\begin{center}
\includegraphics[width=0.7\textwidth]{sic_prec_450_si-si_c-c.ps}
\end{center}
-\caption[Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit\[450\]{$^{\circ}$C} and cooled down to room temperature.]{Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. The bright blue graph shows the Si-Si radial distribution for pure c-Si. The insets show magnified regions of the respective type of bond.}
+\caption[Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of {\unit[450]{$^{\circ}$C}} and cooled down to room temperature.]{Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. The bright blue graph shows the Si-Si radial distribution for pure c-Si. The insets show magnified regions of the respective type of bond.}
\label{fig:md:pc_si-si_c-c}
\end{figure}
\begin{figure}[tp]
\begin{center}
\includegraphics[width=0.7\textwidth]{sic_prec_450_si-c.ps}
\end{center}
-\caption{Radial distribution function of the Si-C distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. Additionally the resulting Si-C distances of a \ci{} \hkl<1 0 0> DB configuration are given.}
+\caption[Radial distribution function of the Si-C distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of {\unit[450]{$^{\circ}$C}} and cooled down to room temperature.]{Radial distribution function of the Si-C distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. Additionally the resulting Si-C distances of a \ci{} \hkl<1 0 0> DB configuration are given.}
\label{fig:md:pc_si-c}
\end{figure}
Fig.~\ref{fig:md:pc_si-c} displays the Si-C radial distribution function for all three insertion volumes together with the Si-C bonds as observed in a \ci{} \hkl<1 0 0> DB configuration.
Clearly, the high-temperature results indicate the precipitation mechanism involving an increased participation of \cs.
Although diamond and graphite like bonds are reduced, no agglomeration of C is observed within the simulated time.
Isolated structures of stretched SiC, which are adjusted to the c-Si host with respect to the lattice constant and alignement, are formed.
-It would be conceivable that by agglomeration of further \cs{} atoms the interfacial energy could be overcome and a transition from a coherent and stretched SiC structure into an incoherent and partially strain-compensated SiC precipitate could occur.
+By agglomeration of \cs{} the interfacial energy could be overcome and a transition from a coherent and stretched SiC structure into an incoherent and partially strain-compensated SiC precipitate could occur.
+Indeed, \si in the near surrounding is observed, which may initially compensate tensile strain in the stretched SiC structure or rearrange the \cs{} sublattice and finally serve as supply for additional C to form further SiC or compensate strain at the interface of the incoherent SiC precipitate and the Si host.
\subsection{High C concentration simulations}
In addition, sharper peaks in the radial distribution functions lead to the assumption of expeditious structural formation.
The increase in temperature leads to the occupation of new defect states, which is particularly evident but not limited to the low C concentration simulations.
+% todo - cut-off effect increases for non-equilibrium processes, thus, to mimic IBS increased temperatures are exceptionally necessary
The question remains, whether these states are only occupied due to the additional supply of kinetic energy and, thus, have to be considered unnatural for temperatures applied in IBS or whether the increase in temperature indeed enables infrequent transitions to occur faster, thus, leading to the intended acceleration of the dynamics and weakening of the unphysical quirks inherent to the potential.
As already pointed out in section~\ref{section:defects:noneq_process_01} and section~\ref{section:defects:noneq_process_02}, IBS is a non-equilibrium process, which might result in the formation of the thermodynamically less stable \cs{} and \si{} configuration.
Indeed, 3C-SiC is metastable and if not fabricated by IBS requires strong deviation from equilibrium and low temperatures to stabilize the 3C polytype.
This is in fact found to be favorable in the absence of the \si{}, which turned out to have a low interaction capture radius with the \cs{} atom and very likely prevents the recombination into a thermodynamically stable \ci{} DB for appropriate separations of the defect pair.
Results gained in this chapter show preferential occupation of Si lattice sites by \cs{} enabled by increased temperatures supporting the assumptions drawn from the defect studies of the last chapter.
-Thus, it is concluded that increased temperatures is not exclusively usefull to accelerate the dynamics approximatively describing the structural evolution.
-Moreover it can be considered a necessary condition to deviate the system out of equilibrium enabling the formation of 3C-SiC, which is obviously realized by a successive agglomeration of \cs{}.
+Moreover, the cut-off effect as detailed in section~\ref{section:md:limit} is particularly significant for non-equilibrium processes.
+Thus, for instance, it is not surprising that short range potentials show overestimated melting temperatures while properties of structures that are only slightly deviated from equilibrium are well described.
+Due to this, increased temperatures are considered exceptionally necessary for modeling non-equilibrium processes and structures such as IBS and 3C-SiC.
+
+Thus, it is concluded that increased temperatures are not exclusively usefull to accelerate the dynamics approximatively describing the structural evolution.
+Moreover, it can be considered a necessary condition to deviate the system out of equilibrium enabling the formation of 3C-SiC, which is obviously realized by a successive agglomeration of \cs{}.
\ifnum1=0
\includegraphics[width=0.7\textwidth]{c_in_si_95_v1_si-c.ps}\\
\includegraphics[width=0.7\textwidth]{c_in_si_95_v1_c-c.ps}
\end{center}
-\caption{Si-C (top) and C-C (bottom) radial distribution for low concentration simulations at 95 \% of the potential's Si melting point at different points in time of the simulation.}
+\caption[Si-C and C-C radial distribution for low concentration simulations at {\unit[95]{\%}} of the potential's Si melting point at different points in time of the simulation.]{Si-C (top) and C-C (bottom) radial distribution for low concentration simulations at \unit[95]{\%} of the potential's Si melting point at different points in time of the simulation.}
\label{fig:md:95_long_time_v1}
\end{figure}
\begin{figure}[tp]
\begin{center}
\includegraphics[width=0.7\textwidth]{c_in_si_95_v2.ps}
\end{center}
-\caption{Si-C and C-C radial distribution for high concentration simulations at 95 \% of the potential's Si melting point at different points in time of the simulation.}
+\caption{Si-C and C-C radial distribution for high concentration simulations at \unit[95]{\%} of the potential's Si melting point at different points in time of the simulation.}
\label{fig:md:95_long_time_v2}
\end{figure}
It is concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.~\cite{nejim95}.
This agrees well with previous results of the {\em ab initio} study on defects in C implanted Si, which show C$_{\text{s}}$ to occur in all probability.
However, agglomeration and rearrangement is enabled by mobile C$_{\text{i}}$, which has to be present at the same time and is formed by recombination of C$_{\text{s}}$ and Si$_{\text{i}}$.
+Indeed, \si{} is observed in the direct surrounding of the stretched SiC structures.
+Next to the rearrangement, \si{} is required as a supply for additional C atoms to form further SiC and to compensate strain, either within the coherent and stretched SiC structure as well as at the interface of the incoherent SiC precipitate and the Si host.
In contrast to assumptions of an abrupt precipitation of an agglomerate of C$_{\text{i}}$ \cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}, however, structural evolution is believed to occur by a successive occupation of usual Si lattice sites with substitutional C.
This mechanism satisfies the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate, whereas 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.
-{\color{red}Si serves as vehicle, for stress compensation (vorallem stress, evtl auch schon vorher rausarbeiten!) and as Si supply for further SiC.}
-
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