SiC CSi antisite pairs in SiC identified as paramagnetic defects with strongly anisotropic orbital quenching

SiCCSi antisite pairs in SiC identified as paramagnetic defects with strongly anisotropic orbital quenching U. Gerstmann,1,2 A. P. Seitsonen,1D. Ceresoli,3F. Mauri,1H. J. von Bardeleben,4J. L. Cantin,4and J. Garcia Lopez5 1Institut de Minéralogie et de Physique des Milieux Condensés, Université Paris 6, 140 rue de Lourmel, F-75015 Paris, France 2Lehrstuhl für Theoretische Physik, Department für Naturwissenschaften, Universität Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany 3Department of Materials Science and Engineering, Massachusetts Institute of Technology (MIT), 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA 4Institut des Nanosciences de Paris, Université Paris 6, 140 rue de Lourmel, F-75015 Paris, France 5Centro Nacional de Aceleradores, Thomas A. Edison, Isla de La Cartuja, E-41092 Sevilla, Spain 共Received 8 April 2010; published 17 May 2010兲 The nearest-neighbor antisite pair defects in 4H-SiC, 6H-SiC, and 3C-SiC single crystals have been identified using electron paramagnetic resonance spectroscopy in combination with a nonperturbative ab initio scheme for the electronic gtensor. Based on the theoretical predictions, the positively charged defect has been found experimentally also in the cubic 3C-SiC polytype where it is characterized by spin 1/2 and highly anisotropic gvalues of gxx=2.0030, gyy=2.0241, and gzz =2.0390 within C1hsymmetry. The exceptional large gvalues are explained by details of the spin-orbit coupling causing a strongly anisotropic quenching of the orbital angular momentum of the p-like unpaired electron. DOI: 10.1103/PhysRevB.81.195208 PACS number共s兲: 71.55.⫺i, 71.15.⫺m, 76.30.⫺v I. INTRODUCTION Intrinsic and irradiation induced defects in solid states have been the object of numerous experimental and theoretical studies since they influence the electronic properties of the materials and act as traps for intentional dopants. The basic intrinsic defects which have been clearly evidenced in many semiconductors are monovacancy and divacancy, and defect complexes related to self-interstitials, e.g., distant vacancy-interstitial pairs, so-called Frenkel pairs which are believed to be the primary irradiation-induced defects. In compound semiconductors, another important class of defects exists: the antisites. These defects, formed by atoms on the “wrong” sublattice, are quite ubiquous in the III-V compounds InP,1GaP,2and GaAs.3Antisites and associated complexes were evidenced as native defects in samples grown under nonstoichiometric conditions as well as irradiationinduced centers. Besides vacancies and some complexes related to carbon interstitials,4–9the antisites10 are believed to be also quite common native defects in silicon carbide 共SiC兲, a promising wide-gap semiconductor for high-power, highfrequency, and high-temperature electronics.5But, interestingly, they have escaped any convincing experimental observation in the various SiC polytypes: initial attributions to the silicon antisite SiChave turned out to be erroneous.9An observation of the isolated CSi antisite in the 6H-SiC has been claimed recently11 but this attribution lacks theoretical support. A complex of a CSi antisite with a carbon vacancy VC has been reported12 but can be regarded as a metastable state of the Si vacancy.13 An involvement of antisite pairs SiCCSi in the omnipresent luminescent DIcenter14,15 or the so-called alphabet lines16 was frequently discussed. The predicted too low thermal stability seems, however, to exclude this attribution.17 To investigate the