+\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 structure 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 necessary 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 diamond 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 in between 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 structure turns into a structure characterized by the occurrence 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 alignment, are formed.
+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}
+
+\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 observable.
+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 successively 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}, which 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.
+
+To summarize, the amorphous phase remains.
+Huge amounts of damage hamper identification.
+The alignment of the investigated structures to the c-Si host is lost in many cases, which suggests the necessity of much more time for structural evolution to maintain the topotactic orientation of the precipitate.
+Though, sharper peaks in the radial distributions at distances expected for a-SiC are observed indicating a slight acceleration of the dynamics due to elevated temperatures.
+
+\subsection{Conclusions concerning the usage of increased temperatures}
+
+Regarding the outcome of both, high and low C concentration simulations at increased temperatures, encouraging conclusions can be drawn.
+With the disappearance of the peaks at the respective cut-off radii, one limitation of the short range potential seems to be accomplished.
+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.
+
+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.
+In IBS, highly energetic C atoms are able to generate vacant sites, which in turn can be occupied by highly mobile \ci{} atoms.
+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.
+
+Moreover, the cut-off effect as detailed in section~\ref{section:md:limit} is particularly significant for configurations that are deviated to a great extent from their equilibrium structures.
+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 useful 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
+
+\section{Long time scale simulations at maximum temperature}
+
+As discussed in section~\ref{section:md:limit} and~\ref{section:md:inct}, a further increase of the system temperature might help to overcome limitations of the short range potential and accelerate the dynamics involved in structural evolution.
+Furthermore, these results indicate that increased temperatures are necessary to drive the system out of equilibrium enabling conditions needed for the formation of a metastable cubic polytype of SiC.
+
+A maximum temperature to avoid melting is determined in section~\ref{section:md:tval} to be 120 \% of the Si melting point but due to defects lowering the transition point a maximum temperature of 95 \% of the Si melting temperature is considered useful.
+This value is almost equal to the temperature of $2050\,^{\circ}\mathrm{C}$ already used in former simulations.
+Since the maximum temperature is reached, the approach is reduced to the application of longer time scales.
+This is considered useful since the estimated evolution of quality in the absence of the cooling down sequence in figure~\ref{fig:md:tot_si-c_q} predicts an increase in quality and, thus, structural evolution is likely to occur if the simulation is proceeded at maximum temperature.
+
+Next to the employment of longer time scales and a maximum temperature, a few more changes are applied.
+In the following simulations, the system volume, the amount of C atoms inserted and the shape of the insertion volume are modified from the values used in first MD simulations.
+To speed up the simulation, the initial simulation volume is reduced to 21 Si unit cells in each direction and 5500 inserted C atoms in either the whole volume or in a sphere with a radius of 3 nm corresponding to the size of a precipitate consisting of 5500 C atoms.
+The \unit[100]{ps} sequence after C insertion intended for structural evolution is exchanged by a \unit[10]{ns} sequence, which is hoped to result in the occurrence of infrequent processes and a subsequent phase transition.
+The return to lower temperatures is considered separately.
+
+\begin{figure}[tp]
+\begin{center}
+\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 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 \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}