Ab initio molecular dynamics simulation of the effects of stacking faults on the radiation response of 3C-SiC

In this study, an ab initio molecular dynamics method is employed to investigate how the existence of stacking faults (SFs) influences the response of SiC to low energy irradiation. It reveals that the C and Si atoms around the SFs are generally more difficult to be displaced than those in unfaulted SiC, and the corresponding threshold displacement energies for them are generally larger, indicative of enhanced radiation tolerance caused by the introduction of SFs, which agrees well with the recent experiment. As compared with the unfaulted state, more localized point defects are generated in faulted SiC. Also, the efficiency of damage production for Si recoils is generally higher than that of C recoils. The calculated potential energy increases for defect generation in SiC with intrinsic and extrinsic SFs are found to be higher than those in unfaulted SiC, due to the stronger screen-Coulomb interaction between the PKA and its neighbors. The presented results provide a fundamental insight into the underlying mechanism of displacement events in faulted SiC and will help to advance the understanding of the radiation response of SiC with and without SFs.

Scientific RepoRts | 6:20669 | DOI: 10.1038/srep20669 to study the fundamental properties of SiC containing intrinsic stacking faults (ISFs) and (or) extrinsic stacking faults (ESFs). Umeno et al. have investigated the SF formation energy and the stress-strain relationship induced by the SF formation 19 . Oda et al. have studied the formation energy and electronic structure of SiC with ISFs 20 . Jamison et al. have investigated how the SFs influence the dose to amorphization in SiC and found that the energy barriers for Si interstitial migration and the rate-limiting defect recovery reaction are reduced by the existence of SFs 18 . In spite of these extensive studies, the dynamic processes for defect generation in SF-contained SiC at an atomic level have not been revealed yet. Besides, the origin of the enhanced radiation tolerance caused by the SF formation needs to be further explored.
In recent years, the ab initio molecular dynamics (AIMD) method, in which the interatomic potential is obtained by electronic structure calculations rather than empirical fitting, has been demonstrated to be a powerful tool in simulating the displacement events in ceramic materials [21][22][23][24][25] . It has been revealed that physical parameters like threshold displacement energy can be determined with ab initio accuracy, and new mechanism for defect generation and new defective states that are different from classical molecular dynamics (MD) can be predicted. In particular, the role of charge transfer during the dynamic process of recoil events can be elucidated. In this study, the AIMD method is employed to study the low-energy recoil events of 3 C-SiC with SFs. Our main aims are (1) to investigate the defect generation mechanism and defect distribution in SiC with SFs; (2) to compare the response of unfaulted and faulted SiC to low energy radiation; and (3) to explore the origin of the difference in the radiation susceptibility between SF-contained SiC and the unfaulted state.

