Stoichiometric Defects in Silicon Carbide - American Chemical Society

J. Phys. Chem. C 2010, 114, 22691–22696

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Stoichiometric Defects in Silicon Carbide Ting Liao,†,‡,§,| Olga Natalia Bedoya-Martı´nez,† and Guido Roma*,† CEA, DEN, SerVice de Recherches de Me´tallurgie Physique, F-91191 Gif sur YVette, France, High-Performance Ceramic DiVision, Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China, and Graduate School of Chinese Academy of Sciences, Beijing 100039, China ReceiVed: August 5, 2010; ReVised Manuscript ReceiVed: NoVember 9, 2010

Defect structures showing odd-membered rings are known features of several tetrahedral semiconductors as well as carbon nanostructures; examples of them are bond defects in crystalline and amorphous silicon, Stone-Wales defects in fullerenes and carbon nanotubes, and the core structure of partial dislocations in some tetrahedral semiconductors. We investigate, using Density Functional Theory, two types of stoichiometryconserving defects, which we call SCD and antiSCD and which are metastable structures presenting fiveand seven-membered rings, both in the cubic and in the hexagonal 4H-SiC polytypes. We also investigate the annealing properties of the two mentioned variants and find that one of them (SCD) easily disappears, turning back to a normal site, while the other (antiSCD) transforms to an antisite pair, overcoming a barrier of 0.21 eV. The very short lifetimes at ambient conditions explain why those defects have not been observed up to now, but they suggest they should be observable at very low temperature, and we provide local vibrational modes to facilitate their identification. Introduction Defects in semiconductors play a major role for their performances as functional materials. The knowledge of their stability, kinetics, and electronic properties is an important challenge to the physics and chemistry of solids. Considering native defects, in addition to vacancies and interstitials and their association to form various defect complexes, as in metals, one has to consider seriously the possibility of bond defects, that is, defects obtained by bond breaking or tilting. In tetrahedrally coordinated semiconductors, bond defects frequently manifest themselves as odd-membered rings,1 which, in the case of binary semiconductors, imply the introduction of homopolar bonds. Many amorphous semiconductors have been shown to contain odd-membered ring structures.2,3 For silicon, a similar kind of bond deformation was first considered as a possible mechanism for diffusion without defects.4 Later, it was recognized that bond tilting could provide stable 4-fold coordinated (FFCD) defects.5,6 It has been suggested that they could provide a mechanism for the amorphization of silicon.7,8 Other authors have shown that it should be present as primary damage induced by ion irradiation in silicon and germanium.9-11 Concerning carbon, similar defects have been studied in graphite as a possible source of the Wigner energy,12 that is, the energy released by defect pairs created by irradiation at low temperature when, raising the temperature, they become mobile and recombine. In general, in carbon nanostructures like nanotubes or fullerenes, these defects take the form of unexpected rings arrangements, for example, a five- and a seven* To whom correspondence should be addressed. E-mail: guido.roma@ cea.fr. † CEA, DEN, SRMP. ‡ IMR, Shenyang. § Graduate School of Chinese Academy of Sciences. | Current address: Centre for Computational Molecular Science, Australian Institute of Bioengineering and Nanotechnology, The University of Queensland, St. Lucia, QLD4072, Australia.

membered ring instead of a pair of six-membered ones.13 They can also be exploited to control the growth of carbon nanostructures.14 Silicon carbide is a semiconductor whose electronic properties make it an interesting candidate for high power, high frequency, and high temperature applications.15 It has also other fields of use, for example, in nuclear environment16 as a cladding material or as a structural material for fusion reactors. Again, the properties of defects, their evolution, and their annealing are crucial to predict the properties of the material under irradiation and in the long term usage. Although most applications of silicon carbide are at high temperature, the material is also considered for space applications where its optical17 or electrical18 performances at cryogenic temperatures and in irradiating environment are important. Most works on defects in SiC have coped with interstitials, vacancies, and, to a lesser extent, antisites, which are nonstoichiometric. Their associations (e.g., a Frenkel pair) can be regarded as stoichiometric defects. Close Frenkel pairs were studied to understand the annealing properties of vacancies and interstitials.19-22 The formation energies of Frenkel defects made by a vacancy and an interstitial very far from each other are very high; for close Frenkel pairs, despite a binding energy of a few electronvolts, most reported stable configurations have formation energies that are still above 10 eV, higher than any single vacancy or interstitial defect. In principle, other stoichiometric defects are possibly relevant, not only stoichiometric associations of vacancies and interstitials, like Schottky or antiSchottky defects, but also coordination defects, like those we have previously mentioned for silicon and carbon. There is also evidence, from experiments23 as well as from theory,24 that oddmembered rings characterize the structure of various type of dislocations in SiC. However, stoichiometric point defects of the type of those that were found in silicon and carbon structures have not been reported up to now in silicon carbide.

