PRL 96, 055501 (2006) PHYSICAL REVIEW LETTERS week ending 10 FEBRUARY 2006 Divacancy in 4H-SiC N. T. Son, P. Carlsson, J. ul Hassan, and E. Janzén Department of Physic, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden T. Umeda and J. Isoya Graduate School of Library, Information and Media Studies, University of Tsukuba, Tsukuba 305-8550, Japan A. Gali Department of Atomic Physics, Budapest University of Technology and Economics, H-1111 Budapest, Hungary M. Bockstedte Universität Erlangen-Nürnberg, D-91058, Erlangen, Germany, and Universidad del Paı́s Vasco, E-20018, San Sebastián, Spain N. Morishita, T. Ohshima, and H. Itoh Japan Atomic Energy Research Institute, Takasaki 370-1292, Japan (Received 22 July 2005; revised manuscript received 12 December 2005; published 6 February 2006; corrected 7 February 2006) Electron paramagnetic resonance and ab initio supercell calculations suggest that the P6=P7 centers, which were previously assigned to the photoexcited triplet states of the carbon vacancy-antisite pairs in the double positive charge state, are related to the triplet ground states of the neutral divacancy. The spin density is found to be located mainly on three nearest C neighbors of the silicon vacancy, whereas it is negligible on the nearest Si neighbors of the carbon vacancy. DOI: 10.1103/PhysRevLett.96.055501 PACS numbers: 61.72.Ji, 61.72.Bb, 71.15.Mb, 76.30.Mi Divacancies are common defects in semiconductors comprised of neighboring isolated vacancies. For SiC, an unambiguous identification of this defect that has been predicted to be thermally stable [1–3] is so far missing. The P6=P7 centers were first observed by electron paramagnetic resonance (EPR) in heat-treated n-type 6H-SiC [4] and were later shown to be a common defect in as-grown n-type [5] and high-purity semi-insulating (HPSI) [6,7] SiC. Based on their symmetry (axial or C3v for P6 and monoclinic or C1h for P7), P6=P7 centers were suggested to be the divacancy [4]. In a study using magnetic circular dichroism of the absorption (MCDA), MCDA-detected EPR, and ab initio calculations [8], P6=P7 centers were instead assigned to the photoexcited triplet state of the carbon vacancy-carbon antisite pair in the doubly positively charged state VC C2
Si . The formation of the center was suggested to be due to the migration of a nearest C neighbor into the silicon vacancy (VSi ) [8]. The process VSi ! VC CSi is theoretically predicted to have a low reaction barrier (1:7 [8] and 2:5 eV [2]) and can therefore be a dominating process. For SiC, so far there is no experimental evidence that the reaction VSi
VC ! VC VSi is important and that the divacancy is a common defect. In a previous EPR study of HPSI SiC substrates [7], a very stable center SI-5 was assigned to the divacancy. However, in a recent EPR study [9], a symmetry lowering of SI-5 from C3v to C1h and additional large hyperfine (hf) interactions with 29 Si were observed that invalidated this model. Indeed, recent EPR studies [9] and supercell calculations [10] 0031-9007=06=96(5)=055501(4)$23.00 identify SI-5 as the carbon vacancy-carbon antisite pair in the negative charge state VC C Si . In this Letter, we present results from EPR studies and ab initio supercell calculations which confirm that P6=P7 are originating from the triplet ground states of the neutral divacancy in the C3v =C1h configurations. Samples used in the study are N-doped n-type (concentration 1  1017 cm3 ), Al-doped p-type (1  1018 cm3 ), and HPSI 4H-SiC. In HPSI samples, the concentration of N is 1  5  1015 cm3 . The irradiation by 3 MeVelectrons was performed at room temperature with a dose of 2  1018 cm2 . For some n-type samples, the irradiation was performed at 850  C with doses of 2  1018 cm2 and 1  1019 cm2 . EPR measurements were performed on Bruker ER200D and E580 X-band spectrometers. For light illumination, a Xenon lamp (150 W) was used in combination with a Jobin-Yvon 0.25 m grating monochromator and/or