PHYSICAL REVIEW B 70, 235212 (2004)

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

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

A. Gali and P. Deák
Department of Atomic Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111, Budapest, Hungary

N. T. Son and E. Janzén
Department of Physics and Measurement Technology, Linköping University, S-581 83 Linköping, Sweden(Received 6 May 2004; revised manuscript received 20 August 2004; published 22 December 2004)
The carbon vacancy is a dominant defect in 4H-SiC, and the “EI5” electron-paramagnetic-resonance (EPR)
spectrum originates from positively charged carbon vacancies 共VC+兲 at quasicubic sites. The observed state for
EI5, however, has been attributed to a motional-averaged state with the C3v symmetry, and its true atomic
structure has not been revealed so far. We here report low temperature 共⬍40 K兲 EPR measurements on EI5 andshow that this center has a C1h-symmetric structure due to Jahn-Teller distortion. We also performed ab inito
calculations of the hyperfine tensors for EI5, and obtained a good agreement between experiment and theory in
not only their principal values but also their principal axis directions. A good agreement was also demonstrated
for the EI6 center (hexagonal-site VC+) in this paper. The transition from EI5共C1h兲 to EI5共C3v兲 was found to be
thermally activated and its activation energy was measured as 0.014 eV.
DOI: 10.1103/PhysRevB.70.235212

PACS number(s): 61.72.Ji, 76.30.Mi, 71.15.⫺m

I. INTRODUCTION

In silicon carbide (SiC), there are a variety of intrinsic
defects not only in radiation-damaged (electron, neutron, ion,etc.) samples but also in as-grown substrates.1 These defects
are of great importance for the doping efficiency, semiinsulating mechanism, and performance/reliability of SiC devices. Among dominant intrinsic defects, vacancies of C or
Si, and in particular, C vacancies 共VC兲 are important becauseof their high thermal stability up to 1000– 1500 ° C.1–5 In
4H-SiC, their positively charged states give rise to “EI5” and“EI6” electron-paramagnetic-resonance (EPR) spectra,2,3
which originate from VC+ at quasicubic 共k兲 and hexagonal
共h兲 sites, respectively.4–7 The VC+ centers at different inequivalent lattice sites [we here denote them as VC+共k兲 andVC+共h兲] exhibited remarkably different Jahn-Teller (JT)distortions.5–7 For EI6 or VC+共h兲, four surrounding Si atoms
共Si1–4兲 were rearranged to separate Si1 a bit further from
Si2,3,4 [Fig. 1(a)], keeping the C3v symmetry.5 The amount of
this distortion, which is manifested by the deviation of ␪ [theSi2,3,4 dangling bond (DB) directions, see Fig. 1(a)] from thetetrahedral angle 共⬇109.2° 兲, increased at low temperatures,
resulting in a strong temperature dependence of the EI6 spectrum. However, EI5 or VC+共k兲 exhibits no largely distorted
structure [Fig. 1(b)] and no strong temperature dependence,5despite the ab initio calculations having predicted that EI5
should deform considerably and have a C1h-symmetricstructure.6 Therefore we previously attributed the observed
C3v configuration for EI5 [Fig. 1(b)] to a motional-averaged
state due to thermally activated reorientation.5 This was suggested by the fact that below 50 K, the EI5 spectrum became
1098-0121/2004/70(23)/235212(6)/$22.50

