Regarding the supposed conversion mechanisms of SiC in c-Si as introduced in section~\ref{section:assumed_prec}, the understanding of C and Si interstitial point defects in c-Si is of fundamental interest.
During implantation, defects such as vacancies (V), substitutional C (C$_{\text{s}}$), interstitial C (C$_{\text{i}}$) and Si self-interstitials (Si$_{\text{i}}$) are created, which are believed to play a decisive role in the precipitation process.
-In the following, these defects are systematically examined by computationally efficient, classical potential as well as highly accurate DFT calculations with the parameters and simulation conditions that are defined in chapter~\ref{chapter:simulation}.
+In the following, these defects are systematically examined by computationally efficient classical potential as well as highly accurate DFT calculations with the parameters and simulation conditions that are defined in chapter~\ref{chapter:simulation}.
Both methods are used to investigate selected diffusion processes of some of the defect configurations.
While the quantum-mechanical description yields results that excellently compare to experimental findings, shortcomings of the classical potential approach are identified.
These shortcomings are further investigated and the basis for a workaround, as proposed later on in the classical MD simulation chapter, is discussed.
However, the implantation of highly energetic C atoms results in a multiplicity of possible defect configurations.
Next to individual Si$_{\text{i}}$, C$_{\text{i}}$, V and C$_{\text{s}}$ defects, combinations of these defects and their interaction are considered important for the problem under study.
-Thus, the study proceeds examining pairs of most probable defect configurations and related diffusion processes exclusively by first-principles methods.
+Thus, investigations proceed examining pairs of most probable defect configurations and related diffusion processes exclusively by first-principles methods.
These systems can still be described by the highly accurate but computationally costly method.
Respective results allow to draw conclusions concerning the SiC precipitation in Si.
For investigating the \si{} structures, a Si atom is inserted or removed according to Fig.~\ref{fig:basics:ins_pos} of section~\ref{section:basics:defects}.
The formation energies of \si{} configurations are listed in Table~\ref{tab:defects:si_self} for both methods used in this work as well as results obtained by other {\em ab initio} studies~\cite{al-mushadani03,leung99}.
-\bibpunct{}{}{,}{n}{}{}
-\begin{table}[tp]
-\begin{center}
-\begin{tabular}{l c c c c c}
-\hline
-\hline
- & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
-\hline
-\multicolumn{6}{c}{Present study} \\
-\textsc{vasp} & 3.39 & 3.42 & 3.77 & 4.41 & 3.63 \\
-\textsc{posic} & 4.39 & 4.48$^*$ & 3.40 & 5.42 & 3.13 \\
-\multicolumn{6}{c}{Other {\em ab initio} studies} \\
-Ref.~\cite{al-mushadani03} & 3.40 & 3.45 & - & - & 3.53 \\
-Ref.~\cite{leung99} & 3.31 & 3.31 & 3.43 & - & - \\
-\hline
-\hline
-\end{tabular}
-\end{center}
-\caption[Formation energies of Si self-interstitials in crystalline Si determined by classical potential MD and DFT calculations.]{Formation energies of Si self-interstitials in crystalline Si determined by classical potential MD and DFT calculations. The formation energies are given in eV. T denotes the tetrahedral and H the hexagonal interstitial configuration. V corresponds to the vacancy configuration. Dumbbell configurations are abbreviated by DB. Formation energies for unstable configurations are marked by an asterisk and determined by using the low kinetic energy configuration shortly before the relaxation into the more favorable configuration starts.}
-\label{tab:defects:si_self}
-\end{table}
-\bibpunct{[}{]}{,}{n}{}{}
-\begin{figure}[tp]
-\begin{center}
-\begin{flushleft}
-\begin{minipage}{5cm}
-\underline{Tetrahedral}\\
-$E_{\text{f}}=3.40\,\text{eV}$\\
-\includegraphics[width=4.0cm]{si_pd_albe/tet_bonds.eps}
-\end{minipage}
-\begin{minipage}{10cm}
-\underline{Hexagonal}\\[0.1cm]
-\begin{minipage}{4cm}
-$E_{\text{f}}^*=4.48\,\text{eV}$\\