10.1021/jp107372w  2010 American Chemical Society Published on Web 12/06/2010

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A defect complex that keeps the stoichiometry, and whose formation energy is lower than that of interstitials and of the silicon vacancy, is the antisite pair (AP), which has been investigated in cubic and hexagonal SiC.25-29 It has been proposed that there is a connection between the APs, the alphabet line,s26 and the DI photoluminescence,27 but according to the calculation of recombination barriers APs should be annealed at temperatures at which the DI defects are still present.29,30 For the alphabet lines, it was suggested that some distorted version of the silicon antisite could play a role,26 but no subsequent study seems to have further investigated this possibility. Although here we do not address the latter hypothesis, the stability of distorted versions of the AP is important to definitely rule out the former one. In this Article, we study stoichiometry conserving defects (SCDs) in SiC, which are similar to the FFCD in silicon; indeed, they share with the latter the characteristic tilted bonds, although the presence of two different atomic species allows a larger number of possible configurations. Previous works on antisite pair recombination29,30 from first principles have reported energy profiles wherein metastable states might occur along the paths. However, these states have not been described nor have been estimated the energy barriers for their annealing, except for a work based on empirical potentials.28 As we will see, our first principles results confirm only partially those results. Moreover, as nothing was known concerning the electronic properties and stable charge states of the bond defects, we provide results for two doubly charged bond defects in cubic SiC. After providing some technical details of our calculations, we will present the results for formation energies and defect structures in the first subsection of the Results. The energy barriers for the annealing of the stoichiometric defects are presented in the second subsection and are followed by a discussion on the physical implications of the results. Theoretical Approach and Technical Details Our first principles calculations are based on the Density Functional Theory (DFT) in the local density approximation (LDA), as implemented in the PWSCF package, part of the Quantum-espresso suite.31 We used an ultrasoft and a normconserving pseudopotential to replace the core electrons of C and Si atoms, respectively. Defect systems considered in this study were mostly modeled using 128- and 72-atom supercells, respectively, for 3C- and 4H-SiC. However, we did calculations with 216 atoms supercells in certain cases for checking the convergence. For example, the formation energy of an antisite pair is 5.21, 5.17, and 5.12 eV in a 64, 128, and 216 atoms supercell, respectively. In the case of an SCD, the error on the formation energy is a bit larger, 5.97 eV in a 128 atoms supercell versus 5.79 eV in a 216 atoms one, but the energy barrier varies only from 0.15 to 0.18 eV, respectively. In all calculations, to provide well-converged results, a 2 × 2 × 2 shifted Monkhorst-Pack k-point mesh was used for the sampling of the Brillouin Zone (the shift was applied only in the z-direction for the hexagonal cells); we checked with a 4 × 4 × 4 k-point grid on an SCD configuration in the 4H polytype and found a difference in formation energy of only 0.011 eV. We used an energy cutoff of 30 Ry for the wave function and of 120 Ry for the density, sufficient to achieve a convergence of 2 × 10-2 eV on total energies. The atomic positions were allowed to relax fully until all residual forces were smaller than 2.6 × 10-2 eV/Å (10-3 Ry/bohr); a lower threshold on forces (10-4 Ry/bohr) led to negligible changes as previously reported32

Liao et al.

Figure 1. Illustration of the creation of SCD defects. On the right, (a) a few atoms of silicon carbide with a bond highlighted in red in the conventional cubic unit cell. Next to it, a view along the [111] direction of the bond. The latter can be tilted toward six possible directions: tilting the Si-C bond toward [100], [010], or [001] (respectively, b,c,d) leads to antiSCD type defects, while tilting toward [1j00], [01j0], or [001j] (e,f,g) produces SCD defects.

