Introduction
Monte Carlo codes, such as GEometry ANd Tracking (GEANT) [1] and Monte Carlo N-Particle (MCNP) [2], are extensively used to model and calculate the response of scintillation detectors used in various applications, such as medical and space applications, nuclear security, and radiation protection. After validation of the Monte Carlo model, the results of such simulations often serve as guidelines for radiation protection practices, detectors’ design or facilities shielding. In the simulation of gamma-ray responses, one of popular tools used to generate the detection efficiency—herein, the absolute peak efficiency, in particular—calibration curve for a radiation detector is the pulse height (f8) tally in MCNP, which records the energy deposited in the detector cell. However, it is often the case that simulated spectral responses do not closely match with the measurement result.
The pulse height tally does not necessarily deliver the same response as the real detector response [3]. For scintillation detectors, in particular, there are lot more processes in generating the detector response signal, as shown in Fig. 1, compared to a simple f8 tally simulation. In general, f8 tally results assume that energy is deposited in the detector as much as the kinetic energy difference of the gamma ray between before and after an event, but, in the case of the actual detector, it is indeed the recoil electron generated by the gamma-ray event who deposit the energy in the detector in reality, producing scintillation photons according to the deposited energy in case of the scintillators, for example. Scintillation photons are often emitted in a random direction inside the scintillator, some of which may directly enter the photomultiplier tube (PMT), but many of them will either reflect at the crystal boundary or exit the scintillator. This can affect overall landscape of the detector response, not just on the energy resolution, but also on the peak efficiency of the scintillation detector. Intuitively, one can also expect the light loss will depend on the location of interaction, therefore, some pulses may not preserve the nominal amplitude even though the same amount of energy is deposited in the scintillator.
In the previous study, the response of the scintillation detector to gamma rays and neutrons of the Cs2LiYCl6:Ce (CLYC) scintillation detector was studied, and the simulation considering the transport of gamma rays with the MCNP6.1 code were compared with measurement results. There was >20% difference between the simulation and measurement results in absolute peak efficiency [3]. In other previous studies, it was confirmed that the results of calculating the absolute peak efficiency using various scintillation detectors (NaI(Tl), CsI(Tl)) using MCNP and GEANT4 code were different from the measurement results [4–9].
Beyond these studies that mainly focus on energy deposition and peak-efficiency calibration, there has been substantial progress in modeling the transport of scintillation photons in scintillation detectors. Recent reviews have emphasized that a realistic description of scintillator optical properties, reflector coatings, and optical coupling media is essential to reproduce measured detector responses and to support detector optimization in both diagnostic imaging and radiotherapy applications [10]. For Geant4 based simulations in particular, the available optical physics processes and their use in optical sensing and dosimetry have been systematically reviewed, showing that the accuracy of the simulation strongly depends on a consistent definition of optical material properties and surface models for scintillators and photosensors [11].
In this study, the gamma-ray response of the CLYC scintillation detector was simulated by including the transport of secondary particles into the simulation using the Monte Carlo codes, MCNP6.1 and GEANT4. Secondary particles considered are recoil electrons and scintillation photons (a few eV), and, as MCNP6.1 does not support the low-energy optical photon transport simulation, the optical transport of scintillation photons was simulated only in GEANT4. The absolute peak efficiency calculated by each simulation was compared with experimental results, and speculation on the difference and implication of the result are discussed.
