+\subsection{C$_{\text{i}}$ next to C$_{\text{s}}$}\r
+\r
+The first row of Table~\ref{table:dc_c-sv} lists the binding energies of C$_{\text{s}}$ next to the C$_{\text{i}}$ \hkl[0 0 -1] DB.\r
+For C$_{\text{s}}$ located at position 1 and 3 the configurations a and A correspond to the naive relaxation of the structure by substituting the Si atom by a C atom in the initial C$_{\text{i}}$ \hkl[0 0 -1] DB structure at positions 1 and 3 respectively.\r
+However, small displacements of the involved atoms near the defect result in different stable structures labeled b and B respectively.\r
+Fig.~\ref{fig:093-095} and \ref{fig:026-128} show structures A, B and a, b together with the barrier of migration for the A to B and a to b transition respectively. \r
+\r
+% 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 inbetween two C$_{\text{s}}$ atoms occupying the lattice sites of the initial DB and position 3 (right). An activation energy of \unit[0.?]{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 next 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 inbetween 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
+% ...\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 next 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 a 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 euqally localized as in the Si$_{\text{i}}$ \hkl<1 0 0> DB structure is observed.\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 missing accounting for 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 \unit[0.2]{eV}.\r
+Obviously a different energy minimum of the electronic system is obatined in that case showing a hysterisis behavior.\r
+However, since the total energy is lower for the magnetic result it is believed to constitute the real, i.e. global, minimum of the electronic minimization.\r
+\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
+However, migration barriers yielding\r
+...\r
+\r
+% mig a-b\r
+% 2 more migs: 051 -> 128 and 026! forgot why ... probably it's about probability of C clustering\r