2.1 Model Description

The Geant4.10.00.p02 version is used to build the model. The planar detector geometry has been constructed using Geometry Category of Geant4. Geometry, as shown in Fig. 1(a), consists of a converter layer of HDPE (density 0.94 g/cm³) with 1 cm x 1 cm front face (XY-plane) and thickness (Z-axis) is varied from one micrometer to few millimeters in order to optimize the thickness of converter layer. Here optimized thickness represents the thickness at which the detector efficiency is maximum. In other words, the thickness at which, maximum number of recoil protons will punch through the converter layer into the SiC semiconductor region to generate a detectable signal. Adjacent to converter is a detector layer made up of SiC with similar XY-plane and thickness is kept at 600 μmm as shown in Fig. 1(b). General Particle Source (GPS), class of particle category has been utilized to generate a spectrum of the ²⁴¹Am-Be neutron source taken from Table 3 of ISO Report 8529-1^[20]. It is positioned at 1 cm distance from the converter face. In practical applications, neutron will not be generated in parallel beams rather fall in random directions on the detector. But in order to achieve maximum efficiency, source is set such that neutrons will impinge perpendicularly and uniformly on the front face of the converter layer (in direction of Z-axis) as illustrated in Fig. 1(b). Standard physics model QGSP_BERT_HP has been used which employs high precision neutron model used for neutron below 20 MeV^[21].

Fig. 1(a)Full-screen View

Visualization of Geant4 simulation of SiC detector with HDPE converter layer. Outer volume is mandatory mother volume; inside is detector geometry and yellow line (online version) shows a trajectory of neutrons passing through detector (b) planar diode detector schematic comprising of HDPE converter and SiC detector volume (c) stacked detector

In order to optimize the converter thickness, five iterations of 10⁹ neutrons have been simulated for different monoenergetic as well as ²⁴¹Am-Be neutron source. This special case of ²⁴¹Am-Be neutron source has been chosen to facilitate the lab-scale experiment of the detector with standard neutron source. Furthermore, five iterations would help in better convergence of results. After determining the optimum thickness, 10⁹ neutrons have been fired to illustrate the energy deposition by recoil protons, other charged particles in converter and detector.

Furthermore, the number of converters and detectors has been increased to implement the stacked detector configuration as depicted in Fig. 1(c), and enhancement in efficiency was estimated. Simulations were performed in GNU HPC clusters and all physics processes were kept on so as to reflect the best practical situation. Dead layer and temperature effect was not considered in this work. It should be noted that these effects would further degrade the detection efficiency.

3.1 Nuclear Interactions in HDPE converter

To determine the reactions that are taking place in converter, a simulation was performed with 1 cm thick HDPE structure. It was irradiated by 10⁶ neutrons of ²⁴¹Am-Be neutron source. List of nuclear reactions along with the reaction Q-value is tabulated in Table 1.

Table 1 represents the reactions which are happening in HDPE material upon interaction with the incident neutrons. It is evident that neutron reaction with hydrogen i.e., (n, p) reaction is dominating (~72 %), which is elastic scattering in nature. This is because, for fast neutrons, elastic scattering cross-section is higher than other reaction cross-sections. In addition to this, neutrons will also undergo elastic scattering reaction with Carbon nuclei, which is the next reaction in terms of dominance (~26 %). Other than these reactions, neutron will also undergo several inelastic scattering reactions with Carbon and hydrogen nuclei [¹²C(n, n')¹²C; ¹²C(n, n')¹³C; ¹H(n, n')²H ] and a very few (n, α) reactions [¹²C(n, α)⁹Be; ¹³C(n, α)¹⁰Be] due to very low cross-section. Some reactions have negative Q-value which shows these reactions will occur only when the incident neutrons will have energy equal to or greater than the threshold energy.

Table 2 shows the list of particles generated due to neutron interaction with HDPE along with their mean kinetic energy and range of the kinetic energies at the time of their production.

3.2 Nuclear Interactions in SiC detector

Similar approach was adopted for simulating the nuclear interactions in SiC material. List of nuclear reactions along with the reaction Q-value is tabulated in Table 3.

From Table 3, it is evident that the elastic scattering reaction with Carbon and Silicon nuclei is dominant with ~ 39 % and ~ 41 % reactions respectively in SiC, followed by inelastic scattering reaction with Si nuclei and other threshold reactions resulting in αa-particles, Mg, Al, Be... as a reaction products. The dominant reaction products produced in SiC have lower energy range (Table 4) than the products generated in HDPE (Table 2). Therefore, an energetic reaction product generated in HDPE converter and transported to SiC, would deposit higher energy in SiC in comparison to the products generated in SiC itself, provided, the thickness of converter is optimized. Thereby, a HDPE converter layer over SiC detector will result in a better detection efficiency and detectable signal. Franceschini et al.^[22], have also reported a better detection efficiency in the presence of converter layer over SiC detector.