Materials and Methods
1. Monte Carlo Simulation
In this study, we simulated the process that gamma rays are detected and measured by a CLYC scintillation detector. Using the MCNP6.1 code, the simulation was performed considering the transport of gamma rays only, to compare with the result considering the transport of both gamma rays and recoil electrons. In MCNP6.1 simulations, photon interactions were modeled with MCPLIB84 and electron transport with EL03; transport cutoff energies were kept at the code defaults. For the gamma-only configuration, we used MODE P with a pulse height tally F8:P. When electron transport was considered, we used MODE P E with F8:P E so that both photons and electrons contributed to the tallied energy deposition. In GEANT4 (version 10.05) simulation, electromagnetic interactions were handled with QGSP_BIC_EMY, and G4OpticalPhysics was enabled to model scintillation photons; the range cuts were left at their default values. For the gamma-only calculation, we recorded the kinetic energy information of secondary electrons without transporting them. When the electron transport was enabled, the energy deposited by transported electrons was used to compute the detector response. The surface of the reflector was set to be polished, and the optical surface model used was GLISUR.
The size of the scintillator crystal is 5.08 cm×5.08 cm (2″×2″), and the crystal volume was equally segmented into 1,000 subsections to investigate the detailed particle transport behavior in each section. The light yield of the CLYC scintillator was set to 20,000 photon/MeV in average [12, 13], and the statistical distribution of the scintillation photon generation was assumed to follow the Poisson distribution. The wavelength of the scintillation photon produced in CLYC was set to 370 nm, and the reflectivity of the reflectors surrounding the scintillator was varied as 90%, 93%, 95%, 99%, and 100% [14–16]. The schematic of the CLYC scintillator geometry and the constituent materials of the internal structure implemented in the simulation are shown in Fig. 2.
The CLYC crystal, the surrounding teflon and neoprene reflectors, and the aluminum housing were explicitly represented with homogeneous bulk properties and idealized polished interfaces. The optical coupling to the PMT was simplified by assigning the refractive index of optical grease at the crystal PMT interface, without modeling a separate grease layer, the photocathode, or any internal PMT structures and electronic response. Possible non-uniformities in crystal surface quality, small air gaps between components were also neglected. Consequently, the reflector reflectivity used in the GEANT4 simulations should be interpreted as an effective parameter that absorbs these unmodeled optical losses, rather than a direct measurement of the physical reflectance of the teflon reflector alone.
In the simulation considering the transport of gamma rays only, using both MCNP6.1 and GEANT4 codes, the energy deposited in the scintillator is calculated by the difference of kinetic energies of gamma rays entering and exiting the detector. Here, it is assumed that the signal amplitude of the scintillator is dependent on the energy deposited in the scintillator, which is as much as the kinetic energy difference before and after the gamma-ray interaction inside the detector. Having consideration on the transport of recoil electrons included, the energy deposition in the scintillator can be calculated by the difference between the initial kinetic energy of the recoil (or primary) electron created from the interaction of gamma rays and the final kinetic energy of the recoil electron escaping the detector.
A two-step simulation was performed by GEANT4 to investigate the overall detector response depending on the consideration of the recoil electron and the scintillation photon transport, respectively. The first step was to calculate the interaction probability of incident gamma rays with each subsection volume of the detector. The simulation geometry coincides with the experimental setup shown in Fig. 3. The radiation source was positioned at 25 cm from the detector face, and the energy spectra or the number distributions of scintillation photons for measuring gamma rays of 122–1,408 keV were obtained. A total history of 1×108 photons were simulated to observe the detector response in each subsection. The probability of gamma-ray interaction in each subsection was calculated, and the simulated gamma-ray peaks of the consolidated spectra were analyzed to calculate the absolute peak efficiency of the detector. The second step was to investigate the light collection efficiency from each subsection of the scintillator entering the PMT face. At each voxel of the scintillator, 1×104 scintillation photons were created and emitted isotropically. The path of scintillation photons undergoing reflection and refraction at surfaces was traced, and the number of photons arriving at the entrance plane of PMT was counted.
