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, the restructuring of strong C-C bonds is affected \cite{deguchi92}.
-These bonds 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}
-
\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.
\fi
+\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, the restructuring of strong C-C bonds is affected \cite{deguchi92}.
+These bonds 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.
+
+{\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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