We report results from spin-polarized ab initio local spin-density calculations for the silicon vacancy (VSi) in 3C– and 2H–SiC in all its possible charge states. The calculated electronic structure for SiC reveals the presence of a stable spin-aligned electron-state t2 near the midgap. The neutral and doubly negative charge states of VSi in 3C–SiC are stabilized in a high-spin configuration with S=1 giving rise to a ground state, which is a many-electron orbital singlet 3T1. For the singly negative VSi, we find a high-spin ground-state4A2 with S=3/2. In the high-spin configuration, VSi preserves the Td symmetry. These results indicate that in neutral, singly, and doubly negative charge states a strong exchange coupling, which prefers parallel electron spins, overcomes the Jahn–Teller energy. In other charge states, the ground state of VSi has a low-spin configuration.Peer reviewe

Laasonen, K. E.

Nieminen, Risto M.

Pöykkö, S.

Torpo, L.

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Author(s): Torpo, L. & Nieminen, Risto M. & Laasonen, K. E. & Pöykkö, S.
Title: Silicon vacancy in SiC: A high-spin state defect
Year: 1999
Version: Final published version
Please cite the original version:
Torpo, L. & Nieminen, Risto M. & Laasonen, K. E. & Pöykkö, S. 1999. Silicon vacancy in
SiC: A high-spin state defect. Applied Physics Letters. Volume 74, Issue 2. 221-223.
ISSN 0003-6951 (printed). DOI: 10.1063/1.123299.
Rights: © 1999 American Institute of Physics. This article may be downloaded for personal use only. Any other use
requires prior permission of the authors and the American Institute of Physics. The following article appeared
in Applied Physics Letters, Volume 74, Issue 2 and may be found at
http://scitation.aip.org/content/aip/journal/apl/74/2/10.1063/1.123299.
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Silicon vacancy in SiC: A high-spin state defect
L. Torpo, R. M. Nieminen, K. E. Laasonen, and S. Pöykkö 
 
Citation: Applied Physics Letters 74, 221 (1999); doi: 10.1063/1.123299 
View online: http://dx.doi.org/10.1063/1.123299 
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/74/2?ver=pdfcov 
Published by the AIP Publishing 
 
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Silicon vacancy in SiC: A high-spin state defect
L. Torpoa) and R. M. Nieminen
Laboratory of Physics, Helsinki University of Technology, 02015 HUT, Finland
K. E. Laasonen
Department of Chemistry, University of Oulu, FIN-09571 Oulu, Finland
S. Po¨ykko¨b)
Laboratory of Physics, Helsinki University of Technology, 02015 HUT, Finland
~Received 29 June 1998; accepted for publication 6 November 1998!
We report results from spin-polarized ab initio local spin-density calculations for the silicon
vacancy (VSi) in 3C– and 2H–SiC in all its possible charge states. The calculated electronic
structure for SiC reveals the presence of a stable spin-aligned electron-state t2 near the midgap. The
neutral and doubly negative charge states of VSi in 3C–SiC are stabilized in a high-spin
configuration with S51 giving rise to a ground state, which is a many-electron orbital singlet 3T1 .
For the singly negative VSi , we find a high-spin ground-state 4A2 with S53/2. In the high-spin
configuration, VSi preserves the Td symmetry. These results indicate that in neutral, singly, and
doubly negative charge states a strong exchange coupling, which prefers parallel electron spins,
overcomes the Jahn–Teller energy. In other charge states, the ground state of VSi has a low-spin
configuration. © 1999 American Institute of Physics. @S0003-6951~99!04702-6#
The electronic structure of a vacancy in a covalent solid
can be simply discussed using a one-electron orbital model
~linear combination of atomic orbitals!.1 Even though the
ground state of the vacancy in silicon can be qualitatively
described within a single-electron picture,2 it is found in
some wide-band-gap semiconductors, such as diamond and
GaP,3,4 that finally, many-electron effects determine the elec-
tronic properties of the vacancy. According to the one-
electron model, the defect molecular orbitals are an a1 sin-
glet and a t2 triplet. By distributing the electrons over the
orbitals, one can determine the ground state as the configu-
ration with the lowest total energy.1 Coulson and Larkins5
predicted a high-spin ground-state 4A2(a12t23) for the vacancy
VC
12 in diamond, which is not subject to Jahn–Teller distor-
tion. The many-electron singlet 4A2 is stabilized by a strong
exchange coupling ~spin–spin interaction!, which is larger
than the corresponding Jahn–Teller energy. For the vacancy
in diamond, the 4A2 state has been confirmed
experimentally.3 A similar high-spin ground state is also
found for the neutral vacancy VGa
0 in GaP.4 Like diamond
and GaP, silicon carbide is a wide-band-gap material. Sev-
eral observations obtained from electron-spin-resonance
~ESR!, optically detected magnetic-resonance ~ODMR!, pho-
toluminescence ~PL!, and electron-nuclear double-resonance
~ENDOR! measurements assigned to silicon vacancy-related
centers, high-spin states S51 and S53/2 have been
reported.6–9 Recently, an all-electron linear muffin-tin orbital
ASA calculation for unrelaxed VSi
12 in SiC has been carried
out,10 in which a large energy separation between the low-
spin (S51/2) and the high-spin (S53/2) configurations was
obtained.
