Ab initio molecular dynamics simulation of low energy radiation responses of α-Al2O3

In this study, an ab initio molecular dynamics method is employed to investigate the response behavior of α-Al2O3 to low energy irradiation. Different from the previous experiments, our calculations reveal that the displacements of oxygen dominate under electron irradiation and the created defects are mainly oxygen vacancy and interstitial. The experimental observation of the absorption peaks appearing at 203, 233 and 256 nm for α-Al2O3 under electron irradiations should be contributed by the oxygen defects and these defects will reduce the transmittance of α-Al2O3, which agrees well with the very recent experiment. This study demonstrates the necessity to reinvestigate the threshold displacement energies of α-Al2O3, and to introduce recombination center for oxygen defects to improve its optical properties and performance under radiation environment.

reported in the case of 90 MeV Xe + ion irradiation 9 , where F + center concentration monotonously increased with the ion fluence in the range up to 10 13 Xe/cm 2 .
Theoretically, Williford et al. have investigated the displacement energies of α-Al 2 O 3 using classical molecular dynamics (MD) method 13 . On the other hand, several density functional theory (DFT) calculations have been carried out to investigate the defect formation and migration in α-Al 2 O 3 3, 14, 16 . In spite of these studies, there still lacks of an atomic-level understanding of the mechanisms for defect generation in α-Al 2 O 3 , as well as the defect distribution and the interaction between defects. In recent years, the ab initio molecular dynamics (AIMD) method has been widely employed to simulate the low energy recoil events in ceramic materials like pyrochlores, fluorite-structure oxides and carbides, in which a number of new defective states and new mechanisms for defect generation that are different from classical MD have been predicted [17][18][19][20] . In this study, the AIMD method is employed to investigate the radiation responses of α-Al 2 O 3 to low energy irradiation. The threshold displacement energies, the pathway for defect generation, the type of created defects, the role of charge transfer during the dynamic process, as well as the impact of created defects on the electronic structure of α-Al 2 O 3 , all have been provided. The presented results will be useful for understanding the structure-property relationship of α-Al 2 O 3 and improving its properties and performances for its application as the substrate material for GaN growth for the production of blue light-emitting diode (LED), thin film passivation material for high-efficiency solar cells, luminescence dosimetry, and so on.