-\includegraphics[width=4.0cm]{si_pd_albe/hex_a_bonds.eps}
-\end{minipage}
-\begin{minipage}{0.8cm}
-\begin{center}
-$\Rightarrow$
-\end{center}
-\end{minipage}
-\begin{minipage}{4cm}
-$E_{\text{f}}=3.96\,\text{eV}$\\
-\includegraphics[width=4.0cm]{si_pd_albe/hex_bonds.eps}
-\end{minipage}
-\end{minipage}\\[0.2cm]
-\begin{minipage}{5cm}
-\underline{\hkl<1 0 0> dumbbell}\\
-$E_{\text{f}}=5.42\,\text{eV}$\\
-\includegraphics[width=4.0cm]{si_pd_albe/100_bonds.eps}
-\end{minipage}
-\begin{minipage}{5cm}
-\underline{\hkl<1 1 0> dumbbell}\\
-$E_{\text{f}}=4.39\,\text{eV}$\\
-\includegraphics[width=4.0cm]{si_pd_albe/110_bonds.eps}
-\end{minipage}
-\begin{minipage}{5cm}
-\underline{Vacancy}\\
-$E_{\text{f}}=3.13\,\text{eV}$\\
-\includegraphics[width=4.0cm]{si_pd_albe/vac.eps}
-\end{minipage}
-\end{flushleft}
-%\hrule
-\end{center}
-\caption[Relaxed Si self-interstitial defect configurations obtained by classical potential calculations.]{Relaxed Si self-interstitial defect configurations obtained by classical potential calculations. Si atoms and bonds are illustrated by yellow spheres and blue lines. Bonds of the defect atoms are drawn in red color.}
-\label{fig:defects:conf}
-\end{figure}
+\bibpunct{}{}{,}{n}{}{}%
+\begin{table}[tp]%
+\begin{center}%
+\begin{tabular}{l c c c c c}%
+\hline%
+\hline%
+ & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\%
+\hline%
+\multicolumn{6}{c}{Present study} \\%
+\textsc{vasp} & 3.39 & 3.42 & 3.77 & 4.41 & 3.63 \\%
+\textsc{posic} & 4.39 & 4.48$^*$ & 3.40 & 5.42 & 3.13 \\%
+\multicolumn{6}{c}{Other {\em ab initio} studies} \\%
+Ref.~\cite{al-mushadani03} & 3.40 & 3.45 & - & - & 3.53 \\%
+Ref.~\cite{leung99} & 3.31 & 3.31 & 3.43 & - & - \\%
+\hline%
+\hline%
+\end{tabular}%
+\end{center}%
+\caption[Formation energies of Si self-interstitials in crystalline Si determined by classical potential MD and DFT calculations.]{Formation energies of Si self-interstitials in crystalline Si determined by classical potential MD and DFT calculations. The formation energies are given in eV. T denotes the tetrahedral and H the hexagonal interstitial configuration. V corresponds to the vacancy configuration. Dumbbell configurations are abbreviated by DB. Formation energies for unstable configurations are marked by an asterisk and determined by using the low kinetic energy configuration shortly before the relaxation into the more favorable configuration starts.}%
+\label{tab:defects:si_self}%
+\end{table}%
+\bibpunct{[}{]}{,}{n}{}{}%
+\begin{figure}[tp]%
+\begin{center}%
+\begin{flushleft}%
+\begin{minipage}{5cm}%
+\underline{Tetrahedral}\\%
+$E_{\text{f}}=3.40\,\text{eV}$\\%
+\includegraphics[width=4.0cm]{si_pd_albe/tet_bonds.eps}%
+\end{minipage}%
+\begin{minipage}{10cm}%
+\underline{Hexagonal}\\[0.1cm]%
+\begin{minipage}{4cm}%
+$E_{\text{f}}^*=4.48\,\text{eV}$\\%
+\includegraphics[width=4.0cm]{si_pd_albe/hex_a_bonds.eps}%
+\end{minipage}%
+\begin{minipage}{0.8cm}%
+\begin{center}%
+$\Rightarrow$%
+\end{center}%
+\end{minipage}%
+\begin{minipage}{4cm}%
+$E_{\text{f}}=3.96\,\text{eV}$\\%
+\includegraphics[width=4.0cm]{si_pd_albe/hex_bonds.eps}%
+\end{minipage}%
+\end{minipage}\\[0.2cm]%
+\begin{minipage}{5cm}%
+\underline{\hkl<1 0 0> dumbbell}\\%
+$E_{\text{f}}=5.42\,\text{eV}$\\%
+\includegraphics[width=4.0cm]{si_pd_albe/100_bonds.eps}%
+\end{minipage}%
+\begin{minipage}{5cm}%
+\underline{\hkl<1 1 0> dumbbell}\\%
+$E_{\text{f}}=4.39\,\text{eV}$\\%
+\includegraphics[width=4.0cm]{si_pd_albe/110_bonds.eps}%
+\end{minipage}%
+\begin{minipage}{5cm}%
+\underline{Vacancy}\\%
+$E_{\text{f}}=3.13\,\text{eV}$\\%
+\includegraphics[width=4.0cm]{si_pd_albe/vac.eps}%
+\end{minipage}%
+\end{flushleft}%
+%\hrule%
+\end{center}%
+\caption[Relaxed Si self-interstitial defect configurations obtained by classical potential calculations.]{Relaxed Si self-interstitial defect configurations obtained by classical potential calculations. Si atoms and bonds are illustrated by yellow spheres and blue lines. Bonds of the defect atoms are drawn in red color.}%
+\label{fig:defects:conf}%
+\end{figure}%
The final configurations obtained after relaxation are presented in Fig.~\ref{fig:defects:conf}.