largely complicated and exhibited a lower symmetry.5 However, the structure of the low-temperature configuration of
EI5 has not been definitely determined so far, because of its
complexity.
In this paper, we report a complete analysis of the lowtemperature spectrum of EI5 and show that the EI5 center
was distorted to a C1h structure, as consistently with the previous theoretical study.6 The EI5 spectrum was measured
using the echo-detected EPR technique of pulsed EPR in the
X-band 共9 – 10 GHz兲 range, which made it possible to observe a complete angular dependence of this spectrum freefrom any disturbances of other signals. We also calculate thehyperfine (HF) tensors including the directions of their principal axes up to the third neighbor atoms (3NN) of the defects by ab initio supercell methods. The calculated HF tensors and JT distortion for EI5 were found to reproduce very
well experimental data. We also found that our calculations
fit nicely to the experimental data for EI6 or VC+共h兲. The
obtained C1h structure for EI5 can explain reasonably thethermally activated reorientation behavior. The activation energy for this reorientation was experimentally estimated to be
0.014 eV, which indicates an “electronic bond switching”
similar to the cases of vacancies in silicon.
II. EPR STUDIESThe EI5 and EI6 centers were created by 3-MeV electron
irradiation in commercial p-type 4H-SiC共0001兲 wafers(room-temperature carrier concentration ⬇1 ⫻ 1015 / cm3) at
850 ° C with a dose of 4 ⫻ 1018 electrons/ cm2. This hightemperature irradiation enables us to observe EI5 and EI6235212-1©2004 The American Physical Society

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T. UMEDA et al.

FIG. 1. (Color online) Atomicmodels for (a) EI6 共C3v兲 (Ref. 5),(b) EI5 共C3v兲 (Ref. 5), and (c) EI5
共C1h兲 determined in this study.

dominantly in the substrates. These substrates were measured
by both X-band continuous-wave (cw) EPR (Bruker E500
system) and pulsed-EPR spectrometers (Bruker E580
system). The X-band range was more useful than the W-band
共95 GHz兲 range2,3 for measuring the angular dependence of
EPR spectra, as will be demonstrated in this paper. At
low temperatures, however, usual cw-EPR spectra were distorted due to saturation and passage effects. Thus we recorded the EI5 spectra at 5 K by X-band echo-detected EPR
method in which the intensity of the two-pulse Hahn echo(␲ / 2 pulse — ␶–␲ pulse — ␶–echo, ␶ = 1.2 ␮s, the repetition
time= 10 ms, the integration window= 1.8 ␮s) was measured
as a function of strength of magnetic field 共B兲.8 Since thespin-lattice relaxation time 共T1兲, phase-memory time 共TM兲,and their temperature dependences differ among different
centers, the echo-detected spectra consisting of a predominant contribution of EI5 were obtained by selecting the conditions such as the pulse separation, the repetition rate, andthe temperature. Pulsed-EPR was also used to measure thespin relaxation times directly in the time domain,8 or to determine whether each of the HF lines originates from 29Si or
13
C (respective natural abundances are 4.7% and 1.1%)
by means of pulsed electron-nuclear-double-resonance(ENDOR) techniques. Pulsed-ENDOR spectra were measured at 5 K by the Mims sequence (␲ / 2 pulse — ␶–␲ / 2
pulse — T–␲ / 2 pulse — ␶–echo, ␶ = 0.8 ␮s, T = 16 ␮s, RFpulse of 10 ␮s duration was inserted between the second andthe third pulses, the repetition time= 10 ms).5
