In contrast, all other investigated configurations show attractive interactions.\r
The most favorable configuration is found for C$_{\text{s}}$ at position 3, which corresponds to the lattice site of one of the upper next neighbored Si atoms of the DB structure that is compressively strained along \hkl[1 -1 0] and \hkl[0 0 1] by the C-Si DB.\r
The substitution with C allows for most effective compensation of strain.\r
-This structure is followed by C$_{\text{s}}$ located at position 2, the next neighbour atom below the two Si atoms bound to the C$_{\text{i}}$ DB atom.\r
+This structure is followed by C$_{\text{s}}$ located at position 2, the next neighbor atom below the two Si atoms bound to the C$_{\text{i}}$ DB atom.\r
As mentioned earlier these two lower Si atoms indeed experience tensile strain along the \hkl[1 1 0] bond chain, however, additional compressive strain along \hkl[0 0 1] exists.\r
The latter is partially compensated by the C$_{\text{s}}$ atom.\r
Yet less of compensation is realized if C$_{\text{s}}$ is located at position 4 due to a larger separation although both bottom Si atoms of the DB structure are indirectly affected, i.e. each of them is connected by another Si atom to the C atom enabling the reduction of strain along \hkl[0 0 1].\r
The eneregtically most favorable configuration (configuration b) forms a strong but compressively strained C-C bond with a separation distance of \unit[0.142]{nm} sharing a Si lattice site.\r
Again, conclusions concerning the probability of formation are drawn by investigating migration paths.\r
Since C$_{\text{s}}$ is unlikely to exhibit a low activation energy for migration the focus is on C$_{\text{i}}$.\r
-Pathways starting from the two next most favored configurations were investigated, all of them showing activation energies above \unit[2.?-2.?]{eV}.\r
-Although lower than the barriers for obtaining the ground state of two C$_{\text{i}}$ defects the activation energy is yet considered too high.\r
+Pathways starting from the two next most favored configurations were investigated, all of them showing activation energies above \unit[2.2-3.5]{eV}.\r
+Although lower than the barriers for obtaining the ground state of two C$_{\text{i}}$ defects the activation energies are yet considered too high.\r
For the same reasons as in the last subsection, structures other than the ground state configuration are, thus, assumed to arise more likely due to much lower activation energies necessary for their formation and still comparatively low binding energies.\r
\r
\subsection{C$_{\text{i}}$ next to V}\r
Even for the largest possible distance (R) achieved in the calculations of the periodic supercell a binding energy as low as \unit[-0.31]{eV} is observed.\r
The ground state configuration is obtained for a V at position 1.\r
The C atom of the DB moves towards the vacant site forming a stable C$_{\text{s}}$ configuration resulting in the release of a huge amount of energy.\r
-The second most favored configuration is accomplished for a V located at position 3 due to the reduction of compressive strain of the Si DB atom and its two upper Si neighbours present in the C$_{\text{i}}$ DB configuration.\r
+The second most favored configuration is accomplished for a V located at position 3 due to the reduction of compressive strain of the Si DB atom and its two upper Si neighbors present in the C$_{\text{i}}$ DB configuration.\r
This configuration is follwed by the structure, in which a vacant site is created at position 2.\r
Similar to the observations for C$_{\text{s}}$ in the last subsection a reduction of strain along \hkl[0 0 1] is enabled by this configuration.\r
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.\r
Thus, the C$_{\text{i}}$ \hkl<1 0 0> DB configuration is assumed to occur more likely.\r
However, only \unit[0.77]{eV} are needed for the reverse process, i.e. the formation of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB out of the ground state.\r
Due to the low activation energy this process must be considered to be activated without much effort either thermally or by introduced energy of the implantation process.\r
-The configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ DBs might be especially important at higher temperatures accompanied by an increase of the entropic contribution.\r
\r
\begin{figure}\r
\includegraphics[width=\columnwidth]{c_sub_si110.ps}\r
The interaction of the defects is well approximated by a Lennard-Jones 6-12 potential, which was used for curve fitting.\r
The binding energy quickly drops to zero with the fit estimating almost zero interaction at \unit[0.6]{nm}.\r
This indicates a low interaction capture radius of the defect pair.\r
-In IBS highly energetic collisions are considered to produce configurations of these defects with separation distances exceeding the capture radius.\r
-\r
-Non-zero temperature, entropy, spatial separation of these defects possible, indeed observed in ab initio MD run.\r
+In IBS highly energetic collisions are assumed to easily produce configurations of these defects with separation distances exceeding the capture radius.\r
+For this reason C$_{\text{s}}$ without a nearby interacting Si$_{\text{i}}$ DB, which are, thus, unable to form the thermodynamically stable C$_{\text{i}}$ \hkl<1 0 0> DB constitutes a most likely configuration to be found in IBS.\r
+\r
+As mentioned above, configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ DBs might be especially important at higher temperatures due to the low activation energy necessary for its formation.\r
+At higher temperatures the contribution of entropy to structural formation increases, which might result in a spatial separation even for defects located within the capture radius.\r
