+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.
+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.
+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.
+
+\begin{figure}[tp]
+\begin{center}
+\subfigure[\underline{$E_{\text{b}}=-2.25\,\text{eV}$}]{\label{fig:defects:225}\includegraphics[width=0.3\textwidth]{00-1dc/2-25.eps}}
+\hspace{0.5cm}
+\subfigure[\underline{$E_{\text{b}}=-2.39\,\text{eV}$}]{\label{fig:defects:239}\includegraphics[width=0.3\textwidth]{00-1dc/2-39.eps}}
+\end{center}
+\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}.
+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}.
+In this configuration the initial Si and C DB atoms are displaced along \hkl[1 0 0] and \hkl[-1 0 0] in such a way that the Si atom is forming tetrahedral bonds with two Si and two C atoms.
+The C and Si atom constituting the second defect are as well displaced in such a way, that the C atom forms tetrahedral bonds with four Si neighbors, a configuration expected in SiC.
+The two carbon atoms, which are spaced by \unit[2.70]{\AA}, do not form a bond but anyhow reside in a shorter distance than expected in SiC.
+Si atom number 2 is pushed towards the C atom, which results in the breaking of the bond to Si atom number 4.
+Breaking of the $\sigma$ bond is indeed confirmed by investigating the charge density isosurface of this configuration.
+
+Apart from that, a more favorable configuration is found for the combination with a \hkl[0 -1 0] and \hkl[-1 0 0] DB respectively, which is assumed to constitute the actual ground-state configuration of two \ci{} DBs in Si.
+The atomic arrangement is shown in Fig.~\ref{fig:defects:239}.
+The initial configuration is still evident in the relaxed configuration.
+The two \ci{} atoms form a strong C-C bond, which is responsible for the large gain in energy resulting in a binding energy of \unit[-2.39]{eV}.
+This bond has a length of \unit[1.38]{\AA} close to the next neighbor distance in diamond or graphite, which is approximately \unit[1.54]{\AA}.
+The minimum of the binding energy observed for this configuration suggests preferred C clustering as a competing mechanism to the \ci{} DB interstitial agglomeration inevitable for the SiC precipitation.
+However, the second most favorable configuration ($E_{\text{f}}=-2.25\,\text{eV}$) is represented four times, i.e. two times more often than the ground-state configuration, within the systematically investigated configuration space.
+Thus, particularly at high temperatures that cause an increase of the entropic contribution, this structure constitutes a serious opponent to the ground state.
+In fact, following results on migration simulations will reinforce the assumption of a low probability for C clustering by thermally activated processes.
+
+\begin{figure}[tp]
+\begin{center}
+\subfigure[\underline{$E_{\text{b}}=-2.16\,\text{eV}$}]{\label{fig:defects:216}\includegraphics[width=0.25\textwidth]{00-1dc/2-16.eps}}
+\hspace{0.2cm}
+\subfigure[\underline{$E_{\text{b}}=-1.90\,\text{eV}$}]{\label{fig:defects:190}\includegraphics[width=0.25\textwidth]{00-1dc/1-90.eps}}
+\hspace{0.2cm}
+\subfigure[\underline{$E_{\text{b}}=-2.05\,\text{eV}$}]{\label{fig:defects:205}\includegraphics[width=0.25\textwidth]{00-1dc/2-05.eps}}
+\end{center}
+\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.
+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].
+The bond of Si atoms 1 and 2 does not persist.
+Instead, the Si atom forms a bond with the initial \ci{} and the second C atom forms a bond with Si atom 1 forming four bonds in total.
+The C atoms are spaced by \unit[3.14]{\AA}, which is very close to the expected C-C next neighbor distance of \unit[3.08]{\AA} in SiC.
+Figure \ref{fig:defects:205} displays the results of a \hkl[0 0 1] DB inserted at position 3.
+The binding energy is \unit[-2.05]{eV}.
+Both DBs are tilted along the same direction remaining aligned in parallel and the second DB is pushed downwards in such a way, that the four DB atoms form a rhomboid.
+Both C atoms form tetrahedral bonds to four Si atoms.
+However, Si atom number 1 and number 3, which are bound to the second \ci{} atom are also bound to the initial C atom.
+These four atoms of the rhomboid reside in a plane and, thus, do not match the situation in SiC.
+The C atoms have a distance of \unit[2.75]{\AA}.
+In Fig. \ref{fig:defects:190} the relaxed structure of a \hkl[0 1 0] DB constructed at position 2 is displayed.
