PHYSICAL REVIEW B 71, 193202 共2005兲

EPR and theoretical studies of negatively charged carbon vacancy in 4H-SiC
T. Umeda, Y. Ishitsuka, and J. Isoya
Research Center for Knowledge Communities, University of Tsukuba, Tsukuba 305-8550, Japan

N. T. Son and E. Janzén
Department of Physics and Measurement Technology, Linköping University, S-581 83 Linköping, Sweden

N. Morishita, T. Ohshima, and H. Itoh
Japan Atomic Energy Research Institute, Takasaki 370-1292, Japan

A. Gali
Department of Atomic Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
共Received 5 October 2004; revised manuscript received 19 November 2004; published 23 May 2005兲
Carbon vacancies 共VC兲 are typical intrinsic defects in silicon carbides 共SiC兲 and so far have been observed
only in the form of positively charged states in p-type or semi-insulating SiC. Here, we present electronparamagnetic-resonance 共EPR兲 and photoinduced EPR 共photo-EPR兲 observations of their negatively charged
state 共V−C兲 in n-type 4H-SiC. This EPR center 共called HEI1兲 is characterized by an electron spin of 1 / 2 in a
Si-Si antibonding state of VC. First-principles calculations confirm that the HEI1 center arises from V−C athexagonal sites. The HEI1 spectrum shows a transition between C1h and C3v symmetries due to a fast reorientation effect reflected in the nature of this defect. The photo-EPR data suggest that V2−
C is the dominant formof VC when the Fermi level lies 1.1 eV below the conduction band.
DOI: 10.1103/PhysRevB.71.193202

PACS number共s兲: 61.72.Ji, 76.30.Mi, 71.15.⫺m

Carbon vacancies 共VC兲 are typical intrinsic defects in radiation 共ion, electron, etc.兲 -damaged or semi-insulating silicon carbides 共SiC兲.1–6 They remain in as-grown wafers ordevice structures because of their high thermal stability,3,4,6
and therefore largely influence the electronic properties of
SiC, such as the doping efficiency, semi-insulating mechanism, and carrier transport and lifetime. They are often observed in p-type or semi-insulating samples by means ofelectron paramagnetic resonance 共EPR兲: electron-spin-1 / 2
centers of EI5 and EI6 in 4H-SiC 共Refs. 1 and 6兲 or ID1 andID2 in semi-insulating 4H-SiC,3 and those of Ky1 to Ky3 in
6H-SiC.5 The EI5 共ID1/Ky1/Ky2兲 and EI6 共ID2/Ky3兲 centers have been identified as positively charged carbon vacancies 共VC+兲 at quasicubic 共k兲 and hexagonal 共h兲 sites,
respectively,5–8 and their electronic levels have been studied
by photoinduced EPR 共photo-EPR兲.2 However, their negatively charged state 共VC−兲, which should also be EPR activewith electron spin S = 1 / 2,9 has not been observed yet. This
state is important for evaluating the electronic role of VC in
n-type or semi-insulating regions. For example, the gap stateof VC− will act as a dominant deep trap in n-type or semiinsulating regions.
In this paper, we present EPR and photo-EPR data on the
VC− state in 4H-SiC. The n-type 4H-SiC samples were prepared by high-temperature electron irradiation. In thesesamples, we found a new EPR center, named HEI1, whose
hyperfine 共HF兲 interactions clearly indicate it originates froma type of VC−. By comparing the HF parameters with those of
first-principles calculations, we conclude that this new center
corresponds to VC− at the h site. The atomic and electronic
structures are strikingly different from those of VC+, and sucha contrast is quite similar to what has earlier been observed
1098-0121/2005/71共19兲/193202共4兲/$23.00

