1.

Introduction

High-energy ($\sim 1\mathrm{MeV}$ and above) detectors serve several important roles in space-based astrophysics missions, yet there are many aspects that still need to be improved. Specifically, detectors that may be built of materials that are low-cost, lightweight, and have the best sensitivity and energy resolution at x-ray and gamma-ray energies are the most ideal. Study of the cosmos at high energies has applications across a broad range of research in astrophysics and space science—from the gamma radiation of distant quasars and black holes, to the x rays of solar storms, to the radioactive decay of minerals in the soil of planets and surfaces of asteroids in our solar system. Similarly, in situ astrobiological and geological investigations of the chemical makeup of planet and asteroid surfaces is optimally performed by probing with pulsed neutrons and measuring the scattered neutrons and gamma rays in this energy range.¹ In this manner, mineralogical assays can be performed to a depth of tens of centimeters below the surface without the need to physically drill, a process that is costly in power consumption.

For scintillators in use as gamma or x-ray detectors, the ionizing event frees an electron, creating a number of electron-hole pairs roughly proportional to the energy of the ionizing radiation. Ideally, each electron-hole pair forms an exciton and then migrates to an activator site, where they recombine and emit a photon in the visible spectrum. These photons are then collected and converted to an electrical signal that is, ideally, proportional to the energy of the ionizing event, since the number of photons should be proportional to the ionizing energy. However, in reality, along each step of this process mitigating factors lead to a loss of excitons, photons, or reduction in the output signal.² This resulting nonproportionality in turn limits the energy resolution.

Indeed, while scintillators used as room temperature radiation detectors have advantages over wide bandgap semiconductors, their limiting factor, at present, is energy resolution. In general, the need for high energy resolution gamma spectrometers is twofold: (1) to recognize structure in spectra (such as the shape of the positronium line) and identify closely located energy lines and (2) improve sensitivity, as the signal-to-background ratio improves with better resolution and the peak identifiability improves even when one energy line is involved.³ For example, in the determination of the subsurface elemental composition of planets and asteroids application using conventional fast neutron activation analysis techniques, the critical advantage comes from both improved energy line identification and improved sensitivity.⁴

Strontium iodide doped with europium [${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$] is a scintillator material that, in particular, shows promise for high energy resolution, as an FWHM energy resolution at 662 keV has been reported as good as $\sim 2.5\%$,⁵ close to the 2% of the semiconductor cadmium zinc telluride (CZT).⁶ An important question, therefore, is whether it is possible to improve the energy resolution of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ to the point that it is even more competitive with CZT. This would lead to a scintillator with a resolution comparable to or better than that of a semiconductor, while less expensive to manufacture and with the capacity to grow much larger single crystals and, therefore, build more efficient detectors compared to those fabricated from semiconductors.⁷

Improving the energy resolution of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ requires characterizing and better understanding the nonproportionality of the material’s light yield. Indeed, some calculations show that, should nonproportionality be minimized, ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ would achieve a fundamental Poisson limit of 1.5% energy resolution.⁸

Nonproportionality is a well-known characteristic of scintillators^9–11 and arises because the incoming photon can deposit its full energy in a variety of ways (e.g., Compton scattering, Auger electrons, etc.) in a cascade process, which causes variations in the amount of light produced within the detector,¹⁰ and the light-yield responses to the individual divisions of energy are not proportional to that energy.¹⁰ It is thought that the underlying cause of nonproportionality is connected to the details of transportation of electric carriers (electrons, holes, and excitons) within the scintillator.^9,10,12,13 The link between the transportation of charge carriers and the amount of light that a scintillator produces (the luminosity of the scintillator) was originally quantified by Birk’s equation.² Attempts at modeling nonproportionality generally begin with this form, or an empirically modified form of Birk’s equation. ² One of these modified forms used by Payne et al. incorporates the Onsager mechanism into their model for light yield of a scintillator.¹³ The Onsager mechanism is a recombination rate that depends on the Onsager radius (separation) where an electron and hole will no longer recombine; this is because the Onsager radius is the distance where the Coulombic and thermal energies are equal.^13–15 While in the Payne et al. study it is implied that perhaps the Onsager radius is connected with a term that pertains to the intrinsic properties of the crystal (and is verified upon comparison to experimental data), we infer that it is possible that there is also a connection between the Onsager radius and nonproportionality. This is further detailed in Sec. 3.