+Indeed an ab initio molecular dynamics run at \unit[900]{$^{\circ}$C} starting from configuration \RM{1}, which -- based on the above findings -- is assumed to recombine into the ground state configuration, results in a separation the C$_{\text{s}}$ and Si$_{\text{i}}$ DB by more than 4 next neighbor distances realized in a repeated migration mechnism of annihilating and arising Si DBs.\r
+The atomic configurations for two different points in time are shown in Fig.~\ref{fig:md}.\r
+Si atoms 1 and 2, which form the initial DB, occupy usual Si lattice sites in the final configuration while atom 3 occupies an interstitial site.\r
+\begin{figure}\r
+\begin{minipage}{0.49\columnwidth}\r
+\includegraphics[width=\columnwidth]{md01.eps}\r
+\end{minipage}\r
+\begin{minipage}{0.49\columnwidth}\r
+\includegraphics[width=\columnwidth]{md02.eps}\\\r
+\end{minipage}\\\r
+\begin{minipage}{0.49\columnwidth}\r
+\begin{center}\r
+$t=\unit[2230]{fs}$\r
+\end{center}\r
+\end{minipage}\r
+\begin{minipage}{0.49\columnwidth}\r
+\begin{center}\r
+$t=\unit[2900]{fs}$\r
+\end{center}\r
+\end{minipage}\r
+\caption{Atomic configurations of an ab initio molecular dynamics run at \unit[900]{$^{\circ}$C} starting from a configuration of C$_{\text{s}}$ located next to a Si$_{\text{i}}$ DB (atoms 1 and 2). Equal atoms are marked by equal numbers. Blue lines correpsond to bonds, which are drawn for substantial atoms.}\r
+\label{fig:md}\r
+\end{figure}\r
\r
\section{Discussion}\r
\r
+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}.\r
+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$_{\text{i}}$.\r
+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.\r
+\r
+The investigation of defect pairs indicates a general trend of defect agglomeration mainly driven by the potential of strain reduction.\r
+Obtained results for the most part compare well with results gained in previous studies\cite{leary97,capaz98,mattoni2002,liu02} and show an astnishingly good agreement with experiment\cite{song90}.\r
+Configurations involving two C impurities indeed exhibit the ground state for structures consisting of C-C bonds, which are responsible for the vast gain in energy.\r
+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 with less high activation energies, which, however, involve intermediate unfavorable configurations.\r
+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.\r
+\r
+In contrast, C$_{\text{i}}$ and V 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 C$_{\text{s}}$ configurations.\r
+In addition, a highly attractive interaction exhibiting a large capture radius was observed, effective independent of the orientation and the direction of separation of the defects.\r
+Thus, the formation of C$_{\text{s}}$ is very likely to occur.\r
+Comparatively high energies necessary for the reverse process reveal this configuration to be extremely stable.\r
+\r
+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.\r
+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.\r
+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.\r
+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.\r
+\r
+These findings allow to draw conclusions on the mechanisms involved in the process of SiC conversion in Si.\r
+Agglomeration of C$_{\text{i}}$ is energetically favored and enabled by a low activation energy for migration.\r
+Although ion implantation is a process far from thermodynamic equlibrium, 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 clusters.\r
+\r
+Unrolling these findings on the initially stated controversy present in the precipitation model, an increased participation of C$_{\text{s}}$ already in the initial stage must be assumed.\r
+Thermally activated C$_{\text{i}}$ might turn into C$_{\text{s}}$.\r
+The associated emission of Si$_{\text{i}}$ serves two needs, as a vehicle for other C$_{\text{s}}$ and as a supply of Si atoms needed elsewhere to form the SiC structure.\r
+As for the vehicle, Si$_{\text{i}}$ is believed to react with C$_{\text{s}}$ turning it into a highly mobile C$_{\text{i}}$ again, allowing for the rearrangement of the C atom.\r
+The rearrangement is crucial to end up in a configuration of C atoms only occupying substitutionally the lattice sites of one of the fcc lattices that build up the diamond lattice as expected in 3C-SiC.\r
+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.\r
+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.\r
+\r
+It is, thus, concluded that precipitation occurs by a successive agglomeration of C$_{\text{s}}$.\r
+However, the process is governed by both, C$_{\text{s}}$ accompanied by Si$_{\text{i}}$ as well as C$_{\text{i}}$.\r
+... HIER WEITER ...\r
+By this, explains the alignment of the \hkl(h k l) lattice planes of the precipitate and the substrate.\r
+No contradiction to ... has Si int ... nice to explain cloudy TEM images indicating atoms in interstitial lattice.\r
+\r
Our calculations show that point defects which unavoidably are present after ion implantation significantly influence the mobility of implanted carbon \r
in the silicon crystal.\r
A large capture radius has been found for... \r
Especially vacancies.... \r
\r
\r
+C$_{\text{s}}$ must be attributed an important role in SiC formation ...\r
+\r
+Spin polarized ... Si or C-C show qualitatively other defect structure than C-Si , in which the C forms almot colinear bond and Si remains 120 ... COOL!\r
+\r
\section{Summary}\r
In summary, we have shown that ...\r
\r
+Interactions ... improved by migration paths and acivation energies ... probability ...\r
+\r
+\r
% ----------------------------------------------------\r
\section*{Acknowledgment}\r
We gratefully acknowledge financial support by the Bayerische Forschungsstiftung (DPA-61/05) and the Deutsche Forschungsgemeinschaft (DFG SCHM 1361/11).\r
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