In Table 4, one can see that significant number of γg-rays is also generating due to various inelastic scatterings and other reactions. Also, neutron fields are generally accompanied with γg-background. These, γg-rays can undergo photoelectric, Compton interactions with atomic electrons and it can also be converted into an electron-positron pair, but it would hardly affect the operation of the SiC detector as it has been reported that change in SiC-based detector response is negligible even after 22.7 MGy exposure to γg-rays^[23].

3.3 Optimization of HDPE converter thickness for wide energy range of neutrons

The recoil proton generated in converter will tend to lose its energy continuously along the path, which limits its range in the material. Figure 2(a) shows the range of proton in HDPE and SiC computed using SRIM^[24]. It is evident that 1 MeV proton can traverse up to 20 μmm while 10 MeV proton can travel up to 1200 μmm. In spite of the fact that having a HDPE converter of around 9 cm will result in approximately 99 % neutron interactions^[10], we could not employ a converter of such thickness because most of the recoil protons will be stopped in converter itself, before reaching the SiC detector volume. Thus, Geant4 simulation has been performed to optimize the HDPE converter thickness for different neutron energies ranging from 0.5 MeV to 10 MeV and a special case of ²⁴¹Am-Be neutron source spectrum as shown in Fig. 2(b). The optimized thickness is the thickness at which the maximum number of recoil protons is detected. It is assumed that each recoil proton, reaching the detector with sufficient energy, will give a detectable signal i.e. proton detection efficiency is 100 %. 10⁹ neutron events have been simulated 5 times to determine the detector's absolute efficiency i.e. number of recoil protons reaching SiC detector volume divided by total incident neutrons^[25].

Fig. 2(a)Full-screen View

Range of protons in HDPE and SiC computed using SRIM (b) Spectrum of ²⁴¹Am-Be neutron source generated using Geant4

Figure 3(a) depicts the detector efficiency for different energy neutrons and different converter thicknesses. It could be observed that after a certain thickness of converter, efficiency is decreasing. This is due to the self-absorption of proton energy in converter itself. This self-absorption limits the efficiency of planar detector. Since, neutrons of different energies, provide maximum efficiency for different thickness, there is a need to select a thickness which could be efficient for a specific energy range that is 0.5-11 MeV in the context of this work. Therefore, in order to accommodate a wide energy range of neutrons, we have considered 400 μmm thickness as an optimized one in this work.

Fig. 3(a)Full-screen View

Optimization of converter thickness for different energy neutron (b) Detector efficiency as a function of HDPE converter thickness for ²⁴¹Am-Be neutron source. (Inset: Zoomed view of plot from origin to 1000 μmm thickness) (c) Efficiency of neutron detector with 400 μmm thick HDPE converter for different monoenergetic neutron sources

From Fig. 3(a), the optimized HDPE converter thickness for different monoenergetic neutron source can also be chosen. For e.g. a thickness of 100 μmm can be selected as an optimized thickness for a 2.5 MeV D-T neutron source. Similarly, for an application which requires 10 MeV neutrons to be detected, a converter layer of ~ 1.1 mm should be considered as an optimum one. Further, a special case has been taken to optimize the HDPE thickness for ²⁴¹Am-Be neutron source and illustrated in Fig. 3(b). It is apparent that for thicknesses of HDPE converter ranging from 400 μmm to 1000 μmm, the detector will provide maximum efficiency of 0.112% to 0.117%.

Thus, we can say that for the thickness of 400 μmm to 1000 μmm, detector efficiency is approximately constant. It should be noted that there are relatively few neutrons significantly higher than 6 MeV in the ²⁴¹Am-Be spectrum. Also, larger thickness would restrict the number of recoil protons reaching the detector. Thus, to cover the wide range of specified source spectrum a 400 μmm thickness could be regarded as the optimum thickness, which is well in agreement with the optimum result for the 6 MeV monoenergetic neutron source obtained in Fig. 3(a). The efficiency of neutron detector with 400 μmm thick HDPE converter with respect to different monoenergetic neutron source is illustrated in Fig. 3(c). It can be observed that with 400 μmm thick HDPE converter, maximum efficiency of ~ 0.18 % can be achieved for up to 7 MeV monoenergetic neutron source. For neutron energies higher than 7 MeV, efficiency is decreasing since the optimized value of HDPE thickness is higher than 400 μmm, for high energy neutron sources as shown in Fig. 3(a).

3.4 Calculation of optimum thickness of SiC for ²⁴¹AmBe neutron source

For ²⁴¹Am-Be neutron source, maximum recoil energy of proton that can be generated in HDPE is 10.726 MeV (Table 2). The range of proton in SiC is computed using SRIM code and it is found to be approximately 571 μmm for proton of energy 11 MeV (Fig. 2a). Thus, to allow the maximum recoil proton to deposit all of its energy in detector volume, the thickness of the SiC detector active volume is chosen to be 600 μmm.

