PHYSICAL REVIEW B 79, 115211 共2009兲

Dicarbon antisite defect in n-type 4H-SiC
T. Umeda and J. Isoya
Graduate School of Library, Information and Media Studies, University of Tsukuba, Tsukuba 305-8550, Japan

N. Morishita and T. Ohshima
Japan Atomic Energy Agency, Takasaki 370-1292, Japan

E. Janzén
Department of Physics, Chemistry, and Biology, Linköping University, SE-581 83 Linköping, Sweden

A. Gali
Department of Atomic Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
共Received 13 August 2008; revised manuscript received 5 January 2009; published 24 March 2009兲
We identify the negatively charged dicarbon antisite defect 共C2 core at silicon site兲 in electron-irradiatedn-type 4H-SiC by means of combined electron paramagnetic resonance 共EPR兲 measurements and firstprinciples calculations. The HEI5 and HEI6 EPR centers 共S = 1 / 2; C1h symmetry兲 are associated with cubic andhexagonal dicarbon antisite defects, respectively. This assignment is based on a comparison of the measured
and calculated hyperfine tensors of 13C and 29Si atoms as far as the second neighborhood around the defects.
Theoretically, the dicarbon antisites are stable in a single negative charge state under a wide range of n-typesamples. We found that the defects can be created under a wide range of irradiation conditions, and ourmeasurements strongly suggest the existence of carbon antisite defects in the as-grown samples. Annealingstudies revealed several atomistic processes such as recombination of carbon interstitials with vacancies andformation of carbon aggregates. These processes were activated at about 1000 ° C, and as theoretically predicted, the dicarbon antisite is much more stable than the dicarbon interstitial defect 共C2 core at carbon site兲.
The measured activation temperature is consistent with the temperature range for forming various carbon
aggregate-related photoluminescence centers.
DOI: 10.1103/PhysRevB.79.115211

PACS number共s兲: 61.72.J⫺, 71.55.Ht, 71.15.Mb, 76.30.Mi

I. INTRODUCTION

Silicon carbide 共SiC兲 is unlike other wide-band-gap semiconductors 共GaN, ZnO, diamond, etc.兲 because largediameter pure single crystals can be grown. Furthermore,
SiC potentially has uses in power electronic devices of highperformance. A problem is that SiC technology has not progressed far enough to be able to control defects that may
affect SiC crystals; even the basic defects are not entirely
understood. In recent years, though, significant progress has
been made in identifying vacancy defects.1 Their identification has mostly been through a combination of electron paramagnetic resonance 共EPR兲 spectroscopy and first-principles
calculations. In fact, we can now list many examples of va−−
共VSi
and TV2a兲,2 VC+ 共EI5/6兲,3 VC−
cancy defects in 4H-SiC: VSi+−
4
5
共HEI1兲, CSiVC 共HEI9/10兲, CSiVC 共SI5兲,6 and VSiVC0 共P6/7兲.7
Some of these defects have also been identified in 6H-SiC
and other polytypes.1 These vacancy defects can be generated by electron, neutron, and ion irradiation and subsequentannealing. They also appear in as-grown crystals.8
In principle, the formation of vacancies must be accompanied by the formation of silicon or carbon interstitials 共Siiand Ci兲. In fact, theoretical studies predict a number of possible interstitial-related defects in SiC.9–13 Carbon interstitials are especially important because they are highly
mobile9,11 and are able to form very stable aggregates owing
to strong C-C bonds.9–13 The Ci atom can be energeticallystabilized by a dumbbell or dicarbon structure 共C2兲 at either
the C site or Si site. The former is a dicarbon interstitial
1098-0121/2009/79共11兲/115211共8兲

defect 共or carbon split interstitial兲 共C2兲C, which is mobile,and it aggregates relatively easy with other interstitials forming clusters9,10 The latter type is called dicarbon antisite
共C2兲Si,9,10 which is produced by pairing Ci and a carbon antisite 共CSi兲, and it exhibits higher thermal stability.9,10,12 At
high temperatures, these dicarbon defects can produce a variety of carbon-interstitial-related defects such as 关共C2兲C兴2,9,11
关共C2兲Si兴2,9,10 共C2兲Si-共C2兲C,9 and 共C3兲Si.9,10,13 They are therefore possible stable defects that are generated by high temperature annealing. For example, some of them are considered to be the origin of the DII center 关a group of 共C2兲Si兴,9,10
P-T centers 关共C2兲C兴,9 and U, Z, HT3, HT4, and HT5 centers关共C3兲Si and their family兴13 in photoluminescence 共PL兲 spectroscopy or to the Z1/2 centers 关a ring structure made of 共C2兲Si
and Ci兴12 in deep-level transient spectroscopy 共DLTS兲. Moreover, Steeds et al.14 recently presented the most successful
assignment so far from PL measurements. For 4H-SiC, they
assigned a set of four 463 nm luminescence lines to the four
neutral states of 共C2兲Si.14 Furthermore, they found that manyother PL centers were possibly related to carbon-interstitialrelated defects.15 Their common signature is high-energy local vibration modes 共ⱖ100 meV兲,15 which can be generated
by strong C-C bonds.9–13
Unfortunately, the PL measurements on the carboninterstitial-related defects were successful in heavy irradiation conditions 共1019 – 1020 e / cm2兲. Moreover, PL signals do
not indicate the absolute concentrations of defects because
their intensity is dependent on a complicated competition
between excitation and emission processes. For example, the115211-1©2009 The American Physical Society

PHYSICAL REVIEW B 79, 115211 共2009兲

UMEDA et al.