microscopic structure of defects, electron paramagnetic resonance 共EPR兲is the experimental technique of choice providing a magnetic fingerprint of the defects including the electronic gtensor and the hyperfine 共HF兲 splittings. The latter have been frequently decisive for the identification of defects in semiconductors. Among the irradiation-induced defects previously reported in SiC, there is one particular class of unidentified EPR centers with exceptionally anisotropic gtensors,18,19 the so-called I,II spectra in 4H-SiC and the I,I,III spectra in 6H-SiC. Their observation in different polytypes with different doping and the fact that they are introduced by electron irradiation without any further annealing, makes a participation of dopants or residual impurities very improbable. Hence, the I,II,III spectra are expected to originate from intrinsic defects introduced by the irradiation. As no HF structure could be clearly resolved in the early reports, however, the spectra could not be attributed to any particular intrinsic defect model. From their multiplicity, they are expected to occupy all inequivalent lattice sites, the hexagonal 共h兲as well as the quasicubic lattice sites 共k1and k2in 6H-SiC; kin 4H-SiC兲. In both polytypes, they have been observed with very similar principal values of the gtensor providing exceptionally large deviations up to 0.0450 from the free-electron value of ge=2.0023. For intrinsic defects in SiC, this deviation is usually by an order of magnitude smaller: due to weak intrinsic spin-orbit coupling of the light elements Si and C, and because of additional quenching of the orbital angular momentum by the crystal lattice, the gvalues lie in the range between 1.9980 and 2.0060. Without exact knowledge of the microscopic origin, the reason for the exceptionally large gvalues in the case of the I,II共,III兲centers has remained a mystery. An analysis of the equivalent center in 3C-SiC, that has a simpler structure with no inequivalent sites could be helpful. However, contrary to the hexagonal polytypes, intrinsic defects have been much less studied in the cubic 3C polytype where the pioneering work by Itoh et al.20 has been followed by only few further investigations21,22 so that in the 3C polytype a similar center has not been reported up to now. PHYSICAL REVIEW B 81, 195208 共2010兲 1098-0121/2010/81共19兲/195208共8兲©2010 The American Physical Society195208-1 In this work, we show that the defects with such large g tensors are not only observed systematically in irradiated 4H/ 6H-SiC but also in 3C-SiC single crystals. Based on two methods,23,24 the latter nonperturbative one developed very recently, we present ab initio g-tensor calculations in the framework of density-functional theory 共DFT兲for a wide range of defect models. This allows us 共1兲to find out an optimized experimental setup to observe the corresponding EPR spectra in the cubic 3C-SiC polytype and 共2兲to identify these centers as positively charged antisite pairs SiCCSi +from their very particular spin Hamiltonian parameters which are shown to originate from an unusually anisotropic orbital quenching of a p-like unpaired electron. II. EXPERIMENTS Commercial p-type 4H and p-type 6H 共0001兲oriented bulk substrates and n-type free standing epitaxial 共001兲ori- ented 3C layers have been used in this study. The EPR measurements were performed with a standard X-band spectrometer at various temperatures between 4 and 300 K. Independent from the dopants, the I,II,III spectra are not observed in the as grown samples, but only after electron or proton irradiation confirming again the intrinsic nature of these defects. In the