(only 0.7 meV on an SCD configuration in 4H-SiC). We applied the nudged elastic band (NEB) method to investigate the transformation paths of the SCDs.33 Our threshold error on the energy of path images is 0.1 eV. We used the climbing image procedure and 5-8 images for each barrier. The starting path was a linear interpolation between the initial and final positions. For the calculation of formation energies, we applied the standard formalism that we already described elsewhere.34 The full vibrational spectra of the supercells were calculated using Density Functional Perturbation Theory35 as implemented in the phonon code included in the Quantum-espresso package.31 The local vibrational modes (LVMs) were extracted from the spectrum by comparison with the bulk density of states. The vibrational contributions to the free energy (including the zero point energy) were obtained from the phonon spectra as detailed elsewhere,32 although, here, we neglect the thermal expansion of the material. From them we can calculate the free energy barrier associated with a jump from a stable position to a saddle point, Fact ) Esaddle - Estable - T(Ssaddle - Sstable), and, using the Eyring equation, a rate of conversion between two minima, in both directions, can be obtained. The lifetime, which is the inverse of the conversion rate, is then calculated as:

τ)

h exp(Fact /kBT) kBT

(1)

where h is Planck’s constant, kB is Boltzmann’s constant, and T is the absolute temperature. Results Formation Energies and Equilibrium Structures of Bond Defects. In the zinc-blende crystalline structure, all covalent Si-C bonds are oriented along 〈111〉 directions. A possible distortion of a Si-C bond consists of tilting toward one of the three equivalent crystallographic directions [100], [010], or [001]; due to the asymmetric character of the Si-C bond, for each axial direction two distorted configurations can exist, depending on the starting atom type in that specified direction (Si-C or C-Si). These configurations are shown in Figure 1. For reasons that will become clear in the following, we call the two defects SCD and antiSCD. We remark that our starting point, prior to relaxation (shown in Figure 1), for the antiSCD defect can be obtained by exchanging the silicon and the carbon atoms in the tilted bond of the SCD. The relaxed structures are

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Figure 3. The calculated electronic density of states (eDOS) of the two neutral stoichiometric defects in β-SiC, as compared to the perfect bulk eDOS (full line). Both SCD (left panel) and antiSCD (right panel) have defect levels in the lower part of the band gap. The zero of the energy scale is the valence band top. The curves are filled when the corresponding DFT states are occupied. Figure 2. Two views of the SCD structures in 3C-SiC. On the left, a view along [100]; on the right, we have extracted the two 〈111〉 planes affected by the defect to visualize the formation of five- and sevenmembered rings.

TABLE 1: Formation Energy of Bond Defects in 3C- and 4H-SiCa type SCD

site

basal, cubic basal, hexagonal axial, type 1 axial, type 2 antiSCD basal, cubic basal, hexagonal axial, type 1* axial, type 2 axial, type 3* antisite pair basal, cubic basal, hexagonal axial, Ccfh axial, Chfc

3C-SiC Ef [eV] 4H-SiC Ef [eV] 5.97

6.87

5.19

5.74 5.70 6.04 6.49 6.88 6.74 6.96 7.25 7.37 5.21 5.15 5.40 5.50

a Four inequivalent sites in 4H-SiC correspond to one in the cubic polytype. The two axial types differ by tilting an axial bond along (x or (y in the xz or yz planes, respectively. We also show the formation energies of antisite pairs for comparison. A star distinguishes two configurations with slightly different bonding arrangement.

