\section{Defect configurations in silicon}
-Table~\ref{tab:defects} summarizes the formation energies of relevant defect structures for the EA and DFT calculations, which are shown in Figs.~\ref{fig:intrinsic_def} and \ref{fig:carbon_def}.
+Table~\ref{tab:defects} summarizes the formation energies of relevant defect structures for the EA and DFT calculations, which are shown in Fig.~\ref{fig:intrinsic_def} and \ref{fig:carbon_def}.
\begin{table*}
\centering
\begin{tabular}{l c c c c c c c c c}
\label{tab:defects}
\end{table*}
\begin{figure}
+\subfloat[Intrinsic Si point defects.]{%
+\begin{minipage}{0.9\columnwidth}
\centering
\begin{minipage}[t]{0.43\columnwidth}
\centering
\underline{Si$_{\text{i}}$ \hkl<1 0 0> DB}\\
\includegraphics[width=0.8\columnwidth]{si100_bonds.eps}
\end{minipage}
-\caption{Configurations of intrinsic Si point defects. Dumbbell configurations are abbreviated by DB.}
+%\caption{Configurations of intrinsic Si point defects. Dumbbell configurations are abbreviated by DB.}
+\end{minipage}
\label{fig:intrinsic_def}
-\end{figure}
-\begin{figure}
+}\\
+\subfloat[C point defects in Si.]{%
+\begin{minipage}{0.9\columnwidth}
\centering
\begin{minipage}[t]{0.43\columnwidth}
\centering
\underline{C$_{\text{i}}$ bond-centered}\\
\includegraphics[width=0.8\columnwidth]{cbc_bonds.eps}
\end{minipage}
-\caption{Configurations of carbon point defects in silicon. Silicon and carbon atoms are illustrated by yellow and gray spheres respectively. Dumbbell configurations are abbreviated by DB.}
+%\caption{Configurations of carbon point defects in silicon. Silicon and carbon atoms are illustrated by yellow and gray spheres respectively. Dumbbell configurations are abbreviated by DB.}
+\end{minipage}
\label{fig:carbon_def}
+}
+\caption{Defect configurations in Si. Si and C atoms are illustrated by yellow and gray spheres respectively. Dumbbell configurations are abbreviated by DB.}
\end{figure}
Regarding intrinsic defects in Si, classical potential and {\em ab initio} methods predict energies of formation that are within the same order of magnitude.
\section{Mobility of the carbon defect}
-The migration barriers of the ground-state C defect are investigated by both, first-principles as well as the empirical method.
-The migration pathways are shown in Figs.\ref{fig:vasp_mig} and \ref{fig:albe_mig} respectively.
+The migration barriers of the ground-state C defect are investigated by both, first-principles as well as the empirical method, their migration pathways shown in Fig.~\ref{fig:mig}.
\begin{figure}
-\begin{center}
+\subfloat[Transition path obtained by first-principles methods.]{%
\includegraphics[width=\columnwidth]{path2_vasp_s.ps}
-\end{center}
-\caption{Migration barrier and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition as obtained by first principles methods.}
-\label{fig:vasp_mig}
-\end{figure}
-\begin{figure}
-\begin{center}
+}\\
+%\caption{Migration barrier and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition as obtained by first principles methods.}
+\subfloat[Transition involving the {\hkl[1 1 0]} DB (center) configuration within the EA description.]{%
\includegraphics[width=\columnwidth]{110mig.ps}
-\end{center}
-\caption{Migration barrier and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the hkl[0 -1 0] DB (right) transition involving the \hkl[1 1 0] DB (center) configuration within EA description. Migration simulations were performed utilizing time constants of \unit[1]{fs} (solid line) and \unit[100]{fs} (dashed line) for the Berendsen thermostat.}
-\label{fig:albe_mig}
+}
+\caption{Migration barriers and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the hkl[0 -1 0] DB (right) transition.}
+%\caption{Migration barrier and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the hkl[0 -1 0] DB (right) transition involving the \hkl[1 1 0] DB (center) configuration within EA description. Migration simulations were performed utilizing time constants of \unit[1]{fs} (solid line) and \unit[100]{fs} (dashed line) for the Berendsen thermostat.}
+\label{fig:mig}
\end{figure}
In qualitative agreement with the results of Capaz~et~al.\ \cite{capaz94}, the lowest migration barrier of the ground-state C$_{\text{i}}$ defect within the quantum-mechanical treatment is found for the path, in which a C$_{\text{i}}$ \hkl[0 0 -1] DB migrates to a C$_{\text{i}}$ \hkl[0 -1 0] DB located at the neighbored Si lattice site in \hkl[1 1 -1] direction.
The second most favorable configuration is accomplished for a V located right next to the Si atom of the DB structure.
This is due to the reduction of compressive strain of the Si DB atom and its two upper Si neighbors present in the isolated C$_{\text{i}}$ DB configuration.