p-type doped hexagonal samples, they can be observed under thermal equilibrium conditions. In the n-type cubic layer, photoexcitation is required 共see below兲. All defects reported here, are stable at room temperature. A set of 4H samples have been irradiated at 77 K with electrons of various energies between 350 keV and 1 MeV at doses of 1⫻1018 e−/cm2. Already in the samples submitted to the lowest energy irradiation, beside the boron acceptor as a contamination of the Al-doped p-type sample and the 共C-C兲C +dumbbell,25 the I,II EPR spectra can be observed. They are characterized by a spin S=1/2, a point symmetry C1hand quite similar, very anisotropic gtensors 共Fig. 1兲. The principal values and the orientation of the axes relative to the crystal lattice are summarized in Table II. For some highsymmetry orientations, different HF splittings could be resolved 关see Figs. 1共b兲and 1共c兲, and Table III兴. In particular, for B 储 关1100兴we observe a strongly anisotropic HF interaction with a single Si nucleus with a maximum value of 101 MHz 关see arrows in Fig. 1共c兲兴. For the corresponding lowfield lines around 3300 G, this value is reduced to 50 MHz. For B 储 关0001兴rather broad HF satellites with a splitting of 11 MHz and with an intensity equivalent to about two Si nuclei are observed instead. The 3C and 6H samples have been irradiated at room temperature with a dose of 1⫻1016p+/cm2of high energy 共6.3 MeV兲protons causing a high introduction rate for primary Frenkel pairs 共distant vacancy—interstitial pairs兲in both, C and also Si sublattices. Both samples show under thermal equilibrium conditions a dominant spectrum of the negatively charged silicon vacancy VSi −. In the 6H crystals 共p-type doped兲, we have equally observed the I,II,III spectra 共Table II, see also Ref. 19兲. In the 3C-SiC samples 共n-type doped兲, low-temperature photoexcitation with near band gap light is needed to observe an additional, very similar S =1/2 spectrum with C1hsymmetry, labeled I. The analysis of the angular variation for a rotation of the magnetic field in a 共−110兲plane 共Fig. 2兲allows us to determine its spin Hamiltonian parameters given in Table II 共gtensor兲and Table III 共HF splittings兲. Independent from the direction of the magnetic field, the low-field lines are less intense and a resolution of HF splittings is not possible. For B 储 关001兴, however, we clearly resolve around the high-field line the HF interaction of 9 MHz with an intensity equivalent to about three Si nuclei 共see inset of Fig. 2兲. Equally we observe a second set of less intense, rather broad satellite lines split by 23 MHz which can be attributed to one or two Si nuclei. HF splittings slightly below 30 MHz are also observed for the midfield 共Mf1,Mf2兲lines for B 储 关110兴共around 3300 G兲. For the corresponding high-field line at 3333 G, a resolution is not possible since the EPR lines are covered by the dominant spectrum of VSi −. Most important, however, we see that the principal gvalues are close to those observed in the 4H and 6H polytypes 共see Ref. 19, this work兲, strongly suggesting a common origin. FIG. 1. 共Color online兲共a兲Angular variation in the resonance lines of the EPR signals I 共blue squares兲and II 共red circles兲in 4H-SiC using a 共11–20兲rotation plane for the magnetic field. Insets: EPR spectra for B 储 关0001兴共b兲and for B 储 关1100兴共c兲. FIG. 2. 