+\section{Increased temperature simulations}
+\label{section:md:inct}
+
+Due to the limitations of short range potentials and conventional MD as discussed above, elevated temperatures are used in the following.
+Increased temperatures are expected to compensate the overestimated diffusion barriers.
+These are overestimated by a factor of 2.4 to 3.5.
+Scaling the absolute temperatures accordingly results in maximum temperatures of \unit[1460-2260]{$^{\circ}$C}.
+Since melting already occurs shortly below the melting point of the potential (\unit[2450]{K}) \cite{albe_sic_pot} due to the presence of defects, temperatures ranging from \unit[450-2050]{$^{\circ}$C} are used.
+The simulation sequence and other parameters except for the system temperature remain unchanged as in section \ref{section:initial_sims}.
+Since there is no significant difference among the $V_2$ and $V_3$ simulations only the $V_1$ and $V_2$ simulations are carried on and referred to as low C and high C concentration simulations.
+
+A simple quality value $Q$ is introduced, which helps to estimate the progress of structural evolution.
+In bulk 3C-SiC every C atom has four next neighbored Si atoms and every Si atom four next neighbored C atoms.
+The quality could be determined by counting the amount of atoms, which form bonds to four atoms of the other species.
+However, the aim of the simulation is to reproduce the formation of a 3C-SiC precipitate embedded in c-Si.
+The amount of Si atoms and, thus, the amount of Si atoms remaining in the c-Si diamond lattice is much higher than the amount of inserted C atoms.
+Thus, counting the atoms, which exhibit proper coordination, is limited to the C atoms.
+The quality value is defined to be
+\begin{equation}
+Q = \frac{\text{Amount of C atoms with 4 next neighbored Si atoms}}
+ {\text{Total amount of C atoms}} \text{ .}
+\label{eq:md:qdef}
+\end{equation}
+By this, bulk 3C-SiC will still result in $Q=1$ and precipitates will also reach values close to one.
+However, since the quality value does not account for bond lengthes, bond angles, crystallinity or the stacking sequence, high values of $Q$ not necessarily correspond to structures close to 3C-SiC.
+Structures that look promising due to high quality values need to be further investigated by other means.
+
+\subsection{Low C concetration simulations}
+
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{tot_pc_thesis.ps}\\
+\includegraphics[width=0.7\textwidth]{tot_ba.ps}
+\end{center}
+\caption[Si-C radial distribution and evolution of quality $Q$ for the low concentration simulations at different elevated temperatures.]{Si-C radial distribution and evolution of quality $Q$ according to equation \ref{eq:md:qdef} for the low concentration simulations at different elevated temperatures. All structures are cooled down to \degc{20}. The grey line shows resulting Si-C bonds in a configuration of \cs{} in c-Si (C$_\text{sub}$) at zero temperature. Arrows in the quality plot mark the end of C insertion and the start of the cooling down step. A fit function according to equation \eqref{eq:md:fit} shows the estimated evolution of quality in the absence of the cooling down sequence.}
+\label{fig:md:tot_si-c_q}
+\end{figure}
+Fig.~\ref{fig:md:tot_si-c_q} shows the radial distribution of Si-C bonds for different temperatures and the corresponding evolution of quality $Q$ as defined above for the low concentration simulaton.
+The first noticeable and promising change in the Si-C radial distribution is the successive decline of the artificial peak at the Si-C cut-off distance with increasing temperature up to the point of disappearance at temperatures above \degc{1650}.
+Obviously, sufficient kinetic energy is provided to affected atoms that are enabled to escape the cut-off region.
+Additionally, a more important structural change is observed, which is illustrated in the two shaded areas in Fig.~\ref{fig:md:tot_si-c_q}.
+%
+In the grey shaded region a decrease of the peak at \unit[0.186]{nm} and of the bump at \distn{0.175} accompanied by an increase of the peak at \distn{0.197} with increasing temperature is visible.
+Similarly, the peaks at \distn{0.335} and \distn{0.386} shrink in contrast to a new peak forming at \distn{0.372} as can be seen in the yellow shaded region.
+Obviously, the structure obtained from the \degc{450} simulations, which is dominated by the existence of \ci{} \hkl<1 0 0> DBs, transforms into a different structure with increasing simulation temperature.