This configuration is followed by the structure, in which the V is created at one of the neighbored lattice site below one of the Si atoms that are bound to the C atom of the initial DB.
-Relaxed structures of the latter two defect combinations are shown in the bottom left of Figs.~\ref{fig:314-539} and \ref{fig:059-539} respectively together with their energetics during transition into the ground state.
+Relaxed structures of the latter two defect combinations are shown in the bottom left of Fig.~\ref{fig:314-539} and \ref{fig:059-539} respectively together with their energetics during transition into the ground state.
\begin{figure}
+\subfloat[V created right next to the Si atom of the initial DB. Activation energy: {\unit[0.1]{eV}}.]{%
\includegraphics[width=\columnwidth]{314-539.ps}
-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created right next to the Si atom of the initial DB (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.1]{eV} is observed.}
\label{fig:314-539}
-\end{figure}
-\begin{figure}
+}\\
+%\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created right next to the Si atom of the initial DB (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.1]{eV} is observed.}
+\subfloat[V created next to one of the Si atoms that is bound to the C atom of the initial DB. Activation energy: {\unit[0.6]{eV}}.]{%
\includegraphics[width=\columnwidth]{059-539.ps}
-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created next to one of the Si atoms that is bound to the C atom of the initial DB (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.6]{eV} is observed.}
\label{fig:059-539}
+}
+%\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created next to one of the Si atoms that is bound to the C atom of the initial DB (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.6]{eV} is observed.}
+\caption{Migration barrier and structures of transitions of an initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V (left) into a C$_{\text{s}}$ configuration (right).}
\end{figure}
These transitions exhibit activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV}.
In the first case the Si and C atom of the DB move towards the vacant and initial DB lattice site respectively.
\end{figure}
A transformation from a structure dominated by C$_{\text{i}}$ into a C$_{\text{s}}$ dominated structure with increasing temperature can clearly be observed if compared with the radial distribution of C$_{\text{s}}$ in c-Si.
Thus, the C$_{\text{s}}$ defect and, thus, stretched coherent structures of SiC, must be considered to play an important role in the IBS at elevated temperatures.
-This, in fact, is in agreement with experimental findings of annealing experiments \cite{nejim95,strane94,serre95} and also with the previous DFT results, which suggest C$_{\text{s}}$ to be involved at higher temperatures and in conditions out of thermodynamic equilibrium.
+This, in fact, is in agreement with experimental findings of annealing experiments \cite{strane94,nejim95,serre95} and also with the previous DFT results, which suggest C$_{\text{s}}$ to be involved at higher temperatures and in conditions out of thermodynamic equilibrium.
\section{Summary and discussion}
-Although investigations of defect combinations show the agglomeration of C$_{\text{i}}$ DBs to be energetically most favorable, configurations that may arise during IBS were presented, their dynamics indicating an C$_{\text{s}}$ to play an important role particularly at high temperatures.
+Although investigations of defect combinations show the agglomeration of C$_{\text{i}}$ DBs to be energetically most favorable, configurations that may arise during IBS were presented, their dynamics indicating C$_{\text{s}}$ to play an important role particularly at high temperatures.
This is supported by the empirical MD results, which show an increased participation of C$_{\text{s}}$ at increased temperatures that allow the system to deviate from the ground state.
-Based on these findings, it is concluded that in IBS at elevated temperatures, the conversion into SiC takes place by an initial agglomeration of C$_{\text{s}}$ into coherent, tensily strained structures of SiC followed by precipitation into incoherent SiC structures once a critical radius is reached.
+Based on these findings, it is concluded that in IBS at elevated temperatures, SiC conversion takes place by an initial agglomeration of C$_{\text{s}}$ into coherent, tensily strained structures of SiC followed by precipitation into incoherent SiC once a critical size is reached and the increasing strain energy of the coherent structure surpasses the interfacial energy of the incoherent precipitate.
Rearrangement of stable C$_{\text{s}}$ is enabled by excess Si$_{\text{i}}$, which not only acts as a vehicle for C but also as a supply of Si atoms needed elsewhere to form the SiC structure and to reduce possible strain at the interface of coherent SiC precipitates and the Si host.
-It is worth to point out that the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate is satisfied by the mechanism of successive positioning of C$_{\text{s}}$.
-In contrast, there is no obvious reason for the topotactic orientation of an agglomerate consisting exclusively of C-Si dimers, which would necessarily involve a much more profound change in structure for the transition into SiC.
+%It is worth to point out that the experimentally observed alignment of the \hkl(h k l) planes of precipitate and substrate is satisfied by this mechanism.
+%In contrast, the topotactic orientation of the SiC precipitate originating from an agglomerate consisting exclusively of C-Si dimers would necessarily involve a much more profound change in structure.
\begin{acknowledgement}
We gratefully acknowledge financial support by the Bayerische Forschungsstiftung (Grant No. DPA-61/05) and the Deutsche Forschungsgemeinschaft (Grant No. DFG SCHM 1361/11).
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