different optical filters. The P6=P7 spectra can be detected after irradiation but are weak. The signals reach the maximum after annealing at 850  C. In irradiated p-type 4H-SiC, the spectra can be detected only under illumination with light of photon energies  1:1 eV. However, in heavily irradiated (1  1019 cm2 ) n-type samples, the spectra can be detected in darkness in the whole temperature range of 4 –293 K. Figure 1 shows the P6=P7 spectra measured in darkness at 8 K. We labeled the P6 spectra according to Ref. [11] and the corresponding C1h spectra as P7b and P70 b. The g value for P6=P7 is 2.003; the axially symmetric D and anisotropic E values of the fine structure parameter 055501-1  2006 The American Physical Society PHYSICAL REVIEW LETTERS EPR Intensity PRL 96, 055501 (2006) 4H-SiC T= 8 K, in dark B c, 9.641 GHz P6b P6c x5 290 P7'b P7'b P7b 310 P7b P6'b P6c 330 350 370 P6b 390 Magnetic Field (mT) FIG. 1. EPR spectrum of P6=P7 centers measured for B k c in irradiated and annealed (850  C) n-type 4H-SiC at 8 K in dark. EPR Intensity (linear scale) (in units of 104 cm1 ) are determined as: DP6b DP70 b 408, DP7b 447, DP60 b 436, 0 EP7b 90, and EP7 b 10. The angle between the principal axis of the fine structure tensor and the c axis for P7b and P70 b is 70.5 and 71 , respectively. Detailed hf structures of the low-field lines of P6b and P60 b spectra measured for the magnetic field B k c are shown in Fig. 2(a). Similar structures are also detected for the high-field lines. The intensity ratio between two outer hf lines and the central lines is 3:3%–3:4%, which is approximately the natural abundance of three 13 C nuclei (I 1=2, 1.1%). These outer hf lines are therefore assigned to the hf interaction with three nearest C neighbors (labeled CI ). The two inner hf structures can be well resolved for P60 b [Fig. 2(a)]. Within the experimental error, the inner hf structures are isotropic and their intensity ratios agree well with the interaction with three and six 29 Si nuclei (I 1=2, 4.7%). For P7b and P70 b, similar hf interactions with three 13 C nuclei can also be detected at some angles. Figure 2(b) shows the hf structures of P7b and P70 b measured at direction of 70 off the c axis. P6'b (a) T= 77 K, B c P6b experiment 3 CI 3 SiI x10 3 SiIIa 290 The axial (C3v ) and monoclinic (C1h ) configurations of the divacancy are illustrated in Figs. 3(a) and 3(b), respectively. For P6b and P60 b, the best fits to the inner hf structures are obtained with the hf tensors of 3 Si atoms on the bonds along the c axis, labeled SiIIa , and 6 Si atoms in the plane, labeled SiIIb [see Fig. 3(a)]. The simulation of the P6b and P60 b lines and their hf structures are plotted in Fig. 2(a). The simulation includes the following hf interactions with: (i) 3 CI nearest neighbors of VSi , (ii) 3 SiIIa and 6 SiIIb second neighbors of VSi , and (iii) 3 nearest SiI neighbors of VC . As can be seen in 10 scale spectra in Fig. 2(a), the simulation describes perfectly the observed spectra, not only the intensity of the hf lines but also their detailed superhyperfine structures. The angular dependences of the CI hf splitting of P6b
plane are shown in and P60 b with B rotating in the (1120) Fig. 3(c). These hf tensors have C1h symmetry and their principal values obtained from the fit are given in Table I. The hf interactions with the nearest CIa and CIb neighbors of P70 b were also observed for some crystal directions as shown in Fig. 3(d). The CIb hf tensor has C1h symmetry and is similar to that observed for the nearest CI neighbors of P6b=P60 b. The principal values of the CI , CIa , and CIb hf tensors are given in Table I. The hf structures of P7b detected at some directions between 60 –90 show to be similar to that of P70 b [Fig. 2(b)]. The broad inner hf lines of P7b and P70 b are unresolved, corresponding to splitting of 0.3– 0.46 mT or 9–13 MHz. Their intensity ratios correspond to the interaction with nine Si atoms. The observation of