To make progress in the effort to improve the nonproportionality and, therefore, the energy resolution of scintillators as a new cost-effective solution for high-energy astrophysical detectors, it is necessary to characterize how factors such as operating temperature and incoming photon energy affect the nonproportionality. Therefore, two studies with ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ are presented in this paper. One is a study of nonproportionality as a function of temperature. The other is a study of nonproportionality as a function of energy at high energies.

The response of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ as a function of temperature has been investigated previously by Lam et al. and Alekhin et al. [both studies are specific to ${\mathrm{SrI}}_2$, doped and un-doped, with ${\mathrm{Eu}}^{2+}$ Refs. 16 and 17], and Boatner et al., who investigated a variety of scintillators up to very high (400°C) temperatures.¹⁸ In the Lam et al. study, they focused on temperatures from 295 down to 5 K, while the Alekhin et al. study went from 80 to 600 K [for ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$] at low energies (up to 100 keV). Our study differs from the above studies in that it focuses on the nonproportionality of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ from 16 to 60°C using gamma-ray sources of energy ranging from 81 to 1275 keV. The focus of the study presented here is the shift of the photopeak with increasing temperature and its implication on how nonproportionality changes as a function of temperature (the Boatner et al. study does not focus on nonproportionality, only on the shift of the photopeak) at a higher temperature range than Lam et al. study and at higher energy ranges than Alekhin et al. Information on the nonproportionality in this energy and temperature range may add information to the underlying physical cause(s) of nonproportionality (such as Onsager mechanism, trapping, etc.).

The high-energy study is unique in that this is the first study of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ at such high energies (to our knowledge). The reason for this experiment was to evaluate the ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ detector as a possible gamma-ray alternative to the lanthanum bromide doped with cerium [${\mathrm{LaBr}}_3({\mathrm{Ce}}^{3+})$] currently used in the Probing in-situ with Neutrons and Gamma-rays Instrument.¹⁹ An interest in an alternative to ${\mathrm{LaBr}}_3({\mathrm{Ce}}^{3+})$ comes from the need to have a scintillator without any self-activity. ${\mathrm{LaBr}}_3({\mathrm{Ce}}^{3+})$ contains self-activity due to the ${}^{138}\mathrm{La}$ (Ref. 20) creating intrinsic photopeaks in the gamma-ray spectrum that increases the background noise and can further interfere with composition analysis if the particular element has a characteristic gamma ray near any of the intrinsic ones coming from the crystal itself.

Both experiments bring new regimes to the previous studies mentioned above. Studies of the electron response, such as Refs. 5, 13, and 16 (to name a few), based on Compton scattering are useful and simpler for probing the effect of nonproportionality on scintillator energy resolution, since the ionization avoids the cascade process that occurs with gamma-ray interactions in inner shell electrons. Studies of the gamma photon response and its temperature variation, while more complicated due to the cascade mentioned above, are directly relevant to high-energy (6 MeV) gamma spectroscopy applications. The experimental setup and results for these studies are shown in Sec. 2, followed by the discussion in Sec. 3, and conclusions in Sec. 4.

2.

Experiments

2.1.

Nonproportionality as a Function of Temperature

2.1.1.