共Color online兲Angular variation in the resonance fields for the EPR spectrum I in 3C-SiC measured for rotating the sample in a 共−110兲plane. The principal gzz axis includes an angle of 69° with 关001兴共right inset兲. Left inset: EPR signal for B 储 关001兴. GERSTMANN et al. PHYSICAL REVIEW B 81, 195208 共2010兲 195208-2 III. COMPUTATIONAL METHOD To find out the origin for this particular class of centers, we perform g-tensor calculations in a wide range of reasonable intrinsic defects 共see Tables Iand II兲. We use two ab initio methods, both implemented in the QUANTUM-ESPRESSO plane wave code:26 the first is based on perturbation theory treating the external magnetic field as well as the spin-orbit coupling as perturbations.23 The approach was already shown to be sufficiently precise to model quantitatively the g tensor of the carbon vacancy VC +in 4H-SiC.27 The second method24 allows to circumvent perturbation theory with respect to spin-orbit coupling. Instead, the Hamiltonian for the spin-orbit coupling is explicitly included in the self-consistent field calculations whereby in the TABLE I. Calculated gtensors for Frenkel pairs in 3C-SiC. The values for the isolated 共C-C兲C +split interstitial and VSi −are also given and compared with experimental data. ␽ is the angle between the principal axis 共gzz兲and the 关001兴axis, otherwise the corresponding axis is given explicitly. Center, model gxx gyy gzz ␽ 共°兲 VC 2+-共C-C兲C +C1h2.0065 2.0039 2.0009 32 VC 2+-共C-C兲C +C12.0031 2.0022 1.9986 19 共C-C兲C +D22.0019 2.0006 1.9869 0 4H-exp 共Ref. 5兲C1h2.0019 2.0015 1.9962 共41兲关0001兴 VCCSi −-Siint 4+ C1h2.0041 2.0075 2.0165 85 VSi −-Siint 4+,S=3/2C 1h2.0022 2.0023 2.0028 65 VSi −Siint 4+,S=3/2C 3v2.0028 2.0028 2.0031 54 VSi −Siint 4+,S=3/2C 2v2.0029 2.0029 2.0030 0 LE1, exp 共Ref. 22兲C2v2.0029 2.0029 2.0029 0 VSi −,S=3/2Td2.0029 2.0029 2.0029 VSi −, exp 共Refs. 21 and 22兲Td2.0029 2.0029 2.0029 TABLE II. gtensors for SiC-related defect models calculated via the nonperturbative method of Ref. 24. The experimental values measured in this work for the I,II,III centers 共error bar ⫾0.0001兲are also given. ␽ is the angle between the principal axis 共gzz兲and the caxis in 4H-/6H-SiC 共关001兴in 3C-SiC兲. We emphasize in boldface the theoretical models which we assign to the observed EPR spectra. Center, model gxx gyy gzz ␽ 共°兲 3C, I Exp. 2.0030 2.0241 2.0390 69 (SiC-CSi)+C1h,a⬙2.0049 2.0210 2.0497 64 C1h,a⬘2.0059 2.0272 2.0591 46 SiC +C2v2.0306 2.0811 2.0866 0 共CSi-SiC-CSi兲+C2v2.0049 2.0216 2.0298 0 4H, I Exp. 2.0030 2.0161 2.0407 63 (SiC,k-CSi,h兲+Basal,a⬙2.0058 2.0278 2.0585 66 共SiC,h-CSi,h兲+Axial,a⬘2.0097 2.0281 2.0697 4 共SiC,k-CSi,k兲+Axial,a⬘2.0117 2.0242 2.0668 3 4H, II Exp. 2.0029 2.0134 2.0337 52 (SiC,h-CSi,k)+Basal,a⬙2.0077 2.0225 2.0439 54 6H, I Exp. 2.0041 2.0161 2.0407 63 (SiC,k1-CSi,h)+Basal,a⬙2.0034 2.0252 2.0507 66 6H, II Exp. 2.0030 2.0139 2.0323 50 (SiC,h-CSi,k1)+Basal,a⬙2.0063 2.0185 2.0413 49 6H, III Exp. 2.0023 2.0077 2.0452 66 (SiC,k2-CSi,k2)+Basal,a⬙2.0060 2.0196 2.0582 68 SiCCSi ANTISITE PAIRS IN SiC…PHYSICAL REVIEW B 81, 195208 共2010兲 195208-3 present implementation this is done within a collinear approximation. The deviation ⌬g ␮ ␯ from the free-electron value geis afterwards calculated via a spin flip within the orbital magnetization24—very similar to that what happens experimentally if the EPR resonance condition is fulfilled.28 For defects in SiC with moderate deviation from the freeelectron value, both methods give the same results. For example, for the isolated Si vacancy VSi −, both methods predict an isotropic value of g=2.0029 that agrees with the experimental value 共see Table I兲. For some defects with large deviation, in contrast, the perturbative approach of Ref. 23 is unable to provide converged results even if large 8⫻8⫻8 equidistant k-point meshes are used. Here, the nonperturbative method comes up to be superior yielding well-converged data for 4⫻4⫻4 samplings. To model the defects, we use supercells containing 144 共6H-SiC兲to 216 共3C-SiC兲atoms, standard norm-conserving pseudopotentials with an energy cutoff of 50 Ry, and the spin-polarized, gradient-corrected functional of Perdew, Burke, and Ernzerhof 共PBE兲共Ref. 