Single PE calibration of the PMT

Single-photoelectron (SPE) calibration was necessary to determine the light yield of the pCsI detector. The online SPE calibration was performed by populating a histogram (Fig. 3 with the PeakQ values of peaks with TS between 7000 and 7999 for all events in dataset. As depicted in Fig. 2, within the 7000-7999 ns range, the pulses are sparse, with each likely corresponding to an SPE. The subplot shows a typical SPE signal. Given the small contributions of multi-PE events, the histogram in Fig. 3 is fitted using a simplified SPE model, similar to the one described in Ref. [19]. $f(q)=\left[Bkg(q)+{\displaystyle \sum _{i=1}^3}{a}_i{g}_i\left(q\mathrm{,}{Q}_{\text{spe}}\mathrm{,}{\sigma }_{\text{spe}}\right)\right]\times Acp(q)$ (1) where $Bkg(q)=a_{\text{bkg}}\cdot e^{-\frac{q}{{\sigma }_{\text{bkg}}}}$ (2) $g_i(q)=\text{Gaus}\left(q\mathrm{,}i{Q}_{\text{spe}}\mathrm{,}\sqrt{i}{\sigma }_{\text{spe}}\right)$ (3) $Acp(q)={\left[1+e^{-k\left(q-q_0\right)}\right]}^{-1}$ (4) The Bkg(q) term describes events generated by electrons emitted from dynodes undergoing incomplete multiplication as well as some electronic noise. The g_i(q) terms represent the i-PE Gaussian responses for fully multiplied electrons. Q_spe is the mean SPE charge and σ_spe represents the spread of SPE charge due to fluctuations in the PMT multiplication process. The Acp(q) term is a sigmoid-shaped function that describes the threshold effect introduced by the peak-searching algorithm discussed in Sect. 3. q₀ represents the edge midpoint and k controls the steepness of the edge. The ai values are not constrained to a Poisson distribution, because the process of populating PeakQ in this histogram is not a Poisson procedure.

Fig. 3Full-screen View

(Color online) SPE histogram filled by the PeakQ values of peaks with TS in range 7000–7999 ns. A simplified SPE model is fitted to the histogram. ${\mu }_{\text{spe}}=32.50\pm 0.03$ and σ_spe = 10.37±0.03 in unit of ADC counts·ns

The fitted curves are shown in Fig. 3. The fitted results are as follows: Q_spe=32.50(3) and σ_spe = 10.37(3) in units of ADC count ·ns.

Light yield and energy resolution of pCsI

The recorded energy spectrum of ²⁴¹Am measured in terms of the number of photoelectrons (NPE) generated during each event is shown in Fig. 4 with the fitting results listed in Table 1 The NPE is computed using the following formula: $NPE=\frac{TotalQ}{Q_{\text{spe}}}.$ (5)

Fig. 4Full-screen View

(Color online) Energy spectrum of ²⁴¹Am measured using a pCsI detector at 77 K. Ten unconstrained Gaussian functions are used for the global fitting of the spectrum. The fitted curve and its components are shown. Fitting results shown in Table 1. The subplot shows the fitting of the 77 keV coincidence peak which is too weak to be visible in the main plot

The spectrum undergoes a global fit by employing ten unconstrained Gaussian functions to accommodate the various components. The 59.54 keV and 26.3 keV gamma peaks originate from intrinsic gamma rays emitted during ²⁴¹Am decay. The K-shell escape and L Shell escape peaks are unique to CsI detectors because of the delayed release or escape of X-rays or Auger electrons after a 59.54 keV gamma ejects a K- or L-shell electron into Cs or I atoms. The 13.95, 17.8, and 20.8 keV X-rays originated from the activated states of ²³⁷Np, a decay product of ²⁴¹Am. These peaks are merged because of nearby X-rays rather than monotonous X-rays. The 77 keV peak arises from the coincidence of the 59.54 keV gamma-rays and X-rays. The Bkg component accounts for events from an environmentally radioactive background. In addition, another X-ray/e component addresses the complex X-ray and electron spectra below 25 keV, requiring more than three Gaussian functions to achieve fitting convergence. However, using a single Gaussian function to describe other X-ray/e spectra remains oversimplified, resulting in an overall χ²/ndf value of 4.0. However, when the χ²/ndf calculation is constrained to the range NPE∈ [600, 3000], the value improves to 1.8. We did not pursue a more refined model for the Other X-ray/e components because their influence on the fitting of the peaks, which are used to determine the light yield, should be minimal because of the significant prominence of the peaks as long as the fitting converges.

