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.
-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.
+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.
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}.
Approximately \unit[2.2]{eV} are needed to turn the \ci{} \hkl[0 0 -1] into the \hkl[1 1 0] DB located at the neighbored lattice site in \hkl[1 1 -1] direction.
Another barrier of \unit[0.90]{eV} exists for the rotation into the \ci{} \hkl[0 -1 0] DB configuration for the path obtained with a time constant of \unit[100]{fs} for the Berendsen thermostat.
Roughly the same amount would be necessary to excite the C$_{\text{i}}$ \hkl[1 1 0] DB to the BC configuration (\unit[0.40]{eV}) and a successive migration into the \hkl[0 0 1] DB configuration (\unit[0.50]{eV}) as displayed in Fig.~\ref{fig:defects:110_mig} and Fig.~\ref{fig:defects:cp_bc_00-1_mig}.
-The former diffusion process, however, would more nicely agree with the {\em ab initio} path, since the migration is accompanied by a rotation of the DB orientation.
+The former diffusion process, however, would more nicely agree with the {\em ab initio} path since the migration is accompanied by a rotation of the DB orientation.
By considering a two step process and assuming equal preexponential factors for both diffusion steps, the probability of the total diffusion event is given by $\exp(\frac{\unit[2.24]{eV}+\unit[0.90]{eV}}{k_{\text{B}}T})$, which corresponds to a single diffusion barrier that is 3.5 times higher than the barrier obtained by {\em ab initio} calculations.
\subsection{Conclusions}
\label{tab:defects:e_of_comb}
\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 the defects.
+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.
%
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.
-By changing the orientation of the second DB interstitial to the \hkl<0 -1 0>-type, the interaction is even more reduced resulting in an energy of \unit[-0.05]{eV} for a distance, which is the maximum that can be realized due to periodic boundary conditions.
+By changing the orientation of the second DB interstitial to the \hkl[0 -1 0]-type, the interaction is even more reduced resulting in an energy of \unit[-0.05]{eV} for a distance, which is the maximum that can be realized due to periodic boundary conditions.
Energetically favorable and unfavorable configurations can be explained by stress compensation and increase respectively based on the resulting net strain of the respective configuration of the defect combination.
Antiparallel orientations of the second defect, i.e.\ \hkl[0 0 1] for positions located below the \hkl(0 0 1) plane with respect to the initial one (positions 1, 2 and 4) form the energetically most unfavorable configurations.
In contrast, the parallel and particularly the twisted orientations constitute energetically favorable configurations, in which a vast reduction of strain is enabled by combination of these defects.
\caption[Relaxed structures of defect combinations obtained by creating {\hkl[1 0 0]} and {\hkl[0 -1 0]} DBs at position 1.]{Relaxed structures of defect combinations obtained by creating \hkl[1 0 0] (a) and \hkl[0 -1 0] (b) DBs at position 1.}
\label{fig:defects:comb_db_01}
\end{figure}
-Mattoni~et~al.~\cite{mattoni2002} predict the ground-state configuration of \ci{} \hkl<1 0 0>-type defect pairs for a \hkl[1 0 0] or equivalently a \hkl[0 1 0] defect created at position 1 with both defects basically maintaining the as-isolated DB structure, resulting in a binding energy of \unit[-2.1]{eV}.
+Mattoni~et~al.~\cite{mattoni2002} predict the ground-state configuration of \ci{} \hkl<1 0 0>-type defect pairs for a \hkl[1 0 0] or equivalently a \hkl[0 1 0] defect created at position 1 with both defects basically maintaining the as-isolated DB structure resulting in a binding energy of \unit[-2.1]{eV}.
In the present study, a further relaxation of this defect structure is observed.
The C atom of the second and the Si atom of the initial DB move towards each other forming a bond, which results in a somewhat lower binding energy of \unit[-2.25]{eV}.
The corresponding defect structure is displayed in Fig.~\ref{fig:defects:225}.
The interaction of \ci{} \hkl<1 0 0> DBs is investigated along the \hkl[1 1 0] bond chain assuming a possible reorientation of the DB atom at each position to minimize its configurational energy.
Therefor, the binding energies of the energetically most favorable configurations with the second DB located along the \hkl[1 1 0] direction and resulting C-C distances of the relaxed structures are summarized in Table~\ref{tab:defects:comb_db110}.