II. EPR ANALYSISThe EPR measurements were carried out with a Bruker
BioSpin X-band cw-EPR spectrometer equipped with an Oxford ESR900 cryostat system. The spectra were measured
using magnetic-field modulation at 100 kHz and a 0.05 mT
width. Most of the measurement temperatures were chosen
to be between 200 and 295 K since the detection of the
HEI5/6 signals at low temperature is affected by a microwave saturation effect. All EPR data shown in this section
were obtained at thermal equilibrium 共without photoillumination兲.
The 1.5-mm-thick 4H-SiC samples were prepared using
commercial nitrogen-doped substrates 共room-temperature
carrier concentration= 1017 / cm3兲. We prepared two types of

HEI6@295K[0001] to [1120]

100%4.8% 5.3%

SiI SiII

HEI6*

4.8% 4.8%

0.6%

SiII SiI

C1(a) 0°SiI SiII

SiII SiIHEI5*SiI SiII

SiII SiI
C1

HEI1(b) 0°

×10

HEI1

HEI3

0.2mW

EPR intensity (arb.units)

463 nm 共2.67 eV兲 signal mentioned above involves an upconversion mechanism 共emitted photon energy⬎ excitation
photon energy兲 owing to a coupling of other unknown
centers.14 Because of this, the formation and annihilation behaviors that can be seen in the 463 nm signal do not simply
reflect those of 共C2兲Si.
Likewise, other spectroscopic techniques have only been
partially successful in identifying carbon-interstitial-related
defects. So far, EPR and theoretical studies have suggested
dicarbon interstitial defects 共C2兲C in as-irradiated SiC. For
instance, the EI1/3 EPR centers 共electron spin S = 1 / 2 or 1;
C1h symmetry兲16 that were observed in room-temperature irradiated p-type 4H-SiC 共ⱖ1 ⫻ 1017 e / cm2兲 are theoretically
due to positive or neutral charge states of 共C2兲C.9 Subsequently, in room-temperature irradiated n-type 6H-SiC 共⬎1⫻ 1018 e / cm2兲, a similar EPR center 共the EIn center, S = 1;C1h symmetry兲 was observed under photoexcitation, and it
was assigned to 共C2兲C in the double positively charged
state.17 These centers were annihilated with a 200– 300 ° C
anneal,16,17 and this result reflects the low thermal stability of
共C2兲C defects. However, the spectroscopic information onthese centers is far from enough for making a conclusive
identification. In particular, hyperfine 共HF兲 interactions ofinterstitial carbon atoms, which are the most crucial information for identification, are not exactly known. Such HF interactions have yet to be detected for EI1/3, and have been
investigated only at a single angle for EIn.16,17
In this paper, we present EPR and first-principles theoretical studies on an important carbon-interstitial defect, dicarbon antisite 共C2兲Si, in 4H-SiC. We found that electron irradiation very easily generated 共C2兲Si defects in n-type
4H-SiC. We labeled the EPR signals of 共C2兲Si as HEI5/6 共S= 1 / 2; C1h symmetry兲. By optimizing experimental conditions, their weak HF interactions due to a 13C atom 共nuclear
spin I = 1 / 2; natural abundance= 1.1%兲 at an interstitial sitewere successfully revealed without isotope enrichments. In
addition, HF interactions due to surrounding 29Si atoms 共I= 1 / 2; natural abundance= 4.7%兲 atoms were also analyzed.
Comparing between the experimental results and theoretical
calculations, the HEI5/6 centers were assigned to negative
charge states of 共C2兲Si at either cubic 共k兲 or hexagonal 共h兲sites of 4H-SiC. Furthermore, we used EPR to reveal theformation and annihilation behaviors of 共C2兲Si.

HEI1

×10

2mW
HEI3

HEI2

(c) 90°, 2mW
4
12 C1

2
12 C1
HEI1

SiI

SiII
SiI

SiI C

HEI6

4

1 12

×10

2
12 C1

HEI1

HEI3

HEI6@200K[0001] to [1100]

SiII

SiII

HEI1

2 ×2
C1 12

HEI1

HEI1

1 ×2
12

**

HEI6

1 ×2
12

HEI1

HEI1

SiII
SiI

**

2 ×2
12 C1

×10

(d) 60°
0.2mW

HEI3

HEI1
HEI2

334

335

336

337

338

339

340

Magnetic field (mT)FIG. 1. 共Color online兲 Hyperfine structures of HEI6 center in
4H-SiC. 共a兲 and 共b兲 0° spectra of HEI6 measured during magneticfield rotation from 关0001兴 共0°兲 to 关112̄0兴 共90°兲 with microwave of
0.2 and 2 mW 共9.452 GHz兲, respectively. In 共b兲, HEI5 signal was
effectively suppressed due to a strong microwave saturation effect.
Both spectra 共a兲 and 共b兲 showed four 29Si HF satellite lines 共SiI and
SiII兲 and a high-field-side 13C HF satellite line 共C1兲 of HEI6. In 共a兲,
we estimated intensity ratio of each satellite line to a central line for
HEI6. Asterisks 共 ⴱ 兲 indicate positions of missing 13C satellite linesthat are hidden by other strong signals. 共c兲 90° spectrum of HEI6.
With this direction, C1 HF structure splits into four satellite lines
with intensity ratio of 2:4:4:2 关see an angular map in Fig. 4共a兲兴,
which were successfully resolved in this spectrum. 共d兲 60° spectrumof HEI6 measured during magnetic-field rotation from 关0001兴 to关1̄100兴 using microwave of 0.2 mW 共9.428 GHz兲 at 200 K. For thisspectrum, magnetic-field values are shifted to adjust to the case of
9.452 GHz. In this rotation experiment, C1 HF structure splits into
eight lines with a ratio of 2:2:1:1:1:1:2:2 关see an angular map in
Fig. 4共c兲兴, and outer four lines can be seen.