The fitted curves and their components are shown in Fig. 4, with fitting results listed in Table 1. The detector light yield (LY) at various energy points is calculated as: $LY[{\text{PE/keV}}_{\text{ee}}]=\frac{{\mu }_{\text{npe}}}{\text{Energy}\left[{\text{keV}}_{\text{ee}}\right]}$ (6) where μ_npe denotes the Gaussian's fitted mean at a given energy point.

The light yield results obtained at various energy points were fitted using a zero-order polynomial function to determine the mean light yield and the associated uncertainties. The fitted results are shown in Fig. 5. The error bars in the graph represent the standard deviation of the Gaussian function fitted at different energy points divided by the energy (σ_npe/Energy). The final mean light yield of the pCsI detector at 77 K is 35.20.6PE/keV_ee, which is slightly higher than the assumed value used in the CLOVERS sensitivity estimation, 33.50.7PE/keV_ee, as reported in Ref. [14], where the CsI crystal was also coupled to an R11065 PMT.

Fig. 5Full-screen View

(Color online) Light yield calculated at different energy points and their averaged value

The most remarkable achievement of this study is the world-leading energy resolution achieved by scintillator detectors. Given that the 59.54 keV gamma peak is monotonic (unlike the X-rays, K/L Shell escape, and coincidence peaks) and is less influenced by nearby peaks (unlike the 26.3 keV gamma peak, which is strongly affected by nearby X-rays and K shell escape peaks), its resolution is chosen to represent the overall resolution of this study. The full width at half maximum (FWHM) energy resolution of this pCsI detector at 77 K at 59.54 keV reached 6.9%, surpassing the reported 9.5% in Ref. [14], 8.8% in Ref. [21] and 7.8% in Refs. [22], making it the best among all the reported resolutions of cryogenic pCsI detectors. This resolution even outperforms that of the brightest inorganic scintillators typically used at room temperature, such as NaI(Tl), CsI(Na), CsI(Tl) or LaBr₃. A summary of the comparison is presented in Fig. 6.

Fig. 6Full-screen View

(Color online) Comparison of energy resolution at 59.54 keV of different crystals from various studies reveals that the 6.9% resolution achieved in this work by the pCsI detector at 77 K is superior to all others. Resolution data were obtained from J. Liu [14], L. Wang [22], R. Hawrami [23], N. Yavuzkanat [24], R. Casanovas [25], W. Chewpraditkul [26], L. Swiderski [27] and P. Feng [28]

Scintllation decay time of pCsI

The scintillation decay time of the pCsI detector at 77 K was determined by fitting the accumulated and normalized waveforms to three exponential components. The waveforms and fitted results are shown in Fig. 7. The decay time of the slowest component of pCsI at 77 K is approximately 1 μs, which is considerably faster than that of the CsI(Na) crystal, which is approximately 17 μs, as shown in Fig. 8. These results are consistent with those in previous studies [29-32]. The considerably shorter decay time of pCsI significantly reduces the afterglow background induced by environmental radioactive events, which contaminates approximately 30% of all events in the COHERENT CsI(Na) experiment [19].

Fig. 7Full-screen View

(Color online) Scintillation decay time fitting of the pCsI detector at 77 K. The waveform fitted is the sum of 100k ²⁴¹Am induced events and normalized to its maximum value. The decay constants and composition fractions of different components are listed

Fig. 8Full-screen View

Scintillation decay time fitting of the CsI(Na) detector at room temperature followed the same setup as the pCsI experiment, except for the crystal type

Influence of temperature on the light yield

The relative light yields of the pCsI detector at different temperatures are shown in Fig. 9, alongside results from V. Mikhailik [33], C. Amsler [29], X. Zhang [34] and W.K.Kim [32]. The results of this study and those of Mikhailik are normalized to the maximum value for each dataset. However, Amsler and Zhang and W.K. Kim do not include data points below 77 K; therefore, their light yields are normalized to the values in this study at 77 K based on their results at the same temperature. All results show good agreement in the overall trend, with slight differences, possibly owing to variations in the PMT setup and crystal used.