+Investigations of the atomic data reveal \cs{} to be responsible for the new Si-C bonds.
+The peak at \distn{0.197} corresponds to the distance of a \cs{} atom and its next neighbored Si atoms.
+The one at \distn{0.372} constitutes the distance of a \cs{} atom to the second next Si neighbor along a \hkl<1 1 0> direction.
+Comparing the radial distribution for the Si-C bonds at \degc{2050} to the resulting Si-C bonds in a configuration of a \cs{} atom in c-Si excludes all possibility of doubt.
+The resulting bonds perfectly match and, thus, explain the peaks observed for the increased temperature simulations.
+To conclude, by increasing the simulation temperature, the structure characterized by the \ci{} \hkl<1 0 0> DB structure transforms into a structure dominated by \cs{}.
+
+This is likewise reflected in the quality values obtained for different temperatures.
+While simulations at \degc{450} exhibit \perc{10} of fourfold coordinated C, simulations at \degc{2050} exceed the \perc{80} range.
+Since \cs{} has four nearest neighbored Si atoms and is the preferential type of defect in elevated temperature simulations, the increase of the quality values become evident.
+The quality values at a fixed temperature increase with simulation time.
+After the end of the insertion sequence marked by the first arrow, the quality is increasing and a saturation behaviour, yet before the cooling process starts, can be expected.
+The evolution of the quality value of the simulation at \degc{2050} inside the range, in which the simulation is continued at constant temperature for \unit[100]{fs}, is well approximated by the simple fit function
+\begin{equation}
+f(t)=a-\frac{b}{t} \text{ ,}
+\label{eq:md:fit}
+\end{equation}
+which results in a saturation value of \perc{93}.
+Obviously, the decrease in temperature accelerates the saturation and inhibits further formation of \cs{}.
+\label{subsubsection:md:ep}
+Conclusions drawn from investigations of the quality evolution correlate well with findings of the radial distribution results.
+
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{tot_pc2_thesis.ps}\\
+\includegraphics[width=0.7\textwidth]{tot_pc3_thesis.ps}
+\end{center}
+\caption[C-C and Si-Si radial distribution for the low concentration simulations at different elevated temperatures.]{C-C and Si-Si radial distribution for the low concentration simulations at different elevated temperatures. All structures are cooled down to $20\,^{\circ}\mathrm{C}$. Arrows with dashed lines mark C-C distances of \hkl<1 0 0> DB combinations and those with solid lines mark C-C distances of combinations of substitutional C. The dashed line corresponds to the distance of a substitutional C with a next neighbored \hkl<1 0 0> DB.}
+\label{fig:md:tot_c-c_si-si}
+\end{figure}
+The formation of \cs{} also affects the Si-Si radial distribution displayed in the lower part of Fig.~\ref{fig:md:tot_c-c_si-si}.
+Investigating the atomic strcuture indeed shows that the peak arising at \distn{0.325} with increasing temperature is due to two Si atoms that form direct bonds to the \cs{} atom.
+The peak corresponds to the distance of next neighbored Si atoms along the \hkl<1 1 0> bond chain with C$_{\text{s}}$ in between.
+Since the expected distance of these Si pairs in 3C-SiC is \distn{0.308}, the existing SiC structures embedded in the c-Si host are stretched.
+
+In the upper part of Fig.~\ref{fig:md:tot_c-c_si-si} the C-C radial distribution is shown.
+The total amount of C-C bonds with a distance inside the displayed separation range does not change significantly.
+Thus, even for elevated temperatures, agglomeration of C atoms neccessary to form a SiC precipitate does not take place within the simulated time scale.
+However, with increasing temperature, a decrease of the amount of next neighbored C pairs can be observed.
+This is a promising result gained by the high-temperature simulations since the breaking of these diomand and graphite like bonds is mandatory for the formation of 3C-SiC.
+Obviously, acceleration of the dynamics occurred by supplying additional kinetic energy.
+A slight shift towards higher distances can be observed for the maximum located shortly above \distn{0.3}.
+Arrows with dashed lines mark C-C distances resulting from \ci{} \hkl<1 0 0> DB combinations while arrows with solid lines mark distances arising from combinations of \cs.
