First-principles studies of defect behaviour in bismuth germanate
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2022-09-23
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Intrinsic defects are known to greatly affect the structural and electronic properties of scintillators thereby impacting performance when these materials are in operation. In order to overcome this effect, an understanding of the defect process is required for the design of more stable materials. Here we employed density functional theory calculations and the PBE0 hybrid functional to study the structural, electronic,defect process and optical properties of Bi4Ge3O12 (BGO), a well know material used as scintillator. We examined possible intrinsic defects and calculated their formation energy and their impact on the properties that affect the scintillation process. Furthermore, we investigated the effect and role of rare earth element (REE = Nd, Pr, Ce and Tm) doping on the properties of the BGO system. While the PBE functional underestimated the band gap, the PBE0 was found to adequately describe the electronic properties of the system. Out of all the defects types considered, it was found that BiGe antisite is the most favourable defect. Analysis of the effect of this defect on the electronic properties of BGO revealed an opening of ingap states within the valence band. This observation suggests that the Bi3+ could be a charge trapping defect in BGO. We found that the calculated dopant substitution formation energy increases with increase in the size of the dopant and it turns out that the formation of O vacancy is easier in doped systems irrespective of the size of the dopant. We analyzed the optical spectra and noted variations in different regions of the photon energy spectra.Scintillators are materials that convert high energy rays such as X-rays and γ rays to light. This characteristic is desirable in so many fields. Over the years there has been increased interest in them especially in fast time measurement in nuclear physics1, for precision calorimetry in high-energy physics2 and for positron emission tomography in medical physics3. The interest has resulted in intense efforts channelled towards discovery, research and development of inorganic scintillator materials1,4. To be considered efficient, a scintillator is required to be stable upon exposure to radiation, posses high light yield, fast response, and high efficiency in absorbing radiation. The scintillation properties are closely linked to the structure of the material used. Moreover, the scintillation efficiency is controlled by the presence of defect and crystallographic properties, isotropic propagation of light in scintillation crystals notwithstanding2. Similarly, the scintillation yield, transport and luminescence yield are all dependent on the crystal structure of the scintillator3. Specifically, the energy transfer in the scintillator is a structure sensitive phenomena governed by carrier capture in deep and shallow traps, as well as other radiation-dependent defects5. Defects serve as trap for electrons and holes, interrupting energy transfer in the process. Indeed, previous investigations confirmed the existence of traps in scintillators, although a complete understanding of the energetics of these defects in most materials is still scarce. In view of the strong performance-structure relationship, it is important to understand the defect chemistry of the material, especially those that can be induced when the material is in operation6,7. This is required to improve existing and in design of resilient materials.One of the most studied material used as scintillator is the Bismuth germanate Bi4Ge3O12 (BGO)8. First synthesized in 1957, BGO is a cubic crystal with space group I43d possessing eulytine-type structure with BiO6 octahedron and GeO4 tetrahedron, an arrangement that can accommodate defects1,9. It has been extensively studied as a scintillator for various applications and found to emit light in the visible region upon exposure to ionizing radiation10. It is also known to possesses high density (7.13 g/cm3) and high light yield (9000 photons/MeV), in addition to impeccable characteristics such as a short radiation length and absence of hygroscopicity11. These characteristics have resulted in the material finding application in tomography scanners and high-precision calorimeters used in the detection of electromagnetic radiation12. This advantages notwithstanding, its wide spread application in fields such as high energy physics is limited due to low response time (about 300 ns). Another issue is the presence of germanium in the system, which raises question about its cost11. Most of the issues encountered in this material is related to its crystal structure13. The arrangement of atoms in BGO is such that a number of charge-trapping sites exist. An understanding of the defect behaviour and formation in the material is required to enhance its performance and minimize deficiencies. Previously, thermo-luminescence experiments have been employed to characterize intrinsic defects in BGO. It was reported that the relative intensities of the glow peaks observed above room temperature depends on radiation dose and the presence of impurities. Certain defect types are suggested as trapping sites with further analysis revealing a range of trapping levels in pristine and doped BGO14. Atomistic simulations employing empirical pair-potential was used to calculate the formation energy of basic defects in BGO. Obtained results supports experiment observation of charge trapping defects in BGO15.Theoretical methods been have applied successfully to describe various material characteristics related to defect and to calculate defect energetics of materials13,16. Specifically, density functional theory has proved to useful in determining band gaps and defect properties of scintillators17. Studies of this nature consider deviation from stoichiometry resulting from formation of intrinsic defects, whose presence determines the stability of the material in operation. The incorporation of dopant ions into perovskite and similar structures in a wide range of concentrations has been reported to improve properties and applicability of materials18,19. Specifically, the introduction of rare-earth elements (REE) has received immense attention due to its ability to modify electronic properties and luminescence in scintillator materials20. Moreover, the doping of BGO attracted attention due to the ability of its photons to interact with the material effectively and combine to form new photons with doubled energy and frequency21. Indeed, REE are interesting dopants for enhancing the properties of BGO. Among REE ions, Pr3+, Nd3+, Tm3+ and Ce3+ have received attention as a result of offering remarkable activator ion for luminescence12,19. Jazmati and coworkers22 investigated BGO: Ce samples implanted at linear no-threshold model at 77 K with He ions for manufacturing waveguides. They observed a phase change in the BGO, modifying its cubic structure to an anisotropic guide layer generated from the ’stress’ of the He beam deployment and, at the same time modifying the optical activity. Besides, Nd doped BGO demonstrates the properties that allow its use in the construction of solid-state lasers23. The advantages reported for these resultant materials notwithstanding, their practical applicability has been hindered by lack of detailed information about their microstructure and the position of the dopant atom in the system. The choice of the REE dopant employed for our investigation is guided by experimental findings. Different REE dopants have been reported to improve scintillation performance12,22. For instance, it has been show that the radiation resistance of BGO crystal was improved by Eu doping leading to faster induced absorption recovery24. In the same vein, Ce doping has been found to lead to occurrence of thermo-luminescence (TSL) peaks around room temperature (RT)25. Similarly, Nd, Tm and Ce are attractive dopant as they have been found to posses emission lines due to 4f–4f transmission from visible to near-infrared wavelength, hence are known as luminescence centers26.Previously, density functional theory (DFT)13,27,28,29 has been employed to study the electronic and optical properties of BGO. Also, attempts have been made to study the doping of BGO with rare earth elements in order to improve its applicability using DFT12. These investigations employed different flavours of the DFT within Generalized gradient approximation (GGA). It was reported that the major part of incoming energy is absorbed by oxygen (O) P electrons and transferred to bismuth (Bi) p states. All of these investigations reported band gaps that are below the experimental reported values. In order to accurately characterize the defect behaviour and optical properties of a system, it is important to obtain electronic properties that are close to experiment30. This work employs the hybrid PBE0 functional to study BGO. The hybrid functional, specifically the PBE0 has been used successfully to study systems where GGA has been found to underestimate band gaps31. In this work, we investigate the defect process in BGO and predict the stability of the different defect type, the effect of the prominent defect on factors affecting scintillation using density functional theory. Although this work focuses on BGO, inferences drawn from this investigation will aid understanding other materials used for similar applications. Moreover, it is expected that understanding of these kind of defects will help to optimize the efficiency of scintillators.The BGO system crystallizes in the cubic symmetry, comprising of a regular arrangement of GeO4 tetrahedra sharing vertices with distorted BiO6 octahedra, see Fig. 1a. The primitive unit cell contains two formula unit of 38 atoms13. Rodriguez and coworkers28 reported the crystal structure of BGO with experimental lattice parameter a = b = c = 10.513 Å. We begin our investigation by calculating the lattice parameter of pristine BGO and obtained a lattice parameter of 10.6 Å which is in good agreement with values reported from previous theoretical work12 and experimentally28,32. The BGO structure is such that two different Bi–O bonds exist due to the distortion of the the BiO6 octahedron. The bond lengths for the pristine system are presented in Table 1. Observation reveals an agreement with values reported by experiment32. After validating our model for the calculation of the structural properties of defect-free BGO, we proceeded to calculate the electronic structure of the pristine system. The density of states in Fig. 2 offers insight into the chemical bonding in pristine BGO. Figure 2a presents the GGA calculated density of states, where we obtained a band gap of 3.4 eV comprising of a O-p states dominated valence band maximum (VBM) and a conduction band that comprises of hybridization of Bi-p and O-p states. Note that the calculated band gap is smaller than the experimental band gap of 4.58–4.7 eV33,34. Previous DFT investigations using GGA12,28 reported a band gap of 3.5 eV. Similar calculations using full-potential linearized augmented plane wave, taking into account spin-orbit interaction yielded similar band gap13. All previous work were unable to reproduce the experimental band gap. Correct prediction of the electronic properties especially fundamental properties of the gap, its width and states is important in determining the defect energetics30, optical properties and characterization of scintillation process13. In view of this, there is a need to consider another functional in a bid to improve the result.The DFT-PBE0 method with 12.5% exchange was employed and the obtained band gap of 4.6 eV is in better agreement with experiment than the one obtained with DFT-PBE. Figure 2b presents PBE0 calculated DOS for pristine BGO. The same features obtained for DFT-PBE are reproduced here with the only difference resulting from increase in the size of the band gap.The band structures (Fig. 2c) calculated along calculated along Γ → H →N → Γ →P → H|P high symmetry path of the Brillouin zone further supports the information obtained from the density of state plot shown in Fig. 2b. It is worth noting that our calculated band gap using the PBE0 significantly improves the band gap previously obtained using PBE-GGA functionals (see Table 1).The electronic band gap of a material is a valuable feature that provides a deep understanding of its electronic, defect and optical properties. From our investigation, it was found that, the PBE0 approximation improves greatly the value of the band gap energy. Infact, PBE0 approximation improves, significantly, the calculated gap value better than the conventional GGA approximation. Llalic and coworkers13 have previously carried out first-principles calculations, including spin orbit coupling on BGO, while certain features were found to be improved in comparison to standard DFT, the band gap was underestimated. Using PBE0, key features of the electronic states are reproduced while a much improved band gap is also obtained. An accurate prediction of the band gap is important for the meaningful characterization of defect energetics35,36. Moreover, several DFT calculations36,37,38 on Bi-containing oxides have been successfully carried out, including investigations involving defect without the employing spin-orbit coupling.
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