In this letter, we present the ab initio characterization of
the silicon vacancy in SiC in all stable charge states. Fully
relaxed vacancies are studied both in cubic ~3C–SiC! and
hexagonal ~2H–SiC! silicon carbide. We have used the
plane-wave pseudopotential method ~PWPP!, where the
exchange-correlation functional of the many-body electron–
electron interaction is described within the local-density
~LDA!10 or local-spin-density ~LSD! approximation.11 All
the calculations are performed using a large 128 atom super-
cell. For the detailed description of the standard formalism
concerning the charged supercell calculations, see Ref. 12.
Further computational details can be found in Refs. 13–17.
We use experimental band-gap values in the formation en-
ergy analysis because of the well-known fact that the gap
calculated from the single-particle Kohn–Sham states under-
estimates severely the true band gap. The experimental band
gap for 3C–SiC is 2.39 eV, while the obtained LDA gap is
1.30 eV.
We find that the silicon vacancy in 3C–SiC has stable
charge states from 21 to 42. In Fig. 1, the formation ener-
gies of different charge states as a function of the electron
chemical potential are shown for C-rich SiC. For neutral VSi ,
the formation energy is relatively high, ;7.1 eV in C-rich
conditions. However, due to the large band gap of SiC, the
formation energy varies strongly with the electron chemical
potential. The ionization levels found for 3C–SiC are listed
in Table I. We find the singly negative vacancy to be the
stablest charge state in the range from 0.5 to 1.2 eV of the
electron chemical potential. The doubly positive vacancy is
stable up to the value of 0.4 eV of the electron chemical
potential. The doubly negative vacancy is stable in ;130
meV wide range, while the 11, neutral, and 32 states are
found to be only marginally stable defects in very narrow
windows of chemical potential. It is possible that negative-U
transitions take place between the states (21/0) and (2
a!Electronic mail: lmt@fyslab.hut.fi
b!Current address: NEC Research Institute, 4 Independence Way, Princeton,
NJ 08540.
APPLIED PHYSICS LETTERS VOLUME 74, NUMBER 2 11 JANUARY 1999
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2/42). Still, because of the restricted accuracy of the den-
sity functional theory ~DFT! LSD method, one cannot con-
firm whether for narrow ranges of the electron chemical po-
tential the charge states 11 and 32 stabilize as well.
Moreover, it is not determined whether the charge state 42
actually exists, because the ionization level of VSi
42 is located
above the LDA band-gap edge.
Figure 1 illustrates the three governing occupations of
the one-electron-state t2 triplet: empty (VSi21), triply occu-
pied by spin-aligned electrons (VSi12), and fully occupied
(VSi42). At the two borderlines of these three zones ~the grey
regions in Fig. 1! we find two stable charge states VSi
0 and
VSi
22 with spin S51. The parallel spin occupation of t2 with
S51 corresponds the ground state of the many-electron or-
bital state 3T1 .1,5 The spin-aligned (t2)3 ground state with
S53/2 stands for the orbitally degenerate singlet 4A2 .1,5 The
exchange energies are most pronounced in the mid-band-gap
region ~see Fig. 1!. The effect of the spin polarization in the
formation energies in different charge states is listed in Table
II. In 3C–SiC, the 12 charge state with spin S53/2 has the
strongest effect of the spin polarization ;0.58 eV. For the
high-spin states S51 of VSi
0 and VSi
22 defects, we find the
exchange energy gain in the spin-polarized calculation as
large as 0.4 eV. For the S51/2 configurations of VSi
11 and
VSi
32
, the gain is remarkably less. Obviously, in the spin-
compensated regions with spin S50, corresponding to the
charge states VSi
21 and VSi
42
, the LDA and LSD results coin-
cide ~see Fig. 1!.
