-\begin{figure}
-\begin{minipage}[t]{0.32\columnwidth}
-\underline{Tetrahedral}\\
-\includegraphics[width=\columnwidth]{tet.eps}
-\end{minipage}
-\begin{minipage}[t]{0.32\columnwidth}
-\underline{Hexagonal}\\
-\includegraphics[width=\columnwidth]{hex.eps}
-\end{minipage}
-\begin{minipage}[t]{0.32\columnwidth}
-\underline{\hkl<1 0 0> dumbbell}\\
-\includegraphics[width=\columnwidth]{100.eps}
-\end{minipage}\\
-\begin{minipage}[t]{0.32\columnwidth}
-\underline{\hkl<1 1 0> dumbbell}\\
-\includegraphics[width=\columnwidth]{110.eps}
-\end{minipage}
-\begin{minipage}[t]{0.32\columnwidth}
-\underline{Substitutional}\\[0.05cm]
-\includegraphics[width=\columnwidth]{sub.eps}
-\end{minipage}
-\begin{minipage}[t]{0.32\columnwidth}
-\underline{Bond-centered}\\
-\includegraphics[width=\columnwidth]{bc.eps}
-\end{minipage}
-\caption{Configurations of carbon point defects in silicon. The silicon/carbon atoms and the bonds (only for the interstitial atom) are illustrated by yellow/grey spheres and blue lines. Bonds are drawn for atoms located within a certain distance and do not necessarily correspond to chemical bonds.}
-\label{fig:defects}
-\end{figure}
+Although discrepancies exist, both methods depict the correct order of the formation energies with regard to C defects in Si.
+Substitutional C (C$_{\text{s}}$) constitutes the energetically most favorable defect configuration.
+Since the C atom occupies an already vacant Si lattice site, C$_{\text{s}}$ is not an interstitial defect.
+The quantum-mechanical result agrees well with the result of another ab initio study\cite{dal_pino93}.
+Clearly, the empirical potential underestimates the C$_{\text{s}}$ formation energy.
+The C interstitial defect with the lowest energy of formation has been found to be the C-Si \hkl<1 0 0> interstitial dumbbell (C$_{\text{i}}$ \hkl<1 0 0> DB), which, thus, constitutes the ground state of an additional C impurity in otherwise perfect c-Si.
+This finding is in agreement with several theoretical\cite{burnard93,leary97,dal_pino93,capaz94} and experimental\cite{watkins76,song90} investigations.
+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.
+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}.
+
+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{Carbon mobility}
+
+To accurately model the SiC precipitation, which involves the agglomeration of C, a proper description of the migration process of the C impurity is required.
+As shown in a previous study\cite{zirkelbach10a} quantum-mechanical results properly describe the C$_{\text{i}}$ \hkl<1 0 0> DB diffusion resulting in a migration barrier height of \unit[0.90]{eV} excellently matching experimental values of \unit[0.70-0.87]{eV}\cite{lindner06,tipping87,song90} and, for this reason, reinforcing the respective migration path as already proposed by Capaz et~al.\cite{capaz94}.
+However, it turned out that the description fails if the EA potential is used, which overestimates the migration barrier (\unit[2.2]{eV}) by a factor of 2.4.
+In addition a different diffusion path is found to exhibit the lowest migration barrier.
+The proposed path involves the C$_{\text{i}}$ BC configuration, which, however, was found to be unstable relaxing into the C$_{\text{i}}$ \hkl<1 1 0> DB configuration.
+