In IBS experiments, the smallest precipitates observed have radii starting from \unit[2]{nm} up to \unit[4]{nm}.
For the initial simulations, a total amount of 6000 C atoms corresponding to a radius of approximately \unit[3.1]{nm} is chosen.
In separated simulations, the 6000 C atoms are inserted in three regions of different volume ($V_1$, $V_2$, $V_3$) within the simulation cell.
-For reasons of simplification these regions are rectangularly shaped.
+For reasons of simplification, these regions are rectangularly shaped.
$V_1$ is chosen to be the total simulation volume.
$V_2$ approximately corresponds to the volume of a minimal 3C-SiC precipitate.
$V_3$ is approximately the volume containing the amount of Si atoms necessary to form such a precipitate, which is slightly smaller than $V_2$ due to the slightly lower Si density of 3C-SiC compared to c-Si.
-The two latter insertion volumes are considered since no diffusion of C atoms is expected within the simulated period of time at prevalent temperatures.
+The two latter insertion volumes are considered since no long-range diffusion of C atoms is expected within the simulated period of time at prevalent temperatures.
This is due to the overestimated activation energy for the diffusion of a \ci \hkl<1 0 0> DB, as pointed out in section~\ref{subsection:defects:mig_classical}.
For rectangularly shaped precipitates with side length $L$ the amount of C atoms in 3C-SiC and Si atoms in c-Si is given by
\begin{equation}
\end{figure}
The radial distribution function $g(r)$ for C-C and Si-Si distances is shown in Fig.~\ref{fig:md:pc_si-si_c-c}.
-\begin{figure}[tp]
-\begin{center}
- \includegraphics[width=0.7\textwidth]{sic_prec_450_si-si_c-c.ps}
-\end{center}
-\caption[Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of {\unit[450]{$^{\circ}$C}} and cooled down to room temperature.]{Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. The bright blue graph shows the Si-Si radial distribution for pure c-Si. The insets show magnified regions of the respective type of bond.}
-\label{fig:md:pc_si-si_c-c}
-\end{figure}
-\begin{figure}[tp]
-\begin{center}
- \includegraphics[width=0.7\textwidth]{sic_prec_450_energy.ps}
-\end{center}
-\caption[Total energy per atom as a function of time for the whole simulation sequence and for all three types of insertion volumes.]{Total energy per atom as a function of time for the whole simulation sequence and for all three types of insertion volumes. Arrows mark the end of C insertion and the start of the cooling process respectively.}
-\label{fig:md:energy_450}
-\end{figure}
+\begin{figure}[tp]%
+\begin{center}%
+ \includegraphics[width=0.7\textwidth]{sic_prec_450_si-si_c-c.ps}%
+\end{center}%
+\caption[Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of {\unit[450]{$^{\circ}$C}} and cooled down to room temperature.]{Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. The bright blue graph shows the Si-Si radial distribution for pure c-Si. The insets show magnified regions of the respective type of bond.}%
+\label{fig:md:pc_si-si_c-c}%
+\end{figure}%
+\begin{figure}[tp]%
+\begin{center}%
+ \includegraphics[width=0.7\textwidth]{sic_prec_450_energy.ps}%
+\end{center}%
+\caption[Total energy per atom as a function of time for the whole simulation sequence and for all three types of insertion volumes.]{Total energy per atom as a function of time for the whole simulation sequence and for all three types of insertion volumes. Arrows mark the end of C insertion and the start of the cooling process respectively.}%
+\label{fig:md:energy_450}%
+\end{figure}%
It is easily and instantly visible that there is no significant difference among the two simulations of high C concentration.
Thus, in the following, the focus can indeed be directed to low ($V_1$) and high ($V_2$, $V_3$) C concentration simulations.
The first C-C peak appears at about \unit[0.15]{nm}, which is comparable to the nearest neighbor distance of graphite or diamond.
The bottom of Fig.~\ref{fig:md:pc_si-si_c-c} shows the radial distribution of Si-Si bonds together with a reference graph for pure c-Si.
Indeed, non-zero $g(r)$ values around \unit[0.31]{nm} are observed while the amount of Si pairs at regular c-Si distances of \unit[0.24]{nm} and \unit[0.38]{nm} decreases.
However, no clear peak is observed but the interval of enhanced $g(r)$ values corresponds to the width of the C-C $g(r)$ peak.
-In addition the abrupt increase of Si pairs at \unit[0.29]{nm} can be attributed to the Si-Si cut-off radius of \unit[0.296]{nm} as used in the present bond order potential.
+In addition, the abrupt increase of Si pairs at \unit[0.29]{nm} can be attributed to the Si-Si cut-off radius of \unit[0.296]{nm} as used in the present bond order potential.
The cut-off function causes artificial forces pushing the Si atoms out of the cut-off region.
Without the abrupt increase, a maximum around \unit[0.31]{nm} gets even more conceivable.
Analyses of randomly chosen configurations, in which distances around \unit[0.3]{nm} appear, identify \ci{} \hkl<1 0 0> DBs to be responsible for stretching the Si-Si next neighbor distance for low C concentrations, i.e.\ for the $V_1$ and early stages of $V_2$ and $V_3$ simulation runs.
