+Although lower than the barriers for obtaining the ground state of two C$_{\text{i}}$ defects, the activation energies are yet considered too high.
+For the same reasons as in the last subsection, structures other than the ground-state configuration are, thus, assumed to arise more likely due to much lower activation energies necessary for their formation and still comparatively low binding energies.
+
+% old c_int - c_substitutional stuff
+
+%Figures~\ref{fig:defects:comb_db_04} and~\ref{fig:defects:comb_db_05} show relaxed structures of substitutional carbon in combination with the \hkl<0 0 -1> dumbbell for several positions.
+%In figure~\ref{fig:defects:comb_db_04} positions 1 (a)), 3 (b)) and 5 (c)) are displayed.
+%A substituted carbon atom at position 5 results in an energetically extremely unfavorable configuration.
+%Both carbon atoms, the substitutional and the dumbbell atom, pull silicon atom number 1 towards their own location regarding the \hkl<1 1 0> direction.
+%Due to this a large amount of tensile strain energy is needed, which explains the high positive value of 0.49 eV.
+%The lowest binding energy is observed for a substitutional carbon atom inserted at position 3.
+%The substitutional carbon atom is located above the dumbbell substituting a silicon atom which would usually be bound to and displaced along \hkl<0 0 1> and \hkl<1 1 0> by the silicon dumbbell atom.
+%In contrast to the previous configuration strain compensation occurs resulting in a binding energy as low as -0.93 eV.
+%Substitutional carbon at position 2 and 4, visualized in figure~\ref{fig:defects:comb_db_05}, is located below the initial dumbbell.
+%Silicon atom number 1, which is bound to the interstitial carbon atom is displaced along \hkl<0 0 -1> and \hkl<-1 -1 0>.
+%In case a) only the first displacement is compensated by the substitutional carbon atom.
+%This results in a somewhat higher binding energy of -0.51 eV.
+%The binding energy gets even higher in case b) ($E_{\text{b}}=-0.15\text{ eV}$), in which the substitutional carbon is located further away from the initial dumbbell.
+%In both cases, silicon atom number 1 is displaced in such a way that the bond to silicon atom number 5 vanishes.
+%In case of~\ref{fig:defects:comb_db_04} a) the carbon atoms form a bond with a distance of 1.5 \AA, which is close to the C-C distance expected in diamond or graphit.
+%Both carbon atoms are highly attracted by each other resulting in large displacements and high strain energy in the surrounding.
+%A binding energy of 0.26 eV is observed.
+%Substitutional carbon at positions 2, 3 and 4 are the energetically most favorable configurations and constitute promising starting points for SiC precipitation.
+%On the one hand, C-C distances around 3.1 \AA{} exist for substitution positions 2 and 3, which are close to the C-C distance expected in silicon carbide.
+%On the other hand stretched silicon carbide is obtained by the transition of the silicon dumbbell atom into a silicon self-interstitial located somewhere in the silicon host matrix and the transition of the carbon dumbbell atom into another substitutional atom occupying the dumbbell lattice site.
+
+
+\subsection[Combinations of a \ci{} \hkl<1 0 0> DB and vacancy]{\boldmath Combinations of a \ci{} \hkl<1 0 0> DB and a vacancy}
+\label{subsection:defects:c-v}
+
+In the last section, configurations of a C$_{\text{i}}$ DB with C$_{\text{s}}$ occupying a vacant site have been investigated.
+Additionally, configurations might arise in IBS, in which the impinging C atom creates a vacant site near a C$_{\text{i}}$ DB, but does not occupy it.
+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}%
+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.
+Even for the largest possible distance (R) achieved in the calculations of the periodic supercell a binding energy as low as \unit[-0.31]{eV} is observed.
+The creation of a vacancy at position 1 results in a configuration of substitutional C on a Si lattice site and no other remaining defects.
+The \ci{} DB atom moves to position 1 where the vacancy is created and the \si{} DB atom recaptures the DB lattice site.
+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}.
+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.
+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.
+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.
+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.
+
+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}%
+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.
+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 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.
+%
+The migration path is best described by the reverse process.
+Starting at \unit[100]{\%}, energy is needed to break the bonds of Si atom 1 to its neighbored Si atoms as well as the bond of the C atom to Si atom number 5.
+At \unit[50]{\%} displacement, these bonds are broken.
+Due to this, and due to the formation of new bonds, e.g.\ the bond of Si atom number 1 to Si atom number 5, a less steep increase of configurational energy is observed.
+In a last step, the just recently formed bond of Si atom number 1 to Si atom number 5 is broken up again as well as the bond of the initial Si DB atom and its Si neighbor in \hkl[-1 -1 -1] direction, which explains the repeated boost in energy.
+Finally, the system gains some configurational energy by relaxation into the configuration corresponding to \unit[0]{\%} displacement.
+%
+The direct migration of the C$_{\text{i}}$ atom onto the vacant lattice site results in a somewhat higher barrier of \unit[1.0]{eV}.
+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.
+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.
+
+\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.
+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{} 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.
+
+\begin{table}[tp]