-\begin{table}[tp]
-\begin{center}
-\begin{tabular}{l c c c c c c}
-\hline
-\hline
- & 1 & 2 & 3 & 4 & 5 & 6\\
-\hline
-$E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
-C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
-Type & \hkl[-1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \hkl[1 0 0], \hkl[0 -1 0]\\
-\hline
-\hline
-\end{tabular}
-\end{center}
-\caption{Binding energies $E_{\text{b}}$, C-C distance and types of energetically most favorable \ci{} \hkl<1 0 0>-type defect pairs separated along the \hkl[1 1 0] bond chain.}
-\label{tab:defects:comb_db110}
-\end{table}
-%
-\begin{figure}[tp]
-\begin{center}
-\includegraphics[width=0.7\textwidth]{db_along_110_cc_n.ps}
-\end{center}
-\caption[Minimum binding energy of DB combinations separated along {\hkl[1 1 0]} with respect to the C-C distance.]{Minimum binding energy of dumbbell combinations separated along \hkl[1 1 0] with respect to the C-C distance. The blue line is a guide for the eye and the green curve corresponds to the most suitable fit function consisting of all but the first data point.}
-\label{fig:defects:comb_db110}
-\end{figure}
+\begin{table}[tp]%
+\begin{center}%
+\begin{tabular}{l c c c c c c}%
+\hline%
+\hline%
+ & 1 & 2 & 3 & 4 & 5 & 6\\%
+\hline%
+$E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\%
+C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\%
+Type & \hkl[-1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \hkl[1 0 0], \hkl[0 -1 0]\\%
+\hline%
+\hline%
+\end{tabular}%
+\end{center}%
+\caption{Binding energies $E_{\text{b}}$, C-C distance and types of energetically most favorable \ci{} \hkl<1 0 0>-type defect pairs separated along the \hkl[1 1 0] bond chain.}%
+\label{tab:defects:comb_db110}%
+\end{table}%
+\begin{figure}[tp]%
+\begin{center}%
+\includegraphics[width=0.7\textwidth]{db_along_110_cc_n.ps}%
+\end{center}%
+\caption[Minimum binding energy of DB combinations separated along {\hkl[1 1 0]} with respect to the C-C distance.]{Minimum binding energy of dumbbell combinations separated along \hkl[1 1 0] with respect to the C-C distance. The blue line is a guide for the eye and the green curve corresponds to the most suitable fit function consisting of all but the first data point.}%
+\label{fig:defects:comb_db110}%
+\end{figure}%
The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:defects:comb_db110}.
The interaction is found to be proportional to the reciprocal cube of the C-C distance for extended separations of the \ci{} DBs and saturates for the smallest possible separation, i.e.\ the ground-state configuration.
The ground-state configuration was ignored in the fitting process.
%\subsection{Diffusion processes among configurations of \ci{} pairs}
To draw further conclusions on the probability of C clustering, transitions into the ground-state configuration are investigated.
-Based on the lowest energy migration path of a single \ci{} \hkl<1 0 0> DB, the configuration, in which the second \ci{} DB is oriented along \hkl[0 1 0] at position 2 is assumed to constitute an ideal starting point for a transition into the ground state.
+Based on the lowest energy migration path of a single \ci{} \hkl<1 0 0> DB, the configuration, in which the second \ci{} DB is oriented along \hkl[0 1 0] at position 2, is assumed to constitute an ideal starting point for a transition into the ground state.
In addition, the starting configuration exhibits a low binding energy (\unit[-1.90]{eV}) and is, thus, very likely to occur.
However, a smooth transition path is not found.
Intermediate configurations within the investigated turbulent pathway identify barrier heights of more than \unit[4]{eV} resulting in a low probability for the transition.
Configuration $\alpha$ is similar to configuration A, except that the C$_{\text{s}}$ atom at position 1 is facing the C DB atom as a neighbor resulting in the formation of a strong C-C bond and a much more noticeable perturbation of the DB structure.
Nevertheless, the C and Si DB atoms remain threefold coordinated.
Although the C-C bond exhibiting a distance of \unit[0.15]{nm} close to the distance expected in diamond or graphite should lead to a huge gain in energy, a repulsive interaction with a binding energy of \unit[0.26]{eV} is observed due to compressive strain of the Si DB atom and its top neighbors (\unit[0.230]{nm}/\unit[0.236]{nm}) along with additional tensile strain of the C$_{\text{s}}$ and its three neighboring Si atoms (\unit[0.198--0.209]{nm}/\unit[0.189]{nm}).