3.5 Simulation of SiC detector in mixed neutron-gamma field

The primary concern of neutron detector in a mixed neutron-gamma field, is the inability of the detector to accurately discriminate between the two. Also, a significant number of γgγ-rays are being generated along with the other charged particles in SiC as well as in HDPE converter. Therefore, to analyze the effect of gamma background over neutron detection, a simulation was performed with gamma and neutron source of energies ranging from 100 keV to 10 MeV with 10⁹ particles. Figure 4(a) represents the comparison of their energy deposition in SiC detector. Gammas would generally undergo photoelectric effect at low energy region while Compton scattering and pair production at high energy region. Pair production reaction generally occurs when the incident gamma energy is greater than 1.02 MeV. On the other hand, neutron induced events are mainly due to energy deposited by recoil protons generated in converter layer. It is evident that such a heavy gamma background signals would be comparable to neutron signals below 1 MeV range. Between 1 MeV to 2 MeV, there would be gamma effect on neutron signals which could be easily distinguishable and can be discriminated with the pulse height spectrum or by applying Low Level Discriminator (LLD). Beyond 3 MeV there is a very minimal effect of gamma events which could be neglected in case of fast neutrons.

Fig. 4(a)Full-screen View

Comparison of energy deposit due to Neutron and Gamma events in SiC (b) Effect of LLD on SiC detector efficiency

Figure 4(b) shows the effect of LLD on detector efficiency. As can be seen, simply increasing the LLD to higher values can limit the background radiation, as from γgγ-rays and other charged particles, but at the same time some proton recoil events will inevitably be discriminated, because the proton recoil energy distribution extends all the way to zero. Therefore, the detector with a finite discrimination level will always have a slightly lower efficiency.

The efficiency achieved with this proton recoil detector is very small. However, for a reliable and consistent monitoring, this kind of detector efficiency is often regarded as unacceptably low. Therefore, to enhance the efficiency of the detector, with major characteristics unaffected, a special configuration consisting several layers of converters and active SiC layers (stacked configuration), as shown in Fig. 1(c), has been considered and assessed.

3.6 Stacked Detector simulation

Converter and detector volume is regarded as a single layer and by using the G4Replica Class of Geant4 it is replicated in order to generate stacked structure as shown in Fig. 1(c). The optimum value of thickness is used for converter and detector i.e. 400 μmm for HDPE and 600 μmm for SiC. Simulations have been performed for 10⁹ neutron events and up to 10 layers. Efficiency, as defined previously, is estimated by increasing the number of layers in the stack. From Fig. 5(a), it is apparent that as we increase the number of stacks, efficiency will also increase but not linearly. As we increase the number of layers from 1 to 2, the increment in efficiency is almost double i.e. 99.33 % increment. Further, from 2^nd layer to 3^rd layer increment is ~ 99 % of the first increment. From 3^rd to 4^th layer increment is ~ 98.22 % of the first increment. Similarly, from 9^th layer to 10^th layer increment is ~ 90.49 % of the first increment. Thus, it appears that adding the 10^th layer is approximately the same increase in total detection as adding the 2^nd layer. Further addition of 50^th layer offers only ~ 48 % increment in efficiency to what we achieved by adding 2^nd layer. It shows that after a certain number of layers efficiency will saturate. This is due to the fact that probability of interaction for neutron with HDPE will saturate at certain thickness^[10]. Also, each HDPE layer will attenuate some fraction of incident neutron flux thereby decreasing the incident flux for subsequent converter layers. D.S. McGregor et al. have shown a similar effect in the case of thermal neutron detector with ¹⁰B and LiF converters^[26]. Thus, we can achieve efficiency of up to 1.04 % with 10 layers of stacked detector. Furthermore, the thickness of converter was varied for 5, 10, 15, 20 and 50 stacks and the maximum efficiency of ~ 3.85 % could be achieved at the converter thickness of around 400 μmm. Efficiency for different stacked numbers with respect to converter thickness is represented in Fig. 5(b).

Fig. 5(a)Full-screen View

Increment in Efficiency of SiC based detector with layers in stack. Percentage increment in efficiency upon increasing the number of layers (b) Efficiency variation with respect to converter thickness for stacked detector with 5, 10, 15, 20 and 50 stacks

Altering the thickness of converter of different layers may help in further enhancing the efficiency, but it is the subject of further detailed study by changing the thicknesses of different layers.

3.7 Calculation of Energy Deposition

A data analysis framework has been integrated with Geant4 in order to illustrate the contribution of recoil protons, alpha particles and other charged particles in SiC detector. Figure 6{(a), (b), (c) & (d)} represents the histograms of the total energy deposited, energy deposited by the recoil protons generated in HDPE converter, energy deposited by alpha particles and energy deposited by other charged reaction products in SiC detector volume respectively. A LDD of 2 MeV would significantly discriminate the signals due to other charged particles while signals due to αa-particles above 2 MeV might provide spurious counts. Furthermore, a discrimination strategy may have to be adopted based on rise time or amplitude to avoid spurious signals. One must find a suitable balance between LLD setting and detector efficiency as per one’s radiation environment.

Fig. 6Full-screen View

Energy deposited in SiC by (a) All particles (b) recoil protons (c) alphas (d) other charged particles