2. Measurement Experiment
Gamma-ray spectra of various radiation sources were obtained using a CLYC scintillator, Trimode (Bubble Technology Industries), of which the experimental setup is as shown in Fig. 3. Like the Monte Carlo simulations, the distance between the detector and the radiation source was set to 25 cm. The sources used in the experiments were 22Na, 152Eu, 137Cs, 133Ba, 60Co, and 54Mn. Signals from the detector was processed by the embedded system of the equipment and stored using the Trimode DAQ software (Bubble Technology Industries). The activity and half-life information of the sources, as well as the measurement time are listed in Table 1. Background counts were measured for 60 minutes to mitigate statistical fluctuation from lower count rates, and 54Mn was measured for a longer period of time, 30 minutes, compared to other sources, because of its relatively weaker activity.
Results and Discussion
1. Gamma-Ray Interaction Probability Distribution
Volumic distribution of gamma-ray interaction probability within the scintillator was calculated using the GEANT4 simulation code. In particular, the probability of the event that all recoil electrons created by the full-energy absorption event of gamma rays deposit their entire energy into the scintillator crystal was calculated and compared with the event probability of the photoelectric effect at each voxel (partial volume region) of the scintillator. Fig. 4A–4C visualize the volumic probability distribution of photoelectric absorption events from the gamma rays of 122, 662, and 1,408 keV. On the other hand, Fig. 4D–4F visualize the event probability distribution in which all recoil electrons deposited their kinetic energy as much as the total energy of the incident gamma rays, for the energies of 122, 662, and 1,408 keV. Two results show slightly different values, as the former was calculated to be up to 1.5% higher at the location of the outer wall of the crystal. It can be anticipated that for the photoelectric effects occurring at the outer wall region of the crystal, the recoil electrons, which received the energy of gamma rays, may not fully deposit their kinetic energy in the crystal and escape out of the crystal instead. Therefore, only partial deposition of the photoelectron’s kinetic energy subsequent to full-energy absorption of gammas would sometimes occur.
2. Light Collection Efficiency Distribution
The light collection efficiency of scintillation photons, which were created at each voxel of the scintillator crystal, arriving at the PMT was calculated by the GEANT4 code simulation, assuming various light reflectivity values at the scintillator surface. Fig. 5 visualizes the volumic probability distribution of the scintillation photons created in each voxel depending on the reflectivity. The light collection efficiency values range between 65% and 80%, and the overall values increase with the reflectivity. The outer region tends to show higher light collection efficiency than the inner region of the scintillator, with higher contrast for poorer reflectance.
3. Effects on Gamma-Ray Spectroscopy
Energy spectra obtained by MCNP6.1 and GEANT4 codes considering the transport of: (1) gamma rays only, (2) gamma rays and recoil electrons, and (3) subsequent scintillation photons are shown in Fig. 6A and 6B. The transport of scintillation photons created in the scintillator was simulated by the GEANT4 code only, and the number distribution of scintillation photons are represented in terms of channel, which corresponds to the interval of 20 scintillation photons each. The number distribution of scintillation photons arriving at PMT was compared to the scintillation photons that were initially created, and plots are overlaid in Fig. 6B. A series of scintillation photon number spectra arriving at PMT depending on the reflectivity at the scintillator surface are shown in Fig. 6C, and Fig. 6D shows an energy spectrum of the 152Eu source obtained by the experiment, as a reference to the simulated spectra.
As it was already indicated in Fig. 4, simulations including the recoil electron transport produced energy spectra with slightly reduced peak counts, while not much altering the overall shape of the spectra. This implies a certain portion of recoil electrons generated at the outer region of the scintillator may escape out of the detector not depositing their full kinetic energy into the scintillator. Introduction of the scintillation photon creation process induced a peak broadening effect in the simulated spectra, as we incorporated statistical fluctuations of information carriers in the photon creation process. In Fig. 6B, red spectrum represents the number distribution of scintillation photons initially created at the scintillation site, and blue spectrum represents the number distribution of scintillation photons arriving at PMT. The location of peak centroids in the red spectrum coincides with the associated original peak location if one converts the peak energy into respective average number of scintillation photons according to the light yield, and the overall spectrum squeezes to lower channels while internal features of the spectrum are blurred even more as we introduce the simulation of scintillation photon transport inside the scintillator. Some peaks start to overlap, as one can also observe the overlapping between 1,086 keV and 1,112 keV peaks, for example, in the measured energy spectrum. The spectra compress even more to lower channels with a decrease of the reflectivity; however, the variation of reflectivity did not provoke any noticeable change in overall shapes of the spectra for identifying specific features in it.
