200 nm. Several thicknesses for the mylar were possible, but showed no differences in light yield. A mylar thickness of 70 µm was selected for its rigidity, which is more convenient when inserting the end of the fibre in the 3D printed connectors. We compared the mirror used in SM1 and the aluminised mylar mirror using the same cube and the same fibre with a single MPPC readout. We measured the light yield for six distances along the fibre in both cases. The result is presented in figure 16. The function used for the fit is given by equation 5.1, which is taking into account the reflection at the end of the fibre with the mirror.
where C is a normalisation coefficient, L att is the attenuation length in cm, R the light reflection coefficient of the mirror and L f ibr e is the total length of the fibre, which is 92.2 cm. In order to compare only the reflection coefficient, the normalisation coefficient and the attenuation length are fixed to 24.7 PA/MeV and 112 cm, respectively, as determined from previous measurements. We find that the SM1 mirror has a reflection coefficient of 73 ± 6 % while it is 98 ± 6 % for the other mirror. Consequently the aluminised mylar mirrors have been selected for the SoLid Phase 1 detector. The effect on the total light yield per cube depends on its position along the fibre because of attenuation. For example this mirror would produce an increase of light yield per fibre of 5 % for the cube farthest to the mirror, 7 % for a cube at the centre and 11 % for the cube closest to the mirror.

Impact of neighbouring cubes
In the SoLid Phase 1 detector the cube and fibre environment is different than that in the test bench. Indeed the fibres will be surrounded by scintillator cubes along their full length. This could have an impact on the light yield for a single cube or on the attenuation length. We performed a test with 16 cubes positioned along one double clad fibre, which is read out by two MPPCs. Considering the central cube, we observe an increase of the light yield of 12 % compared to the same measurement where only one cube was positioned along the fibre ( figure 14). Since the 207 Bi source and the trigger system are free to move along the fibre the light yield of each of the 16 cubes was measured. The measurements are normalised to the sum of the two MPPC signals for each cube to cancel the potential effect of a different response for the cubes. The result of the attenuation measurement for the individual MPPC signals after correction is presented in figure 17. The attenuation length seems to increase a bit although the uncertainty is quite large. The difference between the two MPPCs is partially due to the difference in breakdown voltages. This measurement implies that the light yield will be better in the real detector where 16×16 cubes are assembled in planes compared to our test bench studies. A second effect we measure in this test, is the light escaping to neighbouring cubes. This optical cross-talk could for instance come from light going through the Tyvek, but is more likely to come from leaks through the holes in the Tyvek where the fibres pass. A second cube is placed next to the one interfaced with the calibration source. Two fibres were put through these two cubes perpendicularly to the fibre going through the 16 cubes. Some light has been observed in the neighbouring cube with a peak in the integral spectrum between 1 and 2 PA. After calibrating the light collected by this cube with the 207 Bi source, we conclude that in 90 % of the cases we record less than 10 % (< 100 keV) of the light in the cube next to the source. The correlation with the integral spectrum of the cube with the source is weak (< 0.2) but this might be due to the low number of PA measured. Optical cross-talk should not affect the energy reconstruction for the SoLid experiment since it is very low and the four channel readout per cube will allow for distinguishing the different light origins. We have performed the same test with the next to next cube but no light excess was visible.
6 Summary of the light yield improvements for the SoLid Phase 1 detector Table 5 summarizes all the improvements for the light yield of the Phase 1 detector based on the studies presented in this article. For improvements of the light yield quantified per fibre, one has to take into account that each cube in the SoLid Phase 1 detector will be read out by four fibres. The overall light yield improvement is expected to be around 150 %. In order to validate all these improvements for the SoLid Phase 1 detector design together, we performed two more measurements in a configuration as close as possible to either the SM1 or Phase 1 design. For the SM1 configuration we have used an SM1 cube with one SM1 neutron screen, SM1 Tyvek, two single clad fibres with each an MPPC on one end and an SM1 mirror at the other end. For the SoLid Phase 1 configuration, we have used a Phase 1 cube with two Phase 1 NS, Phase 1 Tyvek, four double-clad fibres with each an MPPC on one end and an aluminised mylar mirrors on the other end. Since the prototype amplifier board has only three channels, the measurement was repeated for the four fibres case changing only position of the MPPC for the two measurements.