+An energy of \unit[-1.90]{eV} is observed.
+The initial DB and especially the C atom is pushed towards the Si atom of the second DB forming an additional fourth bond.
+Si atom number 1 is pulled towards the C atoms of the DBs accompanied by the disappearance of its bond to Si number 5 as well as the bond of Si number 5 to its neighbored Si atom in \hkl[1 1 -1] direction.
+The C atom of the second DB forms threefold coordinated bonds to its Si neighbors.
+A distance of \unit[2.80]{\AA} is observed for the two C atoms.
+Again, the two C atoms and its two interconnecting Si atoms form a rhomboid.
+C-C distances of \unit[2.70-2.80]{\AA} seem to be characteristic for such configurations, in which the C atoms and the two interconnecting Si atoms reside in a plane.
+
+Configurations obtained by adding a \ci{} \hkl<1 0 0> DB at position 4 are characterized by minimal changes from their initial creation condition during relaxation.
+There is a low interaction of the DBs, which seem to exist independent of each other.
+This, on the one hand, becomes evident by investigating the final structure, in which both of the DBs essentially retain the structure expected for a single DB and, on the other hand, is supported by the observed binding energies, which vary only slightly around zero.
+This low interaction is due to the large distance and a missing direct connection by bonds along a chain in the crystallographic \hkl<1 1 0> direction.
+Both, C and Si atoms of the DBs form threefold coordinated bonds to their neighbors.
+The energetically most unfavorable configuration ($E_{\text{b}}=0.26\,\text{eV}$) is obtained for the \ci{} \hkl[0 0 1] DB, which is oppositely orientated with respect to the initial one.
+A DB taking the same orientation as the initial one is less unfavorable ($E_{\text{b}}=0.04\,\text{eV}$).
+Both configurations are unfavorable compared to far-off, isolated DBs.
+Nonparallel orientations, i.e. the \hkl[0 1 0], \hkl[0 -1 0] and its equivalents, result in binding energies of \unit[-0.12]{eV} and \unit[-0.27]{eV}, thus, constituting energetically favorable configurations.
+The reduction of strain energy is higher in the second case, where the C atom of the second DB is placed in the direction pointing away from the initial C atom.
+
+\begin{figure}[tp]
+\begin{center}
+\subfigure[\underline{$E_{\text{b}}=-1.53\,\text{eV}$}]{\label{fig:defects:153}\includegraphics[width=0.25\textwidth]{00-1dc/1-53.eps}}
+\hspace{0.7cm}
+\subfigure[\underline{$E_{\text{b}}=-1.66\,\text{eV}$}]{\label{fig:defects:166}\includegraphics[width=0.25\textwidth]{00-1dc/1-66.eps}}\\
+\subfigure[\underline{$E_{\text{b}}=-1.88\,\text{eV}$}]{\label{fig:defects:188}\includegraphics[width=0.25\textwidth]{00-1dc/1-88.eps}}
+\hspace{0.7cm}
+\subfigure[\underline{$E_{\text{b}}=-1.38\,\text{eV}$}]{\label{fig:defects:138}\includegraphics[width=0.25\textwidth]{00-1dc/1-38.eps}}
+\end{center}
+\caption[Relaxed structures of defect combinations obtained by creating {\hkl[0 0 1]}, {\hkl[0 0 -1]}, {\hkl[0 -1 0]} and {\hkl[1 0 0]} DBs at position 5.]{Relaxed structures of defect combinations obtained by creating \hkl[0 0 1] (a), \hkl[0 0 -1] (b), \hkl[0 -1 0] (c) and \hkl[1 0 0] (d) DBs at position 5.}
+\label{fig:defects:comb_db_03}
+\end{figure}
+Energetically beneficial configurations of defect combinations are observed for interstitials of all orientations placed at position 5, a position two bonds away from the initial interstitial along the \hkl[1 1 0] direction.
+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.
+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.
+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.
+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.
+
+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.
+Therefore, 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}
+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.
+Not considering the previously mentioned elevated barriers for migration, an attractive interaction between the \ci{} \hkl<1 0 0> DB defects indeed is detected with a capture radius that clearly exceeds \unit[1]{nm}.
+The interpolated graph suggests the disappearance of attractive interaction forces, which are proportional to the slope of the graph, in between the two lowest separation distances of the defects.
+This finding, in turn, supports the previously established assumption of C agglomeration and absence of C clustering.
+
+%\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.
+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.
