Materials Science Forum Vols. 527-529 (2006) pp. 539-542
online at http://www.scientific.net© (2006) Trans Tech Publications, Switzerland

Signature of the Negative Carbon Vacancy-Antisite Complex
M. Bockstedte1,a , A. Gali2 , T. Umeda3 , N.T. Son4 , J. Isoya3 , and E. Janzén4
1 Lehrstuhl für Theoretische Festkörperphysik, Unversität Erlangen-Nürnberg, Staudtstr. 7B2,D-91058, Erlangen, Germany and Departamento de Fı́sica de Materiales, Universidad del Paı́sVasco, E-20018 San Sebastián, Spain.
2 Department of Atomic Physics, Budapest University of Technology and Economics, Budafoki ùt 8,H-1111 Budapest, Hungary
3 Graduate School of Library, Information and Media Studies, University of Tsukuba, Tsukuba
305-8550, Japan
4 Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden
abockstedte@physik.uni-erlangen.deKeywords: vacancy complexes, semi insulating SiC, ab initio hyperfine signature

Abstract. The negative carbon vacancy antisite complex is analysed by ab initio theory in view of theSI5 EPR-center. The complex occurs in a Jahn-Teller distorted ground state and a meta stable state.
This and the calculated hyperfine structure agree nicely with the temperature dependent EPR spectraof SI5. An interpretation of the photo-EPR experiments is proposed.
Introduction
In SiC the silicon vacancy (VSi ) is a metastable defect [1, 2] that transforms in p-type and intrinsic
material into the stable carbon vacancy-antisite complex (VC -CSi ). However, direct evidence of theVC -CSi complex is scarce. Recently, the VC -CSi complex was suggested as a model for the P6/P7
center [3]. Our investigations, however, show that this identification has to be revised in favor of
the earlier divacancy model [4]. In recent experiments on high purity semi-insulating (HPSI) andirradiated n-type 4H-SiC the SI5-center was identified as a highly abundant defect [5, 6] with a characteristic temperature dependent hyperfine (HF) signature. At low temperatures (< 50 K) the center
possesses C1h -symmetry and a large HF-tensor due to two Si-atoms, while at higher temperatures C3v symmetry and one large Si HF-tensor is observed. Photo-EPR experiments located the Fermi-level at
EC − 1.1 eV suggesting a negative charge state of the defect center [5, 6]. In this paper we report thetheoretical identification of the SI5-center as the negative VC -CSi complex and the theoretical interpretation of the photo-EPR spectra. We revise the earlier tentative model of a divacancy [5, 7] thatwas suggested by the high symmetry of the previous high temperature EPR-spectra and the missing
large Si HF-tensor.
MethodOur theoretical analysis of the negative carbon vacancy-antisite complex is based on ab initio supercell methods within the framework of the density functional theory and the local density approximation. Large supercells equivalent to 288 lattice sites were used to represent the complex in the 4H
polytype. Its electronic properties and the relaxation were obtained with an efficient pseudopotential

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without thewritten permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 133.51.28.155-22/05/07,11:19:43)

540

Silicon Carbide and Related Materials 2005

(b)

(a)

(c)