shown in Figure 2. For the SCD, the structural relaxation is more pronounced, in agreement with a lower formation energy than for the antiSCD, as shown in Table 1. For the cubic polytype, after relaxation the original 4-fold coordination of the perfect SiC crystal is lost, and dangling bonds appear together with C-C and Si-Si bonds. This can be visualized in Figure 2, where we extract only the two 〈111〉 atomic planes containing the tilted Si-C bond. Another interesting feature of the SCD/antiSCD, as shown in Figure 2, is the presence of odd-membered rings. Instead of the sole sixmembered ring, five- and seven-membered rings emerge as a consequence of bond tilting. We notice that the SCD is characterized by a double pair of five- and seven-membered rings sharing the tilted Si-C bond; while in the case of antiSCD, besides a single pair of five- and seven-membered rings, another larger even-membered ring is present, with 10 atoms running through the two three-coordinated atoms, which are 2.47 Å apart. We find an equilibrium interatomic distance for the tilted Si-C bond in antiSCD, as shown in Figure 2, of 1.75 Å, 7% shorter than the normal Si-C bond length (1.88 Å) in perfect zinc-blende SiC crystal. The C-C and Si-Si homopolar bond lengths are 1.55 and 2.28 Å, respectively; for carbon the value is similar to the corresponding one in diamond, but for silicon

it represents a ∼3% contraction. For SCD, the bond length of the tilted Si-C atomic pair (1.73 Å) is slightly shorter than the counterpart in antiSCD, and although no dangling bond is expected from the figure, there are some bonds that are slightly stretched in comparison to the values estimated from regular atomic covalent radius summation (Si-Si, 2.33 Å; Si-C, 1.97 Å; C-C, 1.62 Å). For 4H-SiC, one can either tilt bonds that lie in one of the two inequivalent basal planes, cubic and hexagonal, or one can act on axial bonds (parallel to the z-direction). These choices, if one tilts by 180°, give rise to four types of antisite pairs, two axial ones, with formation energies of 5.50 and 5.40 eV, and two basal ones, the hexagonal with a formation energy of 5.15 eV and the cubic, whose formation energy is 5.21 eV. The two axial variants arise because the initial C atom can lie in a cubic or a hexagonal plane (and the reverse for silicon), hence the labeling in Table 1. Similarly, several variants of bond defects can be obtained. By tilting the bonds by 55° or 125° in the axial (z) direction and by 0° or 30° in the xy plane, we could find the stable positions indicated in the last column of Table 1. Some of the tilted configurations relaxed to normal sites or to antisites. The two configurations labeled with a star in the table have a slightly different connectivity with respect to the other antiSCDs, the first (axial type 1) has a 10-membered ring and an anomalous six-membered one containing a C-C and a Si-Si bond; the second (axial type 3) still encompasses a five- and sevenmembered ring pair. For both types of bond defects, the formation energies in the 4H polytype are distributed around the corresponding value of the cubic polytype, the average for the 4H being very close to the cubic value (it differs by a few hundredths of an eV). The defect structure of the SCD, as shown in the upper panel of Figure 2, astonishingly resembles the smallest structural unit of the silicon core structure extracted from the 90° Shockley glide partial dislocation of SiC.24 Further similarities can be found between the antiSCD defect and one of the recently proposed topological defect models to explain the StaeblerWronski effect in amorphous silicon.36 The topological defect in Si is also characterized by the formation of the local fiveand seven-membered ring structures with two dangling bonds capable of trapping mobile hydrogens. It would certainly be interesting to investigate the role of these defects for hydrogen trapping in irradiated silicon carbide. The electronic structure analysis in Figure 3 for the defects in the cubic polytype shows a fully occupied midgap state dominated by Si-Si pp bonding for the SCD defective structure. Besides, in accord with the dangling bonds, hybridized Si-sp

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Liao et al. TABLE 2: Formation Energies and Energy Barriers along the Three-Step Process Leading from a Normal Site to an Antisite Pair through the Two-Bond Defects in 3C-SiCa Ef Ef perfect barriers Ef barriers Ef barrier antisite a pair charge SiC SCD a antiSCD a 0

0.00

+2

2.44

-2

1.09

6.12 0.15

6.14 0.08

5.97

7.29

2.31 1.41 6.02 1.33 2.20 1.37

6.87 7.12 7.93

0.21 1.90 0.10 0.32 0.05 1.68

5.19 6.91 6.30

a Energies are in electronvolts. The formation energies are referred to the perfect crystal in the neutral state and the electronic chemical potential at midgap.

