However, the process of formation of SiC precipitates in Si during C implantation is not yet fully understood and controversial ideas exist in the literature.
Based on experimental high resolution transmission electron microscopy (HREM) studies \cite{werner96,werner97,eichhorn99,lindner99_2,koegler03} it is assumed that incorporated C atoms form C-Si dimers (dumbbells) on regular Si lattice sites.
The highly mobile C interstitials agglomerate into large clusters followed by the formation of incoherent 3C-SiC nanocrystallites once a critical size of the cluster is reached.
-In contrast, a couple of other studies \cite{strane94,nejim95,guedj98} suggest initial coherent SiC formation by agglomeration of substitutional instead of interstitial C followed by the loss of coherency once the increasing strain energy surpasses the interfacial energy of the incoherent 3C-SiC precipitate and the c-Si substrate.
+In contrast, a couple of other studies \cite{strane94,nejim95,serre95,guedj98} suggest initial coherent SiC formation by agglomeration of substitutional instead of interstitial C followed by the loss of coherency once the increasing strain energy surpasses the interfacial energy of the incoherent 3C-SiC precipitate and the c-Si substrate.
To solve this controversy and in order to understand the effective underlying processes on a microscopic level atomistic simulations are performed.
% ????
\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 Figs.~\ref{fig:intrinsic_def} and \ref{fig:carbon_def}.
\begin{table*}
\centering
\begin{tabular}{l c c c c c c c c c}
\begin{minipage}[t]{0.43\columnwidth}
\centering
\underline{Si$_{\text{i}}$ \hkl<1 1 0> DB}\\
-\includegraphics[width=0.9\columnwidth]{si110_bonds.eps}
+\includegraphics[width=0.8\columnwidth]{si110_bonds.eps}
\end{minipage}
\begin{minipage}[t]{0.43\columnwidth}
\centering
\underline{Si$_{\text{i}}$ hexagonal}\\
-\includegraphics[width=0.9\columnwidth]{sihex_bonds.eps}
+\includegraphics[width=0.8\columnwidth]{sihex_bonds.eps}
\end{minipage}\\
\begin{minipage}[t]{0.43\columnwidth}
\centering
\underline{Si$_{\text{i}}$ tetrahedral}\\
-\includegraphics[width=0.9\columnwidth]{sitet_bonds.eps}
+\includegraphics[width=0.8\columnwidth]{sitet_bonds.eps}
\end{minipage}
\begin{minipage}[t]{0.43\columnwidth}
\centering
\underline{Si$_{\text{i}}$ \hkl<1 0 0> DB}\\
-\includegraphics[width=0.9\columnwidth]{si100_bonds.eps}
+\includegraphics[width=0.8\columnwidth]{si100_bonds.eps}
\end{minipage}
\caption{Configurations of intrinsic silicon point defects. Dumbbell configurations are abbreviated by DB.}
\label{fig:intrinsic_def}
\centering
\begin{minipage}[t]{0.43\columnwidth}
\centering
-\underline{C$_{\text{s}}$}
-\includegraphics[width=0.9\columnwidth]{csub_bonds.eps}
+\underline{C$_{\text{s}}$}\\
+\includegraphics[width=0.8\columnwidth]{csub_bonds.eps}
\end{minipage}
\begin{minipage}[t]{0.43\columnwidth}
\centering
\underline{C$_{\text{i}}$ \hkl<1 0 0> DB}\\
-\includegraphics[width=0.9\columnwidth]{c100_bonds.eps}
+\includegraphics[width=0.8\columnwidth]{c100_bonds.eps}
\end{minipage}\\
\begin{minipage}[t]{0.43\columnwidth}
\centering
\underline{C$_{\text{i}}$ \hkl<1 1 0> DB}\\
-\includegraphics[width=0.9\columnwidth]{c110_bonds.eps}
+\includegraphics[width=0.8\columnwidth]{c110_bonds.eps}
\end{minipage}
\begin{minipage}[t]{0.43\columnwidth}
\centering
\underline{C$_{\text{i}}$ bond-centered}\\
-\includegraphics[width=0.9\columnwidth]{cbc_bonds.eps}
+\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.}
\label{fig:carbon_def}
\section{Large scale empirical potential MD results}
+Results of the MD simulations at \unit[450]{$^{\circ}$C}, an operative and efficient temperature in IBS \cite{lindner99}, indicate the formation of C$_{\text{i}}$ \hkl<1 0 0> DBs if C is inserted into the total simulation volume.