for vacancies 共V±兲 in silicon.10 The HEI1 center exhibited afast reorientation phenomenon due to the nature of VC−. In thelast part, we show photo-EPR data and evaluate the electronic levels of VC in the energy gap of 4H-SiC 共3.26 eV兲.
The starting samples were prepared from a 1.5-mm-thicknitrogen-doped n-type 4H-SiC共0001兲 wafer 共roomtemperature carrier concentration ⬇1017 cm−3兲 made by Nippon Steel Corporation. The samples were uniformly irradiated by 3.5-MeV electrons with a dose of 共2 – 4兲
⫻ 1018 e / cm2 at 850 ° C. This high-temperature irradiation
created VC dominantly in the samples, which is evidenced byour p-type samples with the same irradiation condition.6 In
addition, the 850 ° C annealing held the Fermi level above
the midgap, which is necessary for detecting VC−. EPR measurements were carried out using a Bruker E500 X-band
共⬇9.452 GHz兲 spectrometer. In the photo-EPR measurements, we used a single-grating 0.25-m Jobin-Yvone monochromator and a 150-W xenon lamp. The EPR spectrum wasmeasured in decreasing steps of 10 nm in wavelength. In thissystem, the uncertainty of the excitation energy was reduced
to less than ±0.06 eV.2
First-principles LSDA-PZ 共local spin density functional
approximation within the parametrization of Perdew and
Zunger11,12兲 calculations were carried out to study the negatively charged carbon vacancies in 4H-SiC. We focused ourinvestigation mainly on the resulting geometry and corresponding HF tensors of the defects. We used a 96-atom supercell to model the 4H-SiC with a 23K Monkhorst-Pack
K-point set.13 We have already shown earlier that this supercell and K-point set provides the convergent geometry andtotal energy for the positively charged carbon vacancies.7
The convergent geometry and HF tensors were calculated

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PHYSICAL REVIEW B 71, 193202 共2005兲

BRIEF REPORTS

TABLE I. Spin-Hamiltonian parameters of HEI1 and calculated
HF tensors for h-site V−C. Principal values of A are expressed in mT
using the conversion factor that 1 mT= 28.02 MHz. ␪ represents themain 共Z兲 principal direction from the c axis.
X共⬜兲FIG. 1. 共Color online兲 EPR measurements of electron-irradiatedn-type 4H-SiC at 60 K. 共a兲 EPR spectrum for B 储 关0001兴. 共b兲 Angular dependence of signal positions for B rotation in the 共112̄0兲
plane. Solid lines are simulated angular patterns. For HEI1, thelines were calculated using spin-Hamiltonian Eq. 共1兲 and the parameters in Table I.

using the CP-PAW code, which utilizes the projector
augmented-wave method.14,15 This makes it possible to use a
relatively small basis set in the plane-wave expansion 共30 Ry
in this case兲 and calculate the HF tensors accurately. During
the geometry optimization, all the atoms were allowed torelax until the forces were below 0.5 mhartree/ bohr. Thismethod has already been successfully used to calculate the
HF tensors of the positively charged carbon vacancies in
4H-SiC.7
An EPR spectrum of the n-type sample at 60 K underroom-light illumination is shown in Fig. 1共a兲. The illumination enhanced the intensities of the EPR signals we want tohighlight. In this sample, several new EPR centers appeared,
which we name HEI1 to HEI8. Among these centers, HEI1
共electron spin S = 1 / 2兲 shows two strong hyperfine 共HF兲 interactions, denoted by “Si1” and “Si2.” The intensity ratio of
the HEI1 spectrum was 100:5:6 for the central line, Si1, andSi2, respectively. This suggests that both HF interactions
originate from a 29Si atom 共nuclear spin I = 1 / 2, naturalabundance= 4.7%兲. Namely, an unpaired electron of the
HEI1 center distributes on two Si atoms. Such a distribution
is well known for a negatively charged vacancy in silicon
共V−, the G2 center兲, where an unpaired electron is located in
the antibonding state of one of two elongated Si-Si bonds ina vacancy.10 This unpaired electron mainly distributes on two
Si atoms of the negatively charged bond, resulting in twostrong 29Si HF interactions. This would suggest that the
HEI1 center arises from a type of VC−, which is confirmed by
the following angular dependence data for the EPR spectrum.
The signal positions as a function of the rotation angle ofmagnetic field 共B兲 in the 共112̄0兲 plane are shown in Fig.
1共b兲, from which the angular pattern of the HEI1 spectrum
共solid lines兲 can be well described by the HamiltonianH = ␮BS · g · B + S · A · I − gn␤nI · B,

