Ionic relaxation was realized by the conjugate gradient algorithm.\r
Spin polarization has been fully accounted for.\r
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-Migration and recombination pathways have been ivestigated utilizing the constraint conjugate gradient relaxation technique (CRT)\cite{kaukonen98}.\r
+Migration and recombination pathways have been investigated utilizing the constraint conjugate gradient relaxation technique (CRT)\cite{kaukonen98}.\r
The defect formation energy $E-N_{\text{Si}}\mu_{\text{Si}}-N_{\text{C}}\mu_{\text{C}}$ is defined by chosing SiC as a particle reservoir for the C impurity, i.e. the chemical potentials are determined by the cohesive energies of a perfect Si and SiC supercell after ionic relaxation.\r
-The binding energy of a defect pair is given by the difference of the formation energy of the complex and the sum of the two separated defect configurations, i.e. energetically favorable configurations show binding energies below zero and non-interacting isolated defects would result in a binding energy of zero.\r
+The binding energy of a defect pair is given by the difference of the formation energy of the complex and the sum of the two separated defect configurations.\r
+Accordingly, energetically favorable configurations show binding energies below zero while non-interacting isolated defects result in a binding energy of zero.\r
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\section{Results}\r
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Configurations a, A and B are not affected by spin polarization and show zero magnetization.\r
Mattoni et~al.\cite{mattoni2002}, in contrast, find configuration b less favorable than configuration A by \unit[0.2]{eV}.\r
Next to differences in the XC-functional and plane-wave energy cut-off this discrepancy might be attributed to the missing accounting for spin polarization in their calculations, which -- as has been shown for the C$_{\text{i}}$ BC configuration -- results in an increase of configurational energy.\r
+Indeed, investigating the migration path from configurations a to b and, in doing so, reusing the wave functions of the previous migration step the final structure, i.e. configuration b, was obtained with zero magnetization and an increase in configurational energy \unit[0.2]{eV}.\r
+Obviously a different energy minimum of the electronic system is obatined in that case showing a hysterisis behavior.\r
+However, since the total energy is lower for the magnetic result it is believed to constitute the real, i.e. global, minimum of the electronic minimization.\r
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A low activation energy of \unit[0.1]{eV} is observed for the a$\rightarrow$b transition.\r
Thus, configuration a is very unlikely to occur in favor of configuration b.\r
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