Astonishingly EA and DFT predict almost equal formation energies.
There are, however, geometric differences with regard to the DB position within the tetrahedron spanned by the four next neighbored Si atoms, as already reported in a previous study\cite{zirkelbach10a}.
Since the energetic description is considered more important than the structural description minor discrepancies of the latter are assumed non-problematic.
-This second most favorable configuration is the C$_{\text{i}}$ \hkl<1 1 0> DB followed by the C$_{\text{i}}$ bond-centered (BC) configuration.
+The second most favorable configuration is the C$_{\text{i}}$ \hkl<1 1 0> DB followed by the C$_{\text{i}}$ bond-centered (BC) configuration.
For both configurations EA overestimates the energy of formation by approximately \unit[1]{eV} compared to DFT.
Thus, nearly the same difference in energy has been observed for these configurations in both methods.
However, we have found the BC configuration to constitute a saddle point within the EA description relaxing into the \hkl<1 1 0> configuration.
Due to the high formation energy of the BC defect resulting in a low probability of occurence of this defect, the wrong description is not posing a serious limitation of the EA potential.
A more detailed discussion of C defects in Si modeled by EA and DFT including further defect configurations are presented in a previous study\cite{zirkelbach10a}.
-
-
-Tersoff indeed predicts a metastable BC configuration.
-However, it is not in the correct order and lower in energy than the \hkl<1 1 0> dumbbell.
-Please note, that Capaz et~al.\cite{capaz94} in turn found this configuration to be a saddle point, which is about \unit[2.1]{eV} higher in energy than the C$_{\text{i}}$ configuration.
-This is assumed to be due to the neglection of the electron spin in these calculations.
-Another DFT calculation without fully accounting for the electron spin results in the smearing of a single electron over two non-degenerate states for the BC configuration.
-This problem is resolved by spin polarized calculations resulting in a net spin of one accompanied by a reduction of the total energy by \unit[0.3]{eV} and the transformation into a metastable local minimum configuration.
-All other configurations are not affected.
-
-To conclude, we observed discrepancies between the results from classical potential calculations and those obtained from first-principles.
-Within the classical potentials EA outperforms Tersoff and is, therefore, used for further comparative studies.
-Both methods (EA and DFT) predict the \hkl<1 0 0> dumbbell interstitial configuration to be most stable.
-%ref mod: language - energetical order
-%Also the remaining defects and their energetical order are described fairly well.
-Also the remaining defects and their relative energies are described fairly well.
-It is thus concluded that -- so far -- modelling of the SiC precipitation by the EA potential might lead to trustable results.
+Regarding intrinsic defects in Si, both methods predict energies of formation that are within the same order of magnitude.
+However discrepancies exist.
+Quantum-mechanical results reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB to compose the energetically most favorabe configuration, which is the consensus view for Si$_{\text{i}}$\cite{leung99,al-mushadani03}.
+The EA potential does not reproduce the correct ground state.
+Instead the tetrahedral defect configuration is favored.
+This limitation is assumed to arise due to the cut-off.
+In the tetrahedral configuration the second neighbors are only slightly more distant than the first neighbors, which creates the particular problem.
+Indeed an increase of the cut-off results in increased values of the formation energies\cite{albe_sic_pot}, which is most significant for the tetrahedral configuration.
+The same issue has already been discussed by Tersoff\cite{tersoff90} with regard to the description of the tetrahedral C defect using his potential.
+While not completely rendering impossible further, more challenging, empirical potential studies on large systems, the artifact has to be taken into account in the following investigations of defect combinations.
+%This artifact does not necessarily render impossible further challenging empirical potential studies on large systems.
+%However, it has to be taken into account in the following investigations of defect combinations.
+
+\subsection{Formation energies of C$_{\text{i}}$ and C$_{\text{s}}$-Si$_{\text{i}}$}
+
+As has been shown in a previous study\cite{zirkelbach10b}, the energetically most favorable configuration of C$_{\text{s}}$ and Si$_{\text{i}}$ is obtained for C$_{\text{s}}$ located at the next neighbored lattice site along the \hkl<1 1 0> bond chain of a Si$_{\text{i}}$ \hkl<1 1 0> DB.