In cubic SiC, the four carbon atoms surrounding VSi ,
forming thus a tetrahedron, stretch their mutual distances,
depending on the charge state, by 8%–14% compared to the
C–C distance of 3.044 Å in the ideal SiC crystal. This dis-
tance tends to get shorter when electrons are added to the
system. Characteristic for the high-spin state (S53/2) and
for the 21 and 11 charge states is a symmetric Td relax-
ation. A small symmetry breaking is found when the charge
increases: other charge states are weakly Jahn–Teller dis-
torted. The volume increase of the tetrahedron, formed by
the C atoms surrounding the Si vacancy, compared to the
ideal case in 3C–SiC, is 30%–47%, depending on the charge
state.
The most common SiC polytypes ~4H and 6H–SiC! are
composed of two inequivalent lattice sites, cubic and hex-
agonal. Our extensive study for 3C–SiC outlines the charac-
teristics of the cubic-site vacancy. Although the local atomic
surroundings of the cubic and hexagonal vacancies do not
considerably differ from each other, the electronic structure
can be altered substantially. In order to understand the quali-
tative difference between the two lattice sites, we also per-
formed a study of the hexagonal-site vacancy in 2H–SiC.14
In 2H–SiC, the formation energy of the silicon vacancy
is found to be 7.8 eV in C-rich conditions, i.e., slightly
higher than in 3C–SiC. Like 3C–SiC, in 2H–SiC the va-
cancy stabilizes in the high-spin configuration in neutral, sin-
gly, and doubly negative charge states. In 2H–SiC, the effect
of spin polarization is qualitatively the same as for 3C–SiC
~see Table II!. The ionization levels for VSi in 2H–SiC are
listed in Table I. Compared to 3C–SiC, the ionization levels
are located lower in the band gap by 0.16–0.39 eV, depend-
ing on the charge state. The 11, neutral, and 32 charge
states are found to be stable in a much wider range of elec-
tron chemical potential in 2H–SiC than in 3C–SiC. The
negative-U behavior is not found for 2H–SiC. The C atoms
surrounding VSi stretch their mutual distances by 8%–12%
compared to the ideal 2H–SiC crystal. Like 3C–SiC, in the
high-spin configuration (S53/2) and 21 charge state, the
defect maintains the Td symmetry, but in the case of VSi
11 the
Jahn–Teller distortion is noticed in 2H–SiC. The rest of the
charge states are weakly Jahn–Teller distorted.
According to the experimental work,6,7,9,18 the silicon
vacancy in SiC is negatively charged, exhibits Td symmetry
and is most often assigned to be VSi
12
. For VSi-related cen-
ters, signals both from a high-spin configuration S53/2 ~Ref.
9! and from a low-spin S51/2 ~Refs. 6 and 18! are observed.
FIG. 1. Formation energy of the silicon vacancy in 3C–SiC grown under
C-rich conditions. The vertical axis shows the formation energy and the
horizontal axis the electron chemical potential. There are two deep levels at
0.5 eV above the valence-band maximum. The rest of the states are about
1.3 eV above the valence-band maximum. The significance of the exchange
to the formation energy can be seen in the mid-band-gap region, where the
results of the high-spin LSD calculations are shown as the lower solid line
and results from the spin-compensated calculation as the dotted line.
TABLE I. Ionization levels for the relaxed Si vacancy in 3C– and 2H–SiC
from LSD calculations ~in eV above the valence-band maximum!.
21/11 11/0 0/12 12/22 22/32 32/42
3C 0.433 0.495 0.561 1.224 1.353 1.403
2H 0.047 0.133 0.317 0.908 1.044 1.242
TABLE II. The effect of spin polarization in 3C– and 2H–SiC in different
charge states of the silicon vacancy. DE5uELSD2ELDAu is evaluated from
the energy difference between the spin-compensated ~LDA! and the spin-
polarized ~LSD! calculation in electron volts ~eV!. In the LDA result
(ELDA), the spin state is always low: either S50 or S51/2, whereas in the
LSD result (ELSD) the total spin in each charge state corresponds to the
ground-state spin configuration and is marked in the second line of Table II.
11 0 12 22 32
S5 12 S51 S5
3
2 S51 S5
1
2
3C 0.076 0.378 0.580 0.419 0.241
2H 0.143 0.317 0.458 0.183 0.090
222 Appl. Phys. Lett., Vol. 74, No. 2, 11 January 1999 Torpo et al.
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Our calculations indicate that the experimentally detected
signal with S53/2 arises from the singly negative VSi and
thus confirms the result of Wimbauer et al.9 Our results fur-
ther suggest that the signals in 3C–SiC with S51/2 ~Refs. 6
and 18! could be explained by VSi
11 or VSi
32
.
