-In the first case the focus is on the migration of silicon atom number 1 towards the vacant site created at position 2, while the carbon atom substitutes the site of the migrating silicon atom.
-An energy of 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 5.4 eV are needed, which make this mechanism very unprobable.
-The migration path is best described by the reverse process.
-Starting at 100 \% energy is needed to break the bonds of silicon atom 1 to its neighboured silicon atoms and that of the carbon atom to silicon atom number 5.
-At a displacement of 60 \% these bonds are broken.
-Due to this and due to the formation of new bonds, that is the bond of silicon atom number 1 to silicon atom number 5 and the bond of the carbon atom to its siliocn neighbour in the bottom left, a less steep increase of free energy is observed.
-At a displacement of approximately 30 \% the bond of silicon atom number 1 to the just recently created siliocn atom is broken up again, which explains the repeated boost in energy.
-Finally the system gains energy relaxing into the configuration of zero displacement.
-
-Due to the low binding energy observed, the configuration of the vacancy created at position 3 is assumed to be stable against transition.
-However, a relatively simple migration path exists, which intuitively seems to be a low energy process.
-The migration path and the corresponding differences in free energy are displayed in figure \ref{fig:defects:comb_mig_02}.
-In fact, migration simulations yield a barrier as low as 0.1 eV.
-This energy is needed to tilt the dumbbell as the displayed structure at 30 \% displacement shows.
-Once this barrier is overcome, the carbon atom forms a bond to the top left silicon atom and the interstitial silicon atom capturing the vacant site is forming new tetrahedral bonds to its neighboured silicon atoms.
-These new bonds and the relaxation into the substitutional carbon configuration are responsible for the gain in free energy.
-For the reverse process approximately 2.4 eV are nedded, which is 24 times higher than the forward process.
-Thus, substitutional carbon is assumed to be stable in contrast to the C-Si dumbbell interstitial located next to a vacancy.
-
-{\color{red}Todo: DB migration calculations along 110 (at the starting of this section)?}
+% kept for nostalgical reason!
+
+%\section{Migration in systems of combined defects}
+
+%\begin{figure}[ht]
+%\begin{center}
+%\includegraphics[width=13cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[2.0cm]
+%\begin{picture}(0,0)(170,0)
+%\includegraphics[width=3cm]{vasp_mig/comb_2-1_init.eps}
+%\end{picture}
+%\begin{picture}(0,0)(80,0)
+%\includegraphics[width=3cm]{vasp_mig/comb_2-1_seq_03.eps}
+%\end{picture}
+%\begin{picture}(0,0)(-10,0)
+%\includegraphics[width=3cm]{vasp_mig/comb_2-1_seq_06.eps}
+%\end{picture}
+%\begin{picture}(0,0)(-120,0)
+%\includegraphics[width=3cm]{vasp_mig/comb_2-1_final.eps}
+%\end{picture}
+%\begin{picture}(0,0)(25,20)
+%\includegraphics[width=2.5cm]{100_arrow.eps}
+%\end{picture}
+%\begin{picture}(0,0)(230,0)
+%\includegraphics[height=2.2cm]{001_arrow.eps}
+%\end{picture}
+%\end{center}
+%\caption{Transition of the configuration of the C-Si dumbbell interstitial in combination with a vacancy created at position 2 into the configuration of substitutional carbon.}
+%\label{fig:defects:comb_mig_01}
+%\end{figure}
+%\begin{figure}[ht]
+%\begin{center}
+%\includegraphics[width=13cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[1.0cm]
+%\begin{picture}(0,0)(150,0)
+%\includegraphics[width=2cm]{vasp_mig/comb_3-1_init.eps}
+%\end{picture}
+%\begin{picture}(0,0)(60,0)
+%\includegraphics[width=2cm]{vasp_mig/comb_3-1_seq_03.eps}
+%\end{picture}
+%\begin{picture}(0,0)(-45,0)
+%\includegraphics[width=2cm]{vasp_mig/comb_3-1_seq_07.eps}
+%\end{picture}
+%\begin{picture}(0,0)(-130,0)
+%\includegraphics[width=2cm]{vasp_mig/comb_3-1_final.eps}
+%\end{picture}
+%\begin{picture}(0,0)(25,20)
+%\includegraphics[width=2.5cm]{100_arrow.eps}
+%\end{picture}
+%\begin{picture}(0,0)(230,0)
+%\includegraphics[height=2.2cm]{001_arrow.eps}
+%\end{picture}
+%\end{center}
+%\caption{Transition of the configuration of the C-Si dumbbell interstitial in combination with a vacancy created at position 3 into the configuration of substitutional carbon.}
+%\label{fig:defects:comb_mig_02}
+%\end{figure}
+
+\clearpage{}
+
+\section{Applicability: Competition of \ci{} and \cs-\si{}}
+\label{section:ea_app}
+
+As has been shown, the energetically most favorable configuration of \cs{} and \si{} is obtained for \cs{} located at the neighbored lattice site along the \hkl<1 1 0> bond chain of a Si$_{\text{i}}$ \hkl<1 1 0> DB.