Figures 2(a) and 2(b) show angular dependences of EI5(labeled by bold type) and EI6 spectra (italic typing) measured in the 共1̄100兲 plane at 150 and 5 K, respectively. At
150 K, both spectra revealed the same C3v symmetry withsimilar angular patterns. 29Si HF structures of EI5 originate
from four 1NN Si atoms (Si1 and Si2,3,4) of VC+ [see Fig.
1(b)]. Also EI6 shows Si1–4 HF structures (however, Si1 HF
structure is out of sight in Fig. 2). For EI6, since theunpaired-electron distribution concentrates in a Si1 atom by
47%,5 the distribution extends appreciably to Si5–7 atoms located behind Si1, making it possible to observe the Si5–7 HF
structure (see Fig. 2). These characteristics of EI5 and EI6
are fully consistent with the VC+ models shown in Fig. 1. At
5 K, however, the angular pattern of EI5 becomes greatly
complicated. The central line of EI5 split into three lines, andfour pairs of Si1–4 HF lines split into 12 pairs [see Fig. 2(b)].
In addition, Si2,3,4 HF lines are separated into two sets of HFlines at the c axis, which will later be attributed to Si2 andSi3,4 HF lines, respectively.
In Fig. 2, solid lines show fitted angular patterns for EI5
which were calculated based on the following spin Hamiltonian:H = ␮BB · g · S + ⌺n关S · A共Sin兲 · I 共Sin兲 − ␮NgNI共Sin兲 · B兴,
where ␮B is the Bohr magneton, g is the g tensor, S is anelectron-spin operator 共S = 1 / 2兲, A共Sin兲 is the HF tensor for
the Sin atom 共n = 1 – 4兲, I共Sin兲 is a nuclear-spin operator 共I= 1 / 2兲, ␮N is the nuclear magnetic moment, and gN is thenuclear g factor for 29Si 共gN = −1.1106兲. The fitted lines reproduced very well the experimental data. We could also fit
the observed line positions for the rotation of B in the 共112̄0兲
plane. The spin-Hamiltonian parameters determined from thefits are given in Table I. Using these parameters, we also
simulated the angular dependence of the EI5 spectrum at the
W band (Fig. 3). The angular dependence at the W band israther difficult to be resolved due to the overlap among alllines, as compared to the case of the X band (Fig. 2). Furthermore, other angular maps such as the EI6’s map should
fully superimpose on this angular map at the W band. This
fact shows that EPR measurements at higher microwave frequencies are not always superior to the conventional X-bandmeasurements. In Table I, all 29Si HF tensors are close to beaxially symmetric with principal values A储 and A⬜, where theA储 principal axis indicates the direction of Si dangling bonds(DB’s). Figure 1(c) shows an atomic model for the lowtemperature state of EI5 constructed from the spinHamiltonian parameters. This structure has C1h symmetry
with a C1 rotation axis and the Si3 and Si4 atoms being
mirror symmetric with respect to the 共112̄0兲 plane. The principal coordinate system of the g tensor is also consistent withthis C1h structure. The DB’s of Si1 and Si2 atoms are tilted toapproach each other, indicating the formation of a Si1-Si2
atomic pair. Also Si3 and Si4 DB’s moved likewise. Thesebehaviors are quite consistent with the theoretical predictionthat the pseudo-JT distortion at VC+共k兲 induces the Si1-Si2
and Si3-Si4 pairs, resulting in the C1h distorted structure.6 In
fact, the principal A values indicated an excellent agreement
between the experiment and previous theoretical calculation
by Bockstedte et al.6 (Table I).
This C1h structure can also explain the reorientation effectobserved at higher temperatures. Since Si2,3,4 atoms are