the P6=P7 spectra in dark at low temperatures confirms that these centers are related to the ground triplet state. From the above analysis of the hf 4H-SiC 9.47508 GHz 6 SiIIb 3 C I simulation 289 week ending 10 FEBRUARY 2006 x10 3 SiI 291 (b) T = 77 K, 70 o off c axis 292 293 4H-SiC 9.47727 GHz P7'b P7b x10 x10 2.07 mT 1 CIa+2 CIb 289 290 291 292 1 CIa 2 CIb 293 2.2 mT 1.87 mT 294 295 296 297 Magnetic Field (mT) FIG. 2 (color online). EPR spectra of P6=P7 centers observed in irradiated and annealed (850  C) HPSI 4H-SiC at 77 K under illumination (photon energies 1:1–1:7 eV), showing hf structures of (a) P6b=P60 b lines at B k c and (b) P7b=P70 b lines at 70 from the c axis. FIG. 3 (color online). Si and C neighbors of the divacancy in (a) axial (C3v ) and (b) monoclinic (C1h ) configurations. Angular
plane of the hf splitting dependence with B rotating in the (1120) of (c) CI nearest neighbors of P6b=P60 b and (d) CIa and CIb nearest neighbors of P70 b. For P6b and P60 b, a misalignment of
plane toward the 1100
direction was taken 1.5 off the (1120) into account in the simulation. 055501-2 PRL 96, 055501 (2006) week ending 10 FEBRUARY 2006 PHYSICAL REVIEW LETTERS TABLE I. Principal values (in MHz) of hf tensors of C and Si neighbors determined for P6b=P60 b and P70 b and calculated for C3v and C1h configurations of the neutral divacancy at cubic (k) and hexagonal (h) sites in 4H-SiC.  is the angle between the principal z axis of the hf tensor and the c axis. The number of equivalent atoms is shown in parentheses. For C1h centers, the calculated hf constants of SiIIa –SiIIe vary in the range 6–10 MHz, and the obtained values for SiIa and SiIb are similar to that of C3v centers. For P7b=P70 b, the hf interactions with 9 Si atoms were measured in the range of 9–13 MHz. CI 3 SiIIa 3 SiI 3 SiIIb 6 C1h center CIa 1 CIb 2 VSi h-VC h P6b C3v center Axx 53 12 3 9 Ayy 50 12 3 9 Azz  110 73 12 3 9 P7b Not determined Not determined Axx 55 9 3 9 51 50 Ayy Azz 56 116 9 9 4 5 9 8 VSi h-VC k 52 118 50 109 interactions, the neutral divacancy appears to be the most probable model for the P6=P7 centers. We have performed ab initio supercell calculations of the neutral divacancy in 4H-SiC using supercells containing 256 lattice sites. For the optimization of the geometry, we employed pseudopotential methods, namely, the SIESTA code with double-
polarized basis set for both C and Si atoms [12] and the FHI96SPIN plane wave code with a wellconverged basis set (cutoff energy of 30 Ry) [13], to check the results. The calculations were based on the local spin density approximation (LSDA: Ceperley-Alder as parametrized by Perdew and Zunger) and norm-conserving Troullier-Martins pseudopotentials [12,13]. We found that the optimized geometries of the divacancies obtained by both codes practically agreed. The hf tensors were then calculated by the all electron projector augmentation wave method using the above LSDA functional [14]. In the latter calculations, we applied a 30 Ry cutoff for the plane-waves basis set and one projector for each angular momentum in the projectors of C and Si atoms. This methodology has proven to be very successful in the study of VC in 4H-SiC [15]. We verified that the well-known band gap failure of the LSDA did not affect our results for the ionization energies beyond the expected accuracy by applying a scissors operator to open the LSDA band gap to the experimental value as suggested by Baraff and Schlüter [16]. With this ad hoc correction, we assured also that the defect spin density is not tightly coupled to the energetic position of the conduction band states. We found the same hf tensors within the achievable accuracy. The obtained hf constants for different configurations are given in Table I. We found that the ground state of the neutral divacancy is a high spin state with S 1. In the axial configurations, two doubly degenerate e levels appear in the band gap: The first one is below the midgap arising