Si2
CSi

CISi3CI
Si 4Si3Si3(d)Si4Si2(i)Si 2CIICIICSi

Si4CIICSiCII(ii)a’aaeaJT−effectFig. 1: The axial VC -CSi complex. Geometry of the complex at (a) cubic and (b) hexagonal sites. (c)equivalent orientations in the Jahn-Teller groundstate (view along c-axis). (d) defect levels, the direct
and indirect ionization (path i and ii, respectively) are indicated by arrows.
method (for details cf. Ref. [8]). To assess the effect of the artifically low band gap we also included ascissors-operator in the calculation. The hyperfine values were than calculated using the all-electron
PAW-method (for details cf. Ref. [9]). The photo excitation spectrum was assessed using the ∆-SCFapproach.
HF-signature and excitation scheme of VC -CSi
In the carbon vacancy-antisite complex, the vacancy and the antisite can occupy neighboring cubicor hexagonal sites. When both sites are cubic or hexagonal the complex is aligned with the c-axis of
the crystal and possesses a lower non-degenerate and a higher doubly degenerate level (a- and e-level,respectively) within the band gap. In the following we address the axially aligned complexes as theHF-signature of the other non-axial configurations has so far not been identified in the EPR-spectra.
In the negative charge state the e-level is occupied by one electron giving rise to a Jahn-Teller distortion that lowers the symmetry to C1h . In the Jahn-Teller ground state (JT) the spin density is mainly
localized on two silicon dangling bonds of VC (on Si3 and Si4 in Fig. 1) with antibonding character. Besides this configuration we have found a metastable (MT) configuration with the spin density
mainly located at one dangling bond (on Si2 in Fig. 1). It has only a slightly higher energy (by 0.02 eV)
and will not be relevant at sufficiently low temperatures. In both states three rotationally equivalent(with respect to the c-axis) configurations exist with a different orientation of the respective danglingbond(s) (cf. Fig. 1c). The thermal motion of the atoms may induce a continuous switching between
the equivalent configurations and a reorientation of the respective dangling bond(s). This leads to temperature dependent HF-tensors as seen for the SI5-center. The calculated HF-tensors of the states JT
and MT are listed in Table 1 together with the experimental values obtained at 30 K (C1h -symmetry)
and at 100 K (C3v -symmetry). We considered the direct ligands of VC and the carbon neighbor as
shown in Fig. 1a,b. For the configuration JT we find large HF-tensors on the two vacancy neighbors
Si3 and Si4 and a much smaller one on Si2 as expected from an inspection of the spin density. Thisfinding nicely agrees with the HF-tensor for two Si atoms deduced from the EPR spectrum at 30 K.
Note, that the difference between the calculated HF-tensors of the cubic and hexagonal complexes issmaller than the expected accuracy. A qualitative destinction between the two sites should be possible
from the HF-tensors of the third and fourth neighbor shell. With the available experimental data for
the SI5-center these HF-tensors could not be resolved and it is well possible that both sites contributed

Materials Science Forum Vols. 527-529

VC -CSi (k), JTA⊥ , A|| [ mT ]
0.3
0.3
0.1
10.8 10.9 13.8
0.5
0.5
0.5
1.3
1.3
1.7

VC -CSi (h), JTA⊥ , A|| [ mT ]
0.8
0.8
0.3
11.2 11.3 14.2
0.4
0.4
0.4
1.4
1.4
1.7

VC -CSi (k), MTA⊥ , A|| [ mT ]Si2
15.9 15.9 20.3
Si3,4
2.7
2.7
3.6
hSi2−4 i 7.2
7.6
8.6
CSi0.1
0.1
0.1
CI
0.9
0.9
1.3

VC -CSi (h), MTA⊥ , A|| [ mT ]15.8 15.8 20.1
3.2
3.3
4.3
7.5
7.9
8.9
0.2
0.2
0.2
1.3
1.3
1.7

Si2
Si3,4CSi
CII

Si (2×)C (2×)

SI5 30K, Ref. [6]A⊥ , A|| [ mT ]10.16 10.04 12.9
1.3
1.3
1.8

Si (1×)C (1×)

SI5 100K, Ref. [6]A⊥ , A|| [ mT ]6.38
6.38 8.02
1.77
1.77 2.22541

Table 1: HF-tensors of VC -C−
Si in comparison with those of the SI5-center. The atoms are labeledaccording to Fig. 1. Angular braces refer to configurational averages (cf. text).

