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

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Abstract

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.

Introduction

Cubic silicon carbide (3C-SiC) exhibits lots of superior electronic and physical properties such as high electron mobility, saturated electron drift velocity, high corrosion resistance, favorable chemical inertness and small neutron absorption cross-section1,2,3,4,5. It is thus desirable for power switching device applications and is often utilized under harsh environment such as high temperature and high pressure. Due to the superior physical properties of 3C-SiC, it has been considered as a vital component in nuclear applications. For example, 3C-SiC has been considered as an inert-matrix material for water-cooled reactors to burn minor actinides or Pu4, a structural material for fusion power reactors6, a cladding material for nuclear fuel, and a structural material for the reactor core in high temperature gas-cooled reactors7. It is therefore of critical importance to understand the phase stability of 3C-SiC under irradiation and explore the way to enhance its radiation tolerance.

In the past decades, a great number of experimental and theoretical studies have been carried out to investigate the radiation damage effects of SiC8,9,10,11,12. Inui et al. have found that crystalline-to-amorphous transition in single crystalline silicon carbide (sc-SiC) can be induced by electron irradiation at temperatures around 300 K13,14. Several ion irradiation studies on nano-crystalline silicon carbide (nc-SiC) have also been reported and it has been suggested that reducing the grain size may improve the mechanical properties of sc-SiC15,16. Recently, Zhang et al. compared the radiation tolerance of sc-SiC and nc-SiC by employing 550 keV Si+ ion irradiation, who found that the sc-SiC readily undergoes irradiation-induced structural amorphization, whereas the nc-SiC with a high-density of stacking faults (SFs) exhibits more than an order of magnitude increase in radiation resistance17. Jamison et al. studied the crystalline-to-amorphous transition in nc-SiC using 1.25 MeV electron irradiation, and found that the nc-SiC has an increased dose to amorphization, as compared with the sc-SiC. They proposed that the addition of a high density of grain boundaries, grain texture, and the presence of SFs may all contribute to the enhanced radiation tolerance18. Theoretically, the density functional theory (DFT) method has been employed 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 formation19. Oda et al. have studied the formation energy and electronic structure of SiC with ISFs20. 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 SFs18. 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 materials21,22,23,24,25. 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 values26,27. The defect formation energy, which is defined by Ef = Edef - Eundef + niµi18, is calculated for ISFs and ESFs. Here, is the energy of the faulted supercell, is the energy of the unfaulted supercell, is the change in the number of species and is the chemical potential of species i. The chemical potentials of silicon () and carbon () obey the following criteria: , and , where and are the chemical potentials of bulk Si and diamond, respectively, and is the total energy of bulk SiC28. The SF formation energies are calculated under both carbon-rich ( and ) condition and silicon-rich ( and ) 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/m2, which agrees well with the value of −3.4 mJ/m2 reported by Käckell et al.29. Umeno et al. have determined the formation energy to be 9.82 mJ/m2 for a single-layer ISF by DFT method19, 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 atoms19. Similarly, the three types of ESFs exhibit very similar stability. The SF formation energy is calculated to be ~1.7 mJ/m2, which differs a lot from the value of −28 mJ/m2 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/m2 30, we find that our calculated value of ~1.7 mJ/m2 is in good agreement with experiments.

Table 1 Calculated lattice constant and cohesive energy for bulk SiC.

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 (Ed), 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 defects12. In the past several years, the Ed values in a number of semiconductors and ceramic materials have been investigated employing the AIMD method23,25. In order to explore how the existence of SFs affects the radiation response of SiC, we first calculate the Eds for C and Si recoils in unfaulted SiC along the and directions, which are perpendicular to the SiC(111) plane and correspond to the and directions in bulk SiC, respectively. A comparison of our results with other theoretical values is provided in Table 2. The Eds for C and C are determined to be 19 and 47.5 eV, respectively. For Si recoils, the Ed values are calculated to be 95 eV for the direction and 63 eV for the 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 Weber31, we find that the Eds obtained by the AIMD method are generally much smaller, except for the case of Si. 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 simulations32.

Table 2 Calculated threshold displacement energies (Eds) and the associated defect types for C and Si recoil events along the direction normal to the SiC(111) surface.

The calculated Eds 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 directions the Ed values for C3 PKAs are generally larger than those for C1 and C2 PKAs. In the case of C recoils around the ESFs, the Ed values for C1 PKAs are the highest for both [001] and 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 Eds 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 Ed values. Comparing the Eds 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 SiC12. These results show that the radiation susceptibility of the C and Si atoms around the SFs is affected significantly by the existence of SFs.

Figure 1
figure1

Illustration of schematic view of SiC containing intrinsic SFs with (a) (ABC)(AC)(ABC); (b) (ABC)(AB)(ABC); (c) (ABC)(BC)(ABC) stacking sequences.

Figure 2
figure2

Illustration of schematic view of SiC containing extrinsic SFs with (a) (ABC)(BABC)(ABC); (b) (ABC)(ACBC)(ABC); (c) (ABC)(ABAC)(ABC) stacking sequences.