sample with different crystal orientations; they exhibited different angular maps of the defect with respect to magneticfield 共B兲 rotations and thus were quite useful for angularmap analyses. The samples were subjected to 3 MeV
electron irradiation at different temperatures 共Tirr兲 inside avacuum chamber of a radiation facility at the Japan Atomic
Energy Agency. As demonstrated in our previous study,5 a
combination of our special thick samples and a high-Q-factor
microwave cavity 共over 10 000 factor under actual measurements兲 enabled us to resolve weak 13C HF structures without
isotope enrichments.
We already reported the HEI5/6 centers as “unknown defects” in Refs. 6 and 18. A typical EPR spectrum of thesecenters is shown in Fig. 1共a兲. They were the dominant paramagnetic defects in the thermal equilibrium state of irradiated n-type 4H-SiC. We found that the two signals had different microwave saturation behaviors. The HEI5 signal was

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PHYSICAL REVIEW B 79, 115211 共2009兲

DICARBON ANTISITE DEFECT IN n-TYPE 4H-SiC
100%

4.1% 4.3%

SiI SiII 0.2%
C1

HEI5

5.3% 4.9%

SiII SiI

(a)

0.6%

C1

(a) 0°
0.02mWSiI SiII

C1

HEI6

×10

C1

336.5

SiII SiI

HEI6
2
C1 12 ×2

SiI~SiII

HEI5
1×2* * 12(b) 60°0.2mW

SiI~SiII

2

1 ×2
12

*

×10

*

SiI~SiII

C1 12 ×2

Magnetic field (mT)EPR intensity (arb.units)

HEI5@295K[0001] to [1100]

SiI~SiII
HEI6

333

334

335

336

337

338

339

340

Magnetic field (mT)FIG. 2. 共Color online兲 Hyperfine structures of HEI5 center in
4H-SiC. 共a兲 0° spectrum of HEI5 measured during magnetic-fieldrotation from 关0001兴 共0°兲 to 关1̄100兴 共90°兲 using microwave of 0.02
mW 共9.428 GHz兲. In this condition, both HEI5 and HEI6 signals
were detected at the same time without microwave saturation behavior. We give intensity ratio of each HF satellite line to a central
line for HEI5, supposing that overlapped HEI6’s HF lines have theirideal intensities 共9.4% for SiI and 0.55% for C1兲. 共b兲 60° spectrumof HEI5. C1 HF structure of HEI5 splits into eight satellite lines
with intensity ratio of 2:2:1:1:1:1:2:2 关see an angular map in Fig.
4共b兲兴, and outer four lines can be resolved. Asterisks 共 ⴱ 兲 indicate
positions of missing 13C satellite lines of HEI5.

rather easily saturated with a high microwave power. Therefore, using strong microwaves, we could selectively observe
the HEI6 signal, as is shown in Figs. 1共b兲–1共d兲. For the best
symmetrical direction 关0° or B 储 关0001兴, Figs. 1共a兲 and 1共b兲兴,
two strong HF doublet structures 共 four HF satellite lines兲
and one weak HF doublet one 共a low-field-side line was hidden by the HEI1 and HEI3 signals兲 can be resolved for HEI6.
We call the strong outer and inner doublets “SiI” and “SiII”,
respectively, because they originate from 29Si HF interactions. The relative intensities of each doublet to the central
line were estimated to be, respectively, 9.6% and 10.1% for
the SiI and SiII doublets 关Fig. 1共a兲; in this spectrum, the HEI6
center exhibited almost no microwave saturation兴. In theother spectrum, the intensity ratios were found to be 8.9%
and 9.2%, respectively. These ratios are close to twice the29
Si concentration 共9.34%兲. Therefore, the wave function of
HEI6 should extend over at least four Si atoms 共two SiI
atoms and two SiII atoms兲. The weak doublet is named “C1”,and it originates from a 13C HF interaction. The high-fieldside C1 line shows a relative intensity of 0.6% to the central
line in Fig. 1共a兲. This value varied between 0.3 and 0.8%
among different spectra. Finally, we judged that the intensity
ratio of the high-field-side C1 line matches half the concentration of 13C 共1.11% ÷ 2 = 0.55%兲. Namely, the HEI6 center
should include one carbon atom in its core. This conclusion
is quite reasonable because later analyses will show that
more than 50% of the wave function of HEI6 is localized on
this carbon atom. Therefore, no one can assume two or morecarbon atoms for the C1 HF structure.
The case of the HEI5 center is shown in Fig. 2. To observe HEI5, we must use a lower microwave power 共e.g.,⬍0.5 mW at 295 K兲. In Fig. 2, both HEI5/6 signals wereobserved at the same time. The features of HEI5 were very

HEI5
336.0

(b)
337.5

HEI6

HEI5

337.0

HEI1
0

Angle (degrees)

90

FIG. 3. 共Color online兲 Angular maps of HEI5/6 centers 共primarylines兲. The magnetic field was rotated by 90° in the following directions: 共a兲 关1̄100兴 and 共b兲 关0001兴 → 关112̄0兴. Solid lines show
simulated angular patterns. EPR measurements were carried out
under the same conditions as in the measurements of Fig. 1共a兲.
These maps were measured using different microwave frequencies.