+However, the energy of formation is slightly higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB, which constitutes the ground state for a C impurity introduced into otherwise perfect c-Si.
+
+For a possible clarification of the controversial views on the participation of C$_{\text{s}}$ in the precipitation mechanism by classical potential simulations, test calculations need to ensure the proper description of the relative formation energies of combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ compared to C$_{\text{i}}$.
+This is particularly important since the energy of formation of C$_{\text{s}}$ is drastically underestimated by the EA potential.
+A possible occurrence of C$_{\text{s}}$ could then be attributed to a lower energy of formation of the C$_{\text{s}}$-Si$_{\text{i}}$ combination due to the low formation energy of C$_{\text{s}}$, which is obviously wrong.
+
+Since quantum-mechanical calculations reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB as the ground-state configuration of Si$_{\text{i}}$ in Si, it was assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$ in the calculations carried out in section \ref{subsection:cs-si}.
+Empirical potentials, however, predict Si$_{\text{i}}$ T to be the energetically most favorable configuration.
+Thus, investigations of the relative energies of formation of defect pairs need to include combinations of C$_{\text{s}}$ with Si$_{\text{i}}$ T.
+Results of {\em ab initio} and classical potential calculations are summarized in Table~\ref{tab:defect_combos}.
+\begin{table}[t]
+\begin{center}
+\begin{tabular}{l c c c}
+\hline
+\hline
+ & C$_{\text{i}}$ \hkl<1 0 0> & C$_{\text{s}}$ \& Si$_{\text{i}}$ \hkl<1 1 0> & C$_{\text{s}}$ \& Si$_{\text{i}}$ T\\
+\hline
+ {\textsc vasp} & 3.72 & 4.37 & 4.17$^{\text{a}}$/4.99$^{\text{b}}$/4.96$^{\text{c}}$ \\
+ {\textsc posic} & 3.88 & 4.93 & 5.25$^{\text{a}}$/5.08$^{\text{b}}$/4.43$^{\text{c}}$\\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption{Formation energies of defect configurations of a single C impurity in otherwise perfect c-Si determined by classical potential and {\em ab initio} methods. The formation energies are given in eV. T denotes the tetrahedral and the subscripts i and s indicate the interstitial and substitutional configuration. Superscripts a, b and c denote configurations of C$_{\text{s}}$ located at the first, second and third nearest neighbored lattice site with respect to the Si$_{\text{i}}$ atom.}
+\label{tab:defect_combos}
+\end{table}
+Obviously the EA potential properly describes the relative energies of formation.
+Combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ T are energetically less favorable than the ground state C$_{\text{i}}$ \hkl<1 0 0> DB configuration.
+With increasing separation distance the energies of formation decrease.
+However, even for non-interacting defects, the energy of formation, which is then given by the sum of the formation energies of the separated defects (\unit[4.15]{eV}) is still higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB.
+Unexpectedly, the structure of a Si$_{\text{i}}$ \hkl<1 1 0> DB and a neighbored C$_{\text{s}}$, which is the most favored configuration of a C$_{\text{s}}$ and Si$_{\text{i}}$ DB according to quantum-mechanical calculations, likewise constitutes an energetically favorable configuration within the EA description, which is even preferred over the two least separated configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ T.
+This is attributed to an effective reduction in strain enabled by the respective combination.
+Quantum-mechanical results reveal a more favorable energy of fomation for the C$_{\text{s}}$ and Si$_{\text{i}}$ T (a) configuration.
+However, this configuration is unstable involving a structural transition into the C$_{\text{i}}$ \hkl<1 1 0> DB interstitial, thus, not maintaining the tetrahedral Si nor the \cs{} defect.
+
+Thus, the underestimated energy of formation of C$_{\text{s}}$ within the EA calculation does not pose a serious limitation in the present context.
+Since C is introduced into a perfect Si crystal and the number of particles is conserved in simulation, the creation of C$_{\text{s}}$ is accompanied by the creation of Si$_{\text{i}}$, which is energetically less favorable than the ground state, i.e. the C$_{\text{i}}$ \hkl<1 0 0> DB configuration, for both, the EA and {\em ab initio} treatment.
+In either case, no configuration more favorable than the C$_{\text{i}}$ \hkl<1 0 0> DB has been found.
+Thus, a proper description with respect to the relative energies of formation is assumed for the EA potential.