ARTICLE IN PRESS

Physica B 376–377 (2006) 334–337
www.elsevier.com/locate/physb

Identiﬁcation of divacancies in 4H-SiC
N.T. Sona,, T. Umedab, J. Isoyab, A. Galic, M. Bockstedted, B. Magnussona,e,A. Ellisone, N. Morishitaf, T. Ohshimaf, H. Itohf, E. JanzénaaDepartment of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden
Graduate School of Library, Information and Media Studies, RCKC, University of Tsukuba, Tsukuba 305-8550, Japanc
Department of Atomic Physics, Budapest University of Technology and Economics, Budafoki út 8, H-1111 Budapest, HungarydLehrstuhl für Theoretische Festkörperphysik, Unversität Erlangen-Nürnberg, Staudtstr. 7B2, D-91058 Erlangen, Germanye
Norstel AB, Hans Meijers väg 2, SE-580 30 Linköping, SwedenfJapan Atomic Energy Research Institute, Takasaki 370-1292, Japanb

Abstract
The P6/P7 centers in 4H-SiC were studied by electron paramagnetic resonance (EPR) and ab initio supercell calculations. The
hyperﬁne coupling constants of C and Si neighbors obtained by EPR are in good agreement with the calculated values for the neutral
divacancy, VC V0Si . Our results suggest that the P6/P7 centers, which were previously assigned to the photo-excited triplet states of the
carbon vacancy–carbon antisite pairs in the double positive charge state ðVC C2þ
Si Þ, are related to the triplet ground states of the C3v =C1h
conﬁgurations of VC V0Si .
r 2006 Elsevier B.V. All rights reserved.
PACS: 61.72.Ji; 76.30.Mi; 71.15.Mb; 61.72.Bb
Keywords: Divacancies; Electron paramagnetic resonance; Ab initio calculations

1. Introduction
One of the most common intrinsic defects observed byelectron paramagnetic resonance (EPR) and opticallydetected EPR in as-grown n-type [1] and high-purity
semi-insulating (HPSI) [2,3] SiC substrates are the P6/P7
centers [4]. These centers were ﬁrst observed by Vainer andIl’in [4] in 6H-SiC substrates, which were heated up to2000 1C and quenched. Based on their symmetry (C3v andC1h for the P6 and P7 centers, respectively), the centerswere suggested to be the divacancy [4], i.e. the close pair of
the carbon and silicon vacancy. In a study using magnetic
circular dichroism of the absorption (MCDA), MCDAdetected EPR (MCDA-EPR) and ab initio calculations [5],the centers were instead assigned to the excited triplet stateof the carbon vacancy–carbon antisite pairs in the doubly
positively charged state, VC C2þ
Si . The divacancy is predicted
Corresponding author. Tel.: +46 13 282531; fax: +46 13 142337.

E-mail address: son@ifm.liu.se (N.T. Son).
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2005.12.086

by theory [6–8] to be a very stable defect, but has not been
experimentally identiﬁed so far. In a previous EPR study ofsemi-insulating SiC substrates [3], a very stable center, SI-5,
was assigned to the divacancy based on the observed
hyperﬁne (hf) interactions. This assignment was later
supported by calculations [8]. However, in recent EPR
studies [9] the symmetry lowering of SI-5 from C3v to C1h
and additional large hf interactions with 29Si wereobserved, that invalidated this model. Both experiments[9] and supercell calculations [10] suggest SI-5 to be thecarbon vacancy–carbon antisite pair in the negative charge
state, VC CSi .
In this work, we present new EPR data on the P6/P7
centers including the hf interactions with C and Si atoms inthe ﬁrst and second neighbor shells. The obtained hf
coupling constants are in good agreement with the values
determined by ab initio supercell calculations, suggestingthat the P6/P7 centers are originating from the triplet
ground states of the neutral divacancy in the C3v =C1h
conﬁgurations.