similar to those of HEI6. In Fig. 2共a兲 关0° or B 储 共0001兲兴, wefound again the SiI and SiII HF doublets as well as the C1
doublet for HEI5. The intensity ratios are also similar to
those of HEI6: 9.0% and 9.6% for the SiI and SiII doublets,
respectively, and 0.8% for the C1 doublet in Fig. 2共a兲.
Namely, both the HEI5/6 centers have the same atomic structure that consists of one carbon atom and four Si atoms.
These atoms correspond to a central carbon interstitial atomand surrounding Si atoms, respectively, as we clarify below.
Furthermore, it is reasonable to assume that the HEI5/6 centers are neither pairing nor clustering defects because we candistinguish only two types or two lattice sites 共k and h sites兲.
Figure 3 plots the angular dependences of the primarylines of HEI5/6. The HEI5/6 centers have an electron spin of
1/2 and C1h symmetry with respect to the 共112̄0兲 plane. FromS = 1 / 2, we expect that their charge is either −1 or +1. The
charge of −1 is reasonable since HEI5/6 was detected in the
n-type samples. Table I shows the g tensors of HEI5/6 asdetermined from the fitting of the angular maps 共solid lines
in Fig. 2兲.19 One notable signature is that the main principal
value 共g储兲 is larger than the other two; this is a general property of negatively charged centers,4,6 and it supports theabove assignment.
The angular dependences of the HF interactions are themost crucial information for unraveling the microscopic origin of the HEI5/6 centers. Figure 4 shows three angular maps
for two rotation planes as well as for two temperatures 295
and 200 K. First, it should be mentioned that the HF inter-

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PHYSICAL REVIEW B 79, 115211 共2009兲

UMEDA et al.

TABLE I. Principal values of g tensor for HEI5/6. ␪ and ␾ indicate main principal axes 共gzz axes兲 in polar
and azimuthal angles. The definition of the Cartesian coordinates is shown in Fig. 5. The g tensors areapproximately axial symmetric 共gxx ⬇ gyy兲 and are temperature independent.
CenterSymmetrygxx

gyy

gzz 共g储兲

␪, ␾

HEI5
HEI6

C1h
C1h

2.002 422.001 85

2.002 58
2.001 75

2.003 45
2.002 39122°,90°127°,90°

actions of HEI6 were temperature dependent above 150 K.
For example, the HF splitting widths of SiI were 2.58, 2.80,
and 2.90 mT at 295, 200, and 150 K, respectively 共forB 储 关0001兴兲. Judging from the experimental merits, we analyzed the HEI6 spectra at 295 and 200 K. The 200 K spectra
are regarded as a low-temperature limit because the spectral
difference between 200 and 150 K was very small
共ⱕ0.1 mT兲. The largest HF interaction of HEI5/6 is givenby the C1 atom 共see Fig. 4兲. This HF splitting is maximized
for the 关112̄0兴 direction, indicating that the carbon 2p orbitalis directed to this direction.
Finally, we performed a fitting of the angular maps bysimulating the following spin Hamiltonian:H = ␮BS · g · B + S · A · I − gn␤nI · B,
where g is a g tensor and A is an HF tensor for either the 13Cor 29Si nuclear spin.1 g was given the values shown in Table
I, and only A was a variable parameter. We assumed axial
symmetry for A; i.e., Azz ⬅ A储 and Axx = Ayy ⬅ A⬜. As shownby the solid lines in Figs. 4共a兲–4共c兲,19 we successfully fitted
the angular patterns of the C1, SiI, and SiII HF doublets of
HEI6. For example, as shown in Fig. 1共c兲, the C1 HF structure splits into four lines with an intensity ratio of 2:4:4:2 forB 储 关1120兴. This feature has been reproduced in Fig. 4共a兲. For
the B rotation in the 共1120兲 plane 关Figs. 4共b兲 and 4共c兲兴, thesimulation shows that the C1 HF structure splits into eight
blanches with an intensity ratio of 2:2:1:1:1:1:2:2, which isconsistent with the observations in Fig. 1共d兲 and Fig. 2共b兲,
respectively. The determined HF tensors are summarized inTable II. Unfortunately, a full determination was impossible
for the SiI and SiII HF tensors for HEI5 because of a large
overlap between the angular patterns of SiI and SiII 关Fig.
4共b兲兴. We extracted their principal values 共corresponding to
the minimum and maximum HF splitting widths兲 and one of
their principal coordinates 共␪ angle兲, but the other coordinate
共␾ angle兲 could not be uniquely determined. However, byusing the ␪ and ␾ values predicted by the first-principles
calculations 共see Table II兲, we obtained a reasonable agreement between the experiment and simulation for the angularpatterns of SiI and SiII. This ensures that our analyses arereasonable.
Since the assumption of axial symmetry of A was satisfactory, we can perform a linear combination of atomic orbitals 共LCAO兲 analysis.1 Namely, the wave function of theunpaired electron of HEI5/6 共⌿兲 is expressed by⌿ = ⌺i␩i关␣i␺s + ␤i␺ p兴,
where ␺s and ␺ p are the s and p orbitals of carbon or silicon,
␣i and ␤i 共␣2i + ␤2i = 1兲 are the s- and p-orbital fractions of the

ith atom, and ␩2i indicates the total spin density on the ith
atom. The LCAO coefficients are calculated as follows:␩2i ␣2i = 共A储 + 2A⬜兲/3A0 ,共1兲