In the case of the vacancy in diamond and GaP, the
high-spin ground state appears only for the charge state,
where the gap state is the spin-aligned (t2)3. For 3C–SiC,
the (t2)3 corresponds to the singly negative charge state. As
a particular character of 3C–SiC, we find the spin-paired
neutral and doubly negative charge states, corresponding to
occupations (t2)2 and (t2)4, stabilize in the high-spin con-
figuration with S51 as well.
In summary, we characterize the silicon vacancy in cu-
bic and hexagonal sites in SiC using the LSD approximation.
In 3C– and 2H–SiC, for neutral, singly, and doubly negative
charge states the exchange coupling overcomes Jahn–Teller
energies, and the silicon vacancy is found in the high-spin
ground state with Td symmetry. In the high-spin configura-
tion the VSi maintains the Td symmetry. A weak Jahn–Teller
effect occurs in the low-spin configuration. Our finding of
the high-spin ground state agrees with recent experiments,9
and can sort out several open questions related to the silicon
vacancy in SiC.6–8,18 Our result also offers a resolution to the
ambiguity, why, in SiC, are both high-spin and low-spin sig-
nals observed for VSi .
This research has been supported by the Academy of
Finland. The authors acknowledged the generous computing
resources of the Center of Scientific Computing ~CSC!, Es-
poo, Finland. One of the authors ~L.T.! wishes to thank Pro-
fessor Weimin Chen, Dr. Nguyen Son, and Dr. Erik So¨rman
for valuable discussions. Especially, the authors are sincerely
grateful to Meri Marlo for her skillful assistance.
1 A. M. Stoneham, Theory of Defects in Solids ~Oxford University Press,
New York, 1975!, p. 860.
2 M. Lannoo, G. A. Baraff, and M. Schlu¨ter, Phys. Rev. B 24, 955 ~1981!.
3 J. Isoya, H. Kanda, Y. Uchida, S. C. Lawson, S. Yamasaki, H. Itoh, and Y.
Morita, Phys. Rev. B 45, 1436 ~1992!.
4 T. A. Kennedy, N. D. Wilsey, J. J. Krebs, and G. H. Stauss, Phys. Rev.
Lett. 50, 1281 ~1983!.
5 C. A. Coulson and F. P. Larkins, J. Phys. Chem. Solids 32, 2245 ~1971!.
6 H. Itoh, A. Kawasuso, T. Ohshima, M. Yoshikawa, I. Nashiyama, S. Tani-
gawa, S. Misawa, H. Okumura, and S. Yoshida, Phys. Status Solidi A 162,
173 ~1997!.
7 E. So¨rman, Ph.D. Thesis, Linko¨ping University, Sweden, 1997.
8 N. Son, E. So¨rman, W. Chen, C. Hallin, O. Kordina, B. Monemar, and E.
Janze´n, Phys. Rev. B 55, 2863 ~1997!.
9 T. Wimbauer, B. Meyer, A. Hofstaetter, A. Scharmann, and H. Overhof,
Phys. Rev. B 56, 7384 ~1997!.
10 D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 ~1980!; J.
Perdew and A. Zunger, Phys. Rev. B 23, 5049 ~1981!.
11 S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 ~1980!.
12 S. Po¨ykko¨, M. J. Puska, and R. M. Nieminen, Phys. Rev. B 53, 3813
~1996!.
13 L. Torpo, S. Po¨ykko¨, and R. M. Nieminen, Phys. Rev. B 57, 6243 ~1998!.
14 The calculations are performed in a large 128 atom site supercell. For
3C–SiC, the fcc basis and for 2H–SiC rectangular superlattice vectors are
used. For Brillouin-zone sampling, the G point is used.
15 For the Si ion standard Bachelet–Hamann–Schlu¨ter pseudopotential ~Ref.
16! and for the C ion the Vanderbilt-type ultrasoft pseudopotential ~Ref.
17! has been employed and good convergence with respect to the basis set
size was obtained at a 20 Ry kinetic-energy cutoff.
16 G. B. Bachelet, D. R. Hamann, and M. Schlu¨ter, Phys. Rev. B 26, 4199
~1982!.
17 K. Laasonen, A. Pasquarello, R. Car, C. Lee, and D. Vanderbilt, Phys.
Rev. B 47, 10 142 ~1993!.
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emar, and E Janze´n, J. Appl. Phys. 79, 3784 ~1996!.
223Appl. Phys. Lett., Vol. 74, No. 2, 11 January 1999 Torpo et al.