Y共⬜兲

Z共储兲

HEI1 共C1h兲, 60 K
g2.00287
2.004072.00459
A共Si1兲
7.76
7.76
10.07
A共Si2兲
11.78
11.67
15.19
HEI1 共C3v兲, 150 K
g2.003812.003812.00401
A共Si1兲
7.79
7.79
10.04
A共Si2兲
Not observed due to broadening
h-site V−C共C1h兲, theory
A共Si1兲
7.78
7.78
10.03
A共Si2兲
11.24
11.24
14.45
A共Si3,4兲
0.14
0.25
0.32

␪
38°
7°
101°
0°
0°

7°
101°

Hamiltonian parameters 共g and A兲 of HEI1 determined fromthe fit are shown in Table I. The HF tensors for Si1 and Si2
are nearly axially symmetric and can therefore be well examined by a simple LCAO 共linear combination of atomic
orbitals兲 analysis of Si’s 3s and 3p orbitals. The directions of
the sp-hybridized orbitals for Si1 and Si2 were determined asshown in Table I or in Fig. 2共a兲. The two Si atoms are wellfitted to one c-axial Si atom 共Si1兲 and one of three Si atoms
in plane 共Si2兲 of a VC. Thus, an unpaired electron of HEI1 isbelieved to be in the antibonding state of the Si1-Si2 bond.
We should mention that this antibonding orbital is repelledby the Si1-Si2 bonding orbital 关the bonding orbital can beseen in the EI5 center, Fig. 2共b兲, where Si1-Si2 atomic pair isformed7兴. This would be a consequence of minimizing theelectron repulsion and is thus quite reasonable in our model.
The atomic structure shown in Fig. 2共a兲 has a C1h symmetry
with respect to the 共112̄0兲 plane. This is also consistent with
the C1h symmetry of the g tensor for HEI1. Consequently, we
conclude that the origin of HEI1 is VC−.
From the LCAO analysis,1,6,7,10 we estimated the distributions of an unpaired electron 共␩2兲 on Si1 and Si2 to be 24.1%
and 36.6%, respectively 关Fig. 2共a兲兴. The ␩2 values were cal-

共1兲

where ␮B is the Bohr magneton, g is a g tensor, S is anelectron spin operator, A is a HF tensor for Si1 or Si2, I is a
nuclear spin operator 共I = 1 / 2兲, gn is the nuclear g value for29
Si 共−1.1106兲, and ␤n is the nuclear magneton. The spin-

FIG. 2. 共Color online兲 Atomic models 共a兲 for V−C 共HEI1兲 and 共b兲
for V+C 共EI5兲.7 For unpaired-electron orbitals on each Si atom, thedirection 共␪兲 and distribution 共␩2兲 are given in the figure.