Figure 4. The calculated vibrational density of states (vDOS) of the two stoichiometric defects in β-SiC, as compared to the perfect bulk vDOS (full line). The inset zooms on the region between 600 and 750 cm-1, where some localized vibrational modes are present.

and single C-p empty states are observed in the energy range around 1 eV above the conduction band edge. On the other hand, for the antiSCD defect, a higher lying occupied midgap state exhibits the character of Si-C pp bonding. For the hexagonal polytype, we expect similar behavior, as the dangling bonds are the same; the last occupied defect level lies at the same distance from the top of the valence band than for the cubic one, both for SCD and antiSCD, for the variants with similar formation energy, and 0.2-0.3 eV higher for the variants with higher formation energy (axial types 2 and 3). The presence of electronic states make the SCD defects candidates for an identification through pholuminescence experiments. The LDA value of the position of the defect states in the gap, which has to be correlated with the energy of the zero-phonon-line (ZPL) of the photoluminescence spectrum, is subject to errors. We can, conversely, rely more safely on the specific vibrational modes associated with the defect as calculated by DFPT. These modes can guide in the interpretation of satellite lines of the spectrum. The vibrational density of states of both stoichiometric defects is shown, together with the bulk one, in Figure 4. Similarly to the antisite pair,30 both stoichiometric defects present LVMs in the gap of the bulk spectra between 610 and 730 cm-1. They are illustrated by the inset of Figure 4. In addition, we detect defect modes above the bulk spectrum, at 924.2, 937.6, 943.9, and 1066.0 cm-1 for SCD, at 970.8 and 1050.8 cm-1 for antiSCD. The phonon modes above 1000 cm-1 clearly distinguish the SCDs from the antisite pair, whose highest mode is at 950 cm-1. Annealing of Bond Defects. The annealing of stoichiometric defects can lead to their disappearance or to their transformation into other stoichiometric defects. We have investigated these kinetic mechanisms, considering the transformation to perfect sites, to antisite pairs and of both bond defects into each other in 3C-SiC. The results are summarized in Table 2. It turns out that the SCD easily transforms to a perfect site, while the antiSCD can be converted to an antisite pair by overcoming a barrier of 0.21 eV, in the neutral state. The conversion of these two bond defects into each other implies a larger barrier to overcome, because it involves the rotation by approximately 180° of a Si-C bond, as can be seen from the left panel of Figure 2. As a consequence, one can view the transformation of a normal site into an antisite pair as a three-jump process: the

first is the tilt of a regular bond to an SCD defect; the second is the switch between the two types of bond defects, and the third is the change from an antiSCD to an antisite pair. The corresponding overall barrier for antisite pair recombination in the neutral state is 3.1 eV, in good agreement with the previous first principles results (3.2 eV in ref 29 and 2.9 eV in ref 30). A similar three-jump scheme was also found in a previous study based on empirical potentials,28 but the sequence of the barriers was even qualitatively different: the highest point in the energy profile for the recombination of an antisite pair was situated between the antisite itself and a bond defect and not between the two bond defects, as in our case. To give a hint on the possible effect of charge states on the energy barriers, we performed NEB calculations for the +2 and -2 charge states. Although we can observe some variations in the barrier heights, with a lowering of the barriers, the overall behavior does not change, except for the fact that the SCD defect is unstable in charge state Q ) +2. Formation energies in the table are referred to the perfect crystal in the neutral state, and for an electronic chemical potential at 1.15 eV (one-half of the experimental band gap) above the valence band edge. The band alignement terms for charged defects (not included in the table) are small and range from -0.20 to -0.15 eV for Q ) +2 and from +0.12 to +0.22 eV for Q ) -2. Because of the known error of Kohn-Sham band gap, the formation energies of the +2 and -2 charged defects need certainly to be corrected; for this reason, we commented only on the qualitative effect on the barriers. The character of the last occupied defect state is kept all along the migration: for Q ) -2 it is hybridized with the conduction band, and for Q ) +2 it merges with the valence band. This is an indication that, even if the correction to be applied may be large, it should not vary much along the jumps. Thus, our calculations for charged SCDs show that there is no reason to expect that charging will enhance their stability. Discussion Our results show that the energy landscape describing bond tilting and rearrangement in silicon carbide is complex and presents some local minima, which were unexpected. In the case of the 4H polytype, the bond defect occurs in several variants, due to geometrical complexity. The analysis of the migration barriers in the cubic polytype suggests that they are annealed at quite low temperature; they could be observed in samples quenched after low temperature irradiation. To give an estimation of the lifetime of these defects as a function of temperature, we used the calculated phonon spectra as described above. For the SCD, the lifetime is of 14 s at 50 K, and 3 h at 40 K, and for the antiSCD, we find 30 s at 70 K and almost 3 h at 60