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EPR AND THEORETICAL STUDIES OF POSITIVELY…

FIG. 2. (Color online) Angular dependence of EI5 and EI6 spectra at (a) 150 K and (b) 5 K, which were measured by cw EPR
共9.452 GHz兲 and echo-detected EPR 共9.665 GHz兲, respectively. In this figure, magnetic field B was rotated in the 共1̄100兲 plane from the[0001] (0°) to the 关112̄0兴 (90°) direction, and the spectra for 90° were displayed. Solid and dashed lines are simulated angular patterns for
EI5 and EI6, respectively, using the spin-Hamiltonian parameters in Table I.

C3v-symmetry related, there should be three equivalent types
of atomic-pair formation (Si1-Si2, Si1-Si3, Si1-Si4 pairs).
Thus at higher temperatures when the thermally activatedreorientation can occur among the three configuration, theEI5 center will exhibit C3v symmetry.
We further examined a dynamics of the reorientation
through EPR and pulsed-EPR measurements (Fig. 4). In thisfigure, low-field-side Si1–4 HF lines measured for B 储 关0001兴
are plotted as a function of temperature. The transition fromthe C3v to C1h configuration started at around 40 K, thengradually proceeded, and finally Si1, Si3,4, Si2 HF lines wereseparated with an intensity ratio of 1:2:1. In this temperature
range, it was found that the linewidth of the Si2,3,4 HF line isstrongly correlated to the reorientation. Above 40 K, thelinewidth decreased with increasing temperature, indicating
the motional narrowing effect. Conversely, below 40 K, thenarrowing of Si3,4 and Si2 HF lines was observed with decreasing temperature, because the characteristic lifetime of
the reorientation 共␶兲 increased and then suppressed the lifetime broadening. These behaviors are common to the reorientation
observedinchargedvacancies(V+ / G1 center and V− / G2 center)9 or a neutral vacancyphosphorous pair [共V + P兲0, E center]10 in silicon. We evaluated ␶ by applying the same treatment as the previous
works.9–11 According to the notations in Ref. 10, we defined␶ = pA共T2兲B = pB共T2兲A

for lifetime broadening regime,␶ = 4/兵共T2兲AB␦␻2⫻关1 − 共pA − pB兲2兴其

for motional narrowing regime,

where T2 is a transverse spin relaxation time (or phasememory time) of each resonance lines. A, B, and AB label for
the Si3,4, Si2, and Si2,3,4 HF lines, respectively. The relative
intensities of A and B are pA = 2 / 3 and pB = 1 / 3, and a separation between A and B is ␦␻ = 2.1⫻ 107 s−1 关=g␮B / ប⫻ 0.12共mT兲兴. The T2 values were experimentally estimatedfrom two methods. One was deduced from measurements ofthe cw-EPR linewidth, ⌬␻共=1 / T2兲, where ⌬␻ was estimatedby a half width at half maximum of A, B, AB lines minus astatic width 共0.032 mT兲. This static width was observed at
5 K. Another method was the direct measurements of T2 by
two-pulse Hahn echo decay of pulsed EPR.8 As shown in theinset of Fig. 3, the data obtained by the two methods coincided excellently. We confirmed that the transition from AB
to A and B is triggered when ␶ ⬇ 1 / ␦␻共4.7⫻ 10−8 s兲, as consistent with the original theory.11 Also in accordance with our
expectation, the lifetime shows a thermally activated behavior (solid line in the figure) and its activation energy Ea wasestimated to be approximately 0.014 eV. This energy is close
to that observed for V± in Si 共0.01 to 0.02 eV兲.9 Therefore,
as similarly to the case of Si, the reorientation should becaused by “electronic bond switching”.9 Namely, an unpaired
electron just hops between electronic levels of equivalentconfigurations. This picture is in line with our reorientation
model.
It should be noted that similar EPR results have been also
obtained in 6H-SiC.12 In this polytype, there are two inequivalent k sites 共k1 , k2兲 and two EPR spectra of Ky1 andKy2 have been assigned to VC+共k1,2兲 (however, the correspondence of each Ky1 / 2 and each k1/2 was not given). For
Ky2, the HF tensors of Si1–4 have been obtained (Table I),
which are quite close to those of EI5 except smaller ␾ of
A共Si3,4兲. Despite the good agreement in the HF tensors be-

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T. UMEDA et al.