+The high activation energy is attributed to the stability of such a low energy configuration, in which the C atom of the second DB is located close to the initial DB.
+Due to an effective stress compensation realized in the respective low energy configuration, which will necessarily be lost during migration, a high energy configuration needs to get passed, which is responsible for the high barrier.
+Low barriers are only identified for transitions starting from energetically less favorable configurations, e.g. the configuration of a \hkl[-1 0 0] DB located at position 2 (\unit[-0.36]{eV}).
+Starting from this configuration, an activation energy of only \unit[1.2]{eV} is necessary for the transition into the ground state configuration.
+The corresponding migration energies and atomic configurations are displayed in Fig.~\ref{fig:036-239}.
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{036-239.ps}
+\end{center}
+\caption[Migration barrier and structures of the transition of a C$_{\text{i}}$ {\hkl[-1 0 0]} DB at position 2 into a C$_{\text{i}}$ {\hkl[0 -1 0]} DB at position 1.]{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[-1 0 0] DB at position 2 (left) into a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 1 (right). An activation energy of \unit[1.2]{eV} is observed.}
+\label{fig:036-239}
+\end{figure}
+Since thermally activated C clustering is, thus, only possible by traversing energetically unfavored configurations, extensive C clustering is not expected.
+Furthermore, the migration barrier of \unit[1.2]{eV} is still higher than the activation energy of \unit[0.9]{eV} observed for a single C$_{\text{i}}$ \hkl<1 0 0> DB in c-Si.
+The migration barrier of a C$_{\text{i}}$ DB in a complex system is assumed to approximate the barrier of a DB in a separated system with increasing defect separation.
+Accordingly, lower migration barriers are expected for pathways resulting in larger separations of the C$_{\text{i}}$ DBs.
+% acknowledged by 188-225 (reverse order) calc
+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.
+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}.
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{188-225.ps}
+\end{center}
+\caption[Migration barrier and structures of the transition of a C$_{\text{i}}$ {\hkl[0 -1 0]} DB at position 5 into a C$_{\text{i}}$ {\hkl[1 0 0]} DB at position 1.]{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 5 (left) into a C$_{\text{i}}$ \hkl[1 0 0] DB at position 1 (right). An activation energy of \unit[0.47]{eV} is observed.}
+\label{fig:188-225}
+\end{figure}
+Finally, as already mentioned above, this type of defect pair is represented two times more often than the ground-state configuration.
+The latter is considered very important at high temperatures, accompanied by an increase in the entropic contribution to structure formation.
+As a result, C defect agglomeration indeed is expected, but only a low probability is assumed for C-C clustering by thermally activated processes with regard to the considered process time in IBS.
+
+\subsection[Combinations of the \ci{} \hkl<1 0 0> and \cs{} type]{\boldmath Combinations of the \ci{} \hkl<1 0 0> and \cs{} type}
+\label{subsection:defects:c-csub}
+
+\begin{table}[tp]
+\begin{center}
+\begin{tabular}{c c c c c c}
+\hline
+\hline
+1 & 2 & 3 & 4 & 5 & R \\
+\hline
+0.26$^a$/-1.28$^b$ & -0.51 & -0.93$^A$/-0.95$^B$ & -0.15 & 0.49
+ & -0.05\\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption[Binding energies of combinations of the \ci{} {\hkl[0 0 -1]} defect with a \cs{} atom 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 \cs{} atom 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-s}
+\end{table}
+%\begin{figure}[tp]
+%\begin{center}
+%\begin{minipage}[t]{5cm}
+%a) \underline{Pos: 1, $E_{\text{b}}=0.26\text{ eV}$}
+%\begin{center}
+%\includegraphics[width=4.8cm]{00-1dc/0-26.eps}
+%\end{center}
+%\end{minipage}
+%\begin{minipage}[t]{5cm}
+%b) \underline{Pos: 3, $E_{\text{b}}=-0.93\text{ eV}$}
+%\begin{center}
+%\includegraphics[width=4.8cm]{00-1dc/0-93.eps}
+%\end{center}
+%\end{minipage}
+%\begin{minipage}[t]{5cm}
+%c) \underline{Pos: 5, $E_{\text{b}}=0.49\text{ eV}$}
+%\begin{center}
+%\includegraphics[width=4.8cm]{00-1dc/0-49.eps}
+%\end{center}
+%\end{minipage}
+%\end{center}
+%\caption{Relaxed structures of defect complexes obtained by creating a carbon substitutional at position 1 (a)), 3 (b)) and 5 (c)).}
+%\label{fig:defects:comb_db_04}
+%\end{figure}
+%\begin{figure}[tp]
+%\begin{center}
+%\begin{minipage}[t]{7cm}
+%a) \underline{Pos: 2, $E_{\text{b}}=-0.51\text{ eV}$}
+%\begin{center}
+%\includegraphics[width=6cm]{00-1dc/0-51.eps}
+%\end{center}
+%\end{minipage}
+%\begin{minipage}[t]{7cm}
+%b) \underline{Pos: 4, $E_{\text{b}}=-0.15\text{ eV}$}
+%\begin{center}
+%\includegraphics[width=6cm]{00-1dc/0-15.eps}
+%\end{center}
+%\end{minipage}
+%\end{center}
+%\caption{Relaxed structures of defect complexes obtained by creating a carbon substitutional at position 2 (a)) and 4 (b)).}
+%\label{fig:defects:comb_db_05}
+%\end{figure}
+%
+Table~\ref{tab:defects:c-s} lists the energetic results of \cs{} combinations with the initial \ci{} \hkl[0 0 -1] DB.