+However, no agglomeration is observed within the simulated time, which was increased up to several nanoseconds.
+To overcome the drastically overestimated migration barriers of the C defect, which hamper C agglomeration, the simulation temperature is successively increased up to ßunit[2050]{$^{\circ}$C}.
+Fig.~\ref{fig:tot} shows the resulting radial distribution function of Si-C bonds for various elevated temperatures.
+\begin{figure}
+\includegraphics[width=\columnwidth]{tot_pc_thesis.ps}
+\caption{Radial distribution function for Si-C pairs for C insertion at various elevated temperatures. Si-C distances of a single C$_{\text{s}}$ defect configuration are plotted.}
+\label{fig:tot}
+\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.
+
\section{Summary and discussion}
-Obtained results for separated point defects in Si are in good agreement to previous theoretical work on this subject, both for intrinsic defects\cite{leung99,al-mushadani03} as well as for C point defects\cite{dal_pino93,capaz94}.
-The ground state configurations of these defects, i.e. the Si$_{\text{i}}$ \hkl<1 1 0> and C$_{\text{i}}$ \hkl<1 0 0> DB, have been reproduced and compare well to previous findings of theoretical investigations on Si$_{\text{i}}$\cite{leung99,al-mushadani03} as well as theoretical\cite{dal_pino93,capaz94,burnard93,leary97,jones04} and experimental\cite{watkins76,song90} studies on C$_{\text{i}}$.
-A quantitatively improved activation energy of \unit[0.9]{eV} for a qualitatively equal migration path based on studies by Capaz et.~al.\cite{capaz94} to experimental values\cite{song90,lindner06,tipping87} ranging from \unit[0.70-0.87]{eV} reinforce their derived mechanism of diffusion for C$_{\text{i}}$ in Si.
-
-The investigation of defect pairs indicated a general trend of defect agglomeration mainly driven by the potential of strain reduction.
-Obtained results for the most part compare well with results gained in previous studies\cite{leary97,capaz98,mattoni2002,liu02} and show an astonishingly good agreement with experiment\cite{song90}.
-For configurations involving two C impurities the ground state configurations have been found to consist of C-C bonds, which are responsible for the vast gain in energy.
-However, based on investigations of possible migration pathways, these structures are less likely to arise than structures, in which both C atoms are interconnected by another Si atom, which is due to high activation energies of the respective pathways or alternative pathways featuring less high activation energies, which, however, involve intermediate unfavorable configurations.
-Thus, agglomeration of C$_{\text{i}}$ is expected while the formation of C-C bonds is assumed to fail to appear by thermally activated diffusion processes.
-
-In contrast, C$_{\text{i}}$ and Vs were found to efficiently react with each other exhibiting activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} resulting in stable C$_{\text{s}}$ configurations.
-In addition, we observed a highly attractive interaction exhibiting a large capture radius, effective independent of the orientation and the direction of separation of the defects.
-Accordingly, the formation of C$_{\text{s}}$ is very likely to occur.
-Comparatively high energies necessary for the reverse process reveal this configuration to be extremely stable.
-
-Investigating configurations of C$_{\text{s}}$ and Si$_{\text{i}}$, formation energies higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB were obtained keeping up previously derived assumptions concerning the ground state of C$_{\text{i}}$ in otherwise perfect Si.
-However, a small capture radius was identified for the respective interaction that might prevent the recombination of defects exceeding a separation of \unit[0.6]{nm} into the ground state configuration.
-In addition, a rather small activation energy of \unit[0.77]{eV} allows for the formation of a C$_{\text{s}}$-Si$_{\text{i}}$ pair originating from the C$_{\text{i}}$ \hkl<1 0 0> DB structure by thermally activated processes.
-Thus, elevated temperatures might lead to configurations of C$_{\text{s}}$ and a remaining Si atom in the near interstitial lattice, which is supported by the result of the molecular dynamics run.
-
-% add somewhere: nearly same energies of C_i -> Si_i + C_s, Si_i mig and C_i mig
-
-These findings allow to draw conclusions on the mechanisms involved in the process of SiC conversion in Si.
