PRL 96, 055501 (2006)

PHYSICAL REVIEW LETTERS

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Divacancy in 4H-SiC
N. T. Son, P. Carlsson, J. ul Hassan, and E. JanzénDepartment 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 isnegligible 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 defectin 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 centerswere 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 siliconvacancy (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 dominatingprocess. For SiC, so far there is no experimental evidence
that the reaction VSi  VC ! VC VSi is important and thatthe 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 toC1h 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 pairin the negative charge state VC CSi .
In this Letter, we present results from EPR studies andab 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 cm3 ), Al-doped p-type (1 
1018 cm3 ), and HPSI 4H-SiC. In HPSI samples, the concentration of N is 1  5  1015 cm3 . The irradiation by
3 MeVelectrons was performed at room temperature with adose of 2  1018 cm2 . For some n-type samples, theirradiation was performed at 850  C with doses of 2 1018 cm2 and 1  1019 cm2 . EPR measurements were
performed on Bruker ER200D and E580 X-band spectrometers. For light illumination, a Xenon lamp (150 W) wasused 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 annealingat 850  C. In irradiated p-type 4H-SiC, the spectra canbe detected only under illumination with light of photon
energies  1:1 eV. However, in heavily irradiated (1 
1019 cm2 ) n-type samples, the spectra can be detectedin 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 inirradiated and annealed (850  C) n-type 4H-SiC at 8 K in dark.

EPR Intensity (linear scale)(in units of 104 cm1 ) are determined as: DP6b
DP70 b 408,
DP7b 447,
DP60 b 436,
0EP7b 90, and EP7 b 10. The angle between theprincipal axis of the fine structure tensor and the c axis forP7b and P70 b is 70.5 and 71 , respectively.
Detailed hf structures of the low-field lines of P6b andP60 b spectra measured for the magnetic field B k c are
shown in Fig. 2(a). Similar structures are also detected forthe high-field lines. The intensity ratio between two outerhf lines and the central lines is 3:3%–3:4%, which isapproximately 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 wellresolved 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 atsome 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 P6bexperiment
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 inFig. 2(a). The simulation includes the following hf interactions with: (i) 3 CI nearest neighbors of VSi , (ii) 3 SiIIaand 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 theirdetailed superhyperfine structures.
The angular dependences of the CI hf splitting of P6b
 plane are shown inand P60 b with B rotating in the (1120)
Fig. 3(c). These hf tensors have C1h symmetry and theirprincipal values obtained from the fit are given in Table I.
The hf interactions with the nearest CIa and CIb neighborsof P70 b were also observed for some crystal directions asshown in Fig. 3(d). The CIb hf tensor has C1h symmetry andis 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 linesof P7b and P70 b are unresolved, corresponding to splittingof 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 theground triplet state. From the above analysis of the hf

4H-SiC
9.47508 GHz

6 SiIIb 3 C
Isimulation289

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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 observedin irradiated and annealed (850  C) HPSI 4H-SiC at 77 K underillumination (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.

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PRL 96, 055501 (2006)

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PHYSICAL REVIEW LETTERSTABLE 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.
C3v centerCI 3
SiIIa 3
SiI 3
SiIIb 6C1h centerCIa 1
CIb 2

Axx
53
12
3
9

Ayy
50
12
3
9

Azz

110
73
12
3
9
P7b
Not determined
Not determined

P60 b

VSi h-VC h 0

P6b
Axx
55
9
3
9
51
50

Ayy
Azz

56
116
73
9
9
4
5
9
8
VSi h-VC k 0
52
118
2
50
109
70

interactions, the neutral divacancy appears to be the mostprobable 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 checkthe 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 foundthat the optimized geometries of the divacancies obtainedby both codes practically agreed. The hf tensors were thencalculated 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 inthe 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 ionizationenergies beyond the expected accuracy by applying ascissors 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 defectspin density is not tightly coupled to the energetic positionof 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 ahigh spin state with S 1. In the axial configurations, twodoubly degenerate e levels appear in the band gap: The firstone is below the midgap arising from C dangling bonds ofVSi , while the second one is above the midgap arising from
Si dangling bonds of VC . In the neutral charge state, thelower e level is occupied by two electrons with parallel
spins making the defect Jahn-Teller stable. As a conse-

Axx
47
13
3
10
52
48

Ayy
Azz
45
104
13
13
3
3
10
10
P70 b
52
110
45
109

VSi k-VC k 0

73

Axx
49
10
1
10

0
70

52
43

Ayy
Azz

49
110
73
10
9
1
2
10
9
VSi k-VC h 0
52
116
2
47
103
70

quence, the spin density is mainly localized on the nearest
carbon neighbors of VSi , whereas the contribution of thedangling bonds at VC is almost negligible. In the off-axis
C1h configurations, the situation is very similar apart fromthe small splitting of the degenerate e levels due to the low
symmetry. The calculated (j0) and (0j) levels are at0:5 and 1:4 eV above the valence band, respectively.
The neutral charge state with S 1 is the ground state ofthe 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 agreementwith the calculated values for the neutral divacancy. Evensmall 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 orbitaland 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 fullanalysis 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

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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 , andP6b=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. Eachannealing 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, theannealing 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 thesample 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 showsthat the annealing characteristics of P6b=P60 b centersdepend on the presence of other defects. Its increase insamples 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 lessefficient 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 ofantisite-vacancy pairs seems to occur, slowing down thedecrease of the VSi signal [Fig. 4(b)]. This annealing
behavior is in accordance with the theoretical predictionsof the formation and dissociation of antisite-vacancy defects [2,8]. In both types of samples, the dissociation of thedivacancy 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 theneutral divacancy in the C3v =C1h configurations and as-

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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 toform divacancies is significant and the divacancy is acommon defect in SiC. Annealing studies suggest thatthe formation of the divacancy is governed mainly bydiffusion 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, theSwedish 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 isacknowledged.

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