\subsection{Combinations of \si{} and \cs}
\label{subsection:si-cs}
-So far the C-Si \hkl<1 0 0> DB interstitial was found to be the energetically most favorable configuration.
+So far, the C-Si \hkl<1 0 0> DB interstitial was found to be the energetically most favorable configuration.
In fact, substitutional C exhibits a configuration more than \unit[3]{eV} lower with respect to the formation energy.
However, the configuration does not account for the accompanying Si self-interstitial that is generated once a C atom occupies the site of a Si atom.
With regard to the IBS process, in which highly energetic C atoms enter the Si target being able to kick out Si atoms from their lattice sites, such configurations are absolutely conceivable and a significant influence on the precipitation process might be attributed to them.
Thus, combinations of \cs{} and an additional \si{} are examined in the following.
The ground-state of a single \si{} was found to be the \si{} \hkl<1 1 0> DB configuration.
-For the following study the same type of self-interstitial is assumed to provide the energetically most favorable configuration in combination with \cs.
+For the following study, the same type of self-interstitial is assumed to provide the energetically most favorable configuration in combination with \cs.
\begin{table}[tp]
\begin{center}
%
The relaxed structure is displayed in the bottom right of Fig.~\ref{fig:162-097}.
Compressive strain originating from the Si$_{\text{i}}$ is compensated by tensile strain inherent to the C$_{\text{s}}$ configuration.
-The Si$_{\text{i}}$ DB atoms are displaced towards the lattice site occupied by the C$_{\text{s}}$ atom in such a way that the Si$_{\text{i}}$ DB atom closest to the C atom does no longer form bonds to its top Si neighbors, but to the next neighbored Si atom along \hkl[1 1 0].
+The Si$_{\text{i}}$ DB atoms are displaced towards the lattice site occupied by the C$_{\text{s}}$ atom in such a way that the Si$_{\text{i}}$ DB atom closest to the C atom does no longer form bonds to its top Si neighbors but to the next neighbored Si atom along \hkl[1 1 0].
%
In the same way the energetically most unfavorable configuration can be explained, which is configuration \RM{3}.
The \cs{} is located next to the lattice site shared by the \si{} \hkl[1 1 0] DB in \hkl[1 -1 1] direction.
An activation energy as low as \unit[0.12]{eV} is necessary for the migration into the ground-state configuration.
Accordingly, the C$_{\text{i}}$ \hkl<1 0 0> DB configuration is assumed to occur more likely.
However, only \unit[0.77]{eV} are needed for the reverse process, i.e.\ the formation of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB out of the ground state.
-Due to the low activation energy this process must be considered to be activated without much effort either thermally or by introduced energy of the implantation process.
+Due to the low activation energy, this process must be considered to be activated without much effort either thermally or by introduced energy of the implantation process.
\begin{figure}[tp]
\begin{center}
The interaction of the defects is well approximated by a Lennard-Jones (LJ) 6-12 potential, which is used for curve fitting.
Unable to model possible positive values of the binding energy, i.e.\ unfavorable configurations, located to the right of the minimum, the LJ fit should rather be thought of as a guide for the eye describing the decrease of the interaction strength, i.e.\ the absolute value of the binding energy, with increasing separation distance.
The binding energy quickly drops to zero.
-The LJ fit estimates almost zero interaction already at \unit[0.6]{nm}.
- indicating a low interaction capture radius of the defect pair.
+The LJ fit estimates almost zero interaction already at \unit[0.6]{nm} indicating a low interaction capture radius of the defect pair.
%As can be seen, the interaction strength, i.e.\ the absolute value of the binding energy, quickly drops to zero with increasing separation distance.
%Almost zero interaction may be assumed already at distances about \unit[0.5-0.6]{nm}, indicating a low interaction capture radius of the defect pair.
In IBS, highly energetic collisions are assumed to easily produce configurations of defects exhibiting separation distances exceeding the capture radius.
-For this reason C$_{\text{s}}$ without a Si$_{\text{i}}$ DB located within the immediate proximity, which is, thus, unable to form the thermodynamically stable C$_{\text{i}}$ \hkl<1 0 0> DB, constitutes a most likely configuration to be found in IBS.
-In particular in IBS, which constitutes a system driven far from equilibrium, respective defect configurations might exist that do not combine into the ground-state configuration.