For the SM1 configuration we obtain a total cube light yield of 18.6 PA/MeV and for the SoLid Phase 1 configuration 51.6 PA/MeV. This is an improvement of almost a factor 2.8, or 180 %, in the light yield for one cube of the new detector. This is better than the prediction computed in Table 5 which was a simple summation and was not taking into account all possible effects and the inter-dependence of effects. With this light yield the energy resolution target of σ E /E = 14 % at 1 MeV has been achieved for the SoLid experiment.
The measured light yield for the SM1 configuration is almost 30 % lower than the observed value for the real SM1 detector, which was 24 PA/MeV [3]. This difference is certainly dominated by the impact of neighbouring cubes in the real SM1 detector (sections 4.2 and 5.4). To lesser extent, it could be due to the different set-up or electronics. The result for the Phase 1 cube is in agreement with the calculation presented in section 5.1 where 60.7 PA/MeV was expected for four fibres in the same cube but without the two neutron screens. Using the results presented in section 4.4 adding two NS would reduce the light yield to 53.6 PA/MeV, which is in agreement with 51.6 PA/MeV measured in this last test given the systematic uncertainty of 5 %.
From this last measurement for a single cube at the central position of the 16×16 cubes detector plane and the attenuation length measurements (section 4.3) we can build the 2D light yield maps for the SM1 and SoLid Phase 1 16×16 cubes planes. These are shown in figure 18. For the SM1 configuration the average light yield of a plane is 19.0 PA/MeV, with values ranging between 16.1 to 23.1 PA/MeV. The difference between these two extreme values is 43 %. For the Phase 1 configuration we observe a much more uniform light yield in the plane with only 6 % difference between the most extreme light yields (51.6 and 54.5 PA/MeV). The average value over the plane is 52.3 PA/MeV. This illustrates the strong improvement in light yield and uniformity expected for the SoLid Phase 1 detector.  Figure 18. 16×16 cubes detector plane light yield maps for SM1 (left) and SoLid Phase 1 (right) extrapolated from the light yield measurements presented in this article. The average light yield is 18.9 and 52.3 PA/MeV for SM1 and SoLid Phase 1, respectively. The maximal difference, is only 6 % for the Phase 1 compared to 43 % for SM1.

Conclusion
A precision test bench based on a 207 Bi calibration source developed to improve the light yield of the SoLid detector has been presented in this article. A trigger system selecting the 1 MeV conversion electrons provides a Gaussian energy peak and allows for precise comparisons of the different detector configurations that were considered. The systematic studies have shown an uncertainty on the light yield measurements of 5 %. The light yield of the SM1 prototype has been measured to be 18.6 PA/MeV on this test bench while the observed value in the real detector was 24 PA/MeV. This 30 % higher efficiency is attributed to the improved reflectivity for cube elements assembled in a real-scale detector module. The reactor antineutrino energy is measured through the energy deposited by the positron produced in the inverse beta decay interaction of the antineutrino in the plastic scintillator of the SoLid detector. The light yield of the Phase 1 cubes has been improved compared to the SM1 detector by a better scintillator machining (+10 % / cube), the choice of wrapping material (+10 % / cube), the type of fibre (+15 % / fibre), the position of the 6 LiF:ZnS(Ag) screen (-3 % / cube), the number of optical fibres (+40 % / cube) and the type of mirror at the end of the fibre (+7 % / fibre). The overall gain results in an expected light yield of 52±2 PA/MeV for the SoLid Phase 1 detector. This is an improvement of almost a factor 2.8, or 180 %, in the light yield for one cube of the new detector. With this light yield the energy resolution target of σ E /E = 14 % at 1 MeV can be achieved. The light yield uniformity of a Phase 1 detector plane, which consists of 16×16 cubes, has also been improved to only 6 % difference between the most extreme cube positions.