␩2i ␤2i = 共A储 − A⬜兲/3b0

共2兲

for each ith atom, where A0 and b0 are the HF constants ofpure s and p orbitals, respectively.1 We used A0= 134.77 mT and b0 = 3.832 mT for 13C and A0= −163.93 mT and b0 = −4.075 mT for 29Si.20 The ␩2i values
for the HEI5 and HEI6 共at 200 K兲 centers were estimated tobe, respectively, 54.0% and 52.9% for the C1 atom, 3.8% and5.9% for each SiI atom, and 2.9% and 4.1% for each SiII
atom. Namely, the wave function of HEI5/6 is strongly localized on the central C1 atom, and it weakly extends to four
surrounding Si atoms 共SiI and SiII兲. The sp hybridization
ratio on C1 共␤2i / ␣2i 兲 is 21.7 共HEI6兲 or 21.9 共HEI5兲, which is
the largest ratio among the known defects in SiC 共␤2i / ␣2i= 9.5⬃ 16.4兲.1 The wave function of HEI5/6 on C1 is very
close to a pure 2p orbital—in other words, an ideal carbon ␲
orbital. This ␲ orbital should be parallel to the 关112̄0兴 axis
共the A储 axis兲. Such a carbon orbital would never exist in anormal SiC lattice, but it can be generated on an interstitialcarbon atom forming sp2 hybridized bonds in the 共112̄0兲
plane. Therefore, we conclude that the HEI5/6 centers involve a carbon interstitial atom at the k and h sites in
4H-SiC.
As mentioned above, the first-principles calculation predicted two types of fundamental carbon interstitial defect:
dicarbon interstitial 共C2兲C and dicarbon antisite 共C2兲Si.9 The
former defect is much less stable 共much more mobile兲 thanthe latter one.9,10,12 Since the HEI5/6 centers are stable athigh temperatures 共ⱕ1000 ° C兲, as will be demonstrated inSec. IV, the latter 共C2兲Si defects at k or h sites are the mostprobable origins of HEI5/6. Their charge states should be −1.
In Sec. III, this identification is completely confirmed bycomparing the HF tensors of the experiment and firstprinciples calculations. The k and h sites are also distinguished with the help of calculations.
Let us further comment on the temperature dependence of
HEI6. Comparing the results for 295 and 200 K, we see that
the SiII atom has the largest difference. As in Table II, themain principal axis of A共SiII兲 exhibits a large variation from共␪ , ␾兲 = 共119° , 24°兲 to 共117° , 7°兲. This implies that there is alarge amount of flexibility or vibration in the vicinity of the
SiII atom. Such a characteristic motion seems to bring afaster spin-lattice relaxation on HEI6, resulting in less microwave saturation for HEI6, as mentioned above. In fact, thedifference in the microwave saturation behavior between

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PHYSICAL REVIEW B 79, 115211 共2009兲

DICARBON ANTISITE DEFECT IN n-TYPE 4H-SiC[0001][0001][1120](a) 295K

HEI5 and HEI6 could no longer be observed after lowering
the temperature to a point 共150 K兲 at which the HEI6 center
became completely frozen.

[1100](b) 295K(c) 200K

HEI1

340

339

III. THEORETICAL IDENTIFICATION

HEI1

6 SiI

339

Magnetic field (mT)

6 SiI
5 SiI
338

6 SiII

6 SiII

338

337
HEI2

HEI6

5 SiII

HEI6

337

HEI5

336
HEI1

HEI3

336

335

6 C1

6 C1

335

6 C1

334
5 C1

HEI1

334
0

90
Angle (degrees)

0

90 0

90

Angle (degrees)

FIG. 4. 共Color online兲 Angular maps for HEI5/6 centers 共13C
and 29Si hyperfine satellite lines兲. B was rotated either in the 共1̄100兲
plane 共关0001兴 → 关112̄0兴兲 or in the 共112̄0兲 plane 共关0001兴 → 关1̄100兴兲.
“+” symbols present resonant positions 共larger and darker symbols
indicate larger resonant peaks兲. Solid lines were calculated by using
the spin-Hamiltonian parameters shown in Tables I and II or byusing those in Ref. 4 共for HEI1兲. “C1” indicates the 13C hyperfine
interaction due to a carbon interstitial atom in HEI5/6. “SiI” and“SiII” denote 29Si hyperfine interactions from four Si atoms surrounding an interstitial atom 共see details in the text兲. 共a兲 Angularpattern for HEI6 at 295 K. This map was produced using a series of
HEI6 spectra shown in Figs. 1共b兲 and 1共c兲. 共b兲 Angular patterns for
a combination of HEI5 and HEI6 at 295 K. This map was produced
using a series of EPR spectra shown in Fig. 2共b兲. Four inner
blanches of C1 were not resolved due to their small intensities andinterferences from many small signals over a middle region 关cf. Fig.
2共b兲兴. Note that the HEI5’s pattern was temperature independent,
but the HEI6’s pattern was temperature dependent above 150 K. 共c兲
Angular pattern of HEI6 at 200 K. This map was produced using aseries of HEI6 spectra shown in Fig. 1共d兲. Four inner blanches of C1
could not be resolved again. Also some branches of SiI and SiII
were unclear in the map due to overlaps between the satellite lines
关cf., Fig. 1共d兲兴. At this temperature, HEI1/2 signals became larger
and disturbed observation of some central lines of HEI6 关cf., Fig.
1共d兲兴.

