RAPID COMMUNICATIONSPHYSICAL REVIEW B 69, 121201共R兲 共2004兲

EPR identification of two types of carbon vacancies in 4H-SiC
T. Umeda,1 J. Isoya,1 N. Morishita,2 T. Ohshima,2 and T. Kamiya2
1

Research Center for Knowledge Communities, University of Tsukuba, Tsukuba 305-8550, Japan
2
Japan Atomic Energy Research Institute, Takasaki 370-1292, Japan
共Received 27 November 2003; published 22 March 2004兲

The EI5 and EI6 centers are typical intrinsic defects in radiation-damaged and semi-insulating 4H-SiC. So
far, their origins have been assigned to positively charged carbon vacancies (V C⫹ ) and silicon antisites (SiC⫹ ),respectively. However, our complete set of 29Si hyperfine 共HF兲 data clearly reveals that both the centers should
originate from V C⫹ but their locations are different, i.e., quasicubic sites for EI5 and hexagonal sites for EI6,
as recently predicted by the first-principle calculation 关M. Bockstedte et al., Phys. Rev. B 67, 193102 共2003兲兴.
The two types of V C⫹ centers showed remarkable differences in their atomic structures as well as in thetemperature dependence of HF interactions, which are closely related to the nature of the two sites.
DOI: 10.1103/PhysRevB.69.121201

PACS number共s兲: 61.72.Ji, 76.30.Mi, 81.05.Hd

Silicon carbide 共SiC兲 has a variety of hexagonal polytypes, represented by 4H- and 6H-SiC. There are quasicubic(k) and hexagonal (h) sites in these polytypes with different
arrangements of next nearest neighbors, leading to great
structural and electronic variations in this material. For example, donors and acceptors have variations in ionizationenergy, that depend on their substitution sites.1–3 Thus, theinfluence of inequivalent sites is not negligible and needs tobe understood to control impurities or defects. Recently, theoretical calculations for carbon vacancies have predicted thatits positively charged state (V C⫹ ) should be strikingly different between k and h sites in 4H-SiC, due to different JahnTeller distortion behaviors.4,5 Thus far, however, only one
type of V C⫹ 共the EI5 center, electron spin S⫽1/2) has been
identified by electron paramagnetic resonance 共EPR兲,6 andanother type is missing. Thus, these theoretical calculations
have suggested that the EI6 center, originally assigned to thepositively charged silicon antisite (SiC⫹ ), 7 will fit the h-site
V C⫹ rather than SiC⫹ , 4 and alternately the EI5 center will bereassigned to be V C⫹ at the k sites.4,5 Also recent highfrequency 共240 GHz兲 EPR measurement has suggested
V C-related origins for the EI6 center.8 The Ky3 center in
6H-SiC with similar features to EI6 has been considered ah-site V C⫹ in this polytype.9 Despite these theoretical andexperimental results, definitive identification has not yet
been obtained, because of a lack of decisive experimental
data on these centers. In particular, the complete angular dependence of 29Si hyperfine 共HF兲 interactions for EI6 is not
yet known, which is necessary to establish the atomic modelfor this defect. Since both EI5 and EI6 centers show highthermal stability and are hence the dominant defects in
4H-SiC, 6 – 8 their assignment is quite significant.
Consequently, we report on complete 29Si HF data for EI5
and EI6 here, and discuss how their atomic structures were
determined. We concluded that both EI5 and EI6 should be
V C⫹ centers but their respective locations were k and h sites,
consistent with theoretical predictions. Despite being thesame type of defect, their atomic structures were found to bequite different. We demonstrate that this difference is connected to the striking contrast in the temperature dependence
for the two V C⫹ centers.
The starting substrates were commercial p-type
4H-SiC(0001) wafers 共room-temperature carrier concen0163-1829/2004/69共12兲/121201共4兲/$22.50