Fig. 9Full-screen View

(Color online) Relative light yield at various temperatures from multiple datasets shows consistent agreement in the overall trend. Both this study and Mikhailik's results indicate that the maximum light yield is achieved at approximately 20 K. The results from Mikhailik are sourced from Ref. [33], Amsler's from Ref. [29], Zhang's from Ref. [34] and W.K.Kim's from Ref. [32]

The light yield increases rapidly as the temperature decreases from room temperature to approximately 100 K. Subsequently, it reached a plateau between 70 K and 100 K, followed by a slight increase at approximately 60 K. The maximum light yield was attained at approximately 20 K, after which it decreased rapidly as the temperature decreased, which is consistent with both our results and those of Mikhailik. Although there is a 20% increase in light yield from 77 K to 20 K, cooling down to 20 K is considerably more challenging than cooling to 77 K, which can be easily achieved with liquid nitrogen, is inexpensive, and safer than liquid hydrogen, which must be obtained to 20 K.

Because the light yield remains relatively stable between 70 K and 100 K, another potential approach is to place pCsI in an 87 K liquid argon environment and utilize liquid argon as an active veto system to reject the background introduced by external particles such as neutrons or gamma rays.

Influence of surface treatment on the light yield

In addition to temperature, another factor that could influence the light yield is the surface treatment of the crystal, which affects the light-collection efficiency of the detector system, as mentioned in Ref. [35]. [36] and Ref. [37]. To optimize the surface treatment (ground or polished), four comparison experiments were conducted.

Experiment A compared the light yields of two cubic crystals subjected to different surface treatments. One crystal had all its surfaces polished, whereas the other had a surface ground, except for the light output surface. The ratio between the light yield of the ground and polished crystals, R_ly, is defined as follows: $R_{\text{ly}}=\frac{L{Y}_{\text{ground}}}{L{Y}_{\text{polished}}}.$ (7) This comparison was conducted at room temperature (293 K) and 77 K. A laser beam passing through the two ground surfaces and two polished surfaces is shown in Fig. 10. The scattering effect of the ground surface on the laser is evident.

Fig. 10Full-screen View

(Color online) Laser beam passing through two ground surfaces (left) and two polished surfaces (right)

Experiment B was identical to Experiment A except that the crystals were cylindrical rather than cubic.

Experiments A and B compared the different crystals. To eliminate differences between crystals, Experiments C and D were conducted. In Experiment C, a cubic crystal was initially ground and then polished, and the light yields were measured before and after polishing. Experiment D was identical to Experiment C, except that a different ground crystal was used. Experiments C and D were conducted at the room temperature.

In addition to these four experiments with pCsI crystals, similar experiments were conducted for CsI(Na) and CsI(Tl) crystals using the same procedure as in Experiments C and D, respectively. The measured R_ly from the experiments are listed in Table 2.

As shown in Table 2, the light yields of the ground crystals are consistent at approximately 60–70% of the polished crystals, regardless of the temperature, crystal shape, or individual crystals. However, the ratio of CsI(Na) to CsI(Tl) are almost 1. We hypothesize that UV light (310 nm at room temperature [38, 39] and 340 nm at 77 K [38]) emitted by pCsI is more likely to be absorbed by microstructures on the ground surface. In contrast, light with longer wavelengths emitted by CsI(Na) (420 nm [40, 41]) and CsI(Tl) (550 nm [42, 43]) is less susceptible to absorption by these microstructures. Although this hypothesis requires further verification, the results suggest that for future 10 kg pCsI detectors in the CLOVERS experiment, all crystal surfaces should be polished to achieve higher light yields.

Influence of crystal shape on the light yield

The crystal shape may also influence the light yield, as reported in Ref. [44] and Ref. [45]. The light yields of cubic and cylindrical crystals were compared for both the ground and polished crystals. The results are presented in Table 3. The light yields and energy resolutions of the cubic crystals are slightly higher than those of the cylindrical crystals under both ground and polished conditions; however, the difference is not significant. Therefore, in future CLOVERS experiments, the choice of the crystal shape may depend on the shape of the photon detector to balance the light collection efficiency and detector mass. For instance, the crystal should be cuboidal for SiPMs with square cathode regions and cylindrical for PMTs with circular cathode regions.