Signal pulse emulation for scintillation detectors using Geant4 Monte Carlo with light tracking simulation Open Access

In radiation measurements the signal pulse generated from a radiation detector is the most fundamental information of incident radiation. Signal pulses are sent to signal processing devices (i.e., discriminator or multi-channel analyzer) with a measurement objective. Particularly, the signal pulse shape is important for pulse shape discrimination (PSD) analysis which aims to improve the measurement accuracy such as energy resolution¹ or background rejection using particle identification.^2,3 The difference in emission properties of scintillation fluorescence caused by an incident particle type could be detected by PSD analysis.^3–7 Similarly, gamma-neutron discrimination by a zero crossing time method is a well-known technique using an organic scintillator in a mixed radiation field.^4,5 Other PSD techniques (i.e., charge comparison method^6,7 or peak-to-charge discrimination (PQD) method with LaBr₃:Ce scintillator⁸) have also been developed for precise signal separation using various scintillators. Recently, PSD analysis has been applied for a depth-of-interaction (DOI) detector in a small positron emission tomography (PET) device aiming at the improvement of image quality.⁹ The DOI detector consists of a multi-layered scintillator with different scintillation properties.^10,11 Moreover, a phoswich (phosphor sandwich) detector which consists of a few scintillators identifies an incident particle type by PSD analysis in a common readout,¹² and applies a background rejection method using anti-Compton analysis.¹³ To evaluate the PSD performance with various detectors, it is essential that the pulse emulation reproduces the exact measured pulse. To the best of our knowledge, the emulation techniques for PMT anode pulse with high accuracy have not yet been developed, since the anode pulse consists of quite complex components.

Scintillation light pulses are generally converted to electric pulses using a photo-electric converter (i.e., photomultiplier tube (PMT) or photodiode). The scintillation light is transported to a PMT photocathode surface from an emission point through a process of complex reflection and refraction in the scintillation crystal and a reflector.¹⁴ The decay curve of the emission and arriving time distribution at the PMT photocathode are different, since a time deviation is added to the emission decay curve in the transport process. The time deviation is considered to be a very complex quantity because it depends on the crystal structure, surface condition, and optical properties of the scintillator. Additionally, the electron transit time spread increases during electron amplification in the PMT.¹⁵ As a result, the PMT anode pulse is spread in the time domain in comparison with the arriving time distribution at the PMT photocathode. A circuit constant of HV divider equipped with the PMT also affects the PMT anode pulse shape. Thus, the arriving time distribution at the PMT photocathode and the PMT response function is required to reproduce the exact measured pulse.

In the present method, in order to achieve the arriving time distribution at the PMT photocathode, the scintillation process and optical photon transport were calculated using the Geant4 Monte Carlo code.^16,17 To simulate the optical photon transport calculation in Geant4, a material surface model was implemented known as DETECT2000.¹⁸ 

In this study, the accuracy of pulse reproducibility was evaluated using pulses of GSO:Ce (0.4, 1.0, 1.5 mol%), LaBr₃:Ce, and BGO scintillators equipped with a R6231-100 PMT. We report the procedure of the proposed pulse emulation technique and its accuracy.

Figure 1 shows the present method based on the Geant4.9.5 Monte Carlo simulation and the measurement of the PMT response function. To obtain the arriving time distribution at the PMT photocathode, a scintillation process and an optical photon transport were calculated using the Geant4 Monte Carlo code. The PMT response function was measured using a BC408 organic scintillator which has fast scintillation properties. The simulated pulse was obtained by a convolution integral of the PMT photocathode arriving time and the PMT response function.

In the present method, an anode pulse of the PMT (R6231-100, Hamamatsu Photonics) equipped with a divider circuit (E1198-26 MOD, Hamamatsu Photonics) was measured directly using a digital oscilloscope (WaveRunner 64xi, LeCroy, 5 GS/s, band width 600 MHz).⁸ This helps to avoid signal distortion from electric devices such as a shaping amplifier. This system was used for the measurement of the PMT response function and for the accuracy assessment of the present method as well.

