Journal of the Korean Physical Society, Vol. 68, No. 9, May 2016, pp. 1069∼1074
Electronic Structure and Optical Properties of CsI, CsI(Ag), and CsI(Tl) Zheng Zhang, Qiang Zhao∗ and Yang Li Beijing Key Laboratory of Passive Safety Technology for Nuclear Energy, School of Nuclear Science and Engineering, North China Electric Power University, Beijing 102206, China
Xiao-Ping Ouyang Beijing Key Laboratory of Passive Safety Technology for Nuclear Energy, School of Nuclear Science and Engineering, North China Electric Power University, Beijing 102206, China, Northwest Institute of Nuclear Technology, Xi’an 710024, China, and School of Materials Science and Engineering, Xiangtan University, Xiangtan 411105, China (Received 11 November 2015, in final form 2 March 2016) The band structure, electronic density of states and optical properties of CsI and of CsI doped with silver or thallium are studied by using a first-principles calculation based on density functional theory (DFT). The exchange and the correlation potentials among the electrons are described by using the generalized gradient approximation (GGA). The results of our study show that the electronic structure changes somewhat when CsI is doped with silver or thallium. The band gaps of CsI(Ag) and CsI(Tl) are smaller than that of CsI, and the width of the conduction band of CsI is increased when CsI is doped with thallium or silver. Two peaks located in the conduction band of CsI(Ag) and CsI(Tl) are observed from their electronic densities of states. The absorption coefficients of CsI, CsI(Ag), and CsI(Tl) are zero when their photon energies are below 3.5 eV, 1.5 eV, and 3.1 eV, respectively. The results show that doping can improve the detection performance of CsI scintillators. Our study can explain why doping can improve the detection performance from a theoretical point of view. The results of our research provide both theoretical support for the luminescent mechanisms at play in scintillator materials when they are exposed to radiation and a reference for CsI doping from the point of view of the electronic structure. PACS numbers: 31.15.Ar, 31.15.Ew, 71.23.-k, 78.20.Ci Keywords: First principles Electronic structure Optical property CsI DOI: 10.3938/jkps.68.1069
I. INTRODUCTION
The cesium-iodide (CsI) crystal, especially when doped with thallium, is widely used as a scintillator material for particle detection due to its high emission efficiency and fast decay time [1–4]. Ag, as a traditional activator, has been used in ZnS(Ag) (zinc sulfide doped with silver). ZnS(Ag) is a well-known material for detecting alpha particles [5]. In some cases, silver is also used as a kind of activator when doped in CsI [6]. CsI has many advantages, such as its strong anti-radiation damaging feature, high stopping power, and slight hygroscopy. CsI is widely used in fields like high-energy physics research, nuclear medicine, environmental monitoring, petroleum surveying, geological survey safety tests, and so on. CsI crystals have an effective nuclear radiation detection property. They are used in many fields, as mentioned above; therefore, research on CsI is essential. ∗ E-mail:
[email protected]
Many experimental studies on CsI are available [7–9]; however, the theoretical research requires further study. To our knowledge, the CsI scintillator can absorb some of photons it produces by de-excitation after it receives some nuclear radiation. Because this undesirable for improving its detection efficiency, many papers [10–13] have discussed the origins of this absorption. The performance of a scintillation detector is closely related to the electronic structure and the optical properties. Firstprinciples calculations are a good method to research the electronic structure [14–18] and optical properties [19– 22] of crystals. Some reseachers [23–26] have used the first-principles calculation method to study CsI and CsI with some defects. Ying [27] et al. studied the absorption spectrum and the electronic structure of CsI crystals with cesium vacancies by using density function theory (DFT). In this paper, we present the results of our study on the band structure, electronic density of states, and optical properties of CsI, CsI(Ag), and CsI(Tl) by using a first-principles calculation method based on DFT. We try to explain the scintillation luminescence mechanism
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Fig. 1. (Color online) A 2 × 2 × 2 supercell of CsI. Brown balls represents iodine atoms, and purple balls represents cesium atoms. The cesium atom, to which the red arrow is pointing, will be replaced by a silver or a thallium atom.
of CsI when it is exposed to radiation and give the reason doping with thallium or silver can improve the detection performance of CsI.
result of hybrid functional calculations. We used the Heyd-Scuseria-Ernzerhof (HSE) [32–36] hybrid function. The hybrid functional calculation results are more consistent with the real situation. In HSE hybrid function, the interaction among the electrons is divided into two parts, short range and long range. In the short range, the interaction among the electrons is split in two parts, the Hartree-Fock and the PBE exchanges. In the long range, the interaction among the electrons is described by the pure PBE. We used ultra-soft pseudo potentials and a plane-wave cutoff of 300 eV for all the other calculations. The basic parameters were chosen as follows: kinetic energy cutoff = 300 eV, space representation = reciprocal, SCF tolerance = 1.0 × 10−6 eV/atom, and k sampling with 5 × 5 × 5 k-point mesh in the Brillouin zone. Optimal atomic positions were determined until the following conditions were satisfied: (1) the maximum force on the atomic positions was smaller than 0.05 eV/nm; (2) the maximum change in the energy per atom was smaller than 1.0 × 10−5 eV; (3) the maximum displacement is smaller than 0.001 ˚ A; and (4) the maximum stress of the crystal was smaller than 0.02 GPa. All the properties we calculated on the basis of the crystal structure were optimized.