Table 3 Calculated threshold displacement energies (Eds) for C and Si in SiC with intrinsic stacking faults (ISFs) and extrinsic stacking faults (ESFs).

In this study, the weighted average Ed values are calculated to be 52.1 eV for C, 59.5 eV for C, >99.6 eV for Si and >122.1 eV for Si in SiC containing ISFs. As for the PKAs in SiC with ESFs, the average Ed values are calculated to be 37.8, 71.6, >128.4 and >88.1 eV for C, C, Si and Si, respectively. Comparing these results with the values of 19, 47.5, 95 and 63 eV for C, C, Siand Si in unfaulted SiC, respectively, we find that the Ed values in faulted SiC are generally larger. The maximum energy transferred to an atom can be expressed as under electron irradiation, where Ee is the incident energy, me is the electronic mass, M is the atomic mass and c is the velocity of light33. 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 Ed 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 resistance17. 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 environment18.

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 (Cvac) and carbon interstitial (Cint), 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 ISFs, we find that C2 PKAs show similar defect distribution to unfaulted SiC. However, the Frenkel pair separation (dFP) between the carbon vacancy and carbon interstitial is somewhat different. As compared with the dFP of 4.02 Å for C in unfaulted SiC, the separations are 3.83, 4.38, 4.42 Å for C2 with (ABC)(AC)(ABC), (ABC)(AB)(ABC) and (ABC)(BC)(ABC) stacking sequences, respectively. For C in unfaulted SiC, the Frenkel pair distance is 1.67 Å, which is much smaller than the values of 2.45, 2.51 and 2.50 Å for C2 in SiC with (ABC)(AC)(ABC), (ABC)(AB)(ABC) and (ABC)(BC)(ABC) stacking sequences, respectively. These results suggest that in spite of similar damage end states, the pathway for defect generation should be different. For C1 and C3 PKAs, the defect generations are more complex. Besides the C FPs, the neighboring Si atoms of the C PKAs are involved in the recoil events, resulting in the additional formation of Si occupying the lattice C site (SiC), C occupying the lattice Si site (CSi), and (or) Si interstitials (Siint). As for C PKAs in SiC with ESFs, the damage end states generated by C2 and C3 PKAs are generally similar to those for C PKAs in unfaulted SiC, except for C2 with (ABC)(ABAC)(ABC) arrangement. In this case, the neighboring Si atom is ejected along the direction and then rebounds along the opposite direction to occupy the original site of C PKA. In the meantime, the vacant Si site is occupied by the C PKA, leading to the formation of SiC and CSi antisite defects. The mechanism for defect generation in C1 recoil events is different from that in C2 and C3 recoils events. The C1 PKA collides directly with its nearest-neighboring Si atom along the (or ) direction and occupies the Si lattice site to form CSi defect. The struck Si atom receives sufficient energy and moves along the (or ) 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 SiC antisite defect and a CSi 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.

Table 4 Defect configurations for C recoil events in SiC with intrinsic stacking faults (ISFs) and extrinsic stacking faults (ESFs).
Table 5 Defect configurations for Si PKA recoil events in SiC with intrinsic stacking faults (ISFs) and extrinsic stacking faults (ESFs).

In unfaulted SiC, the defects created by Si PKAs under low energy irradiation are one C FP, two SiC and two CSi antisite defects for Si, and one Si FP for Si. Comparing the damage end states created by different Si recoils in SiC with ISFs, we find that Si3 show similar defect distribution to unfaulted SiC, whereas Si1, Si2 and Si2 recoil events exhibit different character. For Si1, the damage end states consist of three SiC, two CSi, one Si vacancy and one C interstitial. In the case of Si2, only two antisite defects (and one C FP for SiC with (ABC)(AB)(ABC) stacking sequence) are generated. Regarding Si2, the created defects are one SiC, one Sivac and one Cint for SiC with (ABC)(AC)(ABC) and (ABC)(AB)(ABC) stacking sequences, and one Si FP for SiC with (ABC)(BC)(ABC) stacking sequence.

As for Si PKAs in SiC with ESFs, only one Si FP is generated by Si2 along the direction and two antisite defects are generated by Si2 along the direction in SiC with (ABC)(ACBC)(ABC) stacking sequence. For the Si3, the damage end states in SiC with (ABC)(BABC)(ABC) and (ABC)(ACBC)(ABC) arrangements are similar to those in unfaulted SiC, whereas the recoil events in SiC with (ABC)(ABAC)(ABC) stacking sequence show different end states, i.e., two SiC, one CSi, one Si vacancy and one C interstitial. In the case of Si3 PKAs along the direction, the defect generation are relatively simple, as indicated by CSi + SiC for (ABC)(BABC)(ABC), Si FP for (ABC)(ABAC)(ABC), and SiC + Cint + Sivac for (ABC)(ACBC)(ABC) stacking sequences.