1) Absolute peak efficiency
The absolute peak efficiency calculated from the MCNP6.1 simulation result considering the transport of gamma rays only, exhibited 24.6% higher values in average than that from the measurement result. For example, the absolute peak efficiency was calculated to be 4.04×10−4 and 2.04×10−4 for 662 keV and 1,332 keV photons when only gamma-ray transport was considered in MCNP6.1, whereas the measurement values were 3.26×10−4 and 1.66×10−4, respectively. The values decreased to 3.97×10−4 and 1.98×10−4 when the transport of both gamma rays and electrons was considered, and the overall difference decreased to 21.2% (3.4%p lower) in average, due to the partial energy deposition effect by the primary electrons as aforementioned. In GEANT4 simulations, gamma-only results were calculated to be 13.6% higher than measurements, and introduction of electron transport reduced the difference to 7.9% (5.7%p lower) in average. Absolute peak efficiency curves calculated by both Monte Carlo codes, in comparison with experimental results, are shown in Fig. 7. It was confirmed that consideration of the electron transport would make differences in the calculation of the detector response by the Monte Carlo simulation. The difference between gamma-only and electron transport results tend to become more significant in relatively higher energies, and this also buttresses the phenomena of the partial energy deposition by primary electrons.
On the contrary, consideration of the scintillation photon transport in the simulation did not make an impact on the absolute peak efficiency. It can be intuitively inferred that the peak efficiency would be primarily determined by the number of full-energy absorption events from the gamma-ray interaction with the scintillator and would not be altered for the same measurement configuration. The optical behavior of scintillation photons within a scintillator influences the light collection efficiency and, thus, may cause a discernible impact on the peak efficiency in practice, as an unaccountable irregular loss mechanism of scintillation photons may lead to the overall loss of the detector signals of nominal amplitudes. However, a rigorous consideration on the complex non-linear dynamics of optical photons in the scintillator would be technically challenging and excessive in the scope of the detector response calculation by the Monte Carlo simulation.
2) Energy resolution
Optical behavior of scintillation photons is expected to make a more discernible effect on the energy resolution of the spectrum. Loss of information carriers, i.e., scintillation photons, in the signal formation process will deteriorate the statistics of the final information carrier and lead to poor energy resolution. Adjacent peaks in complex energy spectra may overlap with each other and cause distortion of the spectral shape, which will further complicate the analysis of the spectra. As shown in the example presented in Fig. 6D, energy peaks at 1,086 keV and 1,112 keV overlap in the measured spectrum, whereas two peaks appear to be resolved in the simulated spectra shown in Fig. 6A and 6B until we involved the scintillation photon transport in the simulation. The full-energy deposition probability distribution and the light collection efficiency from each voxel of the scintillator are combined to affect the energy resolution of the simulated spectra. Two peaks started to completely overlap as we applied the limited light collection condition for the simulation inside the scintillator, and the energy resolution of the peaks became comparable to the measured spectra with application of typical reflectivity conditions (~90%) for the scintillator [14–16].
Energy resolution values of various peaks in the simulated and measured spectra of 152Eu are shown in Fig. 8. This result illustrates the combined effect of: (1) creation of scintillation photons according to the energy deposition by the energy loss of the primary electron, and (2) the transport of scintillation photons inside the scintillator crystal. Statistical uncertainties associated with the scintillation process and light collection process were considered as described in the Materials and Methods section. The impact of uncertainty will become more significant if practical concerns such as complex non-linear dynamics of optical photons in scintillators are considered. Literature indicates that quantitative measures related to the defect density within the crystal significantly affect scintillator performance. For example, NaI(Tl) grown using the Bridgman method improved its energy resolution from 7% to 5.4% at 662 keV, while CsI(Tl) exhibited approximately twice the photon yield compared to standard materials, resulting in increased peak emission intensity and enhanced light collection efficiency [17].
