The highest energy is observed for the hexagonal interstitial configuration using classical potentials.
Quantum-mechanical calculations reveal this configuration to be unstable, which is also reproduced by the EA potential.
-In both cases a relaxation towards the \ci{} \hkl<1 0 0> DB configuration is observed.
+In both cases, a relaxation towards the \ci{} \hkl<1 0 0> DB configuration is observed.
Opposed to results of the first-principles calculations, Tersoff finds this configuration to be stable~\cite{tersoff90}.
In fact, the stability of the hexagonal interstitial could not be reproduced in simulations performed in this work using the unmodified Tersoff potential parameters.
Unfortunately, apart from the modified parameters, no more conditions specifying the relaxation process are given in Tersoff's study on C point defects in Si.
\end{table}
Table~\ref{tab:defects:e_of_comb} summarizes resulting binding energies for the combination with a second \ci{} \hkl<1 0 0> DB obtained for different orientations at positions 1 to 5 after structural relaxation.
Most of the obtained configurations result in binding energies well below zero indicating a preferable agglomeration of this type of defects.
-For increasing distances of the defect pair, the binding energy approaches to zero as it is expected for non-interacting isolated defects.
+For increasing distances of the defect pair, the binding energy approaches to zero as it is expected for non-interacting, isolated defects.
%
In fact, a \ci{} \hkl[0 0 -1] DB interstitial created at position R separated by a distance of $\frac{a_{\text{Si}}}{2}\hkl<3 2 3>$ ($\approx$\unit[12.8]{\AA}) from the initial one results in an energy as low as \unit[-0.19]{eV}.
There is still a low interaction remaining, which is due to the equal orientation of the defects.
\caption[Relaxed structures of defect combinations obtained by creating {\hkl[1 0 0]} and {\hkl[0 1 0]} DBs at position 2 and a {\hkl[0 0 1]} DB at position 3.]{Relaxed structures of defect combinations obtained by creating \hkl[1 0 0] (a) and \hkl[0 1 0] (b) DBs at position 2 and a \hkl[0 0 1] (c) DB at position 3.}
\label{fig:defects:comb_db_02}
\end{figure}
-Fig.~\ref{fig:defects:comb_db_02} shows the next three energetically favorable configurations.
+Fig.~\ref{fig:defects:comb_db_02} shows the three next energetically favorable configurations.
The relaxed configuration obtained by creating a \hkl[1 0 0] DB at position 2 is shown in Fig.~\ref{fig:defects:216}.
A binding energy of \unit[-2.16]{eV} is observed.
After relaxation, the second DB is aligned along \hkl[1 1 0].
Relaxed structures of these combinations are displayed in Fig.~\ref{fig:defects:comb_db_03}.
Fig.~\ref{fig:defects:153} and~\ref{fig:defects:166} show the relaxed structures of \hkl[0 0 1] and \hkl[0 0 -1] DBs.
The upper DB atoms are pushed towards each other forming fourfold coordinated bonds.
-While the displacements of the Si atoms in case (b) are symmetric to the \hkl(1 1 0) plane, in case (a) the Si atom of the initial DB is pushed a little further in the direction of the C atom of the second DB than the C atom is pushed towards the Si atom.
+While the displacements of the Si atoms in case (b) are symmetric to the \hkl(1 1 0) plane, in case (a), the Si atom of the initial DB is pushed a little further in the direction of the C atom of the second DB than the C atom is pushed towards the Si atom.
The bottom atoms of the DBs remain in threefold coordination.
The symmetric configuration is energetically more favorable ($E_{\text{b}}=-1.66\,\text{eV}$) since the displacements of the atoms is less than in the antiparallel case ($E_{\text{b}}=-1.53\,\text{eV}$).
In Fig.~\ref{fig:defects:188} and~\ref{fig:defects:138} the non-parallel orientations, namely the \hkl[0 -1 0] and \hkl[1 0 0] DBs, are shown.
Binding energies of \unit[-1.88]{eV} and \unit[-1.38]{eV} are obtained for the relaxed structures.
-In both cases the Si atom of the initial interstitial is pulled towards the near by atom of the second DB.
+In both cases, the Si atom of the initial interstitial is pulled towards the near by atom of the second DB.
Both atoms form fourfold coordinated bonds to their neighbors.
-In case (c) it is the C and in case (d) the Si atom of the second interstitial, which forms the additional bond with the Si atom of the initial interstitial.
+In case (c), it is the C and in case (d) the Si atom of the second interstitial, which forms the additional bond with the Si atom of the initial interstitial.
The respective atom of the second DB, the \ci{} atom of the initial DB and the two interconnecting Si atoms again reside in a plane.
