+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}.
+During transition a C$_{\text{i}}$ \hkl[0 0 -1] DB migrates towards a C$_{\text{i}}$ \hkl[0 -1 0] DB located at the next neighbored lattice site in \hkl[1 1 -1] direction.
+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.
+A C$_{\text{i}}$ \hkl[0 0 -1] DB turns into the \hkl[0 0 1] configuration at the next neighbored lattice site.
+The transition 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.
+If the migration is considered to occur within a single step the kinetic energy of \unit[2.2]{eV} is enough to turn the \hkl<1 0 0> DB into the BC and back into a \hkl<1 0 0> DB configuration.
+If, on the other hand, a two step process is assumed the BC configuration will most probably relax into the C$_{\text{i}}$ \hkl<1 1 0> DB configuration resulting in different relative energies of the intermediate state and the saddle point.
+For the latter case a migration path, which involves a C$_{\text{i}}$ \hkl<1 1 0> DB configuration is proposed and displayed in Fig.~\ref{fig:mig}.
+\begin{figure}
+\begin{center}
+\includegraphics[width=\columnwidth]{110mig.ps}
+\end{center}
+\caption{Migration barrier and structures of the \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition involving the \hkl[1 1 0] DB (center) configuration.}
+\label{fig:mig}
+\end{figure}
+Approximately \unit[2.24]{eV} are needed to turn the C$_{\text{i}}$ \hkl[0 0 -1] DB into the C$_{\text{i}}$ \hkl[1 1 0] DB located at the next neighbored lattice site in \hkl[1 1 -1] direction.
+Another barrier of \unit[0.90]{eV} exists for the rotation into the C$_{\text{i}}$ \hkl[0 -1 0] DB configuration.
+Roughly the same amount would be necessary to excite the C$_{\text{i}}$ \hkl[1 1 0] DB to the BC configuration (\unit[0.40]{eV}) and a successive migration into the \hkl[0 0 1] DB configuration (\unit[0.50]{eV}) as displayed in our previous study\cite{zirkelbach10a}.
+The former diffusion process, however, would more nicely agree to the ab initio path, since the migration is accompanied by a rotation of the DB orientation.
+By considering a two step process and assuming equal preexponential factors for both diffusion steps, the probability of the total diffusion event is given by $\exp(\frac{\unit[2.24]{eV}+\unit[0.90]{eV}}{k_{\text{B}}T})$, which corresponds to a single diffusion barrier that is 3.5 times higher than the barrier obtained by ab initio calculations.
+
+Accordingly the effective barrier of migration of C$_{\text{i}}$ is overestimated by a factor of 2.4 to 3.5 compared to the highly accurate quantum-mechanical methods.
+This constitutes a serious limitation that has to be taken into account for modeling the C-Si system using the EA potential.
+
+\subsection{Molecular dynamics simulations}
+
+Fig.~\ref{fig:450} shows the radial distribution functions of simulations, in which C was inserted at \unit[450]{$^{\circ}$C}, an operative and efficient temperature in IBS, for all three insertion volumes.
+\begin{figure}
+\begin{center}
+\includegraphics[width=\columnwidth]{../img/sic_prec_450_si-si_c-c.ps}\\
+\includegraphics[width=\columnwidth]{../img/sic_prec_450_si-c.ps}
+\end{center}
+\caption{Radial distribution function for C-C and Si-Si (top) as well as Si-C (bottom) pairs for a C insertion temperature of \unit[450]{$^{\circ}$C}. In the latter case the resulting C-Si distances for a C$_{\text{i}}$ \hkl<1 0 0> DB are given additionally.}
+\label{fig:450}
+\end{figure}
+There is no significant difference between C insertion into $V_2$ and $V_3$.
+Thus, in the following, the focus is on low ($V_1$) and high ($V_2$, $V_3$) C concentration simulations only.
+
+In the low C concentration simulation the number of C-C bonds is small.
+On average, there are only 0.2 C atoms per Si unit cell.
+By comparing the Si-C peaks of the low concentration simulation with the resulting Si-C distances of a C$_{\text{i}}$ \hkl<1 0 0> DB it becomes evident that the structure is clearly dominated by this kind of defect.
+One exceptional peak exists, which is due to the Si-C cut-off, at which the interaction is pushed to zero.
+Investigating the C-C peak at \unit[0.31]{nm}, which is also available for low C concentrations as can be seen in the inset, reveals a structure of two concatenated, differently oriented C$_{\text{i}}$ \hkl<1 0 0> DBs to be responsible for this distance.
+Additionally the Si-Si radial distribution shows non-zero values at distances around \unit[0.3]{nm}, which, again, is due to the DB structure stretching two next neighbored Si atoms.
+This is accompanied by a reduction of the number of bonds at regular Si distances of c-Si.
+A more detailed description of the resulting C-Si distances in the C$_{\text{i}}$ \hkl<1 0 0> DB configuration and the influence of the defect on the structure is available in a previous study\cite{zirkelbach09}.
+
+For high C concentrations the defect concentration is likewise increased and a considerable amount of damamge is introduced in the insertion volume.
+A subsequent superposition of defects generates new displacement arrangements for the C-C as well as Si-C pair distances, which become hard to categorize and trace and obviously lead to a broader distribution.
+Short range order indeed is observed, i.e. the large amount of strong next neighbored C-C bonds at \unit[0.15]{nm} as expected in graphite or diamond and Si-C bonds at \unit[0.19]{nm} as expected in SiC, but only hardly visible is the long range order.
+This indicates the formation of an amorphous SiC-like phase.
+In fact resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modifed Tersoff potential\cite{gao02}.
+
+In both cases, i.e. low and high C concentrations, the formation of 3C-SiC fails to appear.
+With respect to the precipitation model the formation of C$_{\text{i}}$ \hkl<1 0 0> DBs indeed occurs for low C concentrations.
+However, sufficient defect agglomeration is not observed.
+For high C concentrations a rearrangment of the amorphous SiC structure, which is not expected at prevailing temperatures, and a transition into 3C-SiC is not observed either.
+On closer inspection two reasons for describing this obstacle become evident.
+Inherent to MD in general ...
+Potential limitation ...
+
+\subsection{Increased temperature simulations}
+
+Foobar ...