ARTICLE IN PRESS
N.T. Son et al. / Physica B 376–377 (2006) 334–337

2. ExperimentStarting materials used in the study are N-doped n-type(concentration 1  1017 cm3 ), Al-doped p-type (1
1018 cm3 ) and HPSI 4H-SiC wafers. In HPSI samples,the concentration of N is 4  1015 cm3 [11]. The
irradiation by 3 MeV electrons was performed at room
temperature with a dose of 2  1018 cm2 . For some n-typesamples, the irradiation was performed at 850 1C withdoses of 2  1018 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 opticalﬁlters.
3. Results and discussion
In our irradiated n-type, HPSI and p-type samples,
typical P6/P7 type EPR spectra [2,5,12,13] were detected.
Fig. 1(a) shows as an example the spectra in irradiatedn-type 4H-SiC measured for the magnetic ﬁeld B along thec-axis at 77 K under illumination with light of photon
energies between 1:1 and 1:7 eV. The P6/P7 signals canbe detected after irradiation but very weak. The spectra
reach their maximum after annealing at about 850 1C. The
P6/P7 spectra can also be detected in dark (the sample
was kept inside the cryostat in completely dark for 1 day

before measurements) at temperatures close to room
temperature (at 77 K, the spectra were not observable indark) in both n-type or HPSI samples irradiated with adose of 2  1018 electrons=cm2 . In heavily irradiated ð1 
1019 electrons=cm2 Þ n-type samples, the P6/P7 spectra canbe detected in dark for the whole temperature range
4–293 K. In irradiated p-type material, however, these
spectra can only be detected under illumination by lightwith the photon energy larger than 1:1 eV. The appearance of the P6/P7 centers in dark strongly suggested thatthey originate from the ground triplet state rather than thephotoexcited positively charged ðþ2Þ state [5]. Fig. 1(b)shows the P6/P7 spectra measured in dark at 8 K. At thislow temperature, the low-ﬁeld lines of P6/P7 spectra areweaker than the corresponding high-ﬁeld lines. The lowﬁeld P6=P60 lines even almost disappear. This indicates thatthe ﬁne structure parameters D of all the P6=P60 and
P7=P70 centers are positive ðD40Þ.
Using on-axis samples we obtained more accurate ﬁne
structure parameters D and E for the P7 type centercompared to that in our previous work using off-axis
samples [12]. We name the P6 spectra according to thelabels used in Ref. [13] and labelled the corresponding C1hspectra as P7b and P70 b. The g-value for P6/P7 centersis 2.003; D and E values (in unit of 104 cm1 ) deduced
from the ﬁts to the angular dependences are, DðP6bÞ ¼
DðP7bÞ ¼ 447, DðP60 bÞ ¼ 436, DðP70 bÞ ¼ 408, EðP7bÞ ¼

4H-SiC
9.47508 GHz

P7'b

B⎜⎜c

P6'b
3 SiI

4H-SiC
9.641 GHzB⎜⎜c

T= 77 K

P6b
P7'b

P7b
P6b

P7b
P6'b
P6c

x5

EPR Intensity (linear scale)EPR Intensity (linear scale)335

experiment
6 Si II

3 CI

3 CI

3 SiII(b) 8 K, in darkx10x10
simulation

P6c

3 SiI
P6'b
P6b
300

(a) 77 K, light on
320

340
360
Magnetic Field (mT)

289

290

291
Magnetic Field (mT)

292

380

Fig. 1. EPR spectra of the P6/P7 centers in electrons irradiated andannealed (850 1C) n-type 4H-SiC measured for Bkc (a) at 77 K underillumination with light of photon energies between 1:1 and 1:7 eV and(b) at 8 K in dark.

Fig. 2. Low-ﬁeld lines of the P6b and P60 b spectra in irradiated andannealed HPSI 4H-SiC measured under illumination with light of photon
energies between 1:1 and 1:7 eV for Bkc, showing the hf interaction
with three 13C nuclei (in 10 scale). The hf interaction with nine Si atoms,of which three are along the c-axis, can be well-resolved (see text for detailsof the simulation).