tration⫽1⫻1015/cm3 ) supplied by Nippon Steel Corporation. The 1.5-mm-thick substrates were irradiated at 850 °C
with a 3-MeV electron beam for 6 h, up to a total dose of
4⫻1018 e/cm2 . This high-temperature irradiation enabled
only EI5 and EI6 to remain dominant in the samples. We
then measured the substrates with X-band EPR 共Bruker E500
system兲 and pulsed EPR spectrometers 共Bruker E580 system兲. Pulsed EPR was used to directly measure spin relaxation times10 and to distinguish HF interactions of 29Si and13
C 共their respective natural abundances are 4.7% and 1.1%,
and nuclear spins for both are 21 ) by means of the pulsed
electron-nuclear-double-resonance 共ENDOR兲 technique. The
pulsed ENDOR spectrum was measured through a combination of microwave and rf 共radio frequency兲 pulses in accordance with the Mims sequence 共␲/2 pulse– ␲/2 pulse–rf
pulse– ␲/2 pulse–echo兲.11
Figure 1共a兲 shows an EPR spectrum of our sample measured for B 共magnetic field兲 储 关 0001兴 (c axis兲. As indicated in
the figure, this spectrum consists of an overlapping central
line for EI5 and EI6, and their HF satellites 共labeled a to g).
Figure 1共b兲 shows their angular dependence when B was
rotated from the c axis to the c-normal direction ( 关 112̄0 兴 ).
The HF satellites a, b, and c have already been reported by
Son et al.6,7 Satellite a is a 29Si HF structure for EI6,7 andsatellites b and c are those for EI5.6 The present angulardependencies for a, b, and c were generally consistent withthose previously reported.6,7
As the angular dependencies of other HF satellites (d tog) have not yet been reported yet, it is unclear whether they
belong to EI5 or EI6. To clarify this, we measured the HF
structures of satellite a 共EI6兲, because this satellite was separate from all of EI5’s lines. In Fig. 1共b兲, the thin light lines
along satellite a indicate its HF structures, which coincide
exactly with satellites d and e. We therefore concluded thatthese satellites are part of the EI6’s HF structures. We applied similar analysis to satellite b or c of EI5. We thenfound that satellites f should originate from EI5, which isdemonstrated by the thin light lines near satellite b 关Fig.
1共b兲兴. Satellite g was found to be isotropic and should arise
from both EI5 and EI6, because we observed the same isotropic HF splittings in satellites a 共EI6兲, b, and c 共EI5兲. We
noted that these results were consistent with the 240-GHz
EPR study by Konovalov et al.8 Although they reported only

69 121201-1©2004 The American Physical Society

RAPID COMMUNICATIONSPHYSICAL REVIEW B 69, 121201共R兲 共2004兲

UMEDA et al.

FIG. 1. 共Color online兲 EPR
measurementsofelectronirradiated p-type 4H-SiC at 150
K. 共a兲 EPR spectrum forB储 关 0001兴 . 共b兲 Angular dependence of signal positions for B rotation in the (1̄100) plane. Solidlines were calculated using thespin-Hamiltonianparameters
given in Table I.

HF splittings for B储 关 0001兴 , their four values for ID1/EI5
共labeled ID1-1– 4兲 were close to the HF splittings for EI5 (b,c, f , and g). Also, the four values labeled ID2-1– 4 for ID2/
EI6 corresponded to those for EI6 (a, d, e, and g), respectively.
Comparing the HF structures of EI5 and EI6, it is immediately clear that satellites a and d for EI6 have the sameangular patterns as those of b and c for EI5. Their intensity
ratios are also the same, i.e., b:c⫽1:3 for EI5 and a:d⫽1:3 for EI6, as is estimated in Fig. 1共a兲. The angular dependence of c and d clearly revealed that these satellites
consist of three HF structures with intensity ratios of 1:1:1.
Furthermore, the symmetry of a and b coincided with that of
the Si dangling bond 共DB兲 on the Si1 atom 共axially symmetrical around the c axis, see Fig. 2兲, and the three HF
structures in d and c were also axially symmetrical aroundthe Si DBs on three Si atoms, i.e., Si2 , Si3 , and Si4 . Summarizing this, both EI5 and EI6 centers revealed four 29Si
HF structures that corresponded to four Si atoms surrounding
a carbon vacancy. Therefore, it is quite reasonable to identify
the EI6 center as a carbon vacancy (V C⫹ ), similar to the EI5
center,6 rather than a silicon antisite (SiC⫹ ). 7 In the original
SiC⫹ model,7 only the EPR spectrum for B储 关 1̄100兴 was measured and then satellite d was assigned to a combination of
two HF structures from the Si1 and Si2 atoms in SiC⫹ . However, this assignment does not fit our complete angular data.
The EI6 center has another HF satellite e. We carried out
pulsed-ENDOR measurements 共10 K兲 on this satellite by fixing a magnetic field at its position and scanning the frequency of the rf pulse. The inset in Fig. 3 shows a typical
ENDOR spectrum, where three 29Si HF splittings can clearlybe observed. The relative intensity of this satellite in the
cw-EPR spectrum 关Fig. 1共a兲兴 also indicates the contributionof three Si atoms. Although the angular dependence of thissatellite indicates an axial symmetry around the c axis 关Fig.
1共b兲兴, looking through the higher resolution ENDOR 共Fig. 3兲
reveals that the symmetry axis is slightly tilted from the caxis. Judging from this symmetry and the number of Si atoms, satellite e should originate from the Si5 , Si6 , and Si7
atoms in a carbon vacancy 共Fig. 2兲.
We determined spin-Hamiltonian parameters, g and A
共HF兲 tensors, for the Si1 to Si7 atoms by simulating the an-gular dependence of corresponding HF satellites. All the gand A tensors were well described by axially symmetricaltensors. The solid lines in Fig. 1共b兲 show an excellent agreement between the experiment and simulation. The spinHamiltonian parameters are summarized in Table I. We also
confirmed that these parameters could perfectly reproduce
the angular-dependence data with respect to different rotation
planes 共B was rotated from 关0001兴 to 关 1̄100兴 ). For EI5, theparameters remained almost unchanged with decreasing thetemperature. For EI6, however, they were obviously temperature dependent above 10 K. The table also shows theoretical A tensors recently calculated by Bockstedte et al.4
Similar theoretical results were also independently reported
by Gali et al.5 Comparing these theoretical values with ourexperimental parameters, the EI5 center is in good agreementwith V C⫹ at the k site, and the EI6 center fits well with thatat the h site. Therefore, we concluded that the origins of EI5
and EI6 are both V C⫹ and their respective locations should
be k and h sites. It should also be noted that the theoretical
calculation4 predicted much smaller A principal values for
SiC⫹ and these were inconsistent with our experimental parameters.
The conclusion that both EI5 and EI6 centers are the same