Setup

The experimental setup consists of (in order from top to bottom in Fig. 1) an outer aluminum sleeve, Teflon, a copper heater, a $0.6{\mathrm{cm}}^3$ ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ crystal encapsulated in an aluminum can, a hollow quartz optical rod (101 mm in length) inside a brass cylindrical core surrounded by copper tubing, and a Hamamatsu photomultiplier tube (PMT) (Ultra-Bialkali model R6231-100). The crystal was grown and encapsulated at Fisk University with an FWHM resolution of 3.9% at 662 keV when tested directly coupled to the PMT (without the light guide). While use of the light guide causes loss of scintillation light, resulting in degradation of the resolution, its use here is to separate the PMT from the heat being applied to the crystal (allowing us to keep the PMT at room temperature). The inset in Fig. 1 shows the assembly of the top portion (everything except the PMT).

Fig. 1

Cross-sectional view of temperature experiment. Figure shows components of temperature study setup.

The method for acquiring data was done using the following three sources (energies ranging from 81 to 1275 keV): ${}^{133}\mathrm{Ba}$, ${}^{137}\mathrm{Cs}$, and ${}^{22}\mathrm{Na}$. The selected temperatures used were 16, 30, 40, 50, and 60°C. Counts from each source were collected for five consecutive runs at each temperature with the exception of ${}^{22}\mathrm{Na}$ at 40 and 60°C. In the case of 40°C, there are only two runs recorded, and in the case of 60°C, there are only four. Each spectrum of the ${}^{133}\mathrm{Ba}$ and ${}^{137}\mathrm{Cs}$ sources was acquired for 300 s, while to achieve good statistics, the ${}^{22}\mathrm{Na}$ spectra were recorded for 900 s.

2.1.2.

Results

Figure 2 shows the full spectra of the final run at each temperature of the ${}^{22}\mathrm{Na}$ source. As temperature increases, the 511 and 1275 keV photopeaks shift to lower channels. Only the ${}^{22}\mathrm{Na}$ source is shown (for brevity), as the same behavior of the photopeak shifting to lower channels with increasing temperature is present for all the sources in all sets of spectra. All values are tabulated in Table 1. The centroid values shown in Table 1 are the weighted averages of all the runs for that energy and temperature.

Fig. 2

${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ ${}^{22}\mathrm{Na}$ spectra as a function of temperature. Figure shows the final run for each temperature with the ${}^{22}\mathrm{Na}$ source. Notice that the photopeaks shift to lower channels with increasing temperature (please see color version online).

Table 1

Summary of averaged centroid values. Below are the weighted average centroid values [in analog to digital converter (ADC) channel] for each temperature.

Energy (keV)	16°C Mean (error)	30°C Mean (error)	40°C Mean (error)	50°C Mean (error)	60°C Mean (error)
81	61.524 (0.023)	58.157 (0.061)	55.803 (0.041)	53.025 (0.035)	50.540 (0.045)
511	375.789 (0.613)	356.011 (0.102)	333.547 (0.781)	323.848 (0.074)	307.630 (0.057)
662	487.596 (0.131)	459.730 (0.082)	439.375 (0.016)	417.655 (0.058)	396.787 (0.120)
1275	925.454 (1.347)	876.264 (0.389)	821.248 (1.414)	797.003 (0.696)	757.137 (2.000)

The fitting and averaging routine that was used was written in Python, with the fitting routine making use of the Python function called curve_fit().²¹ All the spectra are fitted with a Gaussian plus a polynomial (for the background continuum). To obtain the weighted average of the data, another function of Python, called numpy.average()²² was used.

Also, because of the light guide use, the resolution is reduced to $\sim 9.6\%$. This reduction in energy resolution and relative closeness of the 276 and 302 keV photopeaks of the ${}^{133}\mathrm{Ba}$ source is unresolved, along with the 356 and 383 keV peaks. For this reason, we analyze only the 81 keV photopeak of the ${}^{133}\mathrm{Ba}$ source along with the 511 and 1275 keV photopeaks of ${}^{22}\mathrm{Na}$, and the 662 keV photopeak of ${}^{137}\mathrm{Cs}$ (which have no other source peaks nearby and are less affected) for the peak shifts and nonproportionality calculations.