-Agglomeration of C$_{\text{i}}$ is energetically favored and enabled by a low activation energy for migration.
-Although ion implantation is a process far from thermodynamic equilibrium, which might result in phases not described by the Si/C phase diagram, i.e. a C phase in Si, high activation energies are believed to be responsible for a low probability of the formation of C-C clusters.
-
-In the context of the initially stated controversy present in the precipitation model, these findings suggest an increased participation of C$_{\text{s}}$ already in the initial stage due to its high probability of incidence.
-In addition, thermally activated, C$_{\text{i}}$ might turn into C$_{\text{s}}$.
-The associated emission of Si$_{\text{i}}$ serves two needs: as a vehicle for other C$_{\text{s}}$ atoms and as a supply of Si atoms needed elsewhere to form the SiC structure.
-As for the vehicle, Si$_{\text{i}}$ is believed to react with C$_{\text{s}}$ turning it into highly mobile C$_{\text{i}}$ again, allowing for the rearrangement of the C atom.
-The rearrangement is crucial to end up in a configuration of C atoms only occupying substitutionally the lattice sites of one of the two fcc lattices that build up the diamond lattice.
-% TODO: add SiC structure info to intro
-On the other hand, the conversion of some region of Si into SiC by substitutional C is accompanied by a reduction of the volume since SiC exhibits a \unit[20]{\%} smaller lattice constant than Si.
-The reduction in volume is compensated by excess Si$_{\text{i}}$ serving as building blocks for the surrounding Si host or a further formation of SiC.
-
-We conclude that precipitation occurs by successive agglomeration of C$_{\text{s}}$.
-However, the agglomeration and rearrangement of C$_{\text{s}}$ is only possible by mobile C$_{\text{i}}$, which has to be present at the same time.
-Accordingly, the process is governed by both, C$_{\text{s}}$ accompanied by Si$_{\text{i}}$ as well as C$_{\text{i}}$.
-It is worth to mention that there is no contradiction to results of the HREM studies\cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}.
-Regions showing dark contrasts in an otherwise undisturbed Si lattice are attributed to C atoms in the interstitial lattice.
-However, there is no particular reason for the C species to reside in the interstitial lattice.
-Contrasts are also assumed for Si$_{\text{i}}$.
-Once precipitation occurs, regions of dark contrasts disappear in favor of Moir\'e patterns indicating 3C-SiC in c-Si due to the mismatch in the lattice constant.
-Until then, however, these regions are either composed of stretched coherent SiC and interstitials or of already contracted incoherent SiC surrounded by Si and interstitials, where the latter is too small to be detected in HREM.
-In both cases Si$_{\text{i}}$ might be attributed a third role, which is the partial compensation of tensile strain that is present either in the stretched SiC or at the interface of the contracted SiC and the Si host.
-
-In addition, 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.
+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.
+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.
-\section{Summary}
+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.
+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.
-In summary, C and Si point defects in Si, combinations of these defects and diffusion processes within such configurations have been investigated.
-We have shown that C interstitials in Si tend to agglomerate, which is mainly driven by a reduction of strain.
-Investigations of migration pathways, however, allow to conclude that C clustering is hindered due to high activation energies of the respective diffusion processes.
-A highly attractive interaction and a large capture radius has been identified for the C$_{\text{i}}$ \hkl<1 0 0> DB and the vacancy indicating a high probability for the formation of C$_{\text{s}}$.
-In contrast, a rapidly decreasing interaction with respect to the separation distance has been identified for C$_{\text{s}}$ and a Si$_{\text{i}}$ \hkl<1 1 0> DB resulting in a low probability of defects exhibiting respective separations to transform into the C$_{\text{i}}$ \hkl<1 0 0> DB, which constitutes the ground state configuration for a C atom introduced into otherwise perfect Si.
-%Based on these findings conclusions on basic processes involved in the SiC precipitation in bulk Si are drawn.
-Obviously, the precipitation process is governed by the formation of C$_{\text{s}}$ already in the initial stages.
-Agglomeration and rearrangement of C$_{\text{s}}$, however, is only possible by mobile C$_{\text{i}}$, which, thus, needs to be present at the same time.
-Si$_{\text{i}}$ constitutes the vehicle for the rearrangement of C$_{\text{s}}$.
+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.
-\section*{Acknowledgment}
+\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).
+\end{acknowledgement}
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