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culated by the sum of 3s- and 3p-orbital densities, ␩2␣2
+ ␩ 2␤ 2,where␩2␣2 = Aiso共mT兲 / 163.93,
␩ 2␤ 2= Aaniso共mT兲 / 4.08, Aiso = 共A储 + 2A⬜兲 / 3, Aaniso = 共A储 − A⬜兲 / 3,and ␣2 + ␤2 = 1.16 One may assume that the Si1 or Si2 HF
structure originates from three to six 13C atoms 共I = 1 / 2,natural abundance= 1.1%兲, which would make the intensity
ratio of the Si1 or Si2 HF structure about 4.7% 共=ideal intensity ratio for a 29Si HF interaction兲. In this case, however, the␩2 values were calculated to be 26.4% or 40.0% for each C
atom using the atomic coefficients of carbon 关␩2␣2= Aiso共mT兲 / 134.77 for 2s-orbital, ␩2␤2 = Aaniso共mT兲 / 3.83 for
2p-orbital兴.16 Thus, the total distribution was much larger
than 100%. Therefore, we can conclude again that the Si1and Si2 HF structures are due to 29Si.
It is worth noting that there is a close similarity between
V± in Si and VC± in SiC. For V− 共G2兲, an unpaired electron
distributes on two Si atoms by 26.5% ⫻ 2 共totally 53%兲 andfor V+ 共the G1 center兲 the distribution is divided among four
Si atoms by 14.5% ⫻ 4 共totally 58%兲.10 From Figs. 2共a兲 and2共b兲, we can see the same trend in VC− 共HEI1兲 and VC+ 共EI5兲,
although the lower crystal symmetry of 4H-SiC breaks theequality of Si1–4 and causes some deviations from the case ofsilicon. Since both the V± state and the VC± state consist of a
combination of Si dangling-bond orbitals, such a similarity
can naturally be expected.17 However, it is interesting thatthe wave functions of the V± and VC± states were found to bequantitatively close, despite their energetic positions in the
gap being completely different.9,10
In Table I, we compare the measured HF tensors with thecalculated ones for VC− at the h site. The first-principles calculations revealed that h and k sites cause completely different behaviors in VC−. At h sites, Jahn-Teller distortion makesa Si3-Si4 bond and an unpaired electron distributes on the
Si1-Si2 side, which is consistent with what we observed in
the HEI1 center. At k sites, however, an unpaired electron is
located in the Si3-Si4 side, and hence there should appear
another EPR center with quite different angular dependenceof the HF satellites. The obtained geometry of VC− at bothsites agrees very well with the results of an earlier calculation by Zywietz et al.,9 e.g., at h sites, the bond lengths are
2.5 Å for Si3-Si4 and 2.9 Å for Si1-Si2, which are very close
to Zywietz’s values of 2.6 Å and 2.9 Å, respectively. Here,we compare h-site VC− with HEI1. 共Further details of theresults of the calculations will be reported elsewhere.兲 As isseen in the table, perfect agreement between the HEI1 centerand h-site VC− is obtained in both the principal values and the
directions of the HF tensors. Therefore, we conclude that the
HEI1 center originates from VC− at the h site. The reason we
could not observe k-site VC− is still unclear. However, we
speculate that this may be related to dynamic reorientation
effects, because such a dynamics was clearly observed in the
HEI1 center.
The HEI1 spectrum exhibits a thermal-reorientation phenomenon, as shown in Figs. 3共a兲 and 3共b兲. As the temperature was raised, the Si2 HF structure broadened and it eventually disappeared 70 K 关Fig. 3共a兲兴. Simultaneously, the Si1
HF structure is averaged into a single line 关Fig. 3共b兲兴, whenthe magnetic field is aligned at off-angles 共⫽0 ° 兲. Above
70 K, the HEI1 spectrum showed a simple C3v symmetry

FIG. 3. 共Color online兲 Thermally activated reorientation effectof V−C. 共a兲 EPR spectra just for 0° 共B 储 c兲 show the motional narrowing of the Si1 HF line but the lifetime broadening of the Si2 HF line.
共b兲 Off-angle 共20°兲 spectra demonstrate that the Si1 HF structure isaveraged into a single line due to the motional narrowing effect. 共c兲
Temperature dependence of the reorientation lifetime estimated by
the lifetime broadening of the Si2 HF structure. Solid and open
circles were obtained for high-field- and low-field-side Si2 HF lines.
The insets schematically show the reorientation of the defect in the
共0001兲 plane.

共see Table I兲.18 This transition can be explained by the thermal reorientation of the defect. For HEI1, an unpaired electron is located in one of three equivalent bonds, Si1-Si2, Si1-Si3, and Si1-Si4 关see the inset of Fig. 3共c兲兴. Thus, the unpaired electron can hop among these three states by thermal
activation. Since Si2,3,4 atoms are C3v-symmetry related, thethermal-averaging limit also exhibits a C3v symmetry. During the reorientation, the unpaired electron always stays on
Si1 but fully jumps among Si2,3,4. Therefore, only the Si2 HF
structure is strongly affected by the lifetime broadening,which is determined by the reorientation speed. Figure 3共c兲shows the temperature dependence of reorientation lifetime
共␶兲, which was deduced from the inverse of the lifetime
broadening width 共1 / ⌬␻兲7 for the Si2 HF structure. We calculated ⌬␻ from ប⌬␻ = g␮B⌬B, where ⌬B is the half widthat half maximum of the Si2 HF line 共in absorption shape兲
subtracted by the static width 共0.30 mT兲. The static width
was measured at 20– 40 K. The temperature dependence
seems to indicate the thermally activated behavior. The activation energy was roughly estimated to be 0.02 eV. A similar
thermally activated reorientation has been observed for EI5,
in which three equivalent C1h structures were averaged into a
C3v structure with an activation energy of 0.015 eV.6,7 In thatcase, however, the disappearance of particular HF structure共s兲 was not observed,6,7 because the unpaired electronalways stayed on four Si atoms 共Si1–4兲 of VC 关Fig. 2共b兲兴. The
reorientation effects are thus closely related in the nature ofthese defects. By analogy with the “missing” HF structure of
the HEI1 center, the same behavior is also expected for Si3
and Si4 HF structures of k-site VC−. This may be related to thereason we could not observe k-site VC−.
We also carried out photo-EPR measurements at 77 K to193202-3