As observed before, a typical C-C distance of \unit[2.79]{\AA} is, thus, observed for case (c).
In both configurations, the far-off atom of the second DB resides in threefold coordination.
However, if the increase of separation is accompanied by an increase in binding energy, this difference is needed in addition to the activation energy for the respective migration process.
Configurations, which exhibit both, a low binding energy as well as afferent transitions with low activation energies are, thus, most probable C$_{\text{i}}$ complex structures.
On the other hand, if elevated temperatures enable migrations with huge activation energies, comparably small differences in configurational energy can be neglected resulting in an almost equal occupation of such configurations.
-In both cases the configuration yielding a binding energy of \unit[-2.25]{eV} is promising.
+In both cases, the configuration yielding a binding energy of \unit[-2.25]{eV} is promising.
First of all, it constitutes the second most energetically favorable structure.
Secondly, a migration path with a barrier as low as \unit[0.47]{eV} exists starting from a configuration of largely separated defects exhibiting a low binding energy (\unit[-1.88]{eV}).
The migration barrier and corresponding structures are shown in Fig.~\ref{fig:188-225}.
A binding energy of \unit[-0.50]{eV} is observed.
The migration pathways of configuration~\ref{fig:defects:314} and~\ref{fig:defects:059} into the ground-state configuration, i.e.\ the \cs{} configuration, are shown in Fig.~\ref{fig:314-539} and~\ref{fig:059-539} respectively.
-\begin{figure}[tp]
-\begin{center}
-\includegraphics[width=0.7\textwidth]{314-539.ps}
-\end{center}
-\caption[Migration barrier and structures of the transition of the initial C$_{\text{i}}$ {\hkl[0 0 -1]} DB and a V created at position 3 into a C$_{\text{s}}$ configuration.]{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created at position 3 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.1]{eV} is observed.}
-\label{fig:314-539}
-\end{figure}
-\begin{figure}[tp]
-\begin{center}
-\includegraphics[width=0.7\textwidth]{059-539.ps}
-\end{center}
-\caption[Migration barrier and structures of the transition of the initial C$_{\text{i}}$ {\hkl[0 0 -1]} DB and a V created at position 2 into a C$_{\text{s}}$ configuration.]{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created at position 2 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.6]{eV} is observed.}
-\label{fig:059-539}
-\end{figure}
+\begin{figure}[tp]%
+\begin{center}%
+\includegraphics[width=0.7\textwidth]{314-539.ps}%
+\end{center}%
+\caption[Migration barrier and structures of the transition of the initial C$_{\text{i}}$ {\hkl[0 0 -1]} DB and a V created at position 3 into a C$_{\text{s}}$ configuration.]{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created at position 3 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.1]{eV} is observed.}%
+\label{fig:314-539}%
+\end{figure}%
+\begin{figure}[tp]%
+\begin{center}%
+\includegraphics[width=0.7\textwidth]{059-539.ps}%
+\end{center}%
+\caption[Migration barrier and structures of the transition of the initial C$_{\text{i}}$ {\hkl[0 0 -1]} DB and a V created at position 2 into a C$_{\text{s}}$ configuration.]{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created at position 2 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.6]{eV} is observed.}%
+\label{fig:059-539}%
+\end{figure}%
Activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} are observed.
In the first case, the Si and C atom of the DB move towards the vacant and initial DB lattice site respectively.
-In total three Si-Si and one more Si-C bond is formed during transition.
+In total, three Si-Si and one more Si-C bond is formed during transition.
The activation energy of \unit[0.1]{eV} is needed to tilt the DB structure.
Once this barrier is overcome, the C atom forms a bond to the top left Si atom and the \si{} atom capturing the vacant site is forming new tetrahedral bonds to its neighbored Si atoms.
These new bonds and the relaxation into the \cs{} configuration are responsible for the gain in configurational energy.
For the reverse process approximately \unit[2.4]{eV} are needed, which is 24 times higher than the forward process.
In the second case, the lowest barrier is found for the migration of Si number 1, which is substituted by the C$_{\text{i}}$ atom, towards the vacant site.
-A net amount of five Si-Si and one Si-C bond are additionally formed during transition.
+A net amount of five Si-Si bonds and one Si-C bond are additionally formed during transition.
An activation energy of \unit[0.6]{eV} necessary to overcome the migration barrier is found.
This energy is low enough to constitute a feasible mechanism in SiC precipitation.
To reverse this process, \unit[5.4]{eV} are needed, which make this mechanism very improbable.
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.
+Thus, combinations of \cs{} with 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.
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