29兲. All defect structures have been fully relaxed using 2⫻2 ⫻2k-point samplings. IV. RESULTS AND DISCUSSION A. Electronic gtensors We start our theoretical investigations in the cubic 3C polytype. In the irradiated samples, distant vacancyinterstitial pairs 共Frenkel pairs兲are believed to be the primary defects on both Si and C sublattices. For the resulting VSi −-Siint 4+ and VC 2+-共C-C兲C +complexes, however, we calculate much too small gvalues 共Table I兲resembling those of the isolated silicon vacancy VSi −共Refs. 21 and 22兲and the isolated 共C-C兲C +carbon split-interstitial in 4H-SiC,5respectively. Note that this is true for all investigated configuration within various symmetries, i.e., this result holds independent from the relative position of the vacancy and the corresponding interstitial atom. Hence, Frenkel pairs can be excluded as an origin for the large g-value spectrum. The same is true for the isolated carbon antisite CSi since it provides no paramagnetic state in the gap. Interestingly, for a whole class of SiC-including defects 共SiC +,SiCCSi +,CSiSiCCSi +兲exceptionally large gvalues are predicted 共Table II兲. But the orientation of the gtensor relative to the crystal lattice is only well reproduced for the nearestneighbor antisite pair SiCCSi +. Single positively charged, it provides an S=1/2 ground state within C1hsymmetry, whereby the unpaired electron occupies an a⬙-like porbital aligned perpendicular to the mirror plane 共see Fig. 3兲. Within C1hsymmetry, there exist two minima. The unpaired electron occupies either an a⬘or an a⬙orbital, mainly localized at the SiCantisite atom and one 共a⬘兲or two 共a⬙兲of the in C3v symmetry equivalent Si ligands 共see also Fig. 5兲. The competing a⬙-like minimum provides an excited state that is calculated slightly higher in total energy. However, the orientation of its gtensor is far away from the experimentally observed value 共Table II兲. Both, an isolated SiC +as well as antisite trimers CSiSiCCSi +共Ref. 15兲provide similar magnetization densities m共r ជ 兲=n↑共r ជ 兲−n↓共r ជ 兲共mainly localized at the SiCand two equivalent Si ligands兲. But these defects are predicted to have C2vsymmetry with the gtensor oriented along 关001兴, strongly contradicting the experimental finding 共Table II兲. From our g-tensor investigations in 3C-SiC, we can, thus, definitely confirm the antisite pair model and exclude similar antisite-related defects. In the hexagonal polytypes, the nearest-neighbor antisite pairs SiCCSi +may exist in axial 共along the caxis兲and basal configurations but only the basal antisite pairs fit the experimental results. The gtensors of the axial pairs are calculated to be slightly off-axis oriented by 4°—far away from the experimental finding 共Table II兲. We expect that the axial pairs 共and consequently also the isolated Si antisites with the largest gvalues兲are not observable in EPR because of too fast spin-relaxation times. Hence, we attribute the two spectra in 4H-SiC and the three spectra in 6H-SiC to the positively charged basal antisite pairs with the SiCantisite on the hexagonal hand quasicubic k共k1,k2兲lattice sites, respectively 共Fig. 4, Table II兲. B. HF splittings For antisite pairs, our ab initio calculations explain also nicely the observed HF structures 共Table III兲. In the 4H samples and for basal pairs, the maximum HF splitting of C [001] [110] [110] Si C Si Si2 Si2 C2 C2 C C Si FIG. 3. 