-Again a single bond switch, i.e.\ the breaking of the bond of the Si atom bound to the fourfold coordinated C$_{\text{s}}$ atom and the formation of a double bond between the two C atoms, results in configuration b.
+Again, a single bond switch, i.e.\ the breaking of the bond of the Si atom bound to the fourfold coordinated C$_{\text{s}}$ atom and the formation of a double bond between the two C atoms, results in configuration b.
The two C atoms form a \hkl[1 0 0] DB sharing the initial C$_{\text{s}}$ lattice site while the initial Si DB atom occupies its previously regular lattice site.
-The transition is accompanied by a large gain in energy as can be seen in Fig.~\ref{fig:026-128}, making it the ground-state configuration of a C$_{\text{s}}$ and C$_{\text{i}}$ DB in Si yet \unit[0.33]{eV} lower in energy than configuration B.
+The transition is accompanied by a large gain in energy as can be seen in Fig.~\ref{fig:026-128} making it the ground-state configuration of a C$_{\text{s}}$ and C$_{\text{i}}$ DB in Si yet \unit[0.33]{eV} lower in energy than configuration B.
This finding is in good agreement with a combined {\em ab initio} and experimental study of Liu et~al.~\cite{liu02}, who first proposed this structure as the ground state identifying an energy difference compared to configuration B of \unit[0.2]{eV}.
% mattoni: A favored by 0.2 eV - NO! (again, missing spin polarization?)
A net magnetization of two spin up electrons, which are equally localized as in the Si$_{\text{i}}$ \hkl<1 0 0> DB structure is observed.
Configurations $\alpha$, A and B are not affected by spin polarization and show zero magnetization.
Mattoni et~al.~\cite{mattoni2002}, in contrast, find configuration $\beta$ less favorable than configuration A by \unit[0.2]{eV}.
Next to differences in the XC functional and plane-wave energy cut-off, this discrepancy might be attributed to the neglect of spin polarization in their calculations, which -- as has been shown for the C$_{\text{i}}$ BC configuration -- results in an increase of configurational energy.
-Indeed, investigating the migration path from configurations $\alpha$ to $\beta$ and, in doing so, reusing the wave functions of the previous migration step the final structure, i.e.\ configuration $\beta$, is obtained with zero magnetization and an increase in configurational energy by \unit[0.2]{eV}.
-Obviously a different energy minimum of the electronic system is obtained indicating hysteresis behavior.
-However, since the total energy is lower for the magnetic result it is believed to constitute the real, i.e.\ global, minimum with respect to electronic minimization.
+Indeed, investigating the migration path from configurations $\alpha$ to $\beta$ and, in doing so, reusing the wave functions of the previous migration step, the final structure, i.e.\ configuration $\beta$, is obtained with zero magnetization and an increase in configurational energy by \unit[0.2]{eV}.
+Obviously, a different energy minimum of the electronic system is obtained indicating hysteresis behavior.
+However, since the total energy is lower for the magnetic result, it is believed to constitute the real, i.e.\ global, minimum with respect to electronic minimization.
%
% a b transition
A low activation energy of \unit[0.1]{eV} is observed for the a$\rightarrow$b transition.
These structures are investigated in the following.
Resulting binding energies of a C$_{\text{i}}$ DB and a nearby vacancy are listed in the second row of Table~\ref{tab:defects:c-v}.