TABLE I. Spin-Hamiltonian parameters for EI5 共C1h兲 or VC+共k兲 obtained by our EPR experiment and ab initio calculations. Also shown
are HF tensors of the previous theoretical calculation (only principal values were reported) (Ref. 6) and EPR results for Ky1 / Ky2 centers or
VC+共k1,2兲 in 6H-SiC (Ref. 12). Principal values of the HF tensors 共AX,Y,Z兲 are expressed in mT using a conversion factor that 1 mT
= 28.02 MHz. We show the principal direction (polar angles ␪ and ␾) only for the main A储 axis, because the HF tensors are nearly axial
symmetric (see also Fig. 1 for the definition of the coordinate system). The theoretical calculation predicted negative principal values for all
HF tensors, however, this table displays only absolute values for comparison with experimental values. ␩2␣2 and ␩2␤2 indicate 3s- and3p-orbital densities on each Si atom, estimated from the following relations: ␩2␣2 = Aiso共mT兲 / 163.93; ␩2␤2 = Aaniso共mT兲 / 4.08; Aiso
= 关A储共Sin兲 + 2A⬜共Sin兲兴 / 3; Aaniso = 关A储共Sin兲 − A⬜共Sin兲兴 / 3; ␣2 + ␤2 = 1 (Ref. 5). Finally, a comparison between our experiment and calculation is
also demonstrated for EI6 or VC+共h兲.
X共⬜兲
EI5 共C1h兲 at 5 K, our EPR
g
2.0056
A共Si1兲
4.44
3.25
A共Si2兲
A共Si3,4兲
3.85
VC+共k兲 共C1h兲, our calculation
A共Si1兲
4.17
A共Si2兲
3.74
A共Si3,4兲
3.80

Y共⬜兲

Z共储兲

␪共°兲

␾共°兲a

2.0048
4.36
3.19
3.81

2.0030
6.46
4.74
5.52

22.7
7.7
121.5
103.2

0
0
180
±67.4

4.11
3.69
3.75

6.13
5.44
5.51

5.4
117.0
105.7

0
180
±61.0

VC+共k兲 共C1h兲, previous calculation by Bockstedte et al. (Ref. 6)
A共Si1兲
4.35
4.07
7.03
A共Si2兲
3.32
3.10
5.53
A共Si3,4兲
3.89
3.68
5.74
Ky1, Ky2 (both C1h) in 6H-SiC at 4.2 K, EPR by Bratus et al. (Ref. 12)
g (Ky1)2.00582.00232.002531
g (Ky2)2.00482.00372.0022
35
A共Si1兲
4.33
4.33
6.57
7.7
A共Si2兲
3.16
3.16
4.71
122.0
A共Si3,4兲
3.93
3.93
5.59
102.7
EI6 共C3v兲 at 5 K, our EPR
g
2.0026
A共Si1兲
10.61
1.40
A共Si2,3,4兲
A共Si5,6,7兲
0.70
VC+共h兲 共C3v兲, our calculation
A共Si1兲
9.89
A共Si2,3,4兲
0.59
A共Si5,6,7兲
0.92

0
0
0
180
±52

2.0026
10.61
1.40
0.70

2.0052
15.48
2.11
0.87

0
0
98
−16

0
0
0, ±1200, ±120

9.89
0.59
0.92

15.27
1.21
1.17

0
98.8
−18.2

0
0, ±1200, ±120

␩2共%兲

␩2␣2共%兲␩2␤2共%兲

19.9
14.7
16.5

3.1
2.3
2.7

16.8
12.4
13.8

21.4
14.8
16.2

3.1
2.2
2.7

18.3
12.6
13.5

47.3
6.9
1.9

7.5
1.0
0.5

39.8
5.9
1.4

aThere is another equivalent orientation for the defect that is given by adding 180° to this ␾ value, because of the symmetry of 4H-SiC

crystals. For EI6 共C3v兲, ␾ was automatically determined by the restriction of the C3v symmetry.

tween EI5 and Ky2, their g tensors are largely different. The
reason for this discrepancy may be due to different energyband structures in 4H- and 6H-SiC and the g tensor reflects
not only the wave function but also electronic levels of thedefect state.
Using the linear combination of atomic orbital (LCAO)
approximation,2,3,5,9,10 the unpaired-electron densities ␩2
were estimated to be 19.9% on Si1, 14.7% on Si2, and 16.5%
on Si3,4 (Table I). The unpaired electron distributes equallyon the two pairs of Si1-Si2 and Si3-Si4. We note that the total
value of ␩2 for Si1–4 (67.6%) is identical to that for EI6
关VC+共h兲兴 at 5 K,5 because of the same type of origin for EI5