共Color online兲SiCCSi +antisite pair in 3C-SiC, where neighboring Si and C atoms have changed their positions. The resulting magnetization density 共inset兲gives rise to the EPR fingerprint of a p-like hole 共see also Fig. 5兲along 关001兴. FIG. 4. 共Color online兲Sketch of the orientation and position of the basal antisite pairs attributed to the I,II 共,III兲EPR spectra in 4H-SiC and 6H-SiC. The plotted magnetization densities 共red bubbles in the dashed ellipses兲give rise to the EPR fingerprint. Axial pairs along the caxis are not observed. GERSTMANN et al. PHYSICAL REVIEW B 81, 195208 共2010兲 195208-4 about 100 MHz 共as predicted by our ab initio calculations for the Si antisite nucleus兲can be observed for B 储 关1100兴and the high-field line belonging to the defects with a 共1100兲mirror plane. For other defect orientations, the magnetic field reduces the symmetry and, due to their strong anisotropy, also the HF splittings. Calculated values of −51.3 and −51.6 MHz obtained by a projection of the HF tensor onto 关1100兴agree exactly with the values experimentally observed for the low-field lines. For B 储 关0001兴the central HF splitting of the Si antisite nucleus is reduced to a value of −1.6 共I spectrum兲and −1.9 MHz 共II spectrum兲. As a result, these splittings cannot be resolved and contribute to the width of the central line instead. The analysis of the angular dependence of the central HF splitting proves that the magnetization density 共determined by a a⬙-like electronic structure兲is perfectly aligned along 关1100兴, in other words perpendicular to the mirror plane as in the case of the I spectrum in 3C-SiC 共see also Fig. 3兲. For the axial configurations, in contrast, the holelike unpaired electron is aligned within the symmetry plane 共a⬘-like occupation兲and, thus, would give rise to completely different HF parameters.14 Also in the 3C-SiC sample, the Si antisite nucleus is calculated to provide a maximum central HF splitting of about 100 MHz. Again, this splitting is extremely anisotropic 共Table III兲and depends critically on the direction of the applied magnetic field. The maximum can only be expected for the high-field line for B 储 关110兴共perpendicular to a symmetry plane兲. But here, an observation is prevented by the presence of the dominant VSi −spectra. For the two corresponding midfield lines around 3300 G, the HF splittings of the SiCantisite nucleus as well as one of the two 共in absence of the magnetic field兲equivalent Si ligands are calculated to −25.9 and −23.7 MHz, respectively. They, thus, explain nicely the experimentally observed HF splitting 共with two Si nuclei兲 slightly below 30 MHz. For B 储 关001兴the two Si ligands remain equivalent but according to our ab initio calculations their splittings are furthermore reduced to a value of −11.4 MHz. Together with the third Si ligands 共within the nodal plane of the a⬙orbital providing a nearly isotropic splitting around 8 MHz兲they are able to explain an intensity equivalent to three Si nuclei. The HF splitting due to the SiC antisite nucleus, in contrast, has not been clearly resolved. A theoretically predicted splitting of −52.0 MHz would coincide with the tail of the low-field EPR line at 2995 G. Since the central HF tensor is so anisotropic, however, we cannot conclusively exclude a contribution of the SiCantisite nucleus to the 23 MHz splitting. C. Orbital quenching and large g-tensor anisotropy The anisotropic shape of the magnetization density resembling that of a p-like hole 共see inset of Figs. 3and 5兲is also TABLE III. Calculated hyperfine splittings 共MHz兲for antisite pairs in 4H-SiC and 3C-SiC. For the low-field 共Lf兲and high-field 共Hf兲lines 共for B 储 关110兴in 3C-SiC also the midfield lines