+The tetrahedral and the <110> dumbbell self-interstitial configurations can be reproduced as observed in \cite{albe_sic_pot}.
+The formation energies are $3.4\, eV$ and $4.4\, eV$ respectively.
+However the hexagonal one is not stable opposed to what is presented in \cite{albe_sic_pot}.
+The atom moves towards an energetically more favorable position very close to the tetrahedral one but slightly displaced along the three coordinate axes.
+The formation energy of $4.0\, eV$ of this type of interstitial equals the result obtained in the reference for the hexagonal one.
+The same type of interstitial may arise using random insertions.
+In addition variations exist in which the displacement is only along two axes ($E_f=3.8\, eV$) or along a single axis ($E_f=3.6\, eV$) succesively approximating the tetrahedral configuration and formation energy.
+
+The tetrahedral and <110> dumbbel carbon interstitial configurations are stable.
+The formation energies are $2.7\, eV$ and $1.8\, eV$ respectively.
+Again the hexagonal one is found to be unstable.
+The interstitial atom moves to the more favorable <100> dumbbell position which has a formation energy of $0.5\, eV$.
+The interstitial configuration is shown in Fig. 2.
+There is experimental evidence \cite{watkins76} of the existence of this configuration.
+It is frequently generated and has the lowest formation energy of all the defects observed in all the simulation runs in which carbon is inserted at random positions.
+
+\begin{figure}[!h]
+ \begin{center}
+ \includegraphics[width=8cm]{c_in_si_int_001db_0.eps}
+ \caption{Position of a <100> dumbbell carbon interstitial in silicon.
+ Only bonds of the carbon interstitial atom are shown.}
+ \end{center}
+\end{figure}
+
+%\begin{figure}[!h]
+% \begin{center}
+% \includegraphics[width=12cm]{../plot/diff_dep.ps}
+% \caption{Diffusion coefficients of a single carbon atom for different amount of Si selft interstitials}
+% \end{center}
+%\end{figure}
+%The influence of Si self-interstitials on the diffusion of a single carbon atom is displayed in Fig. 3.
+%Diffusion coefficients for different amount of Si self-interstitials are shown.
+%A slight increase is first observed in the case of 30 interstitial atoms.
+%Further increasing the amount of interstitials leads to a tremendous decay of the diffusion coeeficient.
+%Generally there is no long range diffusion of the carbon atom for a temperature of $450\, ^{\circ} \textrm{C}$.
+%The maximal displacement of the carbon atom relativ to its insertion position is between 0.5 and 0.7 \AA.
+
+\begin{figure}[!h]
+ \begin{center}
+ \includegraphics[width=12cm]{pc_si-c_c-c.ps}
+ \caption{Pair correlation functions for Si-C and C-C bonds.
+ Carbon atoms are introduced into the whole simulation volume $V_1$, the region which corresponds to the size of a minimal SiC precipitate $V_2$ and the volume which contains the necessary amount of silicon for such a minimal precipitate $V_2$ respectively.}
+ \end{center}
+\end{figure}
+\begin{figure}[!h]
+ \begin{center}
+ \includegraphics[width=12cm]{pc_si-si.ps}
+ \caption{Si-Si pair correlation function for pure Si and Si with 3000 inserted C atoms.
+ The inset shows a magnified region between 0.28 and 0.36 nm.}
+ \end{center}
+\end{figure}
+Fig. 3 shows resulting pair correlation functions of the simulation runs targeting the observation of precipitation events.
+The contributions of Si-C and C-C pairs are presented separately each of them displaying the pair correlation for the three different volumes $V_1$, $V_2$ and $V_3$ (as explained above) exposed to carbon insertion.
+Results show no signigicant difference between $V_1$ and $V_2$.
+Si-Si pairs for the case of 3000 inserted C atoms inserted into $V_2$ and a reference function for pure Si are displayed in Fig. 4.
+
+The amount of C-C bonds for $V_1$ are much smaller than for $V_2$ and $V_3$ since carbon atoms are spread over the total simulation volume which means that there are only 0.2 carbon atoms per silicon unit cell on average.
+The first C-C peak appears at about 0.15 nm.
+This is comparable to the nearest neighbour distance for graphite or diamond.
+It is assumed that these carbon atoms form strong C-C bonds, which is supported by a decrease of the total energy during carbon insertion for the $V_2$ and $V_3$ in contrast to the $V_3$ simulation.
+
+The peak at 0.31 nm perfectly matches the distance of two carbon atoms in the SiC lattice which in SiC is also expected for the Si-Si bonds.
+After insertion of carbon atoms the Si-Si pair correlation function in fact shows non-zero values in the range of the C-C peak width while the amount of Si pairs at the regular distances at 0.24 and 0.38 nm decreases.
+However no clear peak is observed and random analyses of configurations in which distances around 0.3 nm appear, i.e. visualization of such atom pairs, identify <100> C-Si dumbbells to be responsible for stretching the Si-Si next neighbour distance for low concentrations of carbon, i.e. for the $V_1$ and early stages of $V_2$ and $V_3$ simulation runs.
+For higher carbon concentrations the defect concentration is likewise increased and a considerable amount of damage is introduced into the inserted volume.
+Damage and superposition of defects generate new displacement arrangements which become hard to categorize and trace.
+The slightly higher amount and intense increase of Si-Si pairs at distances smaller 0.31 nm is probably due to the Si-Si cutoff radius of 0.296 nm.
+The cutoff function causes artificial forces pushing the Si atoms out of the cutoff region.
+
+Wieder durch visuelle untersuchungen -> c-c 0.31 paare durch aufeinandertreffen unterschiedlich orientierter 100 dumbbells bzw mit 110.
+C fuer sic schon besser arrangiert. Vorstellung, dass diese zuerst anordnen und spaeter dann evtl am Si ziehen ...
+Nevertheless this might indicate that carbon arranges first, then 'pulls' the Si ...
+\\\\
+On the other hand the Si-C pair correlation function indicates formation of SiC bonds with an increased crystallinity for the simulation in which carbon is inserted into the whole simulation volume.
+There is more carbon forming Si-C bonds than C-C bonds.
+This gives suspect to the competition of Si-C and C-C bond formation in which the predominance of either of them depends on the method handling carbon insertion.
+
+\section*{Summary}
+The supposed conversion mechanism of heavily carbon doped silicon into silicon carbide is presented.
+Molecular dynamics simulation sequences to investigate interstitial configurations
+%, the influence of interstitials on the atomic diffusion
+and the precipitation of SiC are explained.
+The <100> C-Si dumbbel is reproduced and is the energetically most favorable configuration observed by simulation.
+%The influence of silicon self-interstitials on the diffusion of a single carbon atom is demonstrated.
+Two competing bond formations, either Si-C or C-C, seem to coexist, where the strength of either of them depends on the size of the region in which carbon is introduced.
+
+\bibliography{../../bibdb/bibdb}