PHYSICAL REVIEW B 71, 193202 共2005兲

BRIEF REPORTS

estimate the energy position of VC−. The changes in EPR
intensities of the central line 共“main”兲 and HF lines 共“HF”兲
for HEI1 and EI5 are shown in Fig. 4共a兲. For both centers,
the “main” and “HF” curves showed the same behavior,demonstrating that there was no interference from the othersignals. Without illumination, only VC− 共HEI1兲 and other HEI
centers were observed; VC+ 共EI5 and EI6兲 was completely
absent. This is reasonable for our n-type sample. With
1.1-eV light excitation, all EPR signals increased or decreased simultaneously, because it became possible to excite
electrons from levels at the Fermi level 共EF兲 to the conduction band, which caused different charge states for the EPR
centers. This excitation increased the HEI1 signal drastically,
indicating that VC− + e− 共conduction band兲 was generated from

VC2−. Namely, most of the VC were converted to VC2−, when
EF was located at EC 共conduction-band bottom兲 −1.1 eV.
This suggests that the 共− / 2 − 兲 level is located below EC−1.1 eV or EV + 2.2 eV. Alternatively, another explanation
would be that VC2− is slightly more stable than VC− 共the socalled weak negative-U behavior兲, and hence VC2− became
dominant in the dark. In fact, the present calculations predicted U = −0.33 eV for h-site VC−. In the previous
calculation,9 U was also negative for both h-site and k-site
VC− 共−0.29 eV兲. However, we have to note that the total energy of the charged defect represents a problem in the supercell approach. Since the appropriate charge correction for a
defect in a solid is still being debated in the literature,19–21
the negative-U property for VC− is not yet proven entirely bytheory.22 When we further increased the photon energy to
1.8– 1.9 eV, the EI5 signal 共VC+兲 became detectable. This indicates that the 共+ / 0兲 level of VC is located below EC− 1.8 eV or EV 共valence-band top兲 +1.5 eV, which is inagreement with the previous work 共EV + 1.47 eV兲.2 Figure
4共b兲 summarizes these results.
In summary, we have reported EPR measurements of anegatively charged state of carbon vacancies 共VC−兲 in
4H-SiC. We found an EPR center, HEI1, and its 29Si HF
interactions were well described by an unpaired electron 共S= 1 / 2兲 in the antibonding state of Si1 and Si2 of VC. Firstprinciples calculations showed that the HEI1 center corresponds to h-site VC−. It is worth noting that there is a close
similarity between VC−共HEI1兲 / VC+共EI5兲 and V−共G1兲 / V+共G2兲
in silicon. Photo-EPR measurements suggested that VC2− becomes dominant when EF = EC − 1.1 eV. The HEI1 spectrum
revealed a thermally activated reorientation effect, in which
the reorientation caused the lifetime broadening of a particular HF structure 共Si2兲, resulting in a missing HF structure in
the thermally averaging limit.

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FIG. 4. 共Color online兲 共a兲 Photo-EPR measurement on HEI1
共V−C兲 and EI5 共V+C兲 at 77 K. EPR intensities shown here were simply taken by peak heights of the first derivative signals. 共b兲 Anelectronic energy diagram of VC.

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