III. RESULTS AND DISCUSSION
II. METHODOLOGY
1. Optimization of the Crystal Structure
The crystal structure of CsI is a cubic crystal system. Its space group is Pm3m. The crystal structure of CsI is similar to that of CsCl. Figure 1 shows the crystal structure, and this figure contains a 2 × 2 × 2 supercell of CsI. In each CsI cell are eight iodine atoms located in the cubic vertex angle and one cesium atom located in the body center. One cesium atom in the supercell is replaced by a silver atom or thallium atom. We mark them as CsI(Ag) and CsI(Tl) in this paper. The replaced atom’s position is pointed to by a red arrow. In this paper, all of the calculations were carried out by using the Cambridge Serial Total Energy Package (CASTEP) [28]. CASTEP is an ab initio quantum mechanics theory software package based on DFT. It uses a plane-wave pseudo-potential method as a substitute for the ionic potential, and the electron wave function is spread by using plane-wave basis sets. The exchange correlation potentials among the electrons are described by using the local density approximation (LDA) or the generalized gradient approximation (GGA). In this study, we used the GGA with a Perdew-Burke-Ernzerhol (PBE) [29] form in order to describe the exchange correlation potentials among the electrons. The LDA or the GGA often underestimate the width of band gap, and this is a well-known issue [30]. However, the GGA is still a widely used method and has achieved many successes. Results based on the GGA are generally acclaimed [31]. We cross-checked the width of the band gap with the
In order to study the electronic structure and the optical properties of these crystals, first of all, we optimized the crystal structures of CsI, CsI(Ag), and CsI(Tl). The results are that the lattice parameters of the supercells of CsI, CsI(Ag), and CsI(Tl) are 2a0 = 2b0 = 2c0 = 9.37 ˚ A, 9.24 ˚ A, and 9.16 ˚ A, respectively. The angles of all crystals are α = β = γ = 90◦ . Based on these data, we find that the lattice parameter of CsI is in good agreement with the value in Ref. [27]. The lattice parameters of the supercells of CsI(Ag) and CsI(Tl) are smaller due to doping, and the lattice parameter of CsI(Ag) is the smallest of these three scintillation crystals. This is a result of the facts that the size of the cesium atom is different from those of the silver and the thallium atom and that the bonds between atoms in CsI changes somewhat after doping. In the case of CsI more scintillation material is in the same volume when it is doped with silver or thallium. Because of that doping can improve the scintillator’s performance.
2. States
Band Structure and Electronic Density of
The electronic structure is an important parameter of CsI. It determines the performance of the scintillator.
Electronic Structure and Optical Properties · · · – Zheng Zhang et al.
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Fig. 2. (Color online) Band structure, where a, b, and c stand for CsI, CsI(Ag), and CsI(Tl), respectively.
The luminescence spectrum of a scintillator is closely associated with its band structure. The luminescence spectrum comes from de-excitation after the electrons are excited by high-energy particles. We can find the luminescence mechanism from the band structure of these scintillation crystals. When the crystal obtains enough energy from the incident particles, electrons can transit from the valence band to the conduction band. At the same time, the transitions leave a few cavities in the valence band, that is, electron-vacancy pairs. When an electron movies back from the conduction band to the valence band, a photon whose energy is equal to band gap is produced. Therefore, the band gap is a very important parameter for scintillator materials. The band structures of CsI, CsI(Ag), and CsI(Tl) crystals are shown in Fig. 2, and their band gaps of are 3.635 eV, 1.475 eV, and 3.102 eV, respectively. As a crosscheck, we show the results of a hybrid function calculation, for which the band gaps of CsI, CsI(Ag), and CsI(Tl) are 4.948 eV, 2.472 eV, and 4.395 eV, respectively. The trends for the changes in the band gaps for the two calculations are in good agreement. For CsI(Ag) and CsI(Tl), the conduction band edge moves to a lower energy with respect to that of the pure CsI crystals. A CsI crystal doped with silver or thallium can produce more scintillation fluorescent photons, for which the energy is in the visible range (1.61 eV - 3.19 eV), when they are exposed to the same amount of radiation. As we discussed above, doping can improve the detection performance of CsI from this point of view because the best response energy for some photomultiplier tubes is in the range of visible light. In order to further study the electronic structure of these scintillation crystals, we calculated the electronic densities of states of these crystals. We can explain the cause for the formation of their band structures. Figure 3 shows the distributions of the total densities of states (TDOS) and the partial densities of states (PDOS) for
Fig. 3. (Color online) TDOSs and PDOSs of CsI, CsI(Ag), and CsI(Tl).