To quantify the amount of shift in the photopeak, we performed a percent decrease calculation using 16°C as the reference temperature.

Eq. (1)

$$\text{Relative}\text{shift}(\text{in}\%)=\frac{\mathrm{ADC}{\text{Channel}}_{\text{Temperature}}\text{-}\mathrm{ADC}{\text{Channel}}_{16°\mathrm{C}}}{\mathrm{ADC}{\text{Channel}}_{16°\mathrm{C}}}*100\%,$$

Eq. (2)

$${\sigma }_{\text{Relative}\text{shift}(\text{in}\%)}={[{\left(\frac{1}{\mathrm{ADC}{\text{Channel}}_{16°\mathrm{C}}}\right)}^2*{\sigma }_{\mathrm{ADC}{\text{Channel}}_{\text{Temperature}}}^2+{\left(\frac{\mathrm{ADC}{\text{Channel}}_{\text{Temperature}}}{\mathrm{ADC}{\text{Channel}}_{16°\mathrm{C}}^2}\right)}^2*{\sigma }_{\mathrm{ADC}{\text{Channel}}_{16°\mathrm{C}}}^2]}^{1/2}*100\%.$$

The results are presented in Fig. 3 and Table 2. The percent decrease between energies, at each temperature (with the exception of the 511 and 1275 keV peaks of ${}^{22}\mathrm{Na}$ at 40°C, which are addressed in Sec. 3), is 4 to 6%. This decreasing trend seen at all energies can be linearly fit. A possible explanation for this seemingly linear behavior is also addressed in Sec. 3.

Fig. 3

Figure is a graphical representation of the relative shift of the centroid value at different energies, from a reference temperature of 16°C. Values can be found in Table 2. Each energy has a corresponding linear fit to the data points (please see color version online).

Table 2

Relative shift of photopeak in SrI2(Eu2+). Tabulated values for the shift in photopeak of SrI2(Eu2+) as a function of temperature. Values correspond to Fig. 3.

Energy (keV)	Between 30°C and 16°C Relative shift (in %) (error)	Between 40°C and 16°C Relative shift (in %) (error)	Between 50°C and 16°C Relative shift (in %) (error)	Between 60°C and 16°C Relative shift (in %) (error)
81	$-5.468$ (0.105)	$-9.298$ (0.075)	$-13.813$ (0.221)	$-17.852$ (0.079)
511	$-5.262$ (0.157)	$-11.240$ (0.253)	$-13.821$ (0.142)	$-18.137$ (0.134)
662	$-5.714$ (0.030)	$-9.889$ (0.024)	$-14.341$ (0.026)	$-22.605$ (0.033)
1275	$-5.315$ (0.144)	$-11.259$ (0.200)	$-13.879$ (0.187)	$-18.624$ (0.625)

Last, Fig. 4 shows the nonproportionality as a function of temperature. This is calculated by the following equations:

Eq. (3)

$$\text{Nonproportionality}=\frac{\mathrm{ADC}Ch{\#}_{\text{Photopeak}}*\frac{662\mathrm{keV}}{\mathrm{ADC}Ch{\#}_{662\mathrm{keV}\text{Photopeak}}}}{{\text{Energy}}_{\text{Photopeak}}},$$

Eq. (4)

$${\sigma }_{\text{Nonproportionality}}=\{\frac{662\mathrm{keV}}{{\text{Energy}}_{\text{Photopeak}}}*{[{\left(\frac{1}{\mathrm{ADC}Ch{\#}_{662\mathrm{keV}\text{Photopeak}}}\right)}^2*{\sigma }_{\mathrm{ADC}Ch{\#}_{\text{Photopeak}}}^2+{\left(\frac{\mathrm{ADC}Ch{\#}_{\text{Photopeak}}}{\mathrm{ADC}Ch{\#}_{662\mathrm{keV}\text{Photopeak}}^2}\right)}^2*{\sigma }_{662\mathrm{keV}\text{Photopeak}}^2]}^{1/2}\}.$$

Fig. 4

Nonproportionality of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ versus temperature. Figure shows the nonproportionality versus temperature, with data normalized to 662 keV at each temperature. The data points at 511 and 1275 keV are addressed in Sec. 3.1.