We used ab initio supercell calculations to study the 共C2兲Si
defect in detail. Here, we focus mainly on the determinationof the HF tensors. For this purpose, we applied the same
methodology by which we identified vacancy-related defects
in 4H-SiC.4,5 We employed density-functional theory 共DFT兲
within the local-density approximation 共LDA兲 of the Hamiltonian and used the all-electron projector augmented wave
method in the calculation of the HF tensors. A detailed explanation and references can be found in our previous
publications.4,5 Here, we briefly describe only the defectmodeling that was particularly used for this defect. We applied a 576 atom 4H-SiC supercell 共6 ⫻ 6 ⫻ 2 of the primitive
unit cell兲 and the ⌫ point for K-point sampling. This large
supercell is certainly sufficient to study an isolated 共C2兲Si
defect, which has rather delocalized defect states in thegap.9,10,12 Note that the electrical characteristics were alreadystudied in our previous paper in which we used a method
beyond that of standard DFT.12 We found that the 共C2兲Si defect is negatively charged in n-type SiC and that the positively charged state can be disregarded. Thus, here, we restrict our calculation to the HF tensor of the negatively
charged 共C2兲Si defect. Note that the paramagnetic positively
charged state may be detected in moderately doped p-type
SiC.
The label 共C2兲Si indicates a defect in which two carbon
atoms share the same Si site 共Fig. 5兲. Hence, such a defect ispartially an antisite and an interstitial-related defect. The two
carbon atoms in the core 共C1 and C2 in Fig. 5兲 bind to two
carbon atoms among the four first-neighbor carbon atoms of
the Si site. Since the C-C bonds are much shorter than thehost Si-C bonds, this defect does not imply stress in the host
SiC crystal and only the first- and second-neighbor atoms
significantly relax in the lattice. The two carbon atoms in thecore have a 共graphitic兲 sp2-like bonding configuration.
Therefore, these carbon atoms have a strongly localized pelectron pointing perpendicular to the plane defined by the
carbon atom in the core and its two first-neighbor carbon
atoms. In the neutral state, the two carbon atoms in the core
have their own p orbital occupied by one electron. Such p
orbitals are responsible for the defect states appearing in the
middle of the gap in 4H-SiC. This was already explained in
our previous papers9,12 in which the neutral state was analyzed in detail. We found that the formation energies andgeometries of the neutral 共C2兲Si at the k and h sites of
4H-SiC are very similar. In contrast, although the formationenergies of the negatively charged 共C2兲Si at the h and k sites
are within 0.1 eV, their geometries are not the same 关Figs.
5共a兲 and 5共b兲兴. In the negatively charged state, the p orbitalof the C2 atom 共Fig. 5兲 is filled by two electrons and thesystem gets frustrated as this p orbital repels the p orbital of
the C1 atom, and the C2 atom would like to find an additional
partner atom to move from the graphiticlike sp2 bonding
configuration into a sp3 bonding configuration. This becomes

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UMEDA et al.

TABLE II. Spin-Hamiltonian parameters for HEI5/6 centers and negatively charged dicarbon antisites.
Measured and calculated principal values of HF tensors are expressed in mT and absolute values. The
directions of the main principal axis 共A储 axis兲 are indicated with polar and azimuthal angles in Cartesian
coordinates. The coordinate system and associated atoms are defined in Fig. 5.
EPR experimentA⬜ 共Axx , Ayy兲

Atom

C1
C3,4
SiI ⫻ 2
SiII ⫻ 2

1.92
1.78

C1

1.20
共1.08兲

C3,4
SiI ⫻ 22.75
共2.53兲
2.30
共2.07兲

SiII ⫻ 2

␪, ␾A储 共Azz兲90°, 0°
125°
88°

HEI6 at 200 K 共295 K兲
7.02
90°, 0°
共6.37兲
共90°, 0°兲
Not resolved
3.26
108°, −38° / −142°
共3.00兲
共108°, −38° / −142°兲
2.63
118°, 24°/156°
共2.41兲
共117°, 7°/173°兲

possible in the 4H-SiC environment by forming a weak“bond” to a second-neighbor Si atom, labeled Siback in Fig. 5.
The position of this Si atom at the h site is different from its
position at the k site, and this difference is what leads to thedifferent geometry of this defect. We emphasize that despite
the different geometries, the formation energies and oneelectron defect levels in the gap of the two sites agree towithin 0.1 eV. Now that we have established the geometry ofthe defect, we are in the position to determine its HF tensor
at different sites.
The calculated HF tensors are given in Table II. As usual,the principal values and the azimuthal 共␪兲 and polar 共␾兲z[0001] Siback

Si II×2

Si I×2C1

C2_[1120]x

C3,4

Si I×2C1Si II×2_[1100]yCSi(a) k site, HEI5

Axx

C2

Ayy

␪, ␾

Azz
−
共C2兲Siat k site

HEI5
7.15
Not resolved
2.24
2.00

1.21

First-principles calculation

C3,4

Siback(b) h site, HEI6

FIG. 5. 共Color online兲 Atomic structures of dicarbon antisites or
HEI5/6 centers at k and h sites in 4H-SiC. They have a single
negative charge 共S = 1 / 2兲 and C1h symmetry with respect to the
共112̄0兲 plane 共yz plane兲. These figures reproduce the atomic positions obtained from the first-principles calculation. The Cartesian
coordinate system is also shown in the figure. Note the opposite
locations of SiI and SiII atoms with respect to the C1 and C2 atoms
between 共a兲 and 共b兲. The dashed line represents the weak interaction
between the C2 atom and a third-neighbor Si atom labeled Siback.