CsI, CsI(Ag), and CsI(Tl). Figure 3(a) shows the TDOSs of these three crystals. Figures 3(b) and 3(c) show the TDOS and the PDOS of CsI. Figures 3(d), 3(e), and 3(f) show the TDOS and the PDOS of CsI(Ag). Figures 3(g), 3(h), and 3(i) show the TDOS and the PDOS of CsI(Tl). The TDOS is in agreement with the band structure. Based on Fig. 3(a), we can find the parts of the TDOSs of CsI(Ag) and CsI(Tl) that are located in the valence band are generally similar to those of CsI, but some differences are seen in the conduction band. Because the conduction band of CsI extends in the direction of the Fermi level after being doped with thallium or silver, the width of the conduction band becomes bigger, and a small peak is added to the conduction band. In the next parts of this section, we will discuss the reason for these changes. Figures 3(b) and 3(c), show the composition of the TDOS of CsI. The conduction band is composed of sstate electrons of iodine and s, p-state electrons of cesium. The valence band, which is near the Fermi level, is composed by p-state electrons of iodine. In pure CsI,
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Journal of the Korean Physical Society, Vol. 68, No. 9, May 2016
Fig. 4. (Color online) Optical properties of CsI and it doped with Ag or Tl, 4(a), 4(d), and 4(g) stand for CsI, 4(b), 4(e), and 4(h) for CsI(Ag), and 4(c), 4(f), and 4(i) for CsI(Tl).
the electrons in the valence band that are near the Fermi level transit to the conduction band when exposed to radiation. Some photons are produced by the electrons’ de-excitation, and the energy of these photons is equal to the band gap of CsI. In CsI, the energies of the photons put them outside the visible range. This can be deduced from Figs. 3(a) and 3(b). Compared to CsI, we find some changes in CsI(Ag) because it is doped with silver. Some local energy levels near the Fermi level are produced when CsI is doped with silver as an activator. These levels are called exciton bands. The width of the conduction band of CsI(Ag) is bigger than that of the pure CsI crystal, and the band gap of CsI(Ag) becomes smaller than that of CsI. These changes can improve the luminous performance of CsI because it can produce more photons with energies in the visible range after being doped. Doped CsI can produce more photons than pure CsI when exposed to the same amount of radiation because the band gap becomes smaller. Based on Figs. 3(d), 3(e), and 3(f), we can see that a small peak is added in the conduction band due to the s-state electron of silver. The p-state electrons also makes a contribution to the peak near 5 eV. A hybridization between the s-state electrons of cesium and the s-state electron of silver. In addition, a peak is added the valence band near the Fermi level. This peak is the result of a joint function with all state electrons in CsI(Ag). Like CsI(Ag), the band gap of CsI(Tl) becomes smaller than that of CsI, but the width of the band gap is big-
ger than that of CsI(Ag). Although we can conjecture that the energy of the scintillation photons produced by CsI(Tl) should be larger than that of the photons produced by CsI(Ag), the energies of the photons are still in the visible range. In addition, a peak is added near the edge of the original conduction band. This is the contribution of the p-state electrons of thallium. As we discussed above, the band gap of CsI becomes smaller due to doping. Therefore, more photons are produced when the scintillators is exposed to the same amount of radiation. The energy of the scintillation photons is smaller than that of the pure CsI, and most of these photons have energies in the visible range. The detection performance of CsI becomes better when it is doped with thallium or silver.
3. Optical Properties
An excellent scintillator has not only a high luminous efficiency but also a weak absorption capacity for the photons spectra that are produced. The emission spectra and the absorption spectra do not overlap. The greater the distance between them is, the better their detection efficiency is. The optical properties of a scintillator have a significant effect on its detection efficiency. In this study, we calculated the optical properties of CsI when it was doped with thallium or silver, and the results are shown in Fig. 4. Figures 4(a), 4(b), and 4(c) present
Electronic Structure and Optical Properties · · · – Zheng Zhang et al.
