+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.
+
+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.
+
+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{}.
+
+
+\section{Conclusions concerning the SiC conversion mechanism}
+
+MD simulations at temperatures used in IBS result in structures that are dominated by the C$_{\text{i}}$ \hkl<1 0 0> DB and its combinations if C is inserted into the total volume.
+Incorporation into volumes $V_2$ and $V_3$ leads to an amorphous SiC-like structure within the respective volume.
+To compensate overestimated diffusion barriers, simulations at accordingly increased temperatures are performed.
+No significant change is observed for high C concentrations.
+The amorphous phase is maintained.
+Due to the incorporation of a huge amount of C into a small volume within a short period of time, damage is produced, which obviously decelerates structural evolution.
+For the low C concentrations, time scales are still too low to observe C agglomeration sufficient for SiC precipitation, which is attributed to the slow phase space propagation inherent to MD in general.
+However, a phase transition of the C$_{\text{i}}$-dominated into a clearly C$_{\text{s}}$-dominated structure is observed.
+The amount of substitutionally occupied C atoms increases with increasing temperature.
+Isolated structures of stretched SiC adjusted to the c-Si host with respect to the lattice constant and alignement are formed.
+Entropic contributions are assumed to be responsible for these structures at elevated temperatures that deviate from the ground state at 0 K.
+
+Results of the MD simulations at different temperatures and C concentrations can be correlated to experimental findings.
+IBS studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates \cite{kimura82,eichhorn02}.
+In particular, restructuring of strong C-C bonds is affected \cite{deguchi92}, which preferentially arise if additional kinetic energy provided by an increase of the implantation temperature is missing to accelerate or even enable atomic rearrangements.
+This is assumed to be related to the problem of slow structural evolution encountered in the high C concentration simulations.
+The insertion of high amounts of C into a small volume within a short period of time resulting in essentially no time for the system to rearrange.
+% rt implantation + annealing
+Furthermore, C implanted at room temperature was found to be able to migrate towards the surface and form C-rich clusters in contrast to implantations at elevated temperatures, which form stable epitaxially aligned 3C-SiC precipitates \cite{serre95}.
+In simulation, low temperatures result in configurations of highly mobile \ci{} \hkl<1 0 0> DBs whereas elevated temperatures show configurations of \cs{}, which constitute an extremely stable configuration that is unlikely to migrate.
+Indeed, in the optimized recipe to form 3C-SiC by IBS \cite{lindner99}, elevated temperatures are used to improve the epitaxial orientation together with a low temperature implant to destroy stable SiC nanocrystals at the interface, which are unable to migrate during thermal annealing resulting in a rough surface.
+Furtermore, the improvement of the epitaxial orientation of the precipitate with increasing temperature in experiment perfectly conforms to the increasing occurrence of \cs{} in simulation.
+At elevated temperatures, implanted C is therefore expected to occupy substitutionally usual Si lattice sites right from the start.
+
+Thus, elevated temperatures are considered to constitute a necessary condition to deviate the system from equilibrium, as it is the case in IBS.
+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 a 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$_{\text{i}}$.
+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.
+
+\ifnum1=0
+
+\section{Valuation of a practicable temperature limit}
+\label{section:md:tval}
+
+The assumed applicability of increased temperature simulations as discussed above and the remaining absence of either agglomeration of substitutional C in low concentration simulations or amorphous to crystalline transition in high concentration simulations suggests to further increase the system temperature.
+So far, the highest temperature applied corresponds to 95 \% of the absolute Si melting temperature, which is 2450 K and specific to the Erhart/Albe potential.
+However, melting is not predicted to occur instantly after exceeding the melting point due to additionally required transition enthalpy and hysteresis behaviour.
+To check for the possibly highest temperature at which a transition fails to appear plain Si is heated up using a heating rate of $1\,^{\circ}\mathrm{C}/\text{ps}$.
+Fig.~\ref{fig:md:fe_and_t} shows the free energy and temperature evolution in the region around the transition temperature.
+Indeed a transition and the accompanying critical behaviour of the free energy is first observed at approximately 3125 K, which corresponds to 128 \% of the Si melting temperature.
+The difference in free energy is 0.58 eV per atom corresponding to $55.7 \text{ kJ/mole}$, which compares quite well to the Si enthalpy of melting of $50.2 \text{ kJ/mole}$.
+The late transition probably occurs due to the high heating rate and, thus, a large hysteresis behaviour extending the temperature of transition.
+To avoid melting transitions in further simulations system temperatures well below the transition point are considered safe.
+According to this study temperatures of 100 \% and 120 \% of the Si melting point could be used.
+However, defects, which are introduced due to the insertion of C atoms are known to lower the transition point.
+Indeed simulations show melting transitions already at the melting point whenever C is inserted.
+Thus, the system temperature of 95 \% of the Si melting point is considered the maximum limit.
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{fe_and_t.ps}
+\end{center}
+\caption{Free energy and temperature evolution of plain Si at temperatures in the region around the melting transition.}
+\label{fig:md:fe_and_t}
+\end{figure}