In this work, the energy resolution appeared closest to the measured results when the reflector’s reflectivity was assumed to be 93%. This implies that overall effects that were not rigorously accounted for, in the simulation of light collection process, could be combined and assumed to be in an equivalent condition assuming 93% reflectance at the scintillator boundary in this work. Recent review studies have emphasized that detailed optical-transport modeling in scintillation detectors requires a large number of surface- and interface-related parameters, including microscopic surface roughness, air gaps, and optical coupling conditions, many of which are often unavailable for commercial, fully assembled detectors [10, 11]. These studies also point out that introducing an excessive number of free parameters without sufficient experimental constraints can reduce the physical interpretability of simulation results.
In this context, the present study was not intended to optimize or validate a high-fidelity optical surface model, but rather to quantify the relative impact of secondary particle transport, namely recoil electrons and scintillation photons, on the detector spectral response. Accordingly, a simplified and internally consistent optical model was deliberately employed. The fitted reflector reflectivity of approximately 93% should therefore be interpreted as an effective reflectivity that incorporates unmodeled optical losses, rather than as the intrinsic reflectance of the reflector material alone. While this simplification inevitably contributes to residual discrepancies in morphology between simulated and measured spectra, it does not undermine the physical trends observed in peak efficiency and energy resolution within the scope of the present study. Incomplete deposition of full energy due to the escaping electrons at boundaries and loss of scintillation photons in the light collection process will shift nominally full-energy deposition events to lower energy channels, which can become another small factor that accounts for the discrepancy between peak efficiencies by simulation and measurements in practice.
Conclusion
This study compared the simulated gamma-ray response of the CLYC scintillation detector using Monte Carlo codes, MCNP6.1 and GEANT4, with measured values. Consideration of the transport of electrons and scintillation photons inside the scintillator is anticipated to make an impact on the simulated detector responses mainly in two aspects: peak efficiency and energy resolution. The absolute peak efficiency derived as a result of the simulation considering electron transport was analyzed to be about 3.4%p (MCNP6.1) and 5.7%p (GEANT4) lower than the absolute peak efficiency of the simulation that did not consider electron transport. In addition, it was confirmed that the probability of total energy deposition in the micro-volume located on the outer wall of the scintillator was calculated to be lower, if one considers the full-energy absorption events by electron transport, compared to the result of simulation that did not consider electron transport. This indicates that gamma rays are not always destined to deposit their entire energy to the detector when the photoelectric effect occurs. GEANT4 results showed lower values than MCNP6.1 results, and it is speculated to be because of the physical library difference between the two codes. The escaping effect of primary electron from the radiation detector can be an important issue in the fabrication and characterization of a thin-film-based radiation detector responding to gamma rays [18–20]. In particular, X-ray escape peaks make substantial impact as the detector thickness becomes thinner. In the study of nanoparticle-based radiation detector development and their characterization, a notable contribution by X-ray escape peaks in the gamma-ray spectrum obtained was reported [20]. The same argument can be also applied to the discussion of microdosimetry.
In the result of the simulation considering the transport of scintillation photons, the peak efficiency was hardly altered by including the scintillation photon transport, but slightly by varying reflectivity conditions. More significantly, light collection performance makes a considerable impact on the energy resolution of the gamma-ray spectrum. Loss of information carriers can lead to the distortion of photopeaks making it harder to resolve adjacent peaks in spectral analysis. All in all, Monte Carlo simulations for the detector response considering the transport of secondary particles produced results that showed rather similar trend than those without consideration, accounting for a few realistic behaviors of scintillation detector.
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