FIG. 2. 共Color online兲 共a兲 Atomic models for EI5 (k-site V C⫹ )and 共b兲 for EI6 (h-site V C⫹ ). The percentages represent theunpaired-electron densities on each Si atom. The ␪ 储 values for the
Si2 – 4 DBs are also indicated. All these values were estimated at
150 K.

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RAPID COMMUNICATIONSPHYSICAL REVIEW B 69, 121201共R兲 共2004兲

EPR IDENTIFICATION OF TWO TYPES OF CARBON . . .

FIG. 3. 共Color online兲 29Si HF splitting of satellite e for EI6
resolved by pulsed ENDOR at 10 K, and a typical ENDOR spectrum 共inset兲.

type of defect can explain the following facts obtained fromthe experiments. 共i兲 Their g tensors were quite similar, 共ii兲they appeared simultaneously in the form of an overlapping
EPR signal, and 共iii兲 they had similar high thermal stability.
Although it has been reported that the annealing-out temperature is lower for EI5 (450– 850 °C) 共Refs. 6 and 7兲 thanfor EI6 (⭓1000 °C), 7 our isochronal-annealing study 共1000,
1200, and 1500 °C for 30 min兲 revealed that EPR intensities
of EI5 and EI6 were unchanged at 1000 °C, and decreased to
3% at 1200 °C and to almost zero at 1500 °C, as comparedto their initial intensities. A similar but more detailed result
was also reported by the other group.12 In fact, they were
dominant and observed in high-purity semi-insulating
4H-SiC obtained through high-temperature growth.8 Since

V C⫹ can capture an electron of the donor, carbon vacancies
may play an important role for the Fermi-level pining in suchsemi-insulating materials.
The A tensors we determined revealed the atomic structures of two types of V C⫹ , which we found to be greatly
different. For EI5, the direction ␪ 储 of the Si2 – 4 DBs determined from the A(Si2 – 4 ) tensor was 109.2° 共Fig. 2 and TableI兲, which is just the tetrahedral angle (109.28°). Thus, theEI5 center appears to have a tetrahedral structure. Using a
LCAO 共linear combination of atomic orbitals兲 approximation, we could estimate the wave function for this defect interms of the 3s- and 3 p-orbital densities, ␩ 2 ␣ 2 and ␩ 2 ␤ 2 ,on each Sii atom, where ␩ 2 ␣ 2 ⫽A iso(mT)/163.93, ␩ 2 ␤ 2⫽A aniso(mT)/4.08,
A iso⫽ 关 A 储 (Sii )⫹2A⬜ (Sii ) 兴 /3,
A aniso⫽ 关 A 储 (Sii )⫺A⬜ (Sii ) 兴 /3, and ␣ 2 ⫹ ␤ 2 ⫽1.6,7,13 For EI5, theunpaired electron distributes nearly equally on Si1 – 4 atoms
共see Fig. 2兲. For EI6, on the other hand, the direction ␪ 储 ofthe Si2 – 4 atoms decreased towards 90°, indicating a planar
structure, and thus a nonbonding character was expected between Si1 and Si2 – 4 atoms. As a result, the unpaired-electron
density is localized on the Si1 atom by 40% 共Fig. 2兲. However, the sums of unpaired-electron distributions on Si1 – 4
atoms were kept to the same value (⬃66%) for EI5 and EI6.
The structural distortion for EI6 became maximum when
the temperature decreased to 10 K, as can be seen from angle␪ 储 共Table I兲. The 10-K ENDOR data of Fig. 3 reveal distortion at Si5 – 7 atoms in this situation. By simulating the experimental angular pattern 共solid lines in figure兲, the symmetry axis of the A(Si5 – 7 ) tensor was found to have tilted
outward by 15.5° from the c axis. This again indicates that
the EI6 center (h site V C⫹ ) deforms considerably towards aplanar structure. With this deformation, the unpaired electron