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 PKAs34. 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) code34. They suggested that the total damage efficiency for C PKAs is much lower than that for Si PKAs at low damage energies34, 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 configurations17. 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 production17. Comparing the different defect configurations for unfaulted and faulted SiC, we find that antisite defects are the most common defects in faulted SiC, whereas in unfaulted SiC the FPs are dominant. The defect generation in sc-SiC and nc-SiC with a grain size smaller than 12 nm have been investigated by Gao et al. using the MD method, in which the kinetic energies of 10 keV for PKA were simulated. They also found that in nc-SiC the antisite defects are more than other defects, in contrast to those produced in sc-SiC, where the dominant defects are FPs35.

Figure 3
figure3

Total defect number created by (a) C PKAs in SiC with intrinsic SFs; (b) C PKAs in SiC with extrinsic SFs; (c) Si PKAs in SiC with intrinsic SFs; and (d) Si PKAs in SiC with extrinsic SFs. Here, the SFint1, SFint2 and SFint3 represent intrinsic SFs with (ABC)(AC)(ABC), (ABC)(AB)(ABC) and (ABC)(BC)(ABC) atomic arrangements, respectively, and the SFext1, SFext2 and SFext3 represent extrinsic SFs with (ABC)(BABC)(ABC), (ABC)(ABAC)(ABC) and (ABC)(ACBC)(ABC) atomic arrangements, respectively.

Origin of the difference in the radiation response between unfaulted and faulted SiC

Jamison et al. studied the energetics of point defects near the SFs and found that the critical migration and reaction energies are reduced significantly enough to enhance the amorphization resistance by increasing the probability of point defect recombination and annihilation18. To explore the origin of the difference in the radiation response behavior of unfaulted and faulted SiC, we further analyze the potential energy increase for stable defect formation in the recoil events of C3 at 70 eV, C3 at 70 eV, Si2 at 141 eV and Si3 at 152.5 eV. As illustrated in Fig. 4(a), the maximum potential energy increases for C3 are 25.3, 19.2 and 17.2 eV for SiC with (ABC)(AC)(ABC) arrangement, SiC with (ABC)(ACBC)(ABC) arrangement and unfaulted SiC, respectively. In the case of C3, the maximum potential energy increases are 20.8, 17.2 and 12.2 eV, corresponding to SiC with (ABC)(AC)(ABC), (ABC)(ACBC)(ABC) arrangements and unfaulted SiC, respectively. The situation in Si2 at 141 eV and Si3 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 interaction33. 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.

Figure 4
figure4

The calculated potential energy increase for (a) C3 at 70 eV; (b) C3 at 70 eV; (c) Si2 at 141 eV; and (d) Si3 at 152.5 eV.

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. The weighted average Ed values are calculated to be 52.1 eV for C, 59.5 eV for C, >99.6 eV for Si and >122.1 eV for Si in SiC with ISFs. As for SiC containing ESFs, the average Ed values are 37.8, 71.6, >128.4 and >88.1 eV for C, C, Si and Si, respectively. As compared with the Ed values in unfaulted SiC, the Ed values in faulted SiC are generally larger, i.e., the PKAs in faulted SiC are more difficult to be displaced, which may enhance the radiation tolerance of SiC, agreeing well with the recent experiments. In the meantime, the defect generation mechanism for C and Si PKAs in faulted SiC is generally more complex and the defect contribution is very localized. The most common defect configurations in faulted SiC are antisite defects, whereas the Frenkel pairs are dominant in unfaulted SiC. 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 pseudopotential36 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 Ernzerhof37. 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., and . The simulations are conducted with a NVE ensemble and a variable time step scheme is employed to avoid the instability of the system.

Additional Information

How to cite this article: Jiang, M. et al. Ab initio molecular dynamics simulation of the effects of stacking faults on the radiation response of 3C-SiC. Sci. Rep. 6, 20669; doi: 10.1038/srep20669 (2016).

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Acknowledgements

H.Y. Xiao was supported by the NSAF Joint Foundation of China (Grant No. U1530129) and the scientific research starting funding of University of Electronic Science and Technology of China (Grant No. Y02002010401085). Z.J. Liu was supported by National Natural Science Foundation of China (Grant No. 11464025) and the New Century Excellent Talents in University under Grant No. NCET-11-0906. The theoretical calculations were performed using the supercomputer resources at TianHe-1 located at National Supercomputer Center in Tianjin.

Author information

Z.L. and X.Z. designed the calculations. M.J. conducted the calculations and wrote the manuscript. S.P., H.Z., C.X., H.X. and F. Z. contributed to the discussion and interpretation of the results. All authors discussed the results and reviewed the manuscript.

Correspondence to H. Y. Xiao or Z. J. Liu.

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Jiang, M., Peng, S., Zhang, H. et al. Ab initio molecular dynamics simulation of the effects of stacking faults on the radiation response of 3C-SiC. Sci Rep 6, 20669 (2016) doi:10.1038/srep20669

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