1.47
1.51
2.12
1.46

1.50
1.52
2.13
1.47

6.88
1.91
2.54
1.95

90°, 0°52°, −64° / −116°127°, 23°, 23°/157
82°, 40°/140°

1.45−
at h site
共C2兲Si1.47
6.84
90°, 0°

1.89
3.38

1.90
3.39

2.22
4.03

55°,−63° / −117°109°, −36° / −144°

2.51

2.53

2.93

118°, 22°/158°

angles of the main principal value 共Azz兲 are listed. Note thatthe strength of the HF constants has a direct relation to the
localization of the unpaired electron, as shown in Eqs. 共1兲
and 共2兲. The largest HF constants 共hence, the largest localization兲 are possessed by the C1 atom 共see Fig. 5兲, which has
an unpaired p electron, as explained above. We observed
measurable HF constants on C3,4 atoms and on certain
second-neighbor Si atoms, labeled SiI and SiII in Fig. 5. We
measured one large 13C HF signal and two sets of 29Si doublet HF signals.
The HF signal from the C3,4 atoms would have hardly
been observable, judging from the angular-pattern simulation
using the theoretical 13C3,4 HF tensors. For example, the HF
splitting widths of C3,4 for B 储 关0001兴 were estimated to be
1.67 mT for HEI5 and 2.01 mT for HEI6, which are close to
those of SiI 共2.0 or 2.8 mT兲 and SiII 共1.8 or 2.4 mT兲 for
HEI5/6. The C3,4 HF signal would probably be obscured by
the SiI and SiII signals. Because the calculations are valid at
0 K, we compare the low-temperature 共200 K兲 data with thecalculated ones in Table II. We found that these sites hadvery similar HF signals of C1, and the calculations agreewith the experimental data. The SiI and SiII signals characterize the sites: both the calculations and measurements indicate that HF constants of SiI and SiII are appreciably lower
at the k site than at the h site. Therefore, we assigned HEI5 to
the k site and HEI6 to the h site. The calculated angles werealso close to the measured values, further supporting the ideathat the HEI5/6 EPR centers are from negatively charged
共C2兲Si defects in 4H-SiC. In addition, as shown in Figs. 5共a兲and 5共b兲, the orientations of dicarbon 共C1-C2兲 should differ
between the sites. The orientation is more tilted from the caxis at the h site 共HEI6兲. This tilting explains the feature thatthe g储 axis 共␪ angles in Table I兲 is more tilted for HEI6 thanfor HEI5.

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3

Spin density (x10 /cm )DICARBON ANTISITE DEFECT IN n-TYPE 4H-SiC
30
20
10
0
7
6
5
4
3
2
1
0

(c) Tirr=450°C

(b)

(a)

(d) Tirr=800°C

P6(nominal)-

N donorVSi (nominal)
Tv2a (nominal)

HEI1
HEI5/6SI5
HEI1

HEI5/6

17

10

HEI5/6
HEI1
400

18

10

2

Dose (electrons/cm )HEI5/6600

800
oTirr ( C)1000 400

600

800
o

Tann ( C)1000 800

1000 1200oTann ( C)

FIG. 6. 共Color online兲 Formation and annihilation of HEI5/6
and other coexisting centers in n-type 4H-SiC. Panels 共a兲 and 共d兲are replotted from Ref. 6. 共a兲 Electron dose was varied 共zero, 2⫻ 1017 to 4 ⫻ 1018 e / cm2兲 for six n-type 4H-SiC substrates kept at
Tirr = 800 ° C. 共b兲 The same dose 共1 ⫻ 1018 e / cm2兲 was applied andthe irradiation temperature 共Tirr兲 was varied for five n-type 4H-SiC
substrates. 共c兲 and 共d兲 Isochronal annealing measurements forsamples of Tirr = 450 and 800 ° C, respectively. Spin densities of
N共k兲 donors and HEI5/6 were estimated in the dark at 70 K, while
those of SI5 and HEI1 were estimated under photoillumination
共100 W halogen light兲 because these centers were stabilized in EPR−
inactive states in the dark. Those of P6 and VSi/ TV2a are nominal
values 共respectively, estimated at 30 and 295 K under photoillumination兲 because they have a triplet 共S = 1兲 or a quartet spin 共S= 3 / 2兲 and their EPR signals are enhanced by optically induced spinpolarization.

The electronic levels of the 共C2兲Si defects were theoretically investigated in Refs. 9, 11, and 12. In Ref. 12, theelectronic structure of 共C2兲Si was calculated with a correctionof the DFT-LDA gap. The calculated 共0 / −兲 and 共− / 2−兲 levels
in 4H-SiC are at EC − 1.4 eV and EC − 0.4 eV, respectively.12
In the double negatively charged state, the p orbital of the C1
atom is fully occupied, giving rise a larger repulsion than for−. Consequently, the calculated 共− / 2−兲 octhe case of 共C2兲Si
cupation level is about 1.0 eV higher in energy than the−state is expected to be
共− / 0兲 level. Therefore, the 共C2兲Si
stable in a wide range of the Fermi-level positions in n-type
4H-SiC. This explains the observation of HEI5/6 in the thermal equilibrium of our n-type samples.
IV. FORMATION AND ANNEALING OF DICARBONANTISITE

Using the dicarbon antisite model, we examine the formation and annealing of HEI5/6. Figure 6共a兲 plots the formations of the HEI5/6 centers and other defects as a function ofelectron dose. Before the irradiation, only a strong N共k兲 donor signal21 was detectable in the dark, and under photoillumination, a very weak divacancy signal 关P6, VCVSi 共Ref. 7兲兴
could be recognized below 30 K. In this illuminated state, we
did not see the HEI5/6 and other signals. The HEI5/6 centerswere immediately formed by the minimum dose of irradiation 共2 ⫻ 1017 e / cm2兲. At this stage, carbon vacancies
关HEI1, VC− 共Ref. 4兲兴 were not yet detectable. The other typeof carbon vacancies 关SI5, CSiVC− 共Ref. 6兲兴 was weakly detected together with the HEI5/6 and N共k兲 signals.22 This fast
formation of HEI5/6 suggests that a number of carbon antisites 共CSi兲 existed before irradiation. In such a situation, mobile carbon interstitials 共Ci兲 could easily produce 共C2兲Si by