to the SI5-spectrum. The carbon antisite (CSi ) possesses a much smaller HF-tensor than the second
carbon neighbors of the vacancy, since the CSi dangling bond mainly contributes to the fully occupied
non-degenerate a-level. This explains the fact that this HF-interaction was not resolved in the experiment. Instead a HF-interaction with two C-atoms was found, which most likely originated from thesecond carbon neighbors of the vacancy as suggested by the agreement with the tensors CII . For theMT state we find a large HF-tensor on Si2 and smaller ones on Si3 and Si4 as suggested by the spin
density of the e-levels. As for configuration JT only much smaller HF-tensors are found for CSi andthe other ligands of the complex. Qualitatively, these findings agree with the SI5-spectrum measured
at 100 K. In particular only one large Si HF-interaction is observed. The experimentally observed
HF-interaction with one C-atom cannot be explained by the antisite but most likely arises from thecarbon neighbor CI of Si2 . For a more quantitative comparison the motional reorientation is important. We approximately included this effects by taking the average of the respective Si HF-tensors forthe three equivalent reorientations. The principal values were calculated for the averaged HF-tensor
and are denoted by angular braces in Table 1. The averaged Si HF-tensor indeed agrees well with theexperimental one.
In HPSI-SiC [5] and irradiated n-type SiC [6], the SI5-signal could be significantly enhanced byillumination. As a function of the photon energy [6] the SI5-signal (at 77 K) increased in three stepswith thresholds at 0.65 eV, 0.9 eV and 1.1 eV. Experimentally the Fermi-level was located at EC −1.1 eV. The photo-EPR experiments suggest that the concentration of VC -C2−
Si should dominate over
VC -C−.
The
calculated
ionizationlevel(-|2-)
ofE−
1.1eV
(E−0.9eV)of the cubic (hexagonal)
CCSi
complex as obtained for the largest supercell agrees with this conclusion within the limited accuracyof the calculation. We analyzed the photo ionization of the VC -C2−
Si using the approximate ∆-SCF−approach. VC -C2−displays
asimilar
Jahn-Teller
effectasV-C.
Illumination
can directly ionize theCSiSi
complex (path (i) in Fig. 1d), thus recovering the paramagnetic state. Alternatively an excited state of
the complex and a subsequent ionization of this state could occur (path (ii) in Fig. 1d). In the excitedstate each of the split e-levels is occupied by one electron. Due to the Frank-Condon shifts of thisexcited state with respect to the vertical transition a broader band of excitation energies occurs with

542

Silicon Carbide and Related Materials 2005

an optical line shape governed by the Huang-Rhys factors. To estimate the effect we also calculated
the zero-phonon transition including relaxations of the excited state. For the direct vertical ionizationof the Jahn-Teller ground state we obtain 1.4 eV (1.5 eV) for the hexagonal (cubic) complex. Thesevalues are 0.3 eV higher than the experimentally deduced upper threshold but still within the expected
accuracy for such approximate calculations (cf. e.g. [3]). For the vertical internal transition we obtainexcitation energies of 0.9 eV (1.3 eV). The zero phonon transition energy amounts to 0.6 eV (0.6 eV).
For both the vertical and the zero-phonon transition a second photon of the same energy can ionize
the excited defect state. The ionization energies of the metastable configuration are lower by 0.20.3 eV. We obtain 1.1 eV for the direct ionization of the hexagonal complex. The exciation energy of
the indirect process amounts to 0.7 eV (vertical transition) and 0.3 eV (zero-phonon line). Our results
suggest an interpretation of the lower thresholds as the indirect ionization of the complex. The direct
ionization of VC -C2−
Si should account for the highest threshold.
Conclusion
In conclusion, the present theoretical analysis of the negative axial carbon vacancy-antisite complex
provides an identification of the SI5 EPR-center with this complex. A Jahn-Teller effect underlies thetemperature dependent HF-signature. Based on our calculations we propose an interpretation of theobserved photo-EPR thresholds.
Acknowledgments
M.B. acknowledges financial support by the DFG (grant BO1851/2-1 and SiC-research group). A.G.
appreciates the support by the Hungarian OTKA F-038357 and the grants Nr. 2005008 and SNIC02103-20 from the Swedish National Supercomputer Centers.
References[1] E. Rauls et al.: phys. stat. sol. (b) Vol. 217 (2000), p. R1.
[2] M. Bockstedte and O. Pankratov: Mater. Sci. Forum Vol. 338-342 (2000), p. 949.
[3] Th. Lingner et al.: Phys. Rev. B Vol. 64 (2001), p. 245212.
[4] N. T. Son et al.: Mater. Sci. Forum, this volume.
[5] N. T. Son et al.: Mater. Sci. Forum Vol. 457-460 (2004), p. 437.
[6] T. Umeda et al.: Mater. Sci. Forum , this volume.
[7] U. Gerstmann, E. Rauls and H. Overhof: Phys. Rev. B Vol. 70 (2004), p. 201204.
[8] M. Bockstedte, A. Mattausch and O. Pankratov: Phys. Rev. B Vol. 68 (2003), p. 205201.
[9] T. Umeda et al.: Phys. Rev. B Vol. 70 (2005), p. 235212.