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N.T. Son et al. / Physica B 376–377 (2006) 334–337

90 and EðP70 bÞ ¼ 10. The angle between the principal axisof the ﬁne structure tensor and the c-axis for the P7b andP70 b centers is 70:5 and 71 , respectively.
Fig. 2 shows the detailed hf structure of the low-ﬁeldlines P6b and P60 b. The same structure is also observed forcorresponding high-ﬁeld lines. For both P6b and P60 b, theintensity ratio between the two outer hf lines and the mainlines is 3:323:4%, which is approximately the naturalabundance of three 13C nuclei ðI ¼ 1=2; 1:11%Þ. These hflines are therefore assigned to the hf interaction with threenearest C neighbors (labeled CI ). Using a ﬁeld modulation
amplitude of 0.01 mT, the two inner hf structures can bewell-resolved for the P60 b line (Fig. 2). Their intensity
ratios agree well with the interaction with three and six 29Si
nuclei ðI ¼ 1=2; 4:7%Þ. Fig. 3 shows the C and Si
neighbors of a divacancy in axial symmetry. The numberof C and Si neighbors is the same for the general case of apaired complex involving Si and adjacent C site. The hf
interactions with following neighbor atoms may be
distinguishable: 3 CI and 3 SiI in the nearest neighborshells, 9 SiII and 9 CII atoms in the second neighbor shells,of which 3 SiII and 3 CII atoms on the bonds along the caxis may have hf interactions different from that of theother 6 atoms in the basal plane (second neighbors CII of
VC are not shown in Fig. 3). Among different alternatives,
the best ﬁts to the inner hf structures are the interactions
with 3 and 6 Si atoms. The unresolved shoulders of theP60 b line can be well ﬁtted by the interaction with 3 Si
atoms. The simulation of the P6b and P60 b lines and their
hf structures are plotted in Fig. 2. The simulation includes
the hf interactions with following atoms: (i) 3 CI for theouter hf, (ii) 3 SiII (on the bond along the c-axis) and 6 SiII
(in the basal plane) for the two inner hf, (iii) 3 nearest SiI
neighbors of C site for the unresolved shoulders. The linewidth at a half-maximum used in the ﬁt is 0.04 mT. Below
we show the identiﬁcation of these hf structures based on
the ab initio calculations of hf coupling constants. As canbe seen in 10 scale spectra in Fig. 2 the simulation ﬁts
perfectly the observed spectra, not only the intensity of thehf lines but also their detailed superhyperﬁne structures.
The CI hf structure was also detected at some otherdirections and the CI hf tensors of the P6b and P60 b centers
could be determined. Their principal values are summar-

Fig. 3. Carbon and silicon neighbors of a divacancy in axial symmetry.

Table 1The principal values (in MHz) of the hf tensors of C and Si neighbors
determined by EPR for the P6b and P60 b centers and calculated for theneutral divacancy of C3v symmetry at the hexagonal (hh) and cubic (kk)sites in 4H-SiC
Experiment

P60 b

P6b
Axx

Ayy

Azz

y

Axx

Ayy

Azz

y

CI ð3Þ
SiII ð3Þ
SiII ð6Þ
SiI ð3Þ

53
12
9
3

50
12
9
3

110
12
9
3

73

47
13
10
3

45
13
10
3

104
13
10
3

73

TheoryðVSi VC Þ0 (hh)CI ð3Þ
SiII ð3Þ
SiII ð6Þ
SiI ð3Þ

55
9
9
3

110
9
9
2

73

56
9
9
4

ðVSi VC Þ0 (kk)
116
9
8
5

73

49
10
10
1

49
10
10
1

y is the angle between the principal z-axis of the A tensor and the c-axis.
The number of equivalent atoms is shown in parentheses.