simply pairing with as-embedded CSi atoms. This idea is inline with the theoretical prediction that CSi is the most abundant defect because of its lowest formation energy, and despite its existence it is optically and electrically invisible due
to a lack of electronic levels in the band gap.9,23 The formation energy of 共C2兲Si was calculated to be 7.8 eV 共4H-SiC兲,10
which is much higher than 4.0–4.2 eV for VC 共Ref. 24兲 and3.4 eV for CSi.9 However, if CSi existed in the as-grownsamples, the above formation energy for 共C2兲Si should be
reduced to 3–4 eV.9 Existence of CSi in the as-grown samples
was also strongly suggested in the PL study where only 3.8
eV photoradiation formed additional 共C2兲Si 共the 463 nm PL
centers兲.14
Figure 6共b兲 shows the formations of HEI5/6 and otherdefects as a function of the irradiation temperature 共Tirr兲. The
formation of HEI5/6 seems to increase in the range below
650 ° C. This is reasonable because at higher temperatures,
Ci should diffuse more easily, leading to more 共C2兲Si defects.
Furthermore, the formation of HEI5/6 seems to be associated−and TV2a Ref.
with the annihilation of silicon vacancies 关VSi
2兲兴 This can be interpreted as VSi defects being transformed
into CSi defects as well as into 共C2兲Si defects by capturing Ci
atoms.
Figures 6共c兲 and 6共d兲 shows isochronal annealing measurements on two different samples 共Tirr = 450 and 800 ° C兲.
The HEI5/6 centers of both samples were rapidly annihilated
at 1000 ° C. This result suggests that at 1000 ° C, the 共C2兲Si
defects start to dissociate into Ci and CSi, or they themselves
start to diffuse. This temperature is much higher than theannihilation
temperature
of
EI1/3
and
EIn
共200– 300 ° C兲,16,17 which probably correspond to dicarbon
interstitial defects 共C2兲C, and hence the observation is consistent with the theoretical prediction. In Fig. 6共c兲 共Tirr= 450 ° C兲, the HEI5/6 and HEI1 共VC−兲 signals were diminished at 1000 ° C, which suggests that 共C2兲Si 共Ci and CSi兲 and
VC recombine.
On the other hand, Fig. 6共d兲 共Tirr = 800 ° C兲, as well as
previous annealing studies,3,7,25 indicates that the VC centerswere more stable 共i.e., stable up to 1100– 1500 ° C兲 than
共C2兲Si. Accordingly, we expect that the 共C2兲Si defects would
be used for building up carbon aggregates rather than forannihilation of VC. The PL observations strongly support theidea of such an aggregation process occurring. Stable luminescent centers of DI, DII, and many others15 can be generated by annealing irradiated SiC at higher than 1000 ° C. The
DII center is believed to originate from one or more Ci andCSi 关maybe a family of 共C2兲Si兴,9,10 and the DI center is expected to involve one or more CSi 共probably a sort of antisite
clusters兲.26–28 The 共C2兲Si defects are closely related to suchannealing products. A good example is tricarbon antisite,
共C3兲Si,13,15 which consists of one 共C2兲Si site and one Ci atom.
The PL studies showed the tricarbon antisite center 共471.8
nm兲 in irradiated 4H-SiC after a 1100– 1300 ° C anneal15 andthe U center 共525.0 nm兲 in irradiated 6H-SiC after a
1000– 1500 ° C anneal.13 These annealing temperatures are
consistent with the activation temperature of 共C2兲Si observedin the present study.
V. SUMMARY

We identified the negatively charged dicarbon antisite de−, in electron-irradiated n-type 4H-SiC by means offect, 共C2兲Si

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UMEDA et al.

combined electron paramagnetic resonance 共EPR兲 measurements and first-principles calculations. The HEI5/6 EPR centers 共S = 1 / 2; C1h symmetry兲 are associated with cubic andhexagonal dicarbon antisite defects. This assignment is basedon a comparison of the measured and calculated hyperfine
tensors of 13C and 29Si atoms as far as the second neighborhood around the defect. This defect has a C-C core in 共112̄0兲
plane and forms a carbon ␲ orbital perpendicular to thisplane. An unpaired electron is strongly localized in this orbital, showing a characteristic 13C hyperfine interaction. Although the 13C hyperfine signatures of the cubic and hexagonal sites were the same, the second-neighbor Si atoms andthe C-C bond angle were distinguishable between the sites,
and this enabled us to identify the two centers. We found thatthe defects can be created faster than carbon vacancies during electron irradiation. This observation strongly suggeststhat electrically and optically inactive carbon antisite defects
existed in the as-grown samples. The formation of 共C2兲Si via
silicon vacancies was suggested, too. The annealing experi-

ment revealed that the 共C2兲Si defects anneal out through recombination of carbon interstitials with vacancies or throughformation of carbon aggregates. These processes were activated at about 1000 ° C, and this activation temperature isconsistent with the formation temperature of various carboninterstitial-related photoluminescence centers. The calculated
occupation levels of 共C2兲Si were EC − 1.4 eV 共EV + 1.9 eV兲
for 共0 / −兲 and EC − 0.4 eV 共EV + 2.9 eV兲 for 共− / 2−兲. The cal−state was stable in a wide range of the Fermiculated 共C2兲Si
level positions in n-type SiC, and this theoretical prediction
is consistent with the experimental results.

1 J. Isoya, T. Umeda, N. Mizuochi, N. T. Son, E. Janzén, and T.

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The coexistence of the shallow donor signals and the defect signals 共HEI5/6, HEI1, and SI5兲 is a curious behavior because it
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ACKNOWLEDGMENTS

A.G. acknowledges support from the Hungarian OTKA
fund under Contract No. K-67886. We used the Swedish National Super Computer 共NSC兲 共Grant No. snic001-08-22兲 tocarry out the calculations.

115211-8