+For this reason, C$_{\text{s}}$ without a Si$_{\text{i}}$ DB located within the immediate proximity, which is, thus, unable to form the thermodynamically stable C$_{\text{i}}$ \hkl<1 0 0> DB, constitutes a most likely configuration to be found in IBS.
+Particularly in IBS, which constitutes a system driven far from equilibrium, respective defect configurations might exist that do not combine into the ground-state configuration.
Thus, the existence of C$_{\text{s}}$ is very likely.
\label{section:defects:noneq_process_01}
% the ab initio md, where to put
-Similar to what was previously mentioned, configurations of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB might be particularly important at higher temperatures due to the low activation energy necessary for its formation.
+Similar to what was previously mentioned, configurations of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB might be eminently important at higher temperatures due to the low activation energy necessary for its formation.
At higher temperatures, the contribution of entropy to structural formation increases, which might result in a spatial separation even for defects located within the capture radius.
Indeed, an {\em ab initio} MD run at \unit[900]{$^{\circ}$C} starting from configuration \RM{1}, which -- based on the above findings -- is assumed to recombine into the ground state configuration, results in a separation of the C$_{\text{s}}$ and Si$_{\text{i}}$ DB by more than 4 neighbor distances realized in a repeated migration mechanism of annihilating and arising Si$_{\text{i}}$ DBs.
The atomic configurations for two different points in time are shown in Fig.~\ref{fig:defects:md}.
\end{figure}
The barrier, which is even lower than the one for \ci{}, indeed indicates highly mobile \si.
In fact, a similar transition is expected if the \si{} atom, which does not change the lattice site during transition, is located next to a \cs{} atom.
-Due to the low barrier the initial separation of the \cs{} and \si{} atom are very likely to occur.
+Due to the low barrier, the initial separation of the \cs{} and \si{} atom are very likely to occur.
Further investigations revealed transition barriers of \unit[0.94]{eV} for the Si$_{\text{i}}$ \hkl[1 1 0] DB to the hexagonal Si$_{\text{i}}$, \unit[0.53]{eV} for the Si$_{\text{i}}$ \hkl[1 1 0] DB to the tetrahedral Si$_{\text{i}}$ and \unit[0.35]{eV} for the hexagonal Si$_{\text{i}}$ to the tetrahedral Si$_{\text{i}}$ configuration.
The respective configurational energies are shown in Fig.~\ref{fig:defects:si_mig2}.
\begin{figure}[tp]
\section{Applicability: Competition of \ci{} and \cs-\si{}}
\label{section:ea_app}
-As has been shown, the energetically most favorable configuration of \cs{} and \si{} is obtained for \cs{} located at the neighbored lattice site along the \hkl<1 1 0> bond chain of a Si$_{\text{i}}$ \hkl<1 1 0> DB.
+As has been shown, the energetically most favorable configuration of \cs{} and \si{} is obtained for \cs{} located at the neighbored lattice site along the \hkl[1 1 0] bond chain of a Si$_{\text{i}}$ \hkl[1 1 0] DB.
However, the energy of formation is slightly higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB, which constitutes the ground state for a C impurity introduced into otherwise perfect c-Si.
For a possible clarification of the controversial views on the participation of C$_{\text{s}}$ in the precipitation mechanism by classical potential simulations, test calculations need to ensure the proper description of the relative formation energies of combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ compared to C$_{\text{i}}$.
Contrasts are also assumed for Si$_{\text{i}}$.
Once precipitation occurs, regions of dark contrasts disappear in favor of Moir\'e patterns indicating 3C-SiC in c-Si due to the mismatch in the lattice constant.
Until then, however, these regions could either be composed of stretched coherent SiC and interstitials or of already contracted incoherent SiC surrounded by Si and interstitials, where the latter is too small to be detected in HREM.
-In both cases Si$_{\text{i}}$ might be attributed a third role, which is the partial compensation of tensile strain that is present either in the stretched SiC or at the interface of the contracted SiC and the Si host.
+In both cases, Si$_{\text{i}}$ might be attributed a third role, which is the partial compensation of tensile strain that is present either in the stretched SiC or at the interface of the contracted SiC and the Si host.
Furthermore, the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate is satisfied by the mechanism of successive positioning of C$_{\text{s}}$.
In contrast, 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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