Results and Discussion
Ground-state properties of α-Al 2 O 3 . The structural and elastic properties of α-Al 2 O 3 are first calculated and compared with experimental and other theoretical data. The optimized lattice constants for α-Al 2 O 3 are listed in Table 1, which agree well with the theoretical 21  The threshold displacement energies in α-Al 2 O 3 . The threshold displacement energy (E d ), which is defined as the minimum transferred kinetic energy for primary knock-on atom (PKA) to be permanently displaced from its lattice site, is one of the critical physical parameters for estimating damage production rates and predicting the defect profile under electron, neutron and ion irradiation 19,25 The calculated E d s for O and Al recoils along different directions in α-Al 2 O 3 are summarized in Table 2.      [4156] for Al PKA, the E d s are predicted to be larger than 150 eV, i.e., the PKA is not permanently displaced at energy up to 150 eV. Among the determined threshold displacement energies, the E d value of 148 eV for Al [1210] is the largest. The associated defects and the pathway for defect generation for Al [0001] and Al [1210] recoil events are found to be somewhat different. In the case of Al [0001], the Al PKA moves 1.86 Å away from its lattice site to eject its neighboring aluminum atom and occupies its lattice site. Then, the collided aluminum atom moves along the [0001] direction to hit another neighboring Al atom, and forms an interstitial occupying the octahedral site. The third collided aluminum atom also forms an interstitial occupying the octahedral site, which is 2.01 Å away from its original site. As a result, the final defect structure consists of two aluminum Frenkel pairs (FPs). As for Al recoil along the direction of [1210], besides the Al PKA, its neighboring oxygen atom is also involved in the displacement events. Consequently, the damage end state contains one aluminum interstitial occupying the octahedral site, one aluminum vacancy, one oxygen dumbbell and one oxygen vacancy. These results suggest that the displacement events in α-Al 2 O 3 are strongly dependent on the recoil direction and the species of the PKA. Theoretically, Williford et al. have studied the displacement energies of α-Al 2 O 3 employing the classical molecular dynamics (MD) method 13 . It is found that the E d s of 51.4 eV for Al [2110] and 27.7 eV for Al [1010] obtained by the MD method are much smaller than our AIMD results. In the previous AIMD simulation of low energy recoil events in SiC and pyrochlores [18][19][20]25 , it is also found that the threshold displacement energies and the mechanism for defect generation obtained by AIMD method are generally different from the classical MD results. This may be due to the fact that recoil events are dynamic charge transfer processes, while such charge transfer was not considered in classical MD 26 . In this study, the charge transfer for the O and Al PKAs along the [2110] direction during the displacement process as a function of time is illustrated in Fig. 1. In Fig. 1a, the variations of charge difference for O [2110] at the energies of 27 and 26.5 eV are compared, which shows that charge transfer from and to the recoil atom takes place during the whole dynamics process. Especially, the charge changes at 27 eV are more significant than those at 26.5 eV, corresponding to reaching a stable defective state and returning  Fig. 2. Taking the initial charge-density (as shown in Fig. 2a) as a reference, it is clear that electron cloud deformation and charge redistribution takes place in the whole process. In Fig. 2b, when the O PKA is displaced to the interstitial site, it interacts with its neighboring atoms and the electron clouds around the lattice O start to deform toward the O PKA. With time evolution, there is a more significant electron cloud deformation to overcome the energy barrier for stable defect formation. The charge redistribution eventually leads to the formation of one O-O dumbbell, as shown in Fig. 2d.
Under electron irradiation the maximum energy transferred to an atom can be expressed as where E e is the incident energy, m e is the electronic mass, M is the atomic mass and c is the velocity of light 25 . Thus, our calculated minimum E d values of 25 eV for O recoil and 47.5 eV for Al recoil correspond to 152 and 415 keV electron irradiation, respectively. These radiation energies are comparable with the experimental measurements 27, 28 , while discrepancies exist in the threshold displacement energies. Arnold and Compton suggested that at 77 K the threshold radiation energy for α-Al 2 O 3 was 430 keV, and the E d values were 90 ± 5 for O ions and 50 ± 5 eV for Al ions 27 . In their study, the crystal orientation was not considered and the results were strongly dependent on the temperature, i.e., irradiation at 77 K produced many more centers than did a comparable irradiation at 300 K and the ratio of the yields at these two temperatures was at least ten 27 29 . In our study, the threshold displacement energies are determined by the creation of point defects such as oxygen or aluminum Frenkel pair. These defects may be too few to be observed experimentally, for which the threshold displacement energies were determined by the first appearance of defect clusters. Pells and Stathopoulos 30 carried out high voltage electron microscope measurement with optical measurement of electron-irradiation induced color centers on α-Al 2 O 3 . They demonstrated that the threshold radiation energies were independent of the temperature and they were 400 ± 20 and 175 ± 20 keV for the oxygen and aluminum ions, respectively, and the determined E d values were 76 ± 3 eV for O and 18 ± 3 eV for Al 30 . In their work, the crystal orientation was also not considered. Considering that impurities or defects may exist in the sapphire sample and the sapphire has a large band gap, the impurities or defects would make charge transfer process more likely and consequently affect the optical absorption. This may partly cause discrepancy between their work and our simulation.  Table 3, and the defect configurations are illustrated in Fig. 3. As shown in the table, the damage end states after oxygen recoil events generally consist of one oxygen vacancy and one oxygen dumbbell pair with its neighboring oxygen atoms (see Fig. 3a Fig. 3b. For aluminum recoil events, one aluminum vacancy (Al vac ) and one aluminum interstitial occupying the octahedron site (Al octa ) are created in most cases, as shown in Fig. 3c. Similar to the cases of oxygen recoil events, the mechanisms for defect creation and the displacement of Al PKA are generally different. In the cases of Al [0001] , which is also in good agreement with our simulations. Impact of point defects on the electronic structure of α-Al 2 O 3 . Aluminum oxide is one of the earlier materials used in luminescence dosimetry, while the application is limited by its low thermo-luminescence sensitivity. Great efforts have been devoted to study the thermo-luminescence and optical stimulated luminescence   sensitivity, the electronic structure as well as the optical absorption of α-Al 2 O 3 . In order to explore how the radiation damage influences the band gap and optical absorption, first-principles calculations based on density functional theory are further carried out to study the electronic structures of damaged α-Al 2 O 3 . As discussed above, the associated defects are mainly aluminum FP and oxygen FP. The total density of state distribution of damaged α-Al 2 O 3 with oxygen FP and aluminum FP are analyzed and compared with that of pristine state in Fig. 4. The band gap for pristine sapphire phase of alumina is predicted to be 7.7 eV, which is much smaller than the experimental data of 8.7 eV 35 . This underestimation is because of the well-known discontinuity of exchange-correlation energy of the local-density approximation. For the damaged α-Al 2 O 3 with O vac + O-O dumbbell and O vac + O tetra , the Fermi level shifts from 7.6 eV to the higher energy value of 9.9 and 9.3 eV, respectively. Besides, defect levels are observed near the valence band maximum (VBM) and in the forbidden band region. Obviously, the presence of point defect influences the electronic structure of α-Al 2 O 3 significantly, indicating that the optical absorption of α-Al 2 O 3 under irradiation will be affected. As for α-Al 2 O 3 with Al vac + Al octa , the defect levels appear around the VBM and conduction band minimum.
To identify the contribution of the defect to optical absorption, we further analyze the electronic structures of defective α-Al 2 O 3 with single O vacancy and interstitial, as illustrated in Fig. 5. Here, the Al oxygen and interstitial are not considered because the Al recoils have generally much larger threshold displacement energies than oxygen atoms and the oxygen defects dominate under electron irradiation.  36 . Our calculations show that these peaks should be contributed by the oxygen vacancy and interstitial defects. Obviously, the presence of these defects will reduce the transmittance of α-Al 2 O 3 . Ke et al. investigated the change of the surface roughness and transmittance caused by electron and proton irradiation, and found that the transmittance of α-Al 2 O 3 decreased most remarkably in the ultraviolet band under the 100 ~ 150 keV electron irradiation 37 . This is also in good agreement with our simulations. These results suggest that it is necessary to enhance the radiation tolerance of α-Al 2 O 3 or introduce recombination center for oxygen defects to improve its optical properties and performance under radiation environment.