+However the energy of formation is slightly higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB, which constitutes the ground state for a C impurity introduced into otherwise perfect c-Si.
+
+For a possible clarification of the controversial views on the participation of C$_{\text{s}}$ in the precipitation mechanism by classical potential simulations, test calculations need to ensure the proper description of the relative formation energies of combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ compared to C$_{\text{i}}$.
+This is particularly important since the energy of formation of C$_{\text{s}}$ is drastically underestimated by the EA potential.
+A possible occurence of C$_{\text{s}}$ could then be attributed to a lower energy of formation of the C$_{\text{s}}$-Si$_{\text{i}}$ combination due to the low formation energy of C$_{\text{s}}$, which obviously is wrong.
+
+Since quantum-mechanical calculation reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB as the ground state configuration of Si$_{\text{i}}$ in Si it is assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$.
+Empirical potentials, however, predict Si$_{\text{i}}$ T to be the energetically most favorable configuration.
+Thus, investigations of the relative energies of formation of defect pairs need to include combinations of C$_{\text{s}}$ with Si$_{\text{i}}$ T.
+Results of VASP and EA calculations are summarized in Table~\ref{tab:defect_combos}.
+\begin{table}
+\begin{ruledtabular}
+\begin{tabular}{l c c c}
+ & C$_{\text{i}}$ \hkl<1 0 0> & C$_{\text{s}}$ \& Si$_{\text{i}}$ \hkl<1 1 0> & C$_{\text{s}}$ \& Si$_{\text{i}}$ T\\
+\hline
+ VASP & 3.72 & 4.37 & - \\
+ Erhart/Albe & 3.88 & 4.93 & 5.25$^{\text{a}}$/5.08$^{\text{b}}$/4.43$^{\text{c}}$
+\end{tabular}
+\end{ruledtabular}
+\caption{Formation energies of defect configurations of a single C impurity in otherwise perfect c-Si determined by classical potential and ab initio methods. The formation energies are given in electron volt. T denotes the tetrahedral and the subscripts i and s indicate the interstitial and substitutional configuration. Superscripts a, b and c denote configurations of C$_{\text{s}}$ located at the first, second and third next neighbored lattice site with respect to the Si$_{\text{i}}$ atom.}
+\label{tab:defect_combos}
+\end{table}
+Obviously the EA potential properly describes the relative energies of formation.
+Combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ T are energetically less favorable than the ground state C$_{\text{i}}$ \hkl<1 0 0> DB configuration.
+With increasing separation distance the enrgies of formation decrease.
+However, even for non-interacting defects, the energy of formation, which is then given by the sum of the formation energies of the separated defects (\unit[4.15]{eV}) is still higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB.
+Unexpectedly, the structure of a Si$_{\text{i}}$ \hkl<1 1 0> DB and a next neighbored C$_{\text{s}}$, which is the most favored configuration of C$_{\text{s}}$ and Si$_{\text{i}}$ according to quantum-mechanical caluclations\cite{zirkelbach10b} likewise constitutes an energetically favorable configuration within the EA description, which is even preferred over the two least separated configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ T.
+This is attributed to an effective reduction in strain enabled by the respective combination.
+Thus, a proper description with respect to the relative energies of formation is assumed for the EA potential.
\subsection{Mobility}
+To accurately model the SiC precipitation the agglomeration of C the activation energies for the C migration have to be reproduced correctly.
+
A measure for the mobility of the interstitial carbon is the activation energy for the migration path from one stable position to another.
The stable defect geometries have been discussed in the previous subsection.
In the following the migration of the most stable configuration, i.e. C$_{\text{i}}$, from one site of the Si host lattice to a neighboring site has been investigated by both, EA and DFT calculations utilizing the constraint conjugate gradient relaxation technique (CRT)\cite{kaukonen98}.
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