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English

Silicon vacancy in SiC: A high-spin state defect

Aaltodoc Publication Archive

This is an electronic reprint of the original article.This reprint may differ from the original in pagination and typographic detail.Author(s): Torpo, L. & Nieminen, Risto M. & Laasonen, K. E. & Pöykkö, S.Title: Silicon vacancy in SiC: A high-spin state defectYear: 1999Version: Final published versionPlease cite the original version:Torpo, L. & Nieminen, Risto M. & Laasonen, K. E. & Pöykkö, S. 1999. Silicon vacancy inSiC: A high-spin state defect. Applied Physics Letters. Volume 74, Issue 2. 221-223.ISSN 0003-6951 (printed). DOI: 10.1063/1.123299.Rights: © 1999 American Institute of Physics. This article may be downloaded for personal use only. Any other userequires prior permission of the authors and the American Institute of Physics. The following article appearedin Applied Physics Letters, Volume 74, Issue 2 and may be found athttp://scitation.aip.org/content/aip/journal/apl/74/2/10.1063/1.123299.All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, andduplication or sale of all or part of any of the repository collections is not permitted, except that material maybe duplicated by you for your research use or educational purposes in electronic or print form. You mustobtain permission for any other use. Electronic or print copies may not be offered, whether for sale orotherwise to anyone who is not an authorised user.Powered by TCPDF (www.tcpdf.org)Silicon vacancy in SiC: A high-spin state defectL. Torpo, R. M. Nieminen, K. E. Laasonen, and S. Pöykkö  Citation: Applied Physics Letters 74, 221 (1999); doi: 10.1063/1.123299 View online: http://dx.doi.org/10.1063/1.123299 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/74/2?ver=pdfcov Published by the AIP Publishing  Articles you may be interested in Size effects on formation energies and electronic structures of oxygen and zinc vacancies in ZnO nanowires: Afirst-principles study J. Appl. Phys. 109, 044306 (2011); 10.1063/1.3549131  First principles investigation of defect energy levels at semiconductor-oxide interfaces: Oxygen vacancies andhydrogen interstitials in the Si – SiO 2 – HfO 2 stack J. Appl. Phys. 105, 061603 (2009); 10.1063/1.3055347  An ab initio study of structural properties and single vacancy defects in Wurtzite AlN J. Chem. Phys. 120, 4890 (2004); 10.1063/1.1645790  Vacancies in SiGe: Jahn–Teller distortion and spin effects Appl. Phys. Lett. 77, 232 (2000); 10.1063/1.126934  The spin state of the neutral silicon vacancy in 3C–SiC Appl. Phys. Lett. 75, 2103 (1999); 10.1063/1.124930    This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.27 On: Thu, 03 Sep 2015 06:25:45Silicon vacancy in SiC: A high-spin state defectL. Torpoa) and R. M. NieminenLaboratory of Physics, Helsinki University of Technology, 02015 HUT, FinlandK. E. LaasonenDepartment of Chemistry, University of Oulu, FIN-09571 Oulu, FinlandS. Po¨ykko¨b)Laboratory of Physics, Helsinki University of Technology, 02015 HUT, Finland~Received 29 June 1998; accepted for publication 6 November 1998!We report results from spin-polarized ab initio local spin-density calculations for the siliconvacancy (VSi) in 3C– and 2H–SiC in all its possible charge states. The calculated electronicstructure for SiC reveals the presence of a stable spin-aligned electron-state t2 near the midgap. Theneutral and doubly negative charge states of VSi in 3C–SiC are stabilized in a high-spinconfiguration with S51 giving rise to a ground state, which is a many-electron orbital singlet 3T1 .For the singly negative VSi , we find a high-spin ground-state 4A2 with S53/2. In the high-spinconfiguration, VSi preserves the Td symmetry. These results indicate that in neutral, singly, anddoubly negative charge states a strong exchange coupling, which prefers parallel electron spins,overcomes the Jahn–Teller energy. In other charge states, the ground state of VSi has a low-spinconfiguration. © 1999 American Institute of Physics. @S0003-6951~99!04702-6#The electronic structure of a vacancy in a covalent solidcan be simply discussed using a one-electron orbital model~linear combination of atomic orbitals!.1 Even though theground state of the vacancy in silicon can be qualitativelydescribed within a single-electron picture,2 it is found insome wide-band-gap semiconductors, such as diamond andGaP,3,4 that finally, many-electron effects determine the elec-tronic properties