TABLE I. Spin-Hamiltonian parameters of EI5 and EI6 centers. The spin Hamiltonian H is given by H⫽ ␮ BB•g•S⫹ 兺 S•A•I, where ␮ B
is the Bohr magneton, g is a g tensor 共principal values are g 储 and g⬜ ), S is an electron spin operator, A is a HF tensor for each atom in the
wave function, and I is a nuclear spin operator corresponding to each A tensor. Principal values of A are expressed in mT using a conversion
factor that 1 mT⫽28.02 MHz. ␪ 储 is the angle between the A 储 principal axis and the c axis 共see also Fig. 2兲. The table also contains previous
EPR parameters reported by Son et al. 共Refs. 6 and 7兲. The A(Si2,3,4 ) tensor in Ref. 6 was not axial symmetrical and showed a different ␪ 储value (95°); however, this result was obtained using an extra fitting parameter of a misalignment angle. Since we did not use such aparameter and did check the fitting in two different orientation data, our A(Si2,3,4 ) tensor will be more reliable. In the bottom, theoretical A
tensors obtained by the ab initio calculation 共Ref. 4兲 are shown.
g
EI5 (S⫽ 21 , C 3 v )共150 K兲
Ref. 6 共138 K兲

g储
2.003222.00322A(Si1 )g⬜

A储

2.004842.00484

6.49
6.46

HF b

EI6 (S⫽ 21 , C 3 v )共293 K兲
共150 K兲
共50 K兲
共10 K兲
Ref. 7 共138 K兲
k-site V C (C 1h )h-site V C⫹ (C 3 v )A储

A(Si2,3,4 )
A⬜
HF c

␪储

A储

Other A
A⬜
HF f

A iso
HF g

4.47
4.46

5.18
5.02

3.63
3.75

109.2°
95°

0.40

0.29

0.2

HF e 关 A(Si5,6,7 ) 兴

HF g

0.72
0.75
0.82
0.87

0.2
0.2
0.2

HF a
2.00322.00305
2.00279
2.00262.003022.00462.00472
2.004892.00522.00473

Theory 共Ref. 4兲
⫹

A⬜

12.29
13.06
14.26
15.48
13.21

HF d
8.45
8.97
9.77
10.61
9.07

3.21
2.97
2.58
2.11

A(Si1 )
7.04
14.29

4.36
9.82

2.20
2.01
1.72
1.39

103.6°
102.6°
101.0°
97.7°

A(Si2 )
4.07
9.82

5.54
1.54

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3.32
0.79

0.57
0.59
0.64
0.69
A(Si3,4)

3.11
0.71

5.75
1.54

3.89
0.79

3.68
0.71

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UMEDA et al.