Conclusions
In summary, low energy recoil events in α-Al 2 O 3 have been investigated by an initio molecular dynamics method. Generally, the threshold displacement energies for oxygen are smaller than those for aluminum, indicating that the displacement of oxygen dominates under electron irradiation and the created defects are mainly oxygen vacancy and interstitials. Moreover, the oxygen interstitial forms the dumbbell defect configuration or occupies the tetrahedral site. For α-Al 2 O 3 with O vac , there are two defect levels appearing at 232 and 219 nm within the ultraviolet (UV) light region. In the cases of α-Al 2 O 3 with O-O dumbbell and O tetra , the induced defect levels are located at 262 nm and 235 nm, respectively. These defects will influence the optical absorption and reduce the transmittance of α-Al 2 O 3 significantly.

Methods
All calculations are carried out using the Spanish Initiative for Electronic Simulation with Thousands of Atoms (SIESTA) code. The norm-conserving Troullier-Martins pseudopotentials 38 are employed to determine the interaction between ions and electrons, and the exchange-correlation potential is described by the local-density approximation (LDA) in Ceperly-Alder parameterization 39 . The valence electron configurations are 2s 2 2p 4 for O, with cutoff radii of 1.46 bohr for both orbitals. For Al the valence electron configurations are 3s 2 3p 1 , and the cutoff radii are 1.86 and 2.06 bohr for 3 s and 3p orbitals, respectively. The all electron and pseudo valence wave function and the Fourier transfer of ionic pseudo potential for Al and O are presented in Figs 6 and 7, respectively. As shown in Figs 6 and 7, when the cutoff radius is larger than 1.0 bohr, the pseudo valence wave functions for O and Al are in reasonable agreement with the all electron wave functions. A series of test calculations have shown that these relatively hard pseudopotentials can be used to describe the short-range interactions between atoms for recoil energy larger than 100 eV. The valence wave functions are expanded by a basis set of localized atomic orbits, and single-ζbasis sets (SZ) are employed, with a K-point sampling of 1 × 1 × 1 in Brillouin zone and a cutoff energy of 60 Ry. In the displacement events, sixteen directions for α-Al 2 O 3 , as illustrated in Fig. 8b and c, are taken into account. To simulate the low energy recoil events, a 3 × 3 × 1 supercell consisting of 270 atoms is used. The simulations are conducted with a NVE ensemble and a variable time step scheme is employed to avoid the instability of the system.