Stoichiometric Defects in Silicon Carbide K. These temperatures are so low that it is readily explained why these defects have not been observed before, although one cannot exclude to devise an experimental setting allowing for the detection of them. It would be easier to detect the SCDs if they were continuosly created while they are destroyed by thermal vibrations. This is very likely to happen under irradiation by ions or electrons, when silicon carbide is known to amorphize.37-39 As for silicon and germanium, we can expect bond defects to be present at the periferic regions of displacement cascades in ion irradiation, and when the energy of impinging atoms is below the threshold to produce clearly distinguishable vacancies and interstitials. We point out that our SCD structure can be considered as an incompletely recombined (and very strongly bound) carbon Frenkel pair, and indeed we identify it with a metastable structure encountered in studies of recombination paths.19,22 However, it is difficult to recognize a vacancy and an interstitial in the SCD structure, and we think it is more realistic to speak of bond defects. In principle, the production of some (meta)stable defect, like the SCD, certifies overcoming the threshold displacement energy; however, to prove it experimentally, an in situ, and maybe time-resolved, determination of the presence of this defect would be necessary. The threshold for the production of the antiSCD defect is probably a bit higher than for the SCD, but certainly lower than that to produce well-separated Frenkel pairs, whose formation energy is above 10 eV. The annealing of SCD and antiSCD defects will occur before that of Frenkel pairs, as migration energies of vacancies and interstitials are higher than 0.5 eV40 (we exclude here the possibility of accelerated diffusion mechanisms assisted by electronic excitations, which could indeed be possible in silicon carbide). In models for the amorphization of silicon carbide, like the direct impact/defect stimulated (DIDS) one,41 an important role is played by the recombination of those defects which are at the interface between the amorphous and the crystalline regions in the material. In this respect, the bond defects that we have described should be taken into account, precisely because they are expected to form at the interface between heavily damaged regions (the displacement cascade) and portions of the material where no direct creation of defects has occurred. It could be more than a striking coincidence that the activation energy for the annealing of interface defects was estimated at 0.23 eV by fitting existing experimental data on the DIDS model.41 The value is very similar to our calculated annealing energy of bond defects, which can transform to normal sites or to antisite pairs. However, the estimated error on the figure of 0.23 eV was large and would admit also the annealing of defects through the diffusion of neutral carbon interstitials, for which the activation energy is of 0.5 eV.40 In any case, a better knowledge of bond defects from the experimental point of view would be highly desirable. Conclusions In summary, we investigated two types of bond defects in cubic (3C) and hexagonal (4H) silicon carbide. These defects can be generated by tilting one normal Si-C bond from its initial direction along the axis of a tetrahedral unit toward another, which is parallel to the faces of the cubic cell. The subsequent relaxation leads to the formation of five- and seven-membered ring structures, a frequent feature of tetrahedral semiconductors. These defects could be broadly classified into two types, which we call SCD and antiSCD. Their formation energies are close to 6 and 7 eV, respectively, with some variations of a