for EI6 became more localized on the Si1 atom 共47%兲; however, the total ␩ 2 on the Si1 – 4 atoms was found to be almost
unchanged 共68%兲.
Despite being the same type of defect, the EI5 center had
invariant g and A values, while those for EI6 were considerably temperature dependent, as plotted in Fig. 4. We think
this difference is closely related to the symmetry of the distortions. The theoretical calculation for the k site predictedthat the pseudo Jahn-Teller effect generates a pair of Si1 andSi2 atoms 共a Si3 -Si4 pair is also formed兲.4 Although this
distorted configuration indicated a C1h symmetry,4 there arethree equivalent configurations (Si1 -Si2 , Si1 -Si3 , andSi1 -Si4 pairs兲, because the Si2 – 4 atoms are C3 v symmetry
related. Thus, thermally activated reorientation between thethree configurations possibly occurs, which enabled us toobserve their average state with a C3 v symmetry.14 We
speculated that due to the pairing of Si1 and Si2 – 4 atoms, theaverage state of EI5 is always confined and approaches atetrahedral structure at relevant temperatures (⭓50 K), resulting in unchanging g and HF parameters. However, theh-site V C⫹ had only one orientation for distortion 共planar
distortion along c axis兲 retaining C3 v symmetry, and hence
no reorientation effect could take place. Furthermore, thistype of distortion enabled the Si1 atom to move a great deal
because of the nonbonding character of Si1 and Si2 – 4 atoms.
This made it possible to observe structural change in EI6
with decreasing temperature. The theoretical calculation for
EI6 also predicted the presence of a C1h -distorted structure,in addition to the C3 v state. However, we did not observe
such a state even at 4 K, and therefore the C3 v -distorted state
shown here will be energetically preferable.
The presence of reorientation in the symmetry-related
configurations in EI5 and the absence of such dynamic effects in EI6 could also be inferred from the much faster spin
relaxation in the former rather than the latter center. From
three-pulse inversion recovery measurements of pulsed
EPR,10 we found that the spin-lattice relaxation time (T 1 )was three times shorter for EI5 (4.8⫻10⫺6 sec) than for EI6(13.0⫻10⫺6 sec) at 80 K. This can be also confirmed byconventional EPR where the EI6 signal was much more easily saturated to microwave power, compared to the EI5 signal. Also, a similar motional effect was detected in the Ky1and Ky2 centers in 6H-SiC which were assigned to V C⫹ at
the k 1 and k 2 sites 共two inequivalent quasicubic sites兲.9
In summary, we found a complete set of 29Si HF parameters for EI5 and EI6 centers through EPR and pulsed
ENDOR techniques. Although they were originally assigned
to V C⫹ 共for EI5兲 and SiC⫹ 共for EI6兲, our complete data demonstrated that both EI5 and EI6 were V C⫹ centers but theirlocations should have been k and h sites, as recently suggested by the theoretical calculations.4,5 This conclusion was
also supported by facts obtained by experiments, such as
similar g values, their coexistence, and the same thermal
stability. Despite being the same kind of defect, the two typesof V C⫹ were found to be quite different in structural distortion and temperature dependence, which could reasonably be
explained by the symmetry of distortions at k and h sites.

1

9FIG. 4. 共Color online兲 Temperature dependence of spinHamiltonian parameters for EI5 and EI6.

W. Goetz, A. Schöner, G. Pensl, W. Suttrop, W. J. Choyke, R.
Stein, and S. Leibenzeder, J. Appl. Phys. 73, 3332 共1993兲.
2
M. Ikeda, H. Matsunami, and T. Tanaka, J. Lumin. 20, 111
共1979兲.
3
S. Greulich-Weber, F. Feege, E. N. Kalabukhova, S. N. Lukin,
J.-M. Spaeth, and F. J. Adrian, Semicond. Sci. Technol. 13, 59
共1998兲.
4
M. Bockstedte, M. Heid, and O. Pankratov, Phys. Rev. B 67,
193102 共2003兲.
5
A. Gali, P. Deák, N. T. Son, E. Janzén, H. J. von Bardeleben, andJean-Louis Monge, Mater. Sci. Forum 433–436, 511 共2003兲.
6
N. T. Son, P. N. Hai, and E. Janzén, Phys. Rev. B 63, 201201共R兲
共2001兲.
7
N. T. Son, P. N. Hai, and E. Janzén, Phys. Rev. Lett. 87, 045502
共2001兲.
8
V. V. Konovalov, M. E. Zvanut, and J. van Tol, Phys. Rev. B 68,
012102 共2003兲.

V. Ya. Bratus, I. N. Makeeva, S. M. Okulov, T. L. Petrenko, T. T.
Petrenko, and H. J. von Bardeleben, Physica B 308-310, 621
共2001兲.
10
J. Isoya, S. Yamasaki, H. Okushi, A. Matsuda, and K. Tanaka,
Phys. Rev. B 47, 7013 共1993兲.
11
A. Schweiger, in Advanced EPR—Applications in Biology andBiochemistry, edited by A. J. Hoff 共Elsevier, Amsterdam, 1989兲,
pp. 243–276.
12
Z. Zolnai, N. T. Son, B. Magnusson, C. Hallin, and E. Janzén共unpublished兲.
13
J. A. Weil, J. R. Bolton, and J. E. Wertz, in Electron Paramagnetic Resonance 共Wiley, New York, 1994兲.
14
Below 50 K, we found that EI5 exhibited a C1h -symmetric gtensor and complicated HF structures. This C1h symmetry is
consistent with the theoretical prediction 共Ref. 4兲 and supports
our model for the thermally activated reorientation.

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