+For \cs{} located at position 1 and 3, the configurations $\alpha$ and A correspond to the naive relaxation of the structure by substituting the Si atom by a C atom in the initial \ci{} \hkl[0 0 -1] DB structure at positions 1 and 3 respectively.
+However, small displacements of the involved atoms near the defect result in different stable structures labeled $\beta$ and B respectively.
+Fig.~\ref{fig:093-095} and \ref{fig:026-128} show structures A, B and $\alpha$, $\beta$ together with the barrier of migration for the A to B and $\alpha$ to $\beta$ transition respectively.
+
+% A B
+%./visualize_contcar -w 640 -h 480 -d results/c_00-1_c3_csub_B -nll -0.20 -0.4 -0.1 -fur 0.9 0.6 0.9 -c 0.5 -1.5 0.375 -L 0.5 0 0.3 -r 0.6 -A -1 2.465
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{093-095.ps}
+\end{center}
+\caption[Migration barrier and structures of the transition of the initial \ci{} {\hkl[0 0 -1]} DB and C$_{\text{s}}$ at position 3 into a configuration of a twofold coordinated Si$_{\text{i}}$ located in between two C$_{\text{s}}$ atoms occupying the lattice sites of the initial DB and position 3.]{Migration barrier and structures of the transition of the initial \ci{} \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 3 (left) into a configuration of a twofold coordinated Si$_{\text{i}}$ located in between two C$_{\text{s}}$ atoms occupying the lattice sites of the initial DB and position 3 (right). An activation energy of \unit[0.44]{eV} is observed.}
+\label{fig:093-095}
+\end{figure}
+Configuration A consists of a C$_{\text{i}}$ \hkl[0 0 -1] DB with threefold coordinated Si and C DB atoms slightly disturbed by the C$_{\text{s}}$ at position 3, facing the Si DB atom as a neighbor.
+By a single bond switch, i.e. the breaking of a Si-Si in favor of a Si-C bond, configuration B is obtained, which shows a twofold coordinated Si atom located in between two substitutional C atoms residing on regular Si lattice sites.
+This configuration has been identified and described by spectroscopic experimental techniques \cite{song90_2} as well as theoretical studies \cite{leary97,capaz98}.
+Configuration B is found to constitute the energetically slightly more favorable configuration.
+However, the gain in energy due to the significantly lower energy of a Si-C compared to a Si-Si bond turns out to be smaller than expected due to a large compensation by introduced strain as a result of the Si interstitial structure.
+Present results show a difference in energy of states A and B, which exactly matches the experimental value of \unit[0.02]{eV} \cite{song90_2}, reinforcing qualitatively correct results of previous theoretical studies on these structures.
+% mattoni: A favored by 0.4 eV - NO, it is indeed B (reinforce Song and Capaz)!
+%
+% AB transition
+The migration barrier is identified to be \unit[0.44]{eV}, almost three times higher than the experimental value of \unit[0.16]{eV} \cite{song90_2} estimated for the neutral charge state transition in p- and n-type Si.
+Keeping in mind the formidable agreement of the energy difference with experiment, the overestimated activation energy is quite unexpected.
+Obviously, either the CRT algorithm fails to seize the actual saddle point structure or the influence of dopants has exceptional effect in the experimentally covered diffusion process being responsible for the low migration barrier.