The first peak observed for all insertion volumes is at approximately \unit[0.186]{nm}.
This corresponds quite well to the expected next neighbor distance of \unit[0.189]{nm} for Si and C atoms in 3C-SiC.
By comparing the resulting Si-C bonds of a \ci{} \hkl<1 0 0> DB with the C-Si distances of the low concentration simulation, it is evident that the resulting structure of the $V_1$ simulation is clearly dominated by this type of defect.
-This is not surprising, since the \ci{} \hkl<1 0 0> DB is found to be the ground-state defect of a C interstitial in c-Si and, for the low concentration simulations, a C interstitial is expected in every fifth Si unit cell only, thus, excluding defect superposition phenomena.
+This is not surprising since the \ci{} \hkl<1 0 0> DB is found to be the ground-state defect of a C interstitial in c-Si and, for the low concentration simulations, a C interstitial is expected in every fifth Si unit cell only, thus, excluding defect superposition phenomena.
The peak distance at \unit[0.186]{nm} and the bump at \unit[0.175]{nm} corresponds to the distance $r(3C)$ and $r(1C)$ as listed in Table~\ref{tab:defects:100db_cmp} and visualized in Fig.~\ref{fig:defects:100db_cmp}.
In addition, it can be easily identified that the \ci{} \hkl<1 0 0> DB configuration contributes to the peaks at about \unit[0.335]{nm}, \unit[0.386]{nm}, \unit[0.434]{nm}, \unit[0.469]{nm} and \unit[0.546]{nm} observed in the $V_1$ simulation.
Not only the peak locations but also the peak widths and heights become comprehensible.
The consequential superposition of these defects and the high amounts of damage generate new displacement arrangements for the C-C as well as for the Si-C pair distances, which become hard to categorize and trace and obviously lead to a broader distribution.
Short range order indeed is observed, i.e.\ the large amount of strong neighbored C-C bonds at \unit[0.15]{nm} as expected in graphite or diamond and Si-C bonds at \unit[0.19]{nm} as expected in SiC, but only hardly visible is the long range order.
This indicates the formation of an amorphous SiC-like phase.
-In fact the resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modified Tersoff potential~\cite{gao02}.
+In fact, the resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modified Tersoff potential~\cite{gao02}.
In both cases, i.e.\ low and high C concentrations, the formation of 3C-SiC fails to appear.
With respect to the precipitation model, the formation of C$_{\text{i}}$ \hkl<1 0 0> DBs indeed occurs for low C concentrations.
Results of the last section indicate possible limitations of the MD method regarding the task addressed in this study.
Low C concentration simulations do not reproduce the agglomeration of C$_{\text{i}}$ \hkl<1 0 0> DBs.
High concentration simulations result in the formation of an amorphous SiC-like phase, which is unexpected since IBS experiments show crystalline 3C-SiC precipitates at prevailing temperatures.
-Keeping in mind the results
+%Keeping in mind the results
On closer inspection, however, two reasons for describing this obstacle become evident, which are discussed in the following.
The first reason is a general problem of MD simulations in conjunction with limitations in computer power, which results in a slow and restricted propagation in phase space.
One possibility is to simply skip the force contributions containing the derivatives of the cut-off function, which was successfully applied to reproduce the brittle propagation of fracture in SiC at zero temperature~\cite{mattoni2007}.
Another one is to use variable cut-off values scaled by the system volume, which properly describes thermomechanical properties of 3C-SiC~\cite{tang95} but might be rather ineffective for the challenge inherent to this study.
-To conclude the obstacle needed to get passed is twofold.
+To conclude, the obstacle needed to get passed is twofold.
The sharp cut-off of the employed bond order model potential introduces overestimated high forces between next neighbored atoms enhancing the problem of slow phase space propagation immanent to MD simulations.
This obstacle could be referred to as {\em potential enhanced slow phase space propagation}.
Due to this, pushing the time scale to the limits of computational resources or applying one of the above mentioned accelerated dynamics methods exclusively will not be sufficient enough.
The TAD corrections are not applied in coming up simulations.
This is justified by two reasons.
First of all, a compensation of the overestimated bond strengths due to the short range potential is expected.
-Secondly, there is no conflict applying higher temperatures without the TAD corrections, since crystalline 3C-SiC is also observed for higher temperatures than \unit[450]{$^{\circ}$C} in IBS~\cite{nejim95,lindner01}.
+Secondly, there is no conflict applying higher temperatures without the TAD corrections since crystalline 3C-SiC is also observed for higher temperatures than \unit[450]{$^{\circ}$C} in IBS~\cite{nejim95,lindner01}.
It is therefore expected that the kinetics affecting the 3C-SiC precipitation are not much different at higher temperatures aside from the fact that it is occurring much more faster.
Moreover, the interest of this study is focused on structural evolution of a system far from equilibrium instead of equilibrium properties which rely upon proper phase space sampling.
On the other hand, during implantation, the actual temperature inside the implantation volume is definitely higher than the experimentally determined temperature tapped from the surface of the sample.
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.
+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}
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 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.
\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.
+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.
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.
+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.
+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.
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