The displayed structures are the results of the classical potential simulations.
To exclude failures in the implementation of the potential or the MD code itself, the hexagonal defect structure was double-checked with the \textsc{parcas} MD code~\cite{parcas_md}.
The respective relaxation energetics are likewise plotted and look similar to the energetics obtained by \textsc{posic}.
In fact, the same type of interstitial arises using random insertions.
-In addition, variations exist, in which the displacement is only along two \hkl<1 0 0> axes ($E_\text{f}=3.8\,\text{eV}$) or along a single \hkl<1 0 0> axes ($E_\text{f}=3.6\,\text{eV}$) successively approximating the tetrahedral configuration and formation energy.
+In addition, variations exist, in which the displacement is only along two \hkl<1 0 0> axes ($E_\text{f}=3.8\,\text{eV}$) or along a single \hkl<1 0 0> axis ($E_\text{f}=3.6\,\text{eV}$) successively approximating the tetrahedral configuration and formation energy.
The existence of these local minima located near the tetrahedral configuration seems to be an artifact of the analytical potential without physical authenticity revealing fundamental problems of analytical potential models for describing defect structures.
However, the energy barrier required for a transition into the tetrahedral configuration is small.
\begin{figure}[tp]
The \si{} \hkl<1 0 0> DB constitutes the most unfavorable configuration for both, the EA and \textsc{vasp} calculations.
The quantum-mechanical treatment of the \si{} \hkl<1 0 0> DB demands for spin polarized calculations.
The same applies for the vacancy.
-In the \si{} \hkl<1 0 0> DB configuration the net spin up density is localized in two caps at each of the two DB atoms perpendicularly aligned to the bonds to the other two Si atoms respectively.
-For the vacancy the net spin up electron density is localized in caps at the four surrounding Si atoms directed towards the vacant site.
+In the \si{} \hkl<1 0 0> DB configuration, the net spin up density is localized in two caps at each of the two DB atoms perpendicularly aligned to the bonds to the other two Si atoms respectively.
+For the vacancy, the net spin up electron density is localized in caps at the four surrounding Si atoms directed towards the vacant site.
No other intrinsic defect configuration, within the ones that are mentioned, is affected by spin polarization.
In the case of the classical potential simulations, bonds between atoms are displayed if there is an interaction according to the potential model, i.e.\ if the distance of two atoms is within the cut-off radius $S_{ij}$ introduced in equation \eqref{eq:basics:fc}.
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.
The fact that the tetrahedral and hexagonal configurations are the two most unstable configurations in classical potential calculations and, thus, are less likely to arise in MD simulations, acts in concert with the fact that these configurations are found to be unstable in the more accurate quantum-mechanical description.
Just as for \si{}, a \ci{} \hkl<1 1 0> DB configuration exists.
-It constitutes the second most favorable configuration, reproduced by both methods.
+It constitutes the second most favorable configuration, which is reproduced by both methods.
Similar structures arise in both types of simulations.
The Si and C atom share a regular Si lattice site aligned along the \hkl<1 1 0> direction.
The C atom is slightly displaced towards the next nearest Si atom located in the opposite direction with respect to the site-sharing Si atom and even forms a bond with this atom.
The \ci{} \hkl<1 1 0> DB structure is energetically followed by the BC configuration.
-However, even though EA based results yield the same difference in energy with respect to the \hkl<1 1 0> defect as DFT does, the BC configuration is found to be a unstable within the EA description.
+However, even though EA based results yield the same difference in energy with respect to the \hkl<1 1 0> defect as DFT does, the BC configuration is found to be unstable within the EA description.
The BC configuration descends into the \ci{} \hkl<1 1 0> DB configuration.