+% not satisfactory!
+
+% a b
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{comb_mig_026-128_vasp.ps}
+\end{center}
+\caption[Migration barrier and structures of the transition of the initial C$_{\text{i}}$ {\hkl[0 0 -1]} DB and C$_{\text{s}}$ at position 1 into a C-C {\hkl[1 0 0]} DB occupying the lattice site at position 1.]{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 1 (left) into a C-C \hkl[1 0 0] DB occupying the lattice site at position 1 (right). An activation energy of \unit[0.1]{eV} is observed.}
+\label{fig:026-128}
+\end{figure}
+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.
+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.
+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.
+In fact, these two configurations are very similar and are qualitatively different from the C$_{\text{i}}$ \hkl<1 0 0> DB that does not show magnetization but a nearly collinear bond of the C DB atom to its two neighbored Si atoms while the Si DB atom approximates \unit[120]{$^{\circ}$} angles in between its bonds.
+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.
+%
+% a b transition
+A low activation energy of \unit[0.1]{eV} is observed for the a$\rightarrow$b transition.
+Thus, configuration a is very unlikely to occur in favor of configuration b.
+
+% repulsive along 110
+A repulsive interaction is observed for C$_{\text{s}}$ at lattice sites along \hkl[1 1 0], i.e. positions 1 (configuration a) and 5.
+This is due to tensile strain originating from both, the C$_{\text{i}}$ DB and the C$_{\text{s}}$ atom residing within the \hkl[1 1 0] bond chain.
+This finding agrees well with results by Mattoni et~al.~\cite{mattoni2002}.
+% all other investigated results: attractive interaction. stress compensation.
+In contrast, all other investigated configurations show attractive interactions.
+The most favorable configuration is found for C$_{\text{s}}$ at position 3, which corresponds to the lattice site of one of the upper neighbored Si atoms of the DB structure that is compressively strained along \hkl[1 -1 0] and \hkl[0 0 1] by the C-Si DB.
+The substitution with C allows for most effective compensation of strain.
+This structure is followed by C$_{\text{s}}$ located at position 2, the lattice site of one of the neighbor atoms below the two Si atoms that are bound to the C$_{\text{i}}$ DB atom.
+As mentioned earlier, these two lower Si atoms indeed experience tensile strain along the \hkl[1 1 0] bond chain, however, additional compressive strain along \hkl[0 0 1] exists.
+The latter is partially compensated by the C$_{\text{s}}$ atom.
+Yet less of compensation is realized if C$_{\text{s}}$ is located at position 4 due to a larger separation although both bottom Si atoms of the DB structure are indirectly affected, i.e. each of them is connected by another Si atom to the C atom enabling the reduction of strain along \hkl[0 0 1].
+\begin{figure}[tp]
+\begin{center}
+\subfigure[\underline{$E_{\text{b}}=-0.51\,\text{eV}$}]{\label{fig:defects:051}\includegraphics[width=0.25\textwidth]{00-1dc/0-51.eps}}
+\hspace{0.2cm}
+\subfigure[\underline{$E_{\text{b}}=-0.15\,\text{eV}$}]{\label{fig:defects:015}\includegraphics[width=0.25\textwidth]{00-1dc/0-15.eps}}
+\hspace{0.2cm}
+\subfigure[\underline{$E_{\text{b}}=0.49\,\text{eV}$}]{\label{fig:defects:049}\includegraphics[width=0.25\textwidth]{00-1dc/0-49.eps}}
+\end{center}
+\caption[Relaxed structures of defect combinations obtained by creating \cs{} at positions 2, 4 and 5 in the \ci{} {\hkl[0 0 -1]} DB configuration.]{Relaxed structures of defect combinations obtained by creating \cs{} at positions 2 (a), 4 (b) and 5 (c) in the \ci{} \hkl[0 0 -1] DB configuration.}
+\label{fig_defects:245csub}
+\end{figure}
+Fig.~\ref{fig_defects:245csub} lists the remaining configurations and binding energies of the relaxed structures obtained by creating a \cs{} at positions 2, 4 and 5 in the \ci{} \hkl[0 0 -1] DB configuration.
+% todo explain some configurations, source: old text some lines below
+
+% c agglomeration vs c clustering ... migs to b conf
+% 2 more migs: 051 -> 128 and 026! forgot why ... probably it's about probability of C clustering
+Obviously, agglomeration of C$_{\text{i}}$ and C$_{\text{s}}$ is energetically favorable except for separations along one of the \hkl<1 1 0> directions.