-\begin{table}[tp]
-\begin{center}
-\begin{tabular}{c c c c c c}
-\hline
-\hline
-1 & 2 & 3 & 4 & 5 & R \\
-\hline
--5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
-\hline
-\hline
-\end{tabular}
-\end{center}
-\caption[Binding energies of combinations of the \ci{} {\hkl[0 0 -1]} defect with a vacancy located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}.]{Binding energies of combinations of the \ci{} \hkl[0 0 -1] defect with a vacancy located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}. R corresponds to the position located at $\frac{a_{\text{Si}}}{2}\hkl[3 2 3]$ relative to the initial defect position, which is the maximum realizable distance due to periodic boundary conditions.}
-\label{tab:defects:c-v}
-\end{table}
-\begin{figure}[tp]
-\begin{center}
-\subfigure[\underline{$E_{\text{b}}=-0.59\,\text{eV}$}]{\label{fig:defects:059}\includegraphics[width=0.25\textwidth]{00-1dc/0-59.eps}}
-\hspace{0.7cm}
-\subfigure[\underline{$E_{\text{b}}=-3.14\,\text{eV}$}]{\label{fig:defects:314}\includegraphics[width=0.25\textwidth]{00-1dc/3-14.eps}}\\
-\subfigure[\underline{$E_{\text{b}}=-0.54\,\text{eV}$}]{\label{fig:defects:054}\includegraphics[width=0.25\textwidth]{00-1dc/0-54.eps}}
-\hspace{0.7cm}
-\subfigure[\underline{$E_{\text{b}}=-0.50\,\text{eV}$}]{\label{fig:defects:050}\includegraphics[width=0.25\textwidth]{00-1dc/0-50.eps}}
-\end{center}
-\caption[Relaxed structures of defect combinations obtained by creating a vacancy at positions 2, 3, 4 and 5.]{Relaxed structures of defect combinations obtained by creating a vacancy at positions 2 (a), 3 (b), 4 (c) and 5 (d).}
-\label{fig:defects:comb_db_06}
-\end{figure}
+\begin{table}[tp]%
+\begin{center}%
+\begin{tabular}{c c c c c c}%
+\hline%
+\hline%
+1 & 2 & 3 & 4 & 5 & R \\%
+\hline%
+-5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\%
+\hline%
+\hline%
+\end{tabular}%
+\end{center}%
+\caption[Binding energies of combinations of the \ci{} {\hkl[0 0 -1]} defect with a vacancy located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}.]{Binding energies of combinations of the \ci{} \hkl[0 0 -1] defect with a vacancy located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}. R corresponds to the position located at $\frac{a_{\text{Si}}}{2}\hkl[3 2 3]$ relative to the initial defect position, which is the maximum realizable distance due to periodic boundary conditions.}%
+\label{tab:defects:c-v}%
+\end{table}%
+\begin{figure}[tp]%
+\begin{center}%
+\subfigure[\underline{$E_{\text{b}}=-0.59\,\text{eV}$}]{\label{fig:defects:059}\includegraphics[width=0.25\textwidth]{00-1dc/0-59.eps}}%
+\hspace{0.7cm}%
+\subfigure[\underline{$E_{\text{b}}=-3.14\,\text{eV}$}]{\label{fig:defects:314}\includegraphics[width=0.25\textwidth]{00-1dc/3-14.eps}}\\%
+\subfigure[\underline{$E_{\text{b}}=-0.54\,\text{eV}$}]{\label{fig:defects:054}\includegraphics[width=0.25\textwidth]{00-1dc/0-54.eps}}%
+\hspace{0.7cm}%
+\subfigure[\underline{$E_{\text{b}}=-0.50\,\text{eV}$}]{\label{fig:defects:050}\includegraphics[width=0.25\textwidth]{00-1dc/0-50.eps}}%
+\end{center}%
+\caption[Relaxed structures of defect combinations obtained by creating a vacancy at positions 2, 3, 4 and 5.]{Relaxed structures of defect combinations obtained by creating a vacancy at positions 2 (a), 3 (b), 4 (c) and 5 (d).}%
+\label{fig:defects:comb_db_06}%
+\end{figure}%
Figure~\ref{fig:defects:comb_db_06} shows the associated configurations.
All investigated structures are preferred compared to isolated, largely separated defects.
In contrast to C$_{\text{s}}$, this is also valid for positions along \hkl[1 1 0] resulting in an entirely attractive interaction between defects of these types.
With a binding energy of \unit[-5.39]{eV}, this is the energetically most favorable configuration observed.
A great amount of strain energy is reduced by removing the Si atom at position 3, which is illustrated in Fig.~\ref{fig:defects:314}.
The DB structure shifts towards the position of the vacancy, which replaces the Si atom usually bound to and at the same time strained by the \si{} DB atom.
-Due to the displacement into the \hkl[1 -1 0] direction the bond of the DB Si atom to the Si atom on the top left breaks and instead forms a bond to the Si atom located in \hkl[1 -1 1] direction, which is not shown in Fig.~\ref{fig:defects:314}.