Mf1and Mf2兲the projections onto the direction e ជ Bof the magnetic field Bare also given and compared with experiment. For the atomic positions of the contributing nuclei, see also Fig. 3兲. Model Nuclei A1A2A3Ae ជ B Lf/Hf 兩Aexp兩 Lf/Hf e ជ B 4H, I SiC0.0 −3.5 −97.6 −51.3/−97.6 50/99 关1100兴 SiC−1.6 关0001兴 2⫻Si21.5 1.0 −41.4 −1.7 关0001兴 1⫻Si18.6 7.4 6.8 8.6 11 关0001兴 2⫻C214.7 15.9 37.8 14.7 11 关0001兴 4H, II SiC−0.6 −3.5 −99.7 −51.6/−99.7 51/103 关1100兴 SiC−1.9 关0001兴 2⫻Si22.6 1.0 −42.8 −1.6 关0001兴 1⫻Si18.3 7.0 6.3 8.3 11 关0001兴 2⫻C214.7 15.9 37.8 14.7 11 关0001兴 3C, I SiC1.0 −2.0 −102.0 0.2/−52.0 关001兴 2⫻Si20.7 −0.1 −38.7 −8.9/−11.4 –/9 关001兴 1⫻Si16.3 7.6 8.6 7.6/7.4 –/9 关001兴 2⫻C212.3 12.4 39.5 12.9/25.9 –/23 关001兴 Mf1/Mf2Mf1/Mf2 SiC−25.9/−25.9 29/28 关110兴 1⫻Si20.1/−23.2 29/28 关110兴 1⫻Si2−23.9/0.3 29/28 关110兴 1⫻Si17.3/7.7 关110兴 2⫻C2−19.3/−19.3 关110兴 SiCCSi ANTISITE PAIRS IN SiC…PHYSICAL REVIEW B 81, 195208 共2010兲 195208-5 the basic key to explain the exceptionally large gvalues. Defects in solids usually show a large degree of orbital quenching in any direction, especially in covalently bound semiconductors. For the antisite pairs in SiC, in contrast, the orbital quenching is extremely anisotropic: parallel to the p-like hole, the orbital angular momentum is suppressed completely 共gxx⬇ge, see Table II兲. For the other two principal axes perpendicular to the hole 关both lying in the 共110兲 mirror plane of the defect兴, the gtensor can well be presented as gyy=ge+␭ ⌬and gzz=ge+2␭ ⌬, similar to tetragonal systems in ionic crystals.28 Here, ␭denotes the spin-orbit coupling constant and ⌬is the gap between the highestoccupied molecular orbital 共HOMO兲and lowest-unoccupied molecular orbital 共LUMO兲in the minority spin channel, mediating the orbital quenching of the holelike electronic configuration. In the case of an antisite pair, this gap is opened due to the Jahn-Teller distortion toward C1hsymmetry 共crystal-field splitting兲, whereby the spin polarization yields to a considerable enhancement of this value 共for, e.g., 3C- SiC, see Fig. 5兲.30 In Table IV, we have collected the effective spin-orbit coupling constants ␭=⌬·1 3Tr共⌬g兲derived from the k-point averaged31 HOMO-LUMO gap ⌬and the trace of g−geas obtained by our ab initio calculations. For the VC-related defects with Si dangling bond-like 共sp3-hybridized兲unpaired electrons, the values are about two orders of magnitude smaller if compared with the 149 cm−1 for an ionized Si+atom.32 For all SiC-including centers, in contrast, we obtain spin-orbit coupling constants ␭that are only moderately reduced in comparison with the atomic value showing a minor influence of the crystal lattice. This, in semiconductors unusual effect of more or less crystal-field independent orbital quenching is also manifested in the perfect p-like alignment of the magnetization density perpendicular to the symmetry plane 共Fig. 3兲, and gives rise to the extremely anisotropic shape of the HF splittings 共see Sec. IV B兲. D. Defect formation We will now discuss possible formation mechanisms of the antisite pair defect. During the diffusion process of ions, the antisite pair can be easily formed.33 Its observation in low-energy electron-irradiated 4H-SiC is, however, a priori surprising as carbon Frenkel pairs are the expected dominant defects. If the energy is not sufficient to remove a Si atom completely from its lattice site, a tilted structure in which the Si interstitial is stabilized by a CSi antisite 共left part of Fig. 6兲 is predicted by our DFT calculations. In analogy to distant Si CB ∆ (3) (4) ∆ 0 .0 0 .4 spin polarization CSi CSi (SiC) (SiC) 0+ Jahn−Teller distortion ~ 0 .2 e e a’’ a’ E[eV] VB (1) (2) FIG. 5. 