and EI6. Since about 32% of the defect wave function should
extend to Si or C atoms located outside Si1–4 atoms, the EI5
spectra clearly revealed super HF structures from such atoms(see Fig. 5). Using pulsed ENDOR, we identified four 13C
super HF lines 共CI–IV兲 and two 29Si super HF lines 共SiI,II兲. As
similarly to the Si5–7 HF lines for EI6 (see Fig. 2),5 we foundthree Si atoms (SiI and SiII) in the EI5’s HF structures which
possibly correspond to Si5 and S6,7 atoms of EI5 center, respectively. The split to Si5 and Si6,7 HF lines is consistent
with the C1h symmetry of this center. In the C3v configuration observed above 40 K, these super HF structures are averaged out into two HF satellites with the C3v symmetry that

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EPR AND THEORETICAL STUDIES OF POSITIVELY…

FIG. 3. (Color online) Simulation of angular dependence of EI5
at the W band 共94.9 GHz兲 in the 共1̄100兲 plane, using spinHamiltonian parameters in Table I.

have been reported as satellites f and g, respectively, in Ref.
5 (and are also seen in Fig. 2).
III. THEORETICAL CALCULATIONSIn the previous section, we have seen a good agreement inprincipal A values for EI5 共C1h兲 between our EPR analysis
and the previous theoretical work.6 However, principal axesof HF tensors are also the key to construct an atomic modelof the defect, because these parameters directly indicate athree-dimensional structure of the defect. Therefore we have

FIG. 4. (Color online) Temperature dependence of 29Si HF
structures for EI5 measured at 9.452 GHz. These spectra were obtained by integrating cw-EPR spectra for B 储 关0001兴. The inset plots
the lifetime of the reorientation 共␶兲 calculated from T2. Circles denote the data obtained from direct T2 measurements using pulsed
EPR, whereas the other symbols (triangles, pluses, and crosses)
represent data derived through cw-EPR linewidth measurements for
Si2,3,4, Si3,4, and Si2 HF lines, respectively. The solid line represents
the linear fit using the fitting parameters shown in the figure.

FIG. 5. (Color online) Super HF structures for EI5 共C1h兲 measured by echo-detected EPR at 9.665 GHz. We have identified their
origins (Si or C) by pulsed ENDOR. Also shown in the figure is thenumber of atoms corresponding to each super HF line (N), which
was deduced from a relative intensity of the HF line.

investigated VC+共k兲 and VC+共h兲 as well by ab initio quasistatic supercell calculations at 0 K to verify our models.
We have used a density-functional theory in the localdensity approximation13 (DFT-LDA), as implemented in theplane-wave supercell code (FHI98MD) to obtain the optimum geometry.14 Ceperley-Alder exchange correlation
functional15 and norm-conserving Troullier-Martin pseudopotentials16 were used. To determine the HF constants of adefect an extremely accurate geometry is required. We havecarried out comprehensive convergence tests on the basis
size, on the number of relaxed atoms around the defect, on
the K-point sets, on the shape and size of the supercell for
VC+共k兲. The minimum-energy configuration was sought byrelaxing the atoms around the defect until all the forces were
below 0.0005 Hartree/ Bohr. According to our calculations,
VC+ has an electronic configuration of 共a1兲2共a1⬘兲1 under the
crystal field of 4H-SiC. The symmetry of VC+ can be kept to
be C3v or be lowered to C1h due to a pseudo-JT effect involving a nearby e state.6,7,17 With constraint to either ofthese two symmetries we calculated the minimum energy for
VC+共k兲. We have tested the basis size from 36 Ry up to
64 Ry kinetic energy cutoff, the relaxation of atoms from
2NN up to 5NN, the k-point sets from 13 up to 43
Monkhorst-Pack (MP) sets,18 the supercell size from 72 up to
216 atom supercells. We have found that a 96 atom supercell
using a 36 Ry cutoff, 5NN relaxation, and a 23 MP set provides convergent results for the geometry and energy difference between the C1h or C3v symmetry configurations. Accordingly, it was found that the C1h configuration is lower inenergy by 0.06 eV than that of the C3v configuration which isin line with an earlier finding.6 This supports the C1h structure for VC+共k兲 at low temperatures. Since the energy differences is much larger than Ea共=0.014 eV兲 for the thermally
activated reorientation, thus the reorientation occurs directlyfrom one C1h configuration to another one, without passing
the C3v configuration. Our calculations found, however, that
VC+共h兲 has C3v symmetry even at 0 K. To calculate the HF