+Due to the displacement into the \hkl[1 -1 0] direction, the bond of the DB Si atom to the Si atom on the top left breaks and instead forms a bond to the Si atom located in \hkl[1 -1 1] direction, which is not shown in Fig.~\ref{fig:defects:314}.
A binding energy of \unit[-3.14]{eV} is obtained for this structure composing another energetically favorable configuration.
A vacancy created at position 2 enables the relaxation of Si atom number 1 mainly in \hkl[0 0 -1] direction.
The bond to Si atom number 5 breaks.
Hence, the \si{} DB atom is not only displaced along \hkl[0 0 -1] but also and to a greater extent in \hkl[1 1 0] direction.
The C atom is slightly displaced in \hkl[0 1 -1] direction.
A binding energy of \unit[-0.59]{eV} indicates the occurrence of much less strain reduction compared to that in the latter configuration.
-Evidently this is due to a smaller displacement of Si atom 1, which would be directly bound to the replaced Si atom at position 2.
+Evidently, this is due to a smaller displacement of Si atom 1, which would be directly bound to the replaced Si atom at position 2.
In the case of a vacancy created at position 4, even a slightly higher binding energy of \unit[-0.54]{eV} is observed while the Si atom at the bottom left, which is bound to the \ci{} DB atom, is vastly displaced along \hkl[1 0 -1].
-However the displacement of the C atom along \hkl[0 0 -1] is less compared to the one in the previous configuration.
-Although expected due to the symmetric initial configuration, Si atom number 1 is not displaced correspondingly and also the \si DB atom is displaced to a greater extent in \hkl[-1 0 0] than in \hkl[0 -1 0] direction.
+However, the displacement of the C atom along \hkl[0 0 -1] is less compared to the one in the previous configuration.
+Although expected due to the symmetric initial configuration, Si atom number 1 is not displaced correspondingly and also the \si{} DB atom is displaced to a greater extent in \hkl[-1 0 0] than in \hkl[0 -1 0] direction.
The symmetric configuration is, thus, assumed to constitute a local maximum, which is driven into the present state by the conjugate gradient method used for relaxation.
Fig.~\ref{fig:defects:050} shows the relaxed structure of a vacancy created at position 5.
The Si DB atom is largely displaced along \hkl[1 1 0] and somewhat less along \hkl[0 0 -1], which corresponds to the direction towards the vacancy.
-The \si DB atom approaches Si atom number 1.
+The \si{} DB atom approaches Si atom number 1.
Indeed, a non-zero charge density is observed in between these two atoms exhibiting a cylinder-like shape superposed with the charge density known from the DB itself.
Strain reduced by this huge displacement is partially absorbed by tensile strain on Si atom number 1 originating from attractive forces of the C atom and the vacancy.
A binding energy of \unit[-0.50]{eV} is observed.
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.
+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.
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.
In both cases, the formation of additional bonds is responsible for the vast gain in energy rendering almost impossible the reverse processes.
In summary, pairs of C$_{\text{i}}$ DBs and vacancies, like no other before, show highly attractive interactions for all investigated combinations independent of orientation and separation direction of the defects.
-Furthermore, small activation energies, even for transitions into the ground state exist.
+Furthermore, small activation energies, even for transitions into the ground state, exist.
If the vacancy is created at position 1, the system will end up in a configuration of C$_{\text{s}}$ anyways.
Based on these results, a high probability for the formation of C$_{\text{s}}$ must be concluded.
\caption{Formation energies of defect configurations of a single C impurity in otherwise perfect c-Si determined by classical potential and {\em ab initio} methods. The formation energies are given in eV. T denotes the tetrahedral and the subscripts i and s indicate the interstitial and substitutional configuration. Superscripts a, b and c denote configurations of C$_{\text{s}}$ located at the first, second and third nearest neighbored lattice site with respect to the Si$_{\text{i}}$ atom.}
\label{tab:defect_combos}
\end{table}
-Obviously the EA potential properly describes the relative energies of formation.
+Obviously, the EA potential properly describes the relative energies of formation.
Combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ T are energetically less favorable than the ground state C$_{\text{i}}$ \hkl<1 0 0> DB configuration.
With increasing separation distance, the energies of formation decrease.
However, even for non-interacting defects, the energy of formation, which is then given by the sum of the formation energies of the separated defects (\unit[4.15]{eV}) is still higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB.
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