J. Phys. Chem. C, Vol. 114, No. 51, 2010 22695 few tenths of an electronvolt depending on the polytype and the atomic site. The stability of these defects is, however, very fragile. Indeed, by investigating the energy landscape around these local deformations of the SiC network, we find that the SCDs are easily annealed by reverting to perfect SiC by overcoming a barrier of 0.15 eV, while antiSCDs transform to antisite pairs, with a similar barrier of 0.21 eV, in the neutral state and for the cubic polytype. Our calculations of lifetimes confirm that they will be virtually absent above liquid nitrogen temperature. As previously suggested,28 we find that these bond defects can be seen as intermediate states during the recombination of antisite pairs. Our calculations for charged species (Q ) +2 and Q ) -2) suggest that charging these defects is not going to enhance their stability, but weaken it. Nevertheless, at least in the neutral state, these defects should be observable at very low temperature in irradiated silicon carbide and could contribute to the process of amorphization. Both SCDs and antiSCDs present defect levels in the lowest part of the electronic band gap, which should make them visible by photoluminescence; we provide the position of localized vibrational modes to help their identification. We remark that two dangling bonds of the antiSCD structure could be subject to hydrogen passivation and produce effects similar to the Staebler-Wronski effect in silicon. Acknowledgment. We thank Yves Limoge for useful discussions and a critical reading of the manuscript and Franc¸ois Willaime for suggesting we investigate bond defects. Computing time from CCRT (Centre de Calcul de Recherche et Technologie) and from CINES (Centre Informatique National de l’Enseignement Supe´rieur) through grants gen6018 and den0006 is gratefully acknowledged. References and Notes (1) Wooten, F.; Weaire, D. J. Non-Cryst. Solids 1984, 64, 325. (2) Ridgway, M.; Glover, C.; de M. Azevedo, G.; Kluth, S.; Yu, K.; Foran, G. Nucl. Instrum. Methods Phys. Res., Sect. B 2005, 238, 294–301. (3) Glover, C.; Ridgway, M.; Yu, K.; Foran, G.; Lee, T.; Moon, Y.; Yoon, E. Appl. Phys. Lett. 1999, 74, 1713–1715. (4) Pandey, K. C. Phys. ReV. Lett. 1986, 57, 2287–2290. (5) Cargnoni, F.; Gatti, C.; Colombo, L. Phys. ReV. B 1998, 57, 170– 177. (6) Goedecker, S.; Deutsch, T.; Billard, L. Phys. ReV. Lett. 2002, 88, 235501. (7) Marque´s, L. A.; Pelaz, L.; Lo´pez, P.; Aboy, M.; Santos, I.; Barbolla, J. Mater. Sci. Eng., B 2005, 124-125, 72–80. (8) Marque´s, L. A.; Pelaz, L.; Herna´ndez, J.; Barbolla, J.; Gilmer, G. H. Phys. ReV. B 2001, 64, 045214. (9) Holmstro¨m, E.; Kuronen, A.; Nordlund, K. Phys. ReV. B 2008, 78, 045202. (10) Mazzarolo, M.; Colombo, L.; Lulli, G.; Albertazzi, E. Phys. ReV. B 2001, 63, 195207. (11) Holmstro¨m, E.; Nordlund, K.; Kuronen, A. Phys. Scr. 2010, 81, 035601. (12) Ewels, C. P.; Telling, R. H.; El-Barbary, A. A.; Heggie, M. I.; Briddon, P. R. Phys. ReV. Lett. 2003, 91, 025505. (13) Stone, A.; Wales, D. Chem. Phys. Lett. 1986, 128, 501–503. (14) Ewels, C. P.; Heggie, M. I.; Briddon, P. R. Chem. Phys. Lett. 2002, 351, 178–182. (15) Saddow, S. E.; Agarwal, A. AdVances in Silicon Carbide Processing and Applications; Artech House, Inc.: Norwood, MA, 2004. (16) Snead, L. L.; Nozawa, T.; Katoh, Y.; Byun, T.-S.; Kondo, S.; Petti, D. A. J. Nucl. Mater. 2007, 371, 329–377. (17) Kaneda, H.; Onaka, T.; Nakagawa, T.; Enya, K.; Murakami, H.; Yamashiro, R.; Ezaki, T.; Numao, Y.; Sugiyama, Y. Appl. Opt. 2005, 44, 6823–6832. (18) Cheng, L.; Sankin, I.; Merrett, J. N.; Bondarenko, V.; Kelley, R.; Purohit, S.; Koshka, Y.; Casady, J. R. B.; Casady, J. B.; Mazzola, M. S. Cryogenic and High Temperature Performance of 4H-SiC Vertical Junction Field Effect Transistors (VJFETs) for Space Applications. Proceedings of the 17 International Symposium on Power Semiconductor DeVices & IC’s, Santa Barbara, CA, 2005.

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