Results and Discussion
Ground-state properties for bulk SiC and stacking fault formation energy. To test the pseudopotentials of Si and C, the lattice constant and cohesive energy for bulk SiC are first calculated and compared with experimental and other theoretical values in Table 1. It is shown that our results are in excellent agreement with experiments and are comparable with other theoretical values 26,27 . The defect formation energy, which is defined by ) condition. For the three types of ISFs, the calculated formation energies under both conditions are found to be nearly identical to each other, i.e., ~-7.8 mJ/m 2 , which agrees well with the value of -3.4 mJ/m 2 reported by Käckell et al. 29 . Umeno et al. have determined the formation energy to be 9.82 mJ/m 2 for a single-layer ISF by DFT method 19 , which differs greatly from our calculations. Such discrepancy mainly results from the differences in the size of the supercell. In our calculations the supercell for SiC with ISFs consists of 256 atoms, while the supercell employed by Umeno et al. consists of only 10 atoms 19 . Similarly, the three types of ESFs exhibit very similar stability. The SF formation energy is calculated to be ~1.7 mJ/m 2 , which differs a lot from the value of -28 mJ/m 2 reported by Käckell et al. 29 This may be due to the differences in the employed exchange-correlation potentials. Käckell et al. carried out the calculations within the framework of local-density approximation, while our calculations are performed by the generalized gradient approximation. Comparing with the experimental value of 2.5 mJ/m 2 30 , we find that our calculated value of ~1.7 mJ/m 2 is in good agreement with experiments.
Threshold displacement energies for C and Si recoils in unfaulted and faulted SiC. The critical physical parameter for estimating damage production rates under electron, neutron, and ion irradiation and predicting the defect profile is the threshold displacement energy (E d ), which can be defined as the minimum transferred kinetic energy for the primary knock-on atom (PKA) to be permanently displaced from its lattice site and form stable defects 12 . In the past several years, the E d values in a number of semiconductors and ceramic materials have been investigated employing the AIMD method 23,25 . In order to explore how the existence of SFs affects the radiation response of SiC, we first calculate the E d s for C and Si recoils in unfaulted SiC along the [001] and [001] directions, which are perpendicular to the SiC(111) plane and correspond to the [111] and [111] directions in bulk SiC, respectively. A comparison of our results with other theoretical values is provided in  [001] direction and 63 eV for the [001] direction. It is shown that our results are in good agreement with the results reported by Gao et al. 12 . Comparing our results with the classical MD simulation carried out by Devanathan and Weber 31 , we find that the E d s obtained by the AIMD method are generally much smaller, except for the case of Si[001]. This may be due to the fact that charge transfer that occurs during the recoil events is taken into account by the AIMD method while not considered in the classical MD simulations 32 . The calculated E d s for C and Si PKAs in SiC with ISFs and ESFs (see Figs 1 and 2) are summarized in Table 3. As for C recoils around the ISFs, it is found that along both the [001] and [001] directions the E d values for C 3 PKAs are generally larger than those for C 1 and C 2 PKAs. In the case of C recoils around the ESFs, the E d values for C 1 PKAs are the highest for both [001] and [001] directions. Obviously, the three types of C PKAs that have different interlayer spacing from the SFs exhibit different tolerance to irradiation. Similar phenomenon is also observed for Si recoils, for which the E d s in several cases are larger than 150 eV, i.e., the PKA is not permanently displaced at energy up to 150 eV. It is found that the three types of Si recoils around the SFs are affected remarkably and exhibit different E d values. Comparing the E d s for C and Si PKAs, we find that generally considerably higher energies are needed for displacing the Si PKAs than those for displacing the C PKAs, similar to the cases in bulk SiC 12 . These results show that the radiation susceptibility of the C and Si atoms around the SFs is affected significantly by the existence of SFs.
In  E e is the incident energy, m e is the electronic mass, M is the atomic mass and c is the velocity of light 33 . Assuming 300 keV electrons incident on SiC, the maximum energy transferred to Si and C atom are 59.5 and 71 eV, respectively. Our finding that the E d values of C and Si recoils are increased by the existence of SFs, therefore, suggests that SiC with SFs is less susceptible to low energy irradiation. This is consistent with the experiments carried out by Zhang et al. 17 and Jamison et al. 18 . Employing 550 keV Si + ion irradiation, Zhang et al. investigated the radiation tolerance of SiC with and without SFs, and found that the SiC with a high-density of SFs exhibits more than an order of magnitude increase in radiation resistance 17 . Jamison et al. studied the crystalline-to-amorphous transition in SiC using 1.25 MeV electron irradiation, and also found that SiC with ISFs or ESFs behaves more robustly under irradiation environment 18 .
Defect distribution in unfaulted and faulted SiC. The defects created by C and Si PKAs in recoil events are summarized in Tables 4 and 5, respectively. In the case of C PKAs, the defects created in unfaulted SiC mainly consist of the carbon vacancy (C vac ) and carbon interstitial (C int ), as shown in Table 2, which agrees well with the results reported by Gao et al. 12 . Comparing the damage end states created by different carbon recoils in SiC with   direction to replace its neighboring C atom. The replaced C atom then moves away from its lattice site to form stable carbon interstitial. As a result, the final defect structure consists of a C FP, a Si C antisite defect and a C Si antisite defect. Our calculations show that the total defect number generated by C PKAs in faulted SiC is generally not less than that in unfaulted SiC.