ized in Table 1. The angle between the principal z-axis of
the CI hf tensor of P6b and P60 b centers is 73 .
For the P7b and P70 b centers, the hf structure due to theinteraction with three CI atoms was also detected at someangles close to 70 with respect to the c-axis where thespectra are well separated from others. Within experimental
error, the inner hf interactions of P6b and P60 b are isotropic.
Their hf coupling constants are also given in Table 1. In ourprevious work [12] and also in Ref. [5], the signal-to-noise
ratio was rather poor and weak hf lines were likely in thenoise and not detectable. This leads to the incorrect
assignment of the observed hf lines to the interaction withone 13C nucleus [5,12]. Our observation of the P6/P7 signals
at low temperatures in dark and the hf interaction with three
CI neighbors rules out the model of VC CSi for the P6/P7
centers. The most probable model for these centers is thedivacancy in the neutral charge state, VC V0Si .
In order to conﬁrm this model, we have performed abinitio supercell calculations of the divacancy in 4H-SiC.
Large supercells including up to 256 atoms were used. The
optimized geometry was obtained using pseudopotential
method as outlined in Refs. [14,15] and then the HFtensors were calculated by the all electron PAW method[16]. Calculations were performed with a self-consistentscissors operator to assess the effect of the LSDA band gap
failure on the calculated ionization energies. Since thedetailed experimental information is available for thedefects aligned with the c-axis possessing the C3v symmetry
we show here the calculated hf constants for these defects
in Table 1. The calculated hf constants of the defects
possessing C1h symmetry will be published elsewhere. The
divacancy forms six defect levels due to the three carbon
dangling bonds of the VSi part and to the three silicon
dangling bonds of the VC part. In the C3v symmetry two a1
and two doubly degenerate e levels are formed. The two
fully occupied a1 levels falls in the valence band. The two

ARTICLE IN PRESS
N.T. Son et al. / Physica B 376–377 (2006) 334–337

doubly degenerate e levels appear in the band gap: the ﬁrst
one is below the midgap arising due to the carbon dangling
bonds of VSi while the second one is above the midgap
arising due to the silicon dangling bonds of VC . In theneutral charge state of the defect the deeper e level is
occupied by two electrons with parallel spins making thedefect Jahn–Teller stable. As a consequence, the groundstate of the neutral divacancy is a high spin state with
S ¼ 1. The spin density is mainly localized on the carbon
ligands of VSi part and their near neighbor atoms while thecontribution of the VC part is almost negligible. The
calculated ðþ=0Þ and ð0=Þ levels are at 0:5 eV and1:4 eV above the valence band ðEV Þ, respectively. The
neutral charge state with S ¼ 1 is the ground state of thedivacancy when the Fermi-level is in this range.
As can be seen in Table 1, the principal values and the
direction of the symmetry axis of the 13C and 29Si hf
tensors obtained from EPR are in good agreement with thecalculated values for the neutral divacancy. Even small
differences in principal values of hf tensors of P6b and P60 b
are also observed by EPR and calculations. Therefore, weassign P6b and P60 b to the C3v conﬁgurations of the neutral
divacancy at the hexagonal and cubic site, respectively.
In summary, we have identiﬁed the P6/P7 centers as theC3v =C1h conﬁgurations of the neutral divacancy, based on
the electronic structure, including the hf structures of C
and Si neighbors, obtained from EPR and determined by
ab initio supercell calculations. Comparing the hf tensors
obtained from experiments and calculations, we assign the
P6b and P60 b centers to the C3v conﬁgurations of theneutral divacancy at the hexagonal and cubic site,
respectively.
Acknowledgements
Support from the Swedish Foundation for Strategic
Research program SiCMAT, the Hungarian OTKA F-

337

038357, the grant no. 2005008 and SNIC021-03-20 fromthe Swedish National Supercomputer Center, and theGerman DFG (SiC-Research group and BO1851/2-1) is
acknowledged.

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