from C dangling bonds of VSi , while the second one is above the midgap arising from Si dangling bonds of VC . In the neutral charge state, the lower e level is occupied by two electrons with parallel spins making the defect Jahn-Teller stable. As a conse- P60 b 0  73 Axx 47 13 3 10 0  2 70 52 48 Ayy Azz 45 104 13 13 3 3 10 10 P70 b 52 110 45 109 VSi k-VC k  73  0 70 Axx 49 10 1 10 52 43 Ayy Azz 49 110 10 9 1 2 10 9 VSi k-VC h 52 116 47 103 0  73 0 2 70 quence, the spin density is mainly localized on the nearest carbon neighbors of VSi , whereas the contribution of the dangling bonds at VC is almost negligible. In the off-axis C1h configurations, the situation is very similar apart from the small splitting of the degenerate e levels due to the low symmetry. The calculated (
j0) and (0j) levels are at 0:5 and 1:4 eV above the valence band, respectively. The neutral charge state with S 1 is the ground state of the divacancy when the Fermi level is in this range. As can be seen in Table I, the principal values and the direction of the symmetry axis of the hf tensors of nearest C neighbors obtained from EPR are in good agreement with the calculated values for the neutral divacancy. Even small differences in the hf tensors of P6b and P60 b are also observed by EPR and calculations. Therefore, we assign P6b and P60 b to the axial C3v configurations of the neutral divacancy at the hexagonal (h) and cubic (k) sites, respectively. Since the CIa and CIb hf tensors were not determined for P7b, an unambiguous identification of individual C1h configurations is not possible. Using the linear combination of atomic orbital analysis, the spin density on a nearest C neighbor is determined as: 1:8%–1:9% on the s orbital and 18%–19% on the p orbital for P6b, P60 b, and P70 b. The total spin density on the three nearest C neighbors of the neutral divacancy is 60% for the C3v configuration (P6b=P60 b) and 62% for the C1h configuration (P70 b). The spin localization on three nearest Si neighbors of VC (SiI or SiIa and SiIb ) is negligible (  1%). In the previous annealing studies [11,17], the annealing characteristic of the Si vacancy (TV2a center) and P6=P7 centers was interpreted in terms of the theoretically predicted transformation of VSi into VC CSi . The reidentification of the P6=P7 centers with the divacancy demands a reinterpretation of its annealing behavior. Although a full analysis is beyond the scope of the present Letter, we briefly discuss here our annealing experiments performed for two sets of as-grown HPSI 4H-SiC samples: (i) No. 1 with strong signals of VSi (TV2a center), SI-5 (i.e., VC C Si center [9,10]), and VC
(EI5 center [7]); (ii) No. 2 with 055501-3 PHYSICAL REVIEW LETTERS EPR Intensity (arb. unit) PRL 96, 055501 (2006) (a) sample #1 VC + (b) sample #2 TV2a SI-5 SI-5 100 VC+ TV2a P6b 10 600 P6b P6'b 1000 1400 600 P6'b 1000 1400 Annealing Temperature (C) FIG. 4 (color online). Annealing temperature dependence of EPR centers in as-grown HPSI 4H-SiC samples with (a) strong signals of TV2a (or VSi ), SI-5 (i.e., VC CSi  ) and VC
, (b) strong TV2a and SI-5 and weak VC
signals. The VC
, TV2a , and P6b=P60 b signals were detected under illumination (photon energies 1:1–1:7 eV) and the SI-5 signal was detected in dark. strong signals of VSi and SI-5 and a weak VC
signal. Each annealing was conducted in Ar ambient in the chemical vapor deposition reactor for 10 minutes. The natural cooling rate of the reactor after crystal growth was applied here. Since the heating/cooling time varied with temperature, the annealing is not isochronal. In both sample sets, the VC
, TV2a , and P6b=P60 b signals were detected under illumination (photon energies 1:1–1:7 eV), whereas the SI-5 signal can be detected in dark or under illumination. The annealing temperature dependences of EPR centers in the sample sets No. 1 and No. 2 are shown in Figs. 4(a) and 4(b), respectively. Note that the EPR intensity measured under illumination depends also on the excitation efficiency and, hence, may not reflect the real defect concentration. Nevertheless, the experiment clearly shows that the annealing characteristics of P6b=P60 b centers depend on the presence of other defects. Its increase in samples No. 1 [Fig. 4(a)] may be due to two processes: (i) VC