of the vacancy. According to the one-electron model, the defect molecular orbitals are an a1 sin-glet and a t2 triplet. By distributing the electrons over theorbitals, one can determine the ground state as the configu-ration with the lowest total energy.1 Coulson and Larkins5predicted a high-spin ground-state 4A2(a12t23) for the vacancyVC12 in diamond, which is not subject to Jahn–Teller distor-tion. The many-electron singlet 4A2 is stabilized by a strongexchange coupling ~spin–spin interaction!, which is largerthan the corresponding Jahn–Teller energy. For the vacancyin diamond, the 4A2 state has been confirmedexperimentally.3 A similar high-spin ground state is alsofound for the neutral vacancy VGa0 in GaP.4 Like diamondand GaP, silicon carbide is a wide-band-gap material. Sev-eral observations obtained from electron-spin-resonance~ESR!, optically detected magnetic-resonance ~ODMR!, pho-toluminescence ~PL!, and electron-nuclear double-resonance~ENDOR! measurements assigned to silicon vacancy-relatedcenters, high-spin states S51 and S53/2 have beenreported.6–9 Recently, an all-electron linear muffin-tin orbitalASA calculation for unrelaxed VSi12 in SiC has been carriedout,10 in which a large energy separation between the low-spin (S51/2) and the high-spin (S53/2) configurations wasobtained.In this letter, we present the ab initio characterization ofthe silicon vacancy in SiC in all stable charge states. Fullyrelaxed vacancies are studied both in cubic ~3C–SiC! andhexagonal ~2H–SiC! silicon carbide. We have used theplane-wave pseudopotential method ~PWPP!, where theexchange-correlation functional of the many-body electron–electron interaction is described within the local-density~LDA!10 or local-spin-density ~LSD! approximation.11 Allthe calculations are performed using a large 128 atom super-cell. For the detailed description of the standard formalismconcerning the charged supercell calculations, see Ref. 12.Further computational details can be found in Refs. 13–17.We use experimental band-gap values in the formation en-ergy analysis because of the well-known fact that the gapcalculated from the single-particle Kohn–Sham states under-estimates severely the true band gap. The experimental bandgap for 3C–SiC is 2.39 eV, while the obtained LDA gap is1.30 eV.We find that the silicon vacancy in 3C–SiC has stablecharge states from 21 to 42. In Fig. 1, the formation ener-gies of different charge states as a function of the electronchemical potential are shown for C-rich SiC. For neutral VSi ,the formation energy is relatively high, ;7.1 eV in C-richconditions. However, due to the large band gap of SiC, theformation energy varies strongly with the electron chemicalpotential. The ionization levels found for 3C–SiC are listedin Table I. We find the singly negative vacancy to be thestablest charge state in the range from 0.5 to 1.2 eV of theelectron chemical potential. The doubly positive vacancy isstable up to the value of 0.4 eV of the electron chemicalpotential. The doubly negative vacancy is stable in ;130meV wide range, while the 11, neutral, and 32 states arefound to be only marginally stable defects in very narrowwindows of chemical potential. It is possible that negative-Utransitions take place between the states (21/0) and (2a!Electronic mail: lmt@fyslab.hut.fib!Current address: NEC Research Institute, 4 Independence Way, Princeton,NJ 08540.APPLIED PHYSICS LETTERS VOLUME 74, NUMBER 2 11 JANUARY 19992210003-6951/99/74(2)/221/3/$15.00 © 1999 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.27 On: Thu, 03 Sep 2015 06:25:452/42). Still, because of the restricted accuracy of the den-sity functional theory ~DFT! LSD method, one cannot con-firm whether for narrow ranges of the electron chemical po-tential the charge states 11 and 32 stabilize as well.Moreover, it is not determined whether the charge state 42actually exists, because the ionization level of VSi42 is locatedabove the LDA band-gap edge.Figure 1 illustrates the three governing occupations ofthe one-electron-state t2 triplet: empty (VSi21), triply occu-pied by spin-aligned electrons (VSi12), and fully occupied(VSi42). At the two borderlines of these three zones ~the greyregions in Fig. 1! we find two stable charge states VSi0 andVSi22 with spin S51. The parallel spin occupation of t2 withS51 corresponds the ground state of the many-electron or-bital state 3T1 .1,5 The spin-aligned (t2)3 ground state withS53/2 stands for the orbitally degenerate singlet 