+\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 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]
+\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.
+
+However, even configuration \RM{1} is energetically less favorable than the \hkl<1 0 0> C$_{\text{i}}$ DB, which, thus, remains the ground state of a C atom introduced into otherwise perfect c-Si.
+The transition involving the latter two configurations is shown in Fig.~\ref{fig:162-097}.
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{162-097.ps}
+\end{center}
+\caption[Migration barrier and structures of the transition of a {\hkl[1 1 0]} Si$_{\text{i}}$ DB next to C$_{\text{s}}$ into the C$_{\text{i}}$ {\hkl[0 0 -1]} DB configuration.]{Migration barrier and structures of the transition of a \hkl[1 1 0] Si$_{\text{i}}$ DB next to C$_{\text{s}}$ (right) into the C$_{\text{i}}$ \hkl[0 0 -1] DB configuration (left). An activation energy of \unit[0.12]{eV} and \unit[0.77]{eV} for the reverse process is observed.}
+\label{fig:162-097}
+\end{figure}
+An activation energy as low as \unit[0.12]{eV} is necessary for the migration into the ground-state configuration.
+Accordingly, the C$_{\text{i}}$ \hkl<1 0 0> DB configuration is assumed to occur more likely.
+However, only \unit[0.77]{eV} are needed for the reverse process, i.e.\ the formation of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB out of the ground state.
+Due to the low activation energy, this process must be considered to be activated without much effort either thermally or by introduced energy of the implantation process.
+
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{c_sub_si110.ps}
+\end{center}
+\caption[Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance.]{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance. The interaction strength of the defect pairs are well approximated by a Lennard-Jones 6-12 potential, which is used for curve fitting.}
+\label{fig:dc_si-s}
+\end{figure}
+Fig.~\ref{fig:dc_si-s} shows the binding energies of pairs of C$_{\text{s}}$ and a Si$_{\text{i}}$ \hkl<1 1 0> DB with respect to the separation distance.
+The interaction of the defects is well approximated by a Lennard-Jones (LJ) 6-12 potential, which is used for curve fitting.
+Unable to model possible positive values of the binding energy, i.e.\ unfavorable configurations, located to the right of the minimum, the LJ fit should rather be thought of as a guide for the eye describing the decrease of the interaction strength, i.e.\ the absolute value of the binding energy, with increasing separation distance.
+The binding energy quickly drops to zero.
+The LJ fit estimates almost zero interaction already at \unit[0.6]{nm} indicating a low interaction capture radius of the defect pair.
+%As can be seen, the interaction strength, i.e.\ the absolute value of the binding energy, quickly drops to zero with increasing separation distance.
+%Almost zero interaction may be assumed already at distances about \unit[0.5-0.6]{nm}, indicating a low interaction capture radius of the defect pair.
+In IBS, highly energetic collisions are assumed to easily produce configurations of defects exhibiting separation distances exceeding the capture radius.
+For this reason, C$_{\text{s}}$ without a Si$_{\text{i}}$ DB located within the immediate proximity, which is, thus, unable to form the thermodynamically stable C$_{\text{i}}$ \hkl<1 0 0> DB, constitutes a most likely configuration to be found in IBS.
+Particularly in IBS, which constitutes a system driven far from equilibrium, respective defect configurations might exist that do not combine into the ground-state configuration.
+Thus, the existence of C$_{\text{s}}$ is very likely.
+\label{section:defects:noneq_process_01}
+
+
+% the ab initio md, where to put
+
+Similar to what was previously mentioned, configurations of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB might be eminently important at higher temperatures due to the low activation energy necessary for its formation.
+At higher temperatures, the contribution of entropy to structural formation increases, which might result in a spatial separation even for defects located within the capture radius.
+Indeed, an {\em ab initio} MD run at \unit[900]{$^{\circ}$C} starting from configuration \RM{1}, which -- based on the above findings -- is assumed to recombine into the ground state configuration, results in a separation of the C$_{\text{s}}$ and Si$_{\text{i}}$ DB by more than 4 neighbor distances realized in a repeated migration mechanism of annihilating and arising Si$_{\text{i}}$ DBs.
+The atomic configurations for two different points in time are shown in Fig.~\ref{fig:defects:md}.
+\begin{figure}[tp]
+\begin{center}
+\begin{minipage}{0.40\textwidth}
+\includegraphics[width=\columnwidth]{md01_bonds.eps}
+\end{minipage}
+\hspace{1cm}
+\begin{minipage}{0.40\textwidth}
+\includegraphics[width=\columnwidth]{md02_bonds.eps}
+\end{minipage}\\
+\begin{minipage}{0.40\textwidth}
+\begin{center}
+$t=\unit[2230]{fs}$