the dielectric functions of CsI, CsI(Ag), and CsI(Tl), respectively. In the linear response range, the macrooptical response function of a solid can usually be described by a dielectric function in a complex number form ε (ω) = ε1 (ω) + iε2 (ω). The dielectric function, ε (ω), describes the crystal system’s linear response to electromagnetic radiation, and it dominates the behavior of electromagnetic-wave propagation in a medium. We can easily get the spectral information through the ω function. The imaginary part, ε2 (ω), of the dielectric function mainly represents the electron’s transition from occupied to non-occupied states. We can get the imaginary part, ε2 (ω), from the definition of the direct probability transition and get the real part, ε1 (ω), via Kramers-Kronig relations [37,38] after we have gotted the band structure. The optical constant and the reflection coefficient are deduced based on the dielectric function. Figure 4(a) shows the dielectric function of CsI. The absorption edge of ε2 (ω) starts from 3.6 eV. This suggests an optical band gap of 3.6 eV. This result is in agreement with the band structure. ε2 (ω) has two peaks (5.2 eV and 12.4 eV) as dose ε1 (ω) (4.1 eV and 11.2 eV). The peaks that are located at 5.2 eV and 4.1 eV are formed by the electrons that transit from the p-state of iodine to the s-state of iodine. The peaks located at 12.4 eV and 11.2 eV are formed by the electrons that transit from the p-state of cesium to the s-state of cesium or to the s-state of iodine. Figures 4(b), 4(c) show the dielectric functions of CsI(Ag) and CsI(Tl). Their absorption edges of ε2 (ω) are 1.4 eV and 3.2 eV, respectively. The imaginary part, ε2 (ω), has three peaks(2.9 eV, 5.1 eV, and 7.4 eV) for CsI(Ag), and the real part, ε1 (ω), has three peaks(1.9 eV, 4.5 eV, and 6.6 eV). Some added exciton bands are near the Fermi level, which can explain the changes in CsI(Ag). Some changes also occur in CsI(Tl) and can be explained by using the same method that we used earlier in this section. We can understand the reason a certain energy photon can be absorbed by the crystal through the dielectric function associated with the electronic density of states. The absorption spectra of CsI, CsI(Ag), and CsI(Tl) are shown in Figs. 4(d), 4(e), and 4(f), respectively. The absorption peaks of CsI(Ag) and CsI(Tl) are observed to be blue-shift compared to that of CsI. More ultraviolet photons are absorbed, and fewer visible photons are absorbed. The absorption coefficients of CsI, CsI(Ag), and CsI(Tl) are zero if the photons energies are below 3.5 eV, 1.5 eV, and 3.2 eV, respectively. This indicates that these crystals are transparent and that absorption does not occur when the energies of photons are below these values. Although the absorption edge of CsI starts at a smaller value when it is doped with thallium or silver, the total absorption efficiency for visible photons becomes weaker. As a result, we can see that these crystals are transparent to the photons that they produce and that doping can make the CsI crystal more effective at collecting the photons caused by the incident particles. Figures 4(g), 4(h), and 4(i) show the reflection coef-
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ficients of these crystals. Blue shifts in the peak of the reflection coefficient are observed when CsI is doped with thallium or silver. The reflection of visible photons become stronger. From this point of view, doping is beneficial for improving the detection performance of CsI. In short, although the absorption and the reflection of CsI are blue-shifted after the crystal is doped with thallium or silver, the total absorption efficiency for visible photons becomes weaker, and the reflection of visible photons become stronger. Thus doping can improve the detection performance of CsI from the point of view of its optical properties.
IV. CONCLUSIONS In order to explain why doping can improve the detection performance of CsI and discuss which kind of element is the best choice for improving the detection efficiency of CsI, we studied the band structure, electronic density of states, and optical properties of CsI, CsI(Ag), and CsI(Tl) by using the first-principles calculation method based on DFT. The exchange correlation potentials among the electrons were described by using the GGA. The results of our calculations are as follows: (1) The band gaps of CsI(Ag) and CsI(Tl) are smaller than that of pure CsI. The conduction band edges move to lower energy level in CsI(Ag) and CsI(Tl) compare that in CsI. Therefore, when doped with thallium or silver, CsI crystals can produce more scintillation photons with energies in the visible range when exposed to the same amount of radiation. (2) The TDOSs of CsI, CsI(Ag), and CsI(Tl) are in agreement with the band structure very well. Some added peaks near the Fermi level were observed in the electronic density of states. This can help us understand the mechanism and the reason doping can improve the detection performance. (3) The optical band gaps of CsI, CsI(Ag), and CsI(Tl) are 3.5 eV, 1.5 eV, and 3.2 eV, respectively. Although the starting point of absorption becomes smaller, the overall results are that doping makes the absorption of visible photons weaker. All of the results indicate that doping can improve the detection efficiency of CsI crystals. Our work provides both theoretical support for the luminescent mechanism at play in scintillors when they are exposed to radiation and a reference for CsI doping.
ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China under grant Nos. 11275071 and 11305061, and the Fundamental Research Funds for the Central Universities under grant No. 2014MS53.
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