The vast amount of strongly bonded C-C bonds in the high concentration simulations make these configurations energetically more favorable compared to the low concentration configuration.
However, in the same way, a lot of energy is needed to break these bonds to get out of the local energy minimum advancing towards the global minimum configuration.
Thus, such conformational changes are very unlikely to happen.
-This is in accordance with the constant total energy observed in the continuation step of \unit[100]{ps} inbetween the end of C insertion and the cooling process.
+This is in accordance with the constant total energy observed in the continuation step of \unit[100]{ps} in between the end of C insertion and the cooling process.
Obviously, no energetically favorable relaxation is taking place at a system temperature of \unit[450]{$^{\circ}$C}.
The C-C peak at about \unit[0.31]{nm} perfectly matches the nearest neighbor distance of two C atoms in the 3C-SiC lattice.
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}
+\subsection{Low C concentration simulations}
\begin{figure}[tp]
\begin{center}
%
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.
+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.
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 concetration simulations}
+\subsection{High C concentration simulations}
\begin{figure}[tp]
\begin{center}
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}
-
\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 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.
+
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