VSi ! VC VSi governed by the diffusion of VSi (above 700  C) and VC (above 1100  C [17]), and (ii) VC
VC CSi ! VC VSi governed by the migration of VC and VC CSi (above 1100  C). In samples No. 2, below 1500  C the P6 signal is almost unchanged [Fig. 4(b)]. This suggests that both the processes (i) and (ii) are less efficient when the concentration of VC is low. The transformation of the Si vacancy (TV2a ) into the antisite-vacancy pair (SI-5) is observed at temperatures about 1000  C [Fig. 4(b)]. At higher temperatures, the dissociation of antisite-vacancy pairs seems to occur, slowing down the decrease of the VSi signal [Fig. 4(b)]. This annealing behavior is in accordance with the theoretical predictions of the formation and dissociation of antisite-vacancy defects [2,8]. In both types of samples, the dissociation of the divacancy starts at 1600  C. In summary, based on EPR observation and ab initio supercell calculations, we identified the P6=P7 centers in 4H-SiC to be related to the ground triplet state of the neutral divacancy in the C3v =C1h configurations and as- week ending 10 FEBRUARY 2006 signed the P6b and P60 b axial centers to the C3v configuration at the hexagonal and cubic site, respectively. The spin density is found to be located mainly on three nearest C neighbors of VSi , whereas it is negligible on the nearest Si neighbors of VC . The vacancy model for P6=P7 centers also implies that the interaction between VSi and VC to form divacancies is significant and the divacancy is a common defect in SiC. Annealing studies suggest that the formation of the divacancy is governed mainly by diffusion of VC and VSi . Support from the Swedish Foundation for Strategic Research program SiCMAT, the Swedish National Infrastructure for Computing Grant No. SNIC 011/04 –8, the Swedish Foundation for International Cooperation in Research and Higher Education, the Deutsche Forschungsgemeinschaft (SiC-research group and BO 1851/2-1), and the Hungarian OTKA Grant No. F-038357 is acknowledged. [1] L. Torpo, T. E. M. Staab, and R. M. Nieminen, Phys. Rev. B 65, 085202 (2002). [2] M. Bockstedte, A. Mattausch, and O. Pankratov, Phys. Rev. B 69, 235202 (2004). [3] U. Gerstmann, E. Rauls, and H. Overhof, Phys. Rev. B 70, 201204(R) (2004). [4] V. S. Vainer and V. A. Il’in, Sov. Phys. Solid State 23, 2126 (1981). [5] N. T. Son, Mt. Wagner, E. Sörman, W. M. Chen, B. Monemar, and E. Janzén, Semicond. Sci. Technol. 14, 1141 (1999). [6] W. E. Carlos, E. R. Glaser, and B. V. Shanabrook, Physica (Amsterdam) 340B–342B, 151 (2003). [7] N. T. Son, B. Magnusson, Z. Zolnai, A. Ellison, and E. Janzén, Mater. Sci. Forum 457– 460, 437 (2004), and references therein. [8] Th. Lingner et al., Phys. Rev. B 64, 245212 (2001). [9] T. Umeda, N. T. Son, J. Isoya, N. Morishita, T. Ohshima, H. Itoh, and E. Janzén, Mater. Sci. Forum (to be published). [10] M. Bockstedte, A. Gali, T. Umeda, N. T. Son, J. Isoya, and E. Janzén, Mater. Sci. Forum (to be published). [11] M. V. B. Pinheiro et al., Phys. Rev. B 70, 245204 (2004). [12] A. Gali, P. Deák, P. Ordejón, N. T. Son, E. Janzén, and W. J. Choyke, Phys. Rev. B 68, 125201 (2003). [13] M. Bockstedte, A. Mattausch, and O. Pankratov, Phys. Rev. B 68, 205201 (2003). [14] P. E. Blöchl, C. J. Först, and J. Schimpl, Bull. Mater. Sci. 26, 33 (2003). [15] T. Umeda, J. Isoya, N. Morishita, T. Ohshima, T. Kamiya, A. Gali, P. Deák, N. T. Son, and E. Janzén, Phys. Rev. B 70, 235212 (2004); 71, 193202 (2005). [16] G. A. Baraff and M. Schlüter, Phys. Rev. Lett. 55, 1327 (1985). [17] Z. Zolnai, N. T. Son, C. Hallin, and E. Janzén, Mater. Sci. Forum 457– 460, 473 (2004); J. Appl. Phys. 96, 2406 (2004). 055501-4