Stacking sequence Direction
Defect type C 1 C 2 C 3
The total defect number created by C and Si PKAs in faulted SiC is illustrated in Fig. 3. It is found that the Si PKAs are generally more efficient in damage production than C PKAs 34 . Weber et al. have calculated the efficiency of damage production for C, Si and Au PKAs over the energy range from 0.1 to 400 keV using a modified version of the stopping and range of ions in matter (SRIM) code 34 . They suggested that the total damage efficiency for C PKAs is much lower than that for Si PKAs at low damage energies 34 , which is consistent with our results. Comparing the defects generated by Si PKAs in faulted SiC, we find that the defect configurations are similar, i.e., antisite defect, Si FP and C FP. Besides, the defect number for different Si PKA along a certain incident direction is nearly identical to each other. Zhang et al. applied the MD method to study the defect production in sc-SiC, SiC with a high density of ESFs and SiC with a high density of ISFs, and found that there are no great difference among the three simulation cells in defect number and configurations 17 . In the meantime, the distribution of created defects in faulted SiC is shown to be very localized. These results agree well with the study of radiation tolerance of sc-SiC and SiC with SFs performed by Zhang et al., in which it was found that the existence of SFs leads to more localized point defect production 17 3 [001] at 152.5 eV are very similar to those in C recoil events, i.e., the maximum potential energy increases for SiC with SFs are always larger than those for unfaulted SiC. The maximum potential energy increases represent the maximum in screen-Coulomb interactions between PKAs and one or more atomic nuclei on lattice or defect sites, similar to classical two-body interaction 33 . Our results show that the introduction of SFs leads to greater maximum potential energy increase than unfaulted state, i.e., stronger interaction due to more effective screening of Coulomb force between PKA and its neighbors exist in faulted SiC, which may increase the energy barrier for defect generation. Consequently, a greater kinetic energy is necessary to overcome the larger energy barrier for defect generation, corresponding to the larger threshold displacement energies for C and Si PKAs in faulted SiC than those in unfaulted SiC. Another finding is that the maximum potential energy increases for Si PKAs are generally larger than those for C PKAs, which is consistent with our results that generally considerably higher energies are needed for displacing the Si PKAs than those for displacing the C PKAs.

Conclusions
In summary, low-energy recoil events in unfaulted and faulted SiC have been investigated by ab initio molecular dynamics method based on density functional theory. The threshold displacement energies are shown to be dependent on the interlayer spacing between the PKA and the SFs.   Potential energy increase analysis shows that the existence of SFs increases the energy barrier for defect generation, i.e., the C and Si primary knock-on atoms in faulted SiC need to overcome higher energy barrier than those in unfaulted SiC to generate defects.

Methods
All the calculations are carried out using the Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA) code. The norm-conserving Troullier-Martins pseudopotential 36 are employed to determine the interaction between ions and electrons and the exchange-correlation potential is described by the generalized gradient approximation parameterized by Perdew, Burke and Ernzerhof 37 . The valence wave functions are expanded by a basis set of localized atomic orbitals and single-ζ basis sets are employed, with a K-point sampling of 1 × 1 × 1 in the Brillouin zone and a cutoff energy of 90 Ry. In the literature, Zhang et al. 17 and Lin et al. 38 have reported that the SFs lie in the (111) plane of SiC. Hence, both the ISFs and ESFs investigated in this study are created based on the 3C-SiC(111) plane. For SiC with ISFs and ESFs, the supercell consists of 256 and 320 atoms, respectively. Three types of ISFs, i.e., (ABC)(AC)(ABC), (ABC)(AB)(ABC) and (ABC)(BC)(ABC) and three types of ESFs, i.e., (ABC)(BABC)(ABC), (ABC)(ABAC)(ABC) and (ABC)(ACBC)(ABC), as shown in Figs 1 and 2, have been considered. To simulate the low energy recoil events, three types of Si or C on the boundary of the SFs, as denoted in Figs 1 and 2, are selected as PKA and a certain amount of kinetic energy is provided along the direction perpendicular to the SiC(111) surface, i.e., [001] and [001]. The simulations are conducted with a NVE ensemble and a variable time step scheme is employed to avoid the instability of the system.