Materials Science Forum Vols. 527-529 (2006) pp. 523-526
online at http://www.scientific.net© (2006) Trans Tech Publications, Switzerland

Divacancy and its identification: Theory
A. Gali1,a , M. Bockstedte2,b , N. T. Son3,c , T. Umeda4,d , J. Isoya4,e, and E. Janzén3,f
1 Department of Atomic Physics, Budapest University of Technology and Economics, Budafoki út 8,H-1111 Budapest, Hungary
2 Lehrstuhl für Theoretische Festkörperphysik, Unversität Erlangen-Nürnberg, Staudtstr. 7B2, D-91058,Erlangen, Germany; Departamento de Fı́sica de Materiales, Universidad del Paı́s Vasco, E-20018 San
Sebastián, Spain
3 Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden
4 Graduate School of Library, Information and Media Studies, University of Tsukuba, Tsukuba 305-8550,
Japan
aagali@eik.bme.hu , b bockstedte@physik.uni-erlangen.de, c son@ifm.liu.se,
dumeda@slis.tsukuba.ac.jp, e isoya@slis.tsukuba.ac.jp, f erj@ifm.liu.se

Keywords: divacancy, ionization energy, ab initio hyperfine signature

Abstract. Only recently the well-resolved hyperfine structure of the P6/P7 EPR center has
been experimentally observed. Based on the calculated hyperfine tensors we assign the P6/P7
center to the high spin state neutral divacancy, which is the ground state in agreement withthe experiment. We propose a mechanism to explain the loss of divacancy signal at high temperature annealing in semi-insulating SiC samples. We discuss the possible correlation between
the divacancy and some photoluminescence centers.
Introduction
The divacancy (VC -VSi ), the close pair of a carbon vacancy and a silicon vacancy, was considered as the origin of the thermally very stable DI photoluminescence center or of the Z1 /Z2DLTS centers in 6H-SiC [1]. Although the divacancy was indeed found to be a very stabledefect by theory [2], no correlation between the divacancy and the DI or Z1 /Z2 centers could
be established. The P6/P7 centers were first observed in 6H-SiC by electron paramagnetic resonance (EPR) under photo-excitation by Vainer and Il’in [3] and were tentatively assigned tothe excited state of the divacancy. Later, based on a combined experimental and theoretical
study the P6/P7 EPR centers with C3v /C1h symmetry were reassigned to the paramagnetic
excited state of the double positively charged carbon vacancy-antisite complex ((VC -CSi )2+ ) in
n-type 6H-SiC [4]. This reassignment of the P6/P7 centers was based on the observation of a
weak hyperfine (HF) structure assigned to the interaction with one 13 C nucleus (I=1/2, 1.1%
natural abundance). In recent EPR studies by Son and co-workers on P6/P7 centers, however,this HF structure was shown to be due to the HF interaction with three 13 C ligands instead of
one in 6H and 4H-SiC [5]. Hence, the (VC -CSi )2+ -model can no longer be valid and instead themodel of a divacancy was suggested. In the present paper we confirm this model by a theoreticalanalysis based on ab initio supercell methods.

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MethodThe defect was represented by large supercells including up to 256 atoms. First the atomicstructure was obtained using the pseudopotential method as outlined in Refs. [6] and [7] andthen the HF tensors were calculated by the all electron PAW method [8]. Calculations werepreformed with a scissors-operator to assess the effect of the LSDA band gap failure on thecalculated ionization energies. Within the expected accuracy the scissor-correction does notaffect the calculated HF tensors.
Neutral divacancy: electronic structure and its hyperfine signature
In VC -VSi the three C-dangling bonds and three Si-dangling bonds create six defect levels. Inthe axial configuration possessing C3v symmetry two a1 levels fall in the valence band while
two, double degenerate e-levels lie in the gap. The lower e-level is formed by the dangling
bonds of the C-ligands of VSi below the midgap while the higher e-level is due to the Si-ligandsof VC above the midgap. In the neutral charge state of VC -VSi six electrons occupy the tworesonances and the lower e-level. We found that the S=1 state is the ground state of the neutral
divacancy, which hence is Jahn-Teller stable conserving the symmetry. The calculated (+/0)
and (0/-) levels are at about 0.5 eV and 1.4 eV above the valence band edge, respectively. Ifthe Fermi-level of the SiC sample is in this range then the EPR signal of the neutral divacancy
should be detectable in the dark.
In 4H-SiC two configurations with C3v symmetry (P6b, P6’b) and two configurations withC1h symmetry have been detected by EPR [5]. Since detailed experimental information is available for the defects aligned along the c-axis possessing the C3v symmetry we show here thecalculated hf constants for these defects in Table 1. As expected from the analysis of the electronic structure the spin density is mainly localized on the C-ligands of VSi and their neighbors
while the contribution of the VC -ligands is negligible. In the C1h configurations the largest hf
constant was found on one 13 C ligand, about 10 MHz higher than that of CI (cf. Fig 1), while
the other two C-atoms of VSi have a few MHz smaller hf-constants. The hyperfine signals ofthese C-ligands of the non-axial centers were not resolved for all the angles in the experiment,
nevertheless, when the magnetic field was at ∼70 degrees from the c-axis, the hf constant of one
C is about 9 MHz larger than that of the other two C atoms, which also supports our model.
For the axial and non-axial configurations the electronic structure and the overall localization of
the spin density are very similar, except for a small splitting due to the symmetry lowering fromC3v to C1h . For the axial-configurations the small difference between the cubic and hexagonalsites can be distinguished clearly, therefore, we assign P6b and P6’b to the C3v configurationsof the neutral divacancy at the hexagonal and cubic site, respectively.
Divacancy: a step in the formation of large vacancy aggregates?
According to earlier theoretical results [9] vacancy migration is favorable in n-type SiC. The
silicon vacancy should start to diffuse at about 600-700 ◦ C, which then can form a divacancy
with the carbon vacancy. At higher temperatures the migration of the carbon vacancy should
supplement this process. In p-type material the migration of vacancies is less favorable [9]. In
heavily electron irradiated n-type SiC the formed defects can pin the Fermi-level below midgap.
As a consequence, after annealing the EPR signal of the neutral VC -VSi can be detected in theMaterials Science Forum Vols. 527-529