For all energy sources, the nonproportionality increases with the rise in temperature. This increase is $\sim 6\%$ overall. Tabulated values can be found in Table 3.

Table 3

Nonproportionality of SrI2(Eu2+). Tabulated values of the nonproportionality versus temperature as shown in Fig. 4.

Energy (keV)	Nonproportionality (error) 16°C	Nonproportionality (error) 30°C	Nonproportionality (error) 40°C	Nonproportionality (error) 50°C	Nonproportionality (error) 60°C
81	1.031 ($4.768\times {10}^{-4}$)	1.034 ($1.091\times {10}^{-3}$)	1.038 ($7.684\times {10}^{-4}$)	1.038 ($6.991\times {10}^{-4}$)	1.041 ($9.853\times {10}^{-4}$)
511	0.998 ($1.650\times {10}^{-3}$)	1.003 ($3.384\times {10}^{-4}$)	0.983 ($2.302\times {10}^{-3}$)	1.005 ($2.696\times {10}^{-4}$)	1.004 ($3.570\times {10}^{-4}$)
662	1.000 ($3.788\times {10}^{-4}$)	1.000 ($2.529\times {10}^{-4}$)	1.000 ($5.048\times {10}^{-5}$)	1.000 ($1.961\times {10}^{-4}$)	1.000 ($4.286\times {10}^{-4}$)
1275	0.985 ($1.458\times {10}^{-3}$)	0.989 ($4.743\times {10}^{-4}$)	0.970 ($1.672\times {10}^{-3}$)	0.991 ($8.762\times {10}^{-4}$)	0.991 ($2.634\times {10}^{-3}$)

2.2.

Nonproportionality at High Energies

2.2.1.

Setup

As mentioned in Sec. 1, the second experiment was performed at the 6 MeV Gamma-ray Facility at NASA Goddard Space Flight Center with Dr. Ann Parsons and Dr. Suzanne Nowicki.²³ The setup for producing gamma rays is shown in Fig. 5. Piping surrounds the granite monument; starting from the left of the picture, the piping is wrapped in a helical fashion; this is where the pulsed neutron generator is placed. The piping goes across the top of the monument, to a water tank on the right side of the picture, and then comes back across (this is depicted in the schematic also included in Fig. 5). When the neutron generator is turned on, the neutrons excite the oxygen via the ${}^{16}\mathrm{O}{(n,p)}^{16}\mathrm{N}$ reaction. By the time the water has reached the tank, the ${}^{16}\mathrm{N}$ de-excites releasing gamma rays of 2.7, 6.1, and 7.1 MeV (Ref. 24) (with probabilities of 0.82, 67, and 4.9%, respectively²⁵).

Fig. 5

6 MeV gamma-ray facility setup. Picture of the 6 MeV gamma-ray facility at NASA Goddard Space Flight Center. Neutron pulsed generator is on the left, and the water tank is on the right. Gamma rays are produced via the ${}^{16}\mathrm{O}{(n,p)}^{16}\mathrm{N}$ reaction. The schematic shows placement of neutron generator, water tank, and ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ detector for the experiment setup.

Also shown in Fig. 5 is the placement of the ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ detector. The ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ detector was loaned to us from Lawrence Livermore Laboratory and contains a 1 in. by 1 in. crystal [2.95% (19.5 keV) resolution at 662 keV] grown by Radiation Monitoring Devices. For a crystal of this size, we expect $\sim 1$ to 2% efficiency at 6 MeV. For the experiment, the ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ detector was grounded (with foil) and also wrapped in a foil sack to reduce interference from radio waves (used by other groups performing radar ranging at the NASA site). The placement of the ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ detector was $\sim 20.5$ (2) cm and acquisition time was 5 h.