+The energetically most favorable configuration (configuration $\beta$) forms a strong but compressively strained C-C bond with a separation distance of \unit[0.142]{nm} sharing a Si lattice site.
+Again, conclusions concerning the probability of formation are drawn by investigating respective migration paths.
+Since C$_{\text{s}}$ is unlikely to exhibit a low activation energy for migration the focus is on C$_{\text{i}}$.
+Pathways starting from the next most favored configuration, i.e. \cs{} located at position 2, into configuration $\alpha$ and $\beta$ are investigated, which show activation energies above \unit[2.2]{eV} and \unit[2.5]{eV}.
+The respective barriers and structures are displayed in Fig.~\ref{fig:051-xxx}.
+For the transition into configuration $\beta$, as before, the non-magnetic configuration is obtained.
+If not forced by the CRT algorithm, the structures beyond \perc{50} and below \perc{90} displacement of the transition approaching configuration $\alpha$ would settle into configuration $\beta$.
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{comb_mig_051-xxx_conf.ps}
+\end{center}
+\caption{Migration barrier and structures of the transition of a configuration equivalent to the one of the initial \hkl<0 0 -1> \ci{} DB with \cs{} located at position 2 into the $\alpha$ and $\beta$ configurations.}
+\label{fig:051-xxx}
+\end{figure}
+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 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{} 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.
+
+\begin{table}[tp]
+\begin{center}
+\begin{tabular}{l c c c c c c}
+\hline
+\hline
+ & \hkl[1 1 0] & \hkl[-1 1 0] & \hkl[0 1 1] & \hkl[0 -1 1] &
+ \hkl[1 0 1] & \hkl[-1 0 1] \\
+\hline
+1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
+2 & \RM{2} & \RM{6} & \RM{6} & \RM{2} & \RM{8} & \RM{5} \\
+3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
+4 & \RM{4} & \RM{7} & \RM{9} & \RM{10} & \RM{10} & \RM{9} \\
+5 & \RM{5} & \RM{8} & \RM{6} & \RM{2} & \RM{6} & \RM{2} \\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption[Equivalent configurations labeled \RM{1}-\RM{10} of \hkl<1 1 0>-type Si$_{\text{i}}$ DBs created at position I and C$_{\text{s}}$ created at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_si}.]{Equivalent configurations labeled \RM{1}-\RM{10} of \hkl<1 1 0>-type Si$_{\text{i}}$ DBs created at position I and C$_{\text{s}}$ created at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_si}. The respective orientation of the Si$_{\text{i}}$ DB is given in the first row.}
+\label{tab:defects:comb_csub_si110}
+\end{table}
+\begin{table}[tp]
+\begin{center}
+\begin{tabular}{l c c c c c c c c c c}
+\hline
+\hline
+ & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & \RM{6} & \RM{7} & \RM{8} & \RM{9} & \RM{10} \\
+\hline
+$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
+$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
+$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption{Formation energies $E_{\text{f}}$, binding energies $E_{\text{b}}$ and C$_{\text{s}}$-Si$_{\text{i}}$ separation distances of configurations combining C$_{\text{s}}$ and Si$_{\text{i}}$ as defined in Table~\ref{tab:defects:comb_csub_si110}.}
+\label{tab:defects:comb_csub_si110_energy}
+\end{table}
+Table~\ref{tab:defects:comb_csub_si110} classifies equivalent configurations of \hkl<1 1 0>-type Si$_{\text{i}}$ DBs created at position I and C$_{\text{s}}$ created at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_si}.
+Corresponding formation as well as binding energies and the separation distances of the C$_{\text{s}}$ atom and the Si$_{\text{i}}$ DB lattice site are listed in Table~\ref{tab:defects:comb_csub_si110_energy}.
+In total, ten different configurations exist within the investigated range.
+Configuration \RM{1} constitutes the energetically most favorable structure exhibiting a formation energy of \unit[4.37]{eV}.
+Obviously, the configuration of a Si$_{\text{i}}$ \hkl[1 1 0] DB and a neighbored C$_{\text{s}}$ atom along the bond chain, which has the same direction as the alignment of the DB, enables the largest possible reduction of strain.
+%
+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].
+%
+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.
+Thus, the compressive stress along \hkl[1 1 0] of the \si{} \hkl[1 1 0] DB is not compensated but intensified by the tensile stress of the \cs{} atom, which is no longer located along the direction of stress.