525

Si ISi IIbCISi IIaFig. 1: The geometry of the axial (VC -VSi )0 complex (at hexagonal site).

CI (3×)
SiIIa (3×)
SiIIb (6×)
SiI (3×)P6b, Ref. [5]Axx Ayy Azz
53 50 110
12 12 129 9
93 3
3VC (h)-VSi (h)Axx Ayy Azz
55 56 116
9999983
45P6’b, Ref. [5]Axx Ayy Azz
47 45 10413 131310 101033
3

VC (k)-VSi (k)Axx Ayy Azz
49 49 11010 10
910 1091
1
2

Table 1: Principal values of HF-tensors in MHz of axial (VC -VSi )0 defects in comparison withthose of P6-centers. The angle between the principal z-axis of the A-tensor of CI and the c-axis
is 73◦ for both centers in the experiment and in the calculations as well. The atoms are labeledaccording to Fig. 1.
dark even at 4 K [5]. This is consistent with the neutral divacancy model. In as-grown semiinsulating HPSI SiC samples the divacancy signal starts to drop at annealing temperatures
above 1500-1600 ◦ C. This can be explained either by dissociation of the divacancy or forming
larger aggregates of vacancies [9, 10]. The diffusion of VC should contribute to the formationof the aggregates. We have estimated the dissociation barriers of VSi -(VC )n defects (n=1-4)
from the binding energy of additional carbon vacancies and the diffusion barrier of VC . The
dissociation barrier amounts to 7.5 eV. Thus, the kinetic formation of thermally stable vacancy
aggregates is a feasible process to explain the annealing of VC -VSi in SiC. We also note that
EPR signals associated with multivacancy centers were indeed proposed in heavily neutron
irradiated Lely-grown SiC [11].
Divacancy: its excitation and possible correlation with photoluminescence centers
It was found that excitation of about 1.1 eV is needed to detect P6/P7 EPR signals in p-type
SiC [5]. According to the theory if the Fermi-level was below the (+/0) level of the divacancy inthe sample then excitation is required to make the divacancy neutral. We have calculated thevertical ionization energies within the ∆SCF-method. The energies of the (+)→(0) excitation
to the S=1 ground state and to the S=0 excited state are obtained approximately and amount
to 0.9 and 1.0 eV, respectively. These values are consistent with the experimental findings.
The intensity of the P6/P7 EPR signal can be also increased under illumination or using
magnetic circular dichroism under absorption in n-type SiC [4, 5]. In a theoretical analysis
the calculation of the excitation energies of the neutral and the negatively charged divacancy

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are not accessible within the present approach (the inclusion of configurational interaction isrequired), therefore we do not comment on the possible excitation mechanisms in these cases.
Furthermore, photoluminescence centers (PL) were found in the infrared (IR) region associatedwith defects in SiC. The so-called UD-2 and VC -CSi PL centers were proposed to correlatewith the P6/P7 EPR centers [12, 13]. In 4H-SiC four zero-phonon lines (ZPL) were detected
for both PL centers (VC -CSi : ∼1.00-1.05 eV, UD-2: ∼1.10-1.15 eV). Assuming that free holes
are injected during the PL process the VC -CSi and UD-2 PL centers might be related to the(+)→(0)(S=1) and to the (+)→(0)(S=0) transitions. Correlation studies between the P6/P7
EPR centers and these PL centers may reveal the possibility of the afore-mentioned processes.
Conclusion
In conclusion, the P6/P7 EPR centers can be identified as the axial/non-axial configurationof the neutral divacancy in SiC for the following reasons: the theory explains (i) that the S=1
state is the ground state (ii) the number of configurations and their symmetry (iii) the measured
hyperfine tensors (iv) the appearance and disappearance of the P6/P7 signal in annealed SiC
samples by the migration and aggregation of vacancies. We also provided excitation energies
between the (+) and (0) states. The possible relation to the known PL centers and to thephoto-excitation was discussed.
Acknowledgments
A.G. appreciates the support by the Hungarian OTKA F-038357 and the grants Nr. 2005008 andSNIC021-03-20 from the Swedish National Supercomputer Centers. M.B. acknowledges financial
support by the Deutsche Forschungsgemeinschaft (grant BO 1851/2-1 and SiC-research group).
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