2.2.2.

Results

Figure 6 shows the resultant spectra of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ of the 6 MeV experiment. A ${}^{137}\mathrm{Cs}$ source was placed near the detector as a calibration source.

Fig. 6

Spectrum of ${}^{137}\mathrm{Cs}$, and 6 MeV gamma-ray sources obtained with ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$. Peaks seen in the spectra are the ${}^{137}\mathrm{Cs}$ photopeak, and the ${}^{16}\mathrm{O}$ photopeak, see Ref. 24 (${}^{16}\mathrm{O}$ escape peaks are also seen). Inset shows fits (Gaussian + polynomial) to these photopeaks (please see color version online).

Last, the nonproportionality of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ over the range of 662 keV to 6.1 MeV was calculated and is shown in Fig. 7 and in Table 4.

Fig. 7

Nonproportionality versus energy of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$, normalized to 662 keV. The red square (color version online) represents the average nonproportionality in the high-energy range. The error bars of this point in the $x$ axis represent the range of energies measured, while the error bars in the $y$ axis represent the true error in the nonproportionality. Values are shown in Table 4.

Table 4

Nonproportionality values of SrI2(Eu2+) at energies up to 6 MeV (normalized to 662 keV), along with the average nonproportionality (data point in red in Fig. 7). Energies of the O16(n,p)N16 reaction can be found at the National Nuclear Data website (see Ref. 24).

Energy (keV)	Nonproportionality (error)	Energy resolution in % (error)
662	1.000 ($8.746\times {10}^{-5}$)	4.842 (0.012)
5107	0.987 ($5.755\times {10}^{-4}$)	3.955 (0.115)
5618	0.994 ($8.751\mathrm{E}-04$)	4.689 (0.179)
6129	0.979 ($1.272\times {10}^{-3}$)	2.989 (0.278)
Average energy	Average nonproportionality
5618	0.987 ($9.074\times {10}^{-4}$)

3.

Discussion

4.

Conclusions

In this paper, we report findings from two different experiments on the nonproportionality of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$, motivated by the need to develop effective high-energy detectors with energy resolutions comparable to semiconductors for astrophysics applications and future space missions. One study was focused on the change in nonproportionality as a function of temperature; the other was focused on the nonproportionality at high energies.

In the temperature variation study, we found that the photopeak of the ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ crystal shifts to lower channels with increasing temperature and that the nonproportionality increases (up to 6%) with increasing temperature. This could be due to the charge carriers being at a distance equal to or larger than the Onsager radius as their kinetic energy is increased with the higher temperature. This increase in nonproportionality in temperature is in agreement with previous studies¹⁶ and also seems to be a trend when the temperature is decreased;¹⁷ whether or not this is caused by the same mechanism is left for further investigation (and perhaps can be answered with further investigations of the mobilities of the charge carriers in the scintillator).

These results show that increasing temperature increases the nonproportionality; further investigation is needed to tie the specific cause (Onsager mechanism, trapping, and/or mobilities) and determine whether this cause is the same for high or low temperatures. Understanding this cause could give guidance into how to improve the growth (or perhaps correctly compensate for the effect in an already fabricated detector) so that this effect can be mitigated and energy resolution may be improved.

In the high-energy study, we found that ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ has a nonproportionality of $\sim 2\%$ at 6 MeV. Within the energy range of 662 keV to 6.1 MeV, the change in the nonproportionality of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ is $\sim 1.5$ to 2%.

This is the first study of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ at this energy regime, and these preliminary findings seem to be promising for applications in astronomy. If potential improvement in the nonproportionality of ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ is achieved, then ${\mathrm{SrI}}_2({\mathrm{Eu}}^{2+})$ can become a viable detector with low background and no self-activity. This would enable lower-cost high-energy detectors deployable both in space-based platforms and in less temperature-controlled environments, such as planetary surface landers performing compositional analyses.