In this study, five different scintillators, GSO:Ce (Gd₂SiO₅, Ce 0.4, 1.5, 1.0 mol%, Hitachi Chemical/OXIDE), LaBr₃:Ce (Ce 5.0 mol%, B308, BrilLanCe^TM, Saint-Gobain), and BGO (Bi₄Ge₅O₁₂, Saint-Gobain) were used for the evaluation of pulse reproduction accuracy. Additionally, the BC408 organic scintillator (Saint-Gobain) was used for the measurement of the PMT response function. Published scintillation properties for these scintillators are listed in Table I.^18–25 As shown in Figure 2, the structure of the GSO:Ce scintillators is Φ 0.9″ × 1.0″ (Ce 0.4 mol%), 2.5 × 2.5 × 25 mm³ (Ce 1.0 mol%), and Φ12 mm × 12 mm (Ce 1.5 mol%). The LaBr₃:Ce scintillator is a cylinder shape of Φ1.5″ × 1.5″, BGO and BC408 scintillators are rectangle shape of 12 × 14 × 2 mm³ and 20 × 20 × 1 mm³, respectively. The widest flat face of the scintillators was connected to the PMT photocathode using optical grease (BC630, Saint-Gobain). These scintillators were wrapped with PTFE reflector tape (BC642, Saint-Gobain) except the face connected to the PMT photocathode.

In the current work, both the scintillation process and Cerenkov process were included. Cerenkov photons produced in each wavelength were obtained by the theoretical formula which is a function of refractive index of the material and charged particle energy. Scintillation properties of GSO:Ce (Ce 0.4, 1.0, 1.5 mol%),^18–20 LaBr₃:Ce,^21–23 and BGO^24,25 scintillators were reproduced from published data. The envelope function with f(t) = exp(−t/τ_D) and g(t) = (1 − exp(−t/τ_R)) (τ_D and τ_R are decay and rise time constant, respectively) was used for the emission decay curve in the Geant4.9.5 Monte Carlo code. In this simulation, an optical surface model between the scintillator and reflector was ground back painted with specular lobe coefficient 1.0, since this model is recommended for the exact reproducibility of the real surface.¹⁷ Additionally, the quantum efficiency of the PMT photocathode surface was included as a nominal value. Photons were generated by irradiation from an external ¹³⁷Cs gamma-ray source. We calculated time profiles of the scintillation emission and the arriving time at the PMT photocathode using GSO:Ce (Ce 0.4, 1.0, 1.5 mol%), LaBr₃:Ce, and BGO scintillators. For the convolution of the PMT response function, the sampling rate of the arriving time at the PMT photocathode was calculated with 2.5 ns. For the accuracy assessment of the simulated pulse, average pulses of 100 simulation data were used.

The PMT response function is difficult to estimate by simulation because of the complex behavior of transit electrons in a PMT which directly affects the PMT response function. Generally, to obtain the PMT response function, a PMT photocathode is irradiated directly with a fast pulsed laser.¹⁵ Instead of a fast pulsed laser, a BC408 organic scintillator was used to obtain the PMT response function with a ¹³⁷Cs gamma-ray source (235.4 kBq). BC408 has fast scintillation properties with 2.5 ns pulse width. The luminous time of BC408 was assumed to be a 2.5 ns square pulse. The PMT anode pulse of the BC408 scintillator could therefore be assumed to be the PMT response function. The PMT response function was obtained from the average of 100 pulses using events of the same energy deposition. However, the PMT response function measured by the oscilloscope had a sampling rate of 0.2 ns (5 GS/s); thus, the sampling rate of the PMT response function was converted to 2.5 ns from 0.2 ns using a cubic spline interpolation for the convolution integral.

We obtained two response functions with supplied voltages of 1000 V and 1300 V. GSO:Ce (Ce 0.4, 1.5, 1.0 mol%) and LaBr₃:Ce scintillators were used at 1000 V and BGO scintillator at 1300 V. In the case of BGO and GSO:Ce scintillators, the PMT and divider circuit were shared with the measurements of the PMT response function. However, the PMT and divider circuit of the LaBr₃:Ce scintillator were different with the same type of material because the crystal and PMT could not be separated in combined products.

To obtain a simulated pulse, the PMT response functions were convoluted to the arriving time distribution at the PMT photocathode as shown in Fig. 1. To estimate the difference between the measured and the simulated pulse, the sampling rate of the simulated pulse was converted to 0.2 ns from 2.5 ns using a cubic spline interpolation.

The supplied PMT voltage was adjusted to 1000 V for the GSO:Ce and LaBr₃:Ce scintillators, and 1300 V for the BGO scintillator to obtain sufficient signal while avoiding signal saturation. The pulse signals from the scintillators were measured with the oscilloscope with an external ¹³⁷Cs radiation source (235.4 kBq). The energy spectrum was obtained by integrating the pulse signal, which is equivalent to signal charge, using an in-house code. For the analysis, we averaged 100 pulses at 662 keV total absorption peak.