共Color online兲Sketch of the one-particle levels for the antisite pair in 3C-SiC: 共1兲for the neutral charge state 共C3vsym- metry兲the dominant levels of the irreducible representation eare degenerate. 共2兲For SiCCSi +a “hole” arises in the elevel. The potential becomes more attractive, lowering the energetic position of the elevel. 共3兲Occupied with three electrons, the electronic configuration is Jahn-Teller instable, lowering the symmetry toward C1hand splitting up the elevel in two nondegenerate levels 共a⬘and a⬙兲.共4兲 Spin polarization enhances the HOMO-LUMO gap ⌬in the spindown channel, whereby ⌬determines the orbital quenching. TABLE IV. Analysis of the calculated gtensors: spin-orbit coupling constants ␭=⌬·1 3Tr共⌬g兲derived from the trace of g−geand the k-point averaged energy gap ⌬=1 Nk兺k⌬k. Polytype Center Model 1 3Tr共⌬g兲 ⌬ 共eV兲 ␭ 共cm−1兲 3C VC 2+-共C-C兲C +C10.0010 0.656 5.3 3C VCCSi −-Siint 4+ C1h0.0049 0.228 9.0 3C 共SiC-CSi兲+C1h,a⬙0.0299 0.169 31.1 3C I SiC +C2v0.0638 0.080 41.2 3C 共CSi-SiC-CSi兲+C2v0.0165 0.325 43.2 3C 共SiC,h-CSi,h兲+Axial,a⬘0.0335 0.182 47.8 3C 共SiC,k-CSi,k兲+Axial,a⬘0.0326 0.164 43.0 4H I 共SiC,k-CSi,h兲+Basal,a⬙0.0284 0.191 43.6 4H II 共SiC,h-CSi,k兲+Basal,a⬙0.0224 0.211 38.1 6H I 共SiC,k1-CSi,h兲+Basal,a⬙0.0413 0.181 35.2 6H II 共SiC,h-CSi,k1兲+Basal,a⬙0.0197 0.196 31.2 6H III 共SiC,k2-CSi,k2兲+Basal,a⬙0.0256 0.191 39.3 GERSTMANN et al. PHYSICAL REVIEW B 81, 195208 共2010兲 195208-6 Frenkel pairs, the resulting VCCSi −-Siint 4+ complex is initially threefold positively charged 共in total兲. Like the Frenkel pairs, however, this complex itself can by no means explain the observed EPR spectra: the deviations of gzz and gyy from the free-electron value geare much too small 共see also Table I兲. After capture of two electrons, the resulting singly positive charge state is in DFT unstable and relaxes without any barrier into the nearest-neighbor antisite pair 共SiCCSi兲+共Fig. 6兲. From our results it can, however, not be excluded that the antisite pairs could also be native defects which are transformed into a paramagnetic charge state by the electrical compensation accompanying the irradiation. V. SUMMARY In this work, the application of a theoretical ab initio approach24 has allowed us to identify antisite pair defects in SiC from their very particular gtensors. The exceptionally large deviations from the free-electron-value ge, very unusual for intrinsic defects, are shown to originate from an anisotropic quenching of the orbital angular momentum of a p-like hole. By this, remaining doubts concerning the intrinsic character of the responsible defects have been conclusively removed. The antisite pair defects have been detected in various polytypes after electron and proton irradiation, independent from the type of doping and independent from the energy of the irradiation. We have presented a lowenergy scenario for the defect formation where the antisite pairs are generated if the irradiation energies are too low to create distant Si-Frenkel pair. Since they can also be easily formed during growth or during the diffusion process of ions, and since they can be observed in all types of samples, the antisite pairs are believed to be one of the major defects, if the material is not exposed to too high annealing temperatures.17 In the hexagonal polytypes, the multiplicity of the spectra is explained by basal antisite pairs with the silicon antisite atom at the inequivalent hexagonal and quasicubic lattice sites. The axial pairs have not been observed, most probably due to too short spin-relaxation times. 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