Due to the high formation energy of the BC defect resulting in a low probability of occurrence of this defect, the wrong description is not posing a serious limitation of the EA potential.
Tersoff indeed predicts a metastable BC configuration.
The two lower Si atoms are $sp^3$ hybridized and form $\sigma$ bonds to the Si DB atom.
The same is true for the upper two Si atoms and the C DB atom.
In addition, the DB atoms form $\pi$ bonds.
-However, due to the increased electronegativity of the C atom the electron density is attracted by and, thus, localized around the C atom.
+However, due to the increased electronegativity of the C atom, the electron density is attracted by and, thus, localized around the C atom.
In the same figure the Kohn-Sham levels are shown.
There is no magnetization density.
An acceptor level arises at approximately $E_v+0.35\,\text{eV}$ while a band gap of about \unit[0.75]{eV} can be estimated from the Kohn-Sham level diagram for plain Si.
\label{img:defects:c_mig_path}
\end{figure}
Three different migration paths are accounted in this work, which are displayed in Fig.~\ref{img:defects:c_mig_path}.
-The first migration investigated is a transition of a \hkl[0 0 -1] into a \hkl[0 0 1] DB interstitial configuration.
+The first investigated migration is a transition of a \hkl[0 0 -1] into a \hkl[0 0 1] DB interstitial configuration.
During this migration the C atom is changing its Si DB partner.
The new partner is the one located at $a_{\text{Si}}/4 \hkl[1 1 -1]$ relative to the initial one, where $a_{\text{Si}}$ is the Si lattice constant.
Two of the three bonds to the next neighbored Si atoms are preserved while the breaking of the third bond and the accompanying formation of a new bond is observed.
Figures~\ref{fig:defects:cp_00-1_0-10_mig} and~\ref{fig:defects:cp_00-1_ip0-10_mig} show the migration barriers of the \ci{} \hkl[0 0 -1] to \hkl[0 -1 0] DB transition.
In the first case, the transition involves a change in the lattice site of the C atom whereas in the second case, a reorientation at the same lattice site takes place.
In the first case, the pathways for the two different time constants look similar.
-A local minimum exists in between two peaks of the graph.
+A local minimum exists in between the two peaks of the graph.
The corresponding configuration, which is illustrated for the results obtained for a time constant of \unit[1]{fs}, looks similar to the \ci{} \hkl[1 1 0] configuration.
-Indeed, this configuration is obtained by relaxation simulations without constraints of configurations near the minimum.
+Indeed, this configuration is obtained by relaxation simulations without constraints of configurations near this local minimum.
Activation energies of roughly \unit[2.8]{eV} and \unit[2.7]{eV} are needed for migration.
The \ci{} \hkl[1 1 0] configuration seems to play a decisive role in all migration pathways in the classical potential calculations.
As expected, there is no maximum for the transition into the BC configuration.
As mentioned earlier, the BC configuration itself constitutes a saddle point configuration relaxing into the energetically more favorable \hkl[1 1 0] DB configuration.
An activation energy of \unit[2.2]{eV} is necessary to reorientate the \hkl[0 0 -1] into the \hkl[1 1 0] DB configuration, which is \unit[1.3]{eV} higher in energy.
-Residing in this state another \unit[0.90]{eV} is enough to make the C atom form a \hkl[0 0 -1] DB configuration with the Si atom of the neighbored lattice site.
+Residing in this state, another \unit[0.90]{eV} is enough to make the C atom form a \hkl[0 0 -1] DB configuration with the Si atom of the neighbored lattice site.
In contrast to quantum-mechanical calculations, in which the direct transition is the energetically most favorable transition and the transition composed of the intermediate migration steps is very unlikely to occur, the just presented pathway is much more conceivable in classical potential simulations since the energetically most favorable transition found so far is likewise composed of two migration steps with activation energies of \unit[2.2]{eV} and \unit[0.5]{eV}, for which the intermediate state is the BC configuration, which is unstable.
-Thus, the just proposed migration path, which involves the \hkl[1 1 0] interstitial configuration, becomes even more probable than the initially proposed path, which involves the BC configuration that is, in fact, unstable.
+Thus, the just proposed migration path, which involves the \hkl[1 1 0] interstitial configuration, becomes even more probable than the initially proposed path involving the BC configuration.
Due to these findings, the respective path is proposed to constitute the diffusion-describing path.
The evolution of structure and configurational energy is displayed again in Fig.~\ref{fig:defects:involve110}.
\begin{figure}[tp]
\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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