We quantified the accuracy of reproducibility for the simulated signal pulse as a percentage root mean square (RMS) of the difference between the measured and the simulated pulse within a range of measured pulse intensity >10% of the peak value. However, the percentage RMS value depends significantly on the normalized point in the time domain; therefore, we optimized the normalized point in order to obtain the minimum percentage RMS value. Additionally, we compared the integrated charge of the measured and the simulated pulse for the accuracy assessment.

Figures 3(a.1,2)–3(e.1,2) shows the time profile of the emission decay curve and the PMT photocathode arriving time calculated by Geant4 Monte Carlo simulation using GSO:Ce (0.4, 1.0, 1.5 mol%), LaBr₃:Ce, and BGO scintillators. The sampling rate of Figs. 3(a.2)–3(e.2) was calculated to be 0.2 ns in order to maximize the rising edge of the pulses. The contribution of the photons produced by the Cerenkov process was less than 1% in all scintillators. It is difficult to differentiate between the emission decay curve and the arriving time at the PMT photocathode using small crystal structures such as GSO:Ce 1.0 mol% and BGO scintillators. We found the maximum difference using the LaBr₃:Ce scintillator which was the largest structure in this study.

The signal deviation was determined by the photon yield with intensity ratio of fast and slow components in the simulation. Therefore, the signal deviation of the LaBr₃:Ce scintillator which has a large photon yield was obtained with much lower value than the other scintillators. A large deviation of GSO:Ce (Ce 0.4, 1.0, 1.5 mol%) in a range of >200 ns was due to a lower photon yield caused by the 10% slow component.

The response functions of R6231-100 PMT with supplied voltages of 1000 V and 1300 V were obtained by using a BC408 scintillator with external ¹³⁷Cs radiation source as shown in Figure 4. The pulse shape normalized with a peak value was unchanged in the energy spectrum using constant supplied voltage. Figure 4 shows that the PMT response function of 1000 V spread slightly more than that of 1300 V, since the electron transit time spread in the PMT is in inverse relation with the supplied voltage.¹⁵ 

Figures 5-7(a) show the energy spectra obtained by the integrated charge of pulses acquired with the oscilloscope using GSO:Ce (0.4, 1.0, 1.5 mol%), LaBr₃:Ce, and BGO scintillators. The peak to Compton ratio of energy spectrum depends on the crystal structure, its density, and energy resolution. A lower threshold level of these spectra was determined by a rising edge trigger level of the oscilloscope. Energy resolution estimated by a fitting analysis with a gauss function was 10.8%, 14.1%, 9.79% (GSO:Ce 0.4, 1.0, 1.5 mol%), 3.36% (LaBr₃:Ce), and 13.1% (BGO) using full width at half-maximum (FWHM) at total absorption peak (662 keV). The comparison between the measured and the simulated pulses of GSO:Ce (0.4, 1.0, 1.5 mol%), LaBr₃:Ce, and BGO scintillators with the optimization of a normalized point in a time domain are shown in Figures 5(a)-5(c), Figures 6(b) and 7(b), respectively. The accuracy of the pulse reproducibility was assessed by the percentage RMS value of difference between measured and simulated pulse as shown in Table II. The difference in the integrated charge is also summarized in Table II.

Scintillation properties of a GSO:Ce scintillator depend on a dopant concentration as shown in Figs. 5(b)-5(d). The percentage RMS value for the GSO:Ce (0.4, 1.0, 1.5 mol%) scintillators were 3.60%, 2.60%, 10.6% and the difference in the integrated charge wsa 4.93%, 3.37%, 16.75%, respectively. The simulated pulses for the GSO:Ce 0.4, 1.0 mol% scintillators were reproduced almost the same as the measured pulse except for the range of 120-300 ns. However, the simulated pulse shape of the GSO:Ce 1.5 mol% scintillator shows relatively large difference from the measured pulse as shown in Fig. 5(d). The difference in the integrated charge and the percentage RMS value indicate a similar tendency as shown in Table II.

The LaBr₃:Ce scintillator performed with excellent energy resolution and fast signal response as shown in Figs. 6(a) and 6(b). Moreover, we obtained the highest accuracy of pulse reproducibility, the percentage RMS value of 2.41%, and a difference in integrated charge of −2.09% as shown in Table II. Even though the PMT and the divider circuit of the LaBr₃:Ce scintillator were different from the device of the PMT response function measurement, a high accuracy of pulse reproducibility was achieved.