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constants of VC+ we have used the supercell code CP-PAW,
which is based on the projector augmentation wave method
in determining the true wave function close to the nuclei.19
We have used the same supercell and MP set as with the
FHI98MD code. Two projector functions were used for eachangular momentum. The tests on HF constants have shownthat even 30 Ry kinetic energy cutoff provides convergent
results with using the appropriate projectors.
For VC+共k兲, the calculated HF tensors including both principal values and principal axes are compared to the experimental ones in Table I. It is immediately obvious that thecalculated and measured HF of the 1NN Si atoms 共Si1,2,3,4兲
coincide very well in both principal values and axes. For theouter shell of VC, the calculations found that Si5 shows detectable HF interactions (principal values= 0.24, 0.27,
0.45 mT) and Si6,7 does too (principal values= 0.44, 0.45,
0.59 mT). These values are in the same order of the observed
HF splittings for SiI 共Si5兲 and SiII 共Si6,7兲 (note that the experimental values are not principal values and hence only
their orders should be discussed). Among the 12 2NN C
atoms around the vacancy, the spin density on eight C atoms
are detectable according to the calculations. That is in linewith the experimental observation in Fig. 4.
Finally, we also calculated the principal A values as wellas their directions for the case of VC+共h兲. The results are
summarized in Table I. The calculated HF tensors are again
in agreement with the experimental values of EI6 center,even for the 3NN atoms 共Si5,6,7兲, which demonstrates a highreliability of our calculations. In the calculation, the spin

density on the first three neighbor C atoms of Si1 (CI: principal A values= 0.29, 0.31, 0.67 mT) and on one neighbor C
atom for each Si2–4 atom along the c axis (CII: principal A
values= 0.28, 0.30, 0.50 mT) were also large, although they
have not been observed in experiments. We have found thatthe HF constants of 3NN atoms other than Si5,6,7 are below
0.02 mT, as consistent with EPR measurements.

1 For example, N. T. Son, B. Magnusson, Z. Zolnai, A. Ellison, andD. Watkins, Radiation Effects in Semiconductors (Plenum
Press, New York, 1968).
10 G. D. Watkins and J. W. Corbett, Phys. Rev. 134, A1359 (1964).
11 H. S. Gutowsky and A. Saika, J. Chem. Phys. 21, 1688 (1953).
12 V. Ya. Bratus, I. N. Makeeva, S. M. Okulov, T. L. Petrenko, T. T.
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IV. SUMMARY

We have revealed the C1h-symmetric atomic structure for
the EI5 center 关VC+共k兲兴, which was observable below 40 K,
by means of the optimized X-band echo-detected EPR measurements. This structure was characterized by pairing offour Si atoms (Si1-Si2 and Si3-Si4) of VC due to JT distortion.
We also carried out the first-principle calculations and demonstrated that the HF tensors (both principal values and axes)
for VC+共k兲 were in good agreement with those in our EPR
experiments. Also this paper demonstrated a good correspondence between the EI6 center and theoretical calculation for
VC+共h兲, ensuring the reliability of our calculations. Above
40 K, the EI5 center transformed from the C1h-symmetriccenter to the C3v-symmetric one. This phenomenon was attributed to a thermally activated reorientation of VC+共k兲. The
presence of such reorientation was consistent with the atomic
structure of VC+共k兲 determined here. The activation energy
for this reorientation was found to be 0.014 eV, which indicated “electronic bond switching” behavior the same as observed for vacancies in silicon.

9 G.

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