+The continuous dashed line corresponds to the distance of \cs{} and a next neighbored \ci{} \hkl<1 0 0> DB.
+%
+Obviously, the shift of the peak is caused by the advancing transformation of the C$_{\text{i}}$ DB into the C$_{\text{s}}$ defect.
+Next to combinations of two \cs{} atoms or \ci{} \hkl<1 0 0> DBs, combinations of \ci{} \hkl<1 0 0> DBs with a \cs{} atom arise.
+In addition, structures form that result in distances residing inbetween the ones obtained from combinations of mixed defect types and the ones obtained by \cs{} configurations, as can be seen by quite high $g(r)$ values in between the continuous dashed line and the first arrow with a solid line.
+For the most part, these structures can be identified as configurations of \cs{} with either another C atom that basically occupies a Si lattice site but is displaced by a \si{} atom residing in the very next surrounding or a C atom that nearly occupies a Si lattice site forming a defect other than the \hkl<1 0 0>-type with the Si atom.
+Again, this is a quite promising result since the C atoms are taking the appropriate coordination as expected in 3C-SiC.
+%However, this is contrary to the initial precipitation model proposed in section \ref{section:assumed_prec}, which assumes that the transformation into 3C-SiC takes place in a very last step once enough C-Si DBs agglomerated.
+
+To summarize, results of low concentration simulations show a phase transition in conjunction with an increase in temperature.
+The \ci{} \hkl<1 0 0> DB dominated struture turns into a structure characterized by the occurence of an increasing amount of \cs{} with respect to temperature.
+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.
+
+\subsection{High C concetration simulations}
+
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{12_pc_thesis.ps}\\
+\includegraphics[width=0.7\textwidth]{12_pc_c_thesis.ps}
+\end{center}
+\caption[Si-C and C-C radial distribution for the high concentration simulations at different elevated temperatures.]{Si-C (top) and C-C (bottom) radial distribution for the high concentration simulations at different elevated temperatures. All structures are cooled down to \degc{20}.}
+\label{fig:md:12_pc}
+\end{figure}
+Fig.~\ref{fig:md:12_pc} displays the radial distribution for Si-C and C-C pairs obtained from high C concentration simulations at different elevated temperatures.
+Again, in both cases, the cut-off artifact decreases with increasing temperature.
+Peaks that already exist for the low temperature simulations get slightly more distinct for elevated temperatures.
+This is also true for peaks located past distances of next neighbors indicating an increase in the long range order.
+However, this change is rather small and no significant structural change is observeable.
+Due to the continuity of high amounts of damage, atomic configurations remain hard to identify even for the highest temperature.
+Other than in the low concentration simulation, analyzed defect structures are no longer necessarily aligned to the primarily existing but succesively disappearing c-Si host matrix inhibiting or at least hampering their identification and classification.
+As for low temperatures, order in the short range exists decreasing with increasing separation.
+The increase of the amount of Si-C pairs at \distn{0.186} could be positively interpreted since this type of bond also exists in 3C-SiC.
+On the other hand, the amount of next neighbored C atoms with a distance of approximately \distn{0.15}, which is the distance of C in graphite or diamond, is likewise increased.
+Thus, higher temperatures seem to additionally enhance a conflictive process, i.e. the formation of C agglomerates, obviously inconsistent with the desired process of 3C-SiC formation.
+This is supported by the C-C peak at \distn{0.252}, which corresponds to the second next neighbor distance in the diamond structure of elemental C.
+Investigating the atomic data indeed reveals two C atoms, which are bound to and interconnected by a third C atom, to be responsible for this distance.
+The C-C peak at about \distn{0.31}, wich is slightly shifted to higher distances (\distn{0.317}) with increasing temperature still corresponds quite well to the next neighbor distance of C in 3C-SiC as well as a-SiC and indeed results from C-Si-C bonds.
+The Si-C peak at \distn{0.282}, which is pronounced with increasing temperature, is constructed out of a Si atom and a C atom, which are both bound to another central C atom.
+This is similar for the Si-C peak at approximately \distn{0.35}.
+In this case, the Si and the C atom are bound to a central Si atom.