4A2 .1,5 Theexchange energies are most pronounced in the mid-band-gapregion ~see Fig. 1!. The effect of the spin polarization in theformation energies in different charge states is listed in TableII. In 3C–SiC, the 12 charge state with spin S53/2 has thestrongest effect of the spin polarization ;0.58 eV. For thehigh-spin states S51 of VSi0 and VSi22 defects, we find theexchange energy gain in the spin-polarized calculation aslarge as 0.4 eV. For the S51/2 configurations of VSi11 andVSi32, the gain is remarkably less. Obviously, in the spin-compensated regions with spin S50, corresponding to thecharge states VSi21 and VSi42, the LDA and LSD results coin-cide ~see Fig. 1!.In cubic SiC, the four carbon atoms surrounding VSi ,forming thus a tetrahedron, stretch their mutual distances,depending on the charge state, by 8%–14% compared to theC–C distance of 3.044 Å in the ideal SiC crystal. This dis-tance tends to get shorter when electrons are added to thesystem. Characteristic for the high-spin state (S53/2) andfor the 21 and 11 charge states is a symmetric Td relax-ation. A small symmetry breaking is found when the chargeincreases: other charge states are weakly Jahn–Teller dis-torted. The volume increase of the tetrahedron, formed bythe C atoms surrounding the Si vacancy, compared to theideal case in 3C–SiC, is 30%–47%, depending on the chargestate.The most common SiC polytypes ~4H and 6H–SiC! arecomposed of two inequivalent lattice sites, cubic and hex-agonal. Our extensive study for 3C–SiC outlines the charac-teristics of the cubic-site vacancy. Although the local atomicsurroundings of the cubic and hexagonal vacancies do notconsiderably differ from each other, the electronic structurecan be altered substantially. In order to understand the quali-tative difference between the two lattice sites, we also per-formed a study of the hexagonal-site vacancy in 2H–SiC.14In 2H–SiC, the formation energy of the silicon vacancyis found to be 7.8 eV in C-rich conditions, i.e., slightlyhigher than in 3C–SiC. Like 3C–SiC, in 2H–SiC the va-cancy stabilizes in the high-spin configuration in neutral, sin-gly, and doubly negative charge states. In 2H–SiC, the effectof spin polarization is qualitatively the same as for 3C–SiC~see Table II!. The ionization levels for VSi in 2H–SiC arelisted in Table I. Compared to 3C–SiC, the ionization levelsare located lower in the band gap by 0.16–0.39 eV, depend-ing on the charge state. The 11, neutral, and 32 chargestates are found to be stable in a much wider range of elec-tron chemical potential in 2H–SiC than in 3C–SiC. Thenegative-U behavior is not found for 2H–SiC. The C atomssurrounding VSi stretch their mutual distances by 8%–12%compared to the ideal 2H–SiC crystal. Like 3C–SiC, in thehigh-spin configuration (S53/2) and 21 charge state, thedefect maintains the Td symmetry, but in the case of VSi11 theJahn–Teller distortion is noticed in 2H–SiC. The rest of thecharge states are weakly Jahn–Teller distorted.According to the experimental work,6,7,9,18 the siliconvacancy in SiC is negatively charged, exhibits Td symmetryand is most often assigned to be VSi12. For VSi-related cen-ters, signals both from a high-spin configuration S53/2 ~Ref.9! and from a low-spin S51/2 ~Refs. 6 and 18! are observed.FIG. 1. Formation energy of the silicon vacancy in 3C–SiC grown underC-rich conditions. The vertical axis shows the formation energy and thehorizontal axis the electron chemical potential. There are two deep levels at0.5 eV above the valence-band maximum. The rest of the states are about1.3 eV above the valence-band maximum. The significance of the exchangeto the formation energy can be seen in the mid-band-gap region, where theresults of the high-spin LSD calculations are shown as the lower solid lineand results from the spin-compensated calculation as the dotted line.TABLE I. Ionization levels for the relaxed Si vacancy in 3C– and 2H–SiCfrom LSD calculations ~in eV above the valence-band maximum!.21/11 11/0 0/12 12/22 22/32 32/423C 0.433 0.495 0.561 1.224 1.353 1.4032H 0.047 0.133 0.317 0.908 1.044 1.242TABLE II. The effect of spin polarization in 3C– and 2H–SiC in differentcharge states of the silicon vacancy. DE5uELSD2ELDAu is evaluated fromthe energy difference between the spin-compensated ~LDA! and the spin-polarized ~LSD! calculation in electron volts ~eV!. In the LDA result(ELDA), the spin state is always low: either S50 or S51/2, whereas in theLSD result (ELSD) the total spin in each charge state corresponds to theground-state spin configuration and is marked in the second line of Table II.11 0 12 22 32S5 12 S51 S532 S51 S5123C 0.076 0.378 0.580 0.419 0.2412H 0.143 0.317 0.458 0.183 0.090222 Appl. Phys. Lett., Vol. 74, No. 2, 11 January 1999 Torpo et al. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.27 On: Thu, 03 Sep 2015 06:25:45Our calculations indicate that the experimentally detectedsignal with S53/2 arises from the singly negative VSi andthus confirms the result of Wimbauer et al.9 Our results fur-ther suggest that the signals in 3C–SiC with S51/2 ~Refs. 6and 18! could be explained by VSi11 or VSi32.In the case of the vacancy in diamond and GaP, thehigh-spin ground state appears only for the charge state,where the gap state is the spin-aligned (t2)3. For 3C–SiC,the (t2)3 corresponds to the singly negative charge state. Asa particular character of 3C–SiC, we find the spin-pairedneutral and doubly negative charge states, corresponding tooccupations (t2)2 and (t2)4, stabilize in the high-spin con-figuration with S51 as well.In summary, we characterize the silicon vacancy in cu-bic and hexagonal sites in SiC using the LSD approximation.In 3C– and 2H–SiC, for neutral, singly, and doubly negativecharge states the exchange coupling overcomes Jahn–Tellerenergies, and the silicon vacancy is found in the high-spinground state with Td symmetry. In the high-spin configura-tion the VSi maintains the Td symmetry. A weak Jahn–Tellereffect occurs in the low-spin configuration. Our finding ofthe high-spin ground state agrees with recent experiments,9and can sort out several open questions related to the siliconvacancy in SiC.6–8,18 Our result also offers a resolution to theambiguity, why, in SiC, are both high-spin and low-spin sig-nals observed for VSi .This research has been supported by the Academy ofFinland. The authors acknowledged the generous computingresources of the Center of Scientific Computing ~CSC!, Es-poo, Finland. One of the authors ~L.T.! wishes to thank Pro-fessor Weimin Chen, Dr. Nguyen Son, and Dr. Erik So¨rmanfor valuable discussions. Especially, the authors are sincerelygrateful to Meri Marlo for her skillful assistance.1 A. M. Stoneham, Theory of Defects in Solids ~Oxford University Press,New York, 1975!, p. 860.2 M. Lannoo, G. A. Baraff, and M. Schlu¨ter, Phys. Rev. B 24, 955 ~1981!.3 J. Isoya, H. Kanda, Y. Uchida, S. C. Lawson, S. Yamasaki, H. Itoh, and Y.Morita, Phys. Rev. B 45, 1436 ~1992!.4 T. A. Kennedy, N. D. Wilsey, J. J. Krebs, and G. H. Stauss, Phys. Rev.Lett. 50, 1281 ~1983!.5 C. A. Coulson and F. P. Larkins, J. Phys. Chem. Solids 32, 2245 ~1971!.6 H. Itoh, A. Kawasuso, T. Ohshima, M. Yoshikawa, I. Nashiyama, S. Tani-gawa, S. Misawa, H. Okumura, and S. Yoshida, Phys. Status Solidi A 162,173 ~1997!.7 E. So¨rman, Ph.D. Thesis, Linko¨ping University, Sweden, 1997.8 N. Son, E. So¨rman, W. Chen, C. Hallin, O. Kordina, B. Monemar, and E.Janze´n, Phys. Rev. B 55, 2863 ~1997!.9 T. Wimbauer, B. Meyer, A. Hofstaetter, A. Scharmann, and H. Overhof,Phys. Rev. B 56, 7384 ~1997!.10 D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 ~1980!; J.Perdew and A. Zunger, Phys. Rev. B 23, 5049 ~1981!.11 S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 ~1980!.12 S. Po¨ykko¨, M. J. Puska, and R. M. Nieminen, Phys. Rev. B 53, 3813~1996!.13 L. Torpo, S. Po¨ykko¨, and R. M. Nieminen, Phys. Rev. B 57, 6243 ~1998!.14 The calculations are performed in a large 128 atom site supercell. For3C–SiC, the fcc basis and for 2H–SiC rectangular superlattice vectors areused. For Brillouin-zone sampling, the G point is used.15 For the Si ion standard Bachelet–Hamann–Schlu¨ter pseudopotential ~Ref.16! and for the C ion the Vanderbilt-type ultrasoft pseudopotential ~Ref.17! has been employed and good convergence with respect to the basis setsize was obtained at a 20 Ry kinetic-energy cutoff.16 G. B. Bachelet, D. R. Hamann, and M. Schlu¨ter, Phys. Rev. B 26, 4199~1982!.17 K. Laasonen, A. Pasquarello, R. Car, C. Lee, and D. Vanderbilt, Phys.Rev. B 47, 10 142 ~1993!.18 N. Son, E. So¨rman, W. Chen, M. Sight, C. Hallin, O. Kordina, B. Mon-emar, and E Janze´n, J. Appl. Phys. 79, 3784 ~1996!.223Appl. Phys. Lett., Vol. 74, No. 2, 11 January 1999 Torpo et al. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.27 On: Thu, 03 Sep 2015 06:25:45

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Silicon vacancy in SiC: A high-spin state defect

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