+% A B\r
+%./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\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{093-095.ps}\r
+\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 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.}\r
+\label{fig:093-095}\r
+\end{figure}\r
+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.\r
+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.\r
+This configuration has been identified and described by spectroscopic experimental techniques\cite{song90_2} as well as theoretical studies\cite{leary97,capaz98}.\r
+Configuration B is found to constitute the energetically slightly more favorable configuration.\r
+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.\r
+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.\r
+% mattoni: A favored by 0.4 eV - NO, it is indeed B (reinforce Song and Capaz)!\r
+%\r
+% AB transition\r
+The migration barrier was 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.\r
+Keeping in mind the formidable agreement of the energy difference with experiment, the overestimated activation energy is quite unexpected.\r
+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.\r
+% not satisfactory!\r
+\r
+% a b\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{026-128.ps}\r
+\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 (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.}\r
+\label{fig:026-128}\r
+\end{figure}\r
+Configuration a 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.\r
+Nevertheless, the C and Si DB atoms remain threefold coordinated.\r
+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}).\r
+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.\r
+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.\r
+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.\r
+This finding is in good agreement with a combined 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}.\r
+% mattoni: A favored by 0.2 eV - NO! (again, missing spin polarization?)\r
+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.\r
+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.\r
+Configurations a, A and B are not affected by spin polarization and show zero magnetization.\r
+Mattoni et~al.\cite{mattoni2002}, in contrast, find configuration b less favorable than configuration A by \unit[0.2]{eV}.\r
+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.\r
+Indeed, investigating the migration path from configurations a to b and, in doing so, reusing the wave functions of the previous migration step the final structure, i.e. configuration b, was obtained with zero magnetization and an increase in configurational energy by \unit[0.2]{eV}.\r
+Obviously a different energy minimum of the electronic system is obtained indicating hysteresis behavior.\r
+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.\r
+%\r
+% a b transition\r
+A low activation energy of \unit[0.1]{eV} is observed for the a$\rightarrow$b transition.\r
+Thus, configuration a is very unlikely to occur in favor of configuration b.\r
+\r
+% repulsive along 110\r
+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.\r
+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.\r
+This finding agrees well with results by Mattoni et~al.\cite{mattoni2002}.\r
+% all other investigated results: attractive interaction. stress compensation.\r
+In contrast, all other investigated configurations show attractive interactions.\r
+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.\r
+The substitution with C allows for most effective compensation of strain.\r
+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.\r
+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.\r
+The latter is partially compensated by the C$_{\text{s}}$ atom.\r
+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].\r
+\r
+% c agglomeration vs c clustering ... migs to b conf\r
+% 2 more migs: 051 -> 128 and 026! forgot why ... probably it's about probability of C clustering\r
+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.\r
+The energetically most favorable configuration (configuration b) forms a strong but compressively strained C-C bond with a separation distance of \unit[0.142]{nm} sharing a Si lattice site.\r
+Again, conclusions concerning the probability of formation are drawn by investigating migration paths.\r
+Since C$_{\text{s}}$ is unlikely to exhibit a low activation energy for migration the focus is on C$_{\text{i}}$.\r
+Pathways starting from the two next most favored configurations were investigated, which show activation energies above \unit[2.2]{eV} and \unit[3.5]{eV} respectively.\r
+Although lower than the barriers for obtaining the ground state of two C$_{\text{i}}$ defects the activation energies are yet considered too high.\r
+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.\r
+\r
+\subsection{C$_{\text{i}}$ next to V}\r
+\r
+In the last subsection configurations of a C$_{\text{i}}$ DB with C$_{\text{s}}$ occupying a vacant site have been investigated.\r
+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.\r
+Resulting binding energies of a C$_{\text{i}}$ DB and a nearby vacancy are listed in the second row of Table~\ref{table:dc_c-sv}.\r
+All investigated structures are preferred compared to isolated largely separated defects.\r
+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.\r
+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.\r
+The ground state configuration is obtained for a V at position 1.\r
+The C atom of the DB moves towards the vacant site forming a stable C$_{\text{s}}$ configuration resulting in the release of a huge amount of energy.\r
+The second most favorable configuration is accomplished for a V located at position 3 due to the reduction of compressive strain of the Si DB atom and its two upper Si neighbors present in the C$_{\text{i}}$ DB configuration.\r
+This configuration is followed by the structure, in which a vacant site is created at position 2.\r
+Similar to the observations for C$_{\text{s}}$ in the last subsection a reduction of strain along \hkl[0 0 1] is enabled by this configuration.\r
+Relaxed structures of the latter two defect combinations are shown in the bottom left of Fig.~\ref{fig:314-539} and \ref{fig:059-539} respectively together with their energetics during transition into the ground state.\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{314-539.ps}\r
+\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 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.1]{eV} is observed.}\r
+\label{fig:314-539}\r
+\end{figure}\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{059-539.ps}\r
+\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 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.6]{eV} is observed.}\r
+\label{fig:059-539}\r
+\end{figure}\r
+Activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} are observed.\r
+In the first case the Si and C atom of the DB move towards the vacant and initial DB lattice site respectively.\r
+In total three Si-Si and one more Si-C bond is formed during transition.\r
+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.\r
+A net amount of five Si-Si and one Si-C bond are additionally formed during transition.\r
+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}.\r
+In both cases, the formation of additional bonds is responsible for the vast gain in energy rendering almost impossible the reverse processes.\r
+\r
+In summary, pairs of C$_{\text{i}}$ DBs and Vs, like no other before, show highly attractive interactions for all investigated combinations independent of orientation and separation direction of the defects.\r
+Furthermore, small activation energies, even for transitions into the ground state exist.\r
+Based on these results, a high probability for the formation of C$_{\text{s}}$ must be concluded.\r
+\r
+\subsection{C$_{\text{s}}$ next to Si$_{\text{i}}$}\r
+\r
+As shown in section~\ref{subsection:sep_def}, C$_{\text{s}}$ exhibits the lowest energy of formation.\r
+Considering a perfect Si crystal and conservation of particles, however, the occupation of a Si lattice site by a slowed down implanted C atom is necessarily accompanied by the formation of a Si self-interstitial.\r
+There are good reasons for the existence of regions exhibiting such configurations with regard to the IBS process.\r
+Highly energetic C atoms are able to kick out a Si atom from its lattice site, resulting in a Si self-interstitial accompanied by a vacant site, which might get occupied by another C atom that lost almost all of its kinetic energy.\r
+%Thus, configurations of C$_{\text{s}}$ and Si self-interstitials are investigated in the following.\r
+Provided that the first C atom, which created the V and Si$_{\text{i}}$ pair has enough kinetic energy to escape the affected region, the C$_{\text{s}}$-Si$_{\text{i}}$ pair can be described as a separated defect complex.\r
+The Si$_{\text{i}}$ \hkl<1 1 0> DB, which was found to exhibit the lowest energy of formation within the investigated self-interstitial configurations, is assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$.\r