A percentage RMS value of 4.75% and a difference in the integrated charge of 4.25% were obtained using the BGO scintillator as shown in Table II. A difference between the measured and the simulated pulse was observed in the signal rise region (Fig. 7(b)). On the other hand, the simulated pulse shape of the signal decay region reproduced the exact measured pulse.

Fig. 5(d) shows that sufficient accuracy of pulse reproduction was not achieved using the GSO:Ce 1.5 mol% scintillator. Similarly, Figs. 5(b) and 5(c) indicate a slight difference between the measured and the simulated pulse using GSO:Ce 0.4, 1.0 mol% scintillators. This suggests that the preset scintillation properties were not precise in the Geant4 Monte Carlo simulation, since the Ce concentration, which determines the scintillation properties, depends on the fraction of melt solidification in the crystal ingot grown by the Czochralski technique.^26,27 Moreover, the gradient of the Ce concentration in the crystal ingot increases with the amount of CeO₂ in the starting material.²⁸ Therefore, we tried to estimate the scintillation properties of GSO:Ce (0.4, 1.0, 1.5 mol%) scintillators for the exact measured pulse reproduction. The estimated parameters using GSO:Ce scintillators improved the accuracy of pulse reproduction as shown in Figures 8(a)-8(c) and Table II. It seems that the GSO:Ce scintillators used in the present method have a higher Ce concentration than the nominal value, since the decay time constant and Ce concentration are in inverse relation. For the present pulse emulation method using scintillators grown by the Czochralski technique, it is recommended to use precise scintillation properties obtained by measurements rather than the nominal value.

To improve the pulse reproducibility of LaBr₃:Ce scintillators, we estimated a suitable decay time constant as shown in Table II. As a result, the difference in the integrated charge of simulated pulse with estimated time constant is quite smaller than the simulated pulse with nominal time constant. The sufficient accuracy of pulse reproducibility using the LaBr₃:Ce scintillator was obtained with a nominal decay constant, but it was also possible to improve the pulse reproducibility with an estimated decay constant.

According to previous research, light collection time due to the scintillator volume might affect the rise time.²⁴ Moreover, the scintillation time properties of the BGO scintillator strongly depend on the temperature.²⁹ Thus, the time constant of the BGO scintillator is estimated to reproduce the exact measured pulse. The estimated parameters of the BGO scintillator which reproduced accurately the measured pulse are shown in Fig. 8(d) and Table II.

Precise emission decay curves for the GSO:Ce and BGO scintillators are more difficult to reproduce than for the LaBr₃:Ce scintillator, since the scintillation time properties of the GSO:Ce and BGO scintillators have two major decay constants. Moreover the properties vary due to several reasons. However, high accuracy pulse reproduction with the nominal scintillation properties was obtained except for the crystals with large dopant concentrations such as the GSO:Ce 1.5 mol%.

In the present method, the PMT response function was obtained using a BC408 organic scintillator which is assumed to have a square pulse of 2.5 ns. However, the luminous time structure of BC408 is actually based on its scintillation properties. It is considered that the accuracy of pulse reproducibility is reduced by the luminous time structure of the BC408 scintillator. Particularly, the accuracy reduction occurred in the case of a scintillator with fast time properties such as an organic scintillator in the present method. However, the simulated pulse of the LaBr₃:Ce scintillator, which has a short decay time constant of 16 ns in inorganic scintillators, reproduced the exact measured pulse as shown in Fig. 6(b). This means that the measurement of the PMT response function using the BC408 scintillator can be applied to the present pulse simulation of various inorganic scintillators.

The present method can be applied to a simulation study of radiation measurements using a scintillator equipped with a PMT, particularly for the estimation of an optimized scintillator and performance evaluation for PSD analysis. Moreover, a simulation of a subsequent circuit of a PMT can be achieved by combining a SPICE simulation and the current method. Recently, development of an avalanche photodiode (APD) has been considered as a subsequent device coupled with a scintillator. In the future, we are planning to investigate the accuracy of pulse reproducibility with an APD device using the present simulation method.

We have developed a novel emulation method for a PMT anode pulse with sufficient accuracy. The accuracy of pulse reproducibility was demonstrated by using various scintillators. The authors believe that the present method will be used as one of the standard techniques for a simulation study using a scintillator equipped with a PMT.

The authors would like to express deep gratitude to Hitachi Chemical/OXIDE for providing GSO:Ce (0.4, 1.5 mol%) scintillators for long time, and gratefully acknowledge the Graduate School of Health Science, Hokkaido University for facilitating experiment facilities and external radiation sources.