-Figure \ref{fig:defects:comb_db_06} displays relaxed structures of vacancies in combination with the \hkl<0 0 -1> dumbbell interstital.
-The creation of a vacancy at position 1 results in a configuration of substitutional carbon on a silicon lattice site and no other remaining defects.
-The carbon dumbbell atom moves to position 1 where the vacancy is created and the silicon dumbbell atom recaptures the dumbbell lattice site.
-With a binding energy of -5.39 eV, this is the energetically most favorable configuration observed.
-A great amount of strain energy is reduced by removing the silicon atom at position 3, which is illustrated in figure \ref{fig:defects:comb_db_06} b).
-The dumbbell structure shifts towards the position of the vacancy which replaces the silicon atom usually bond to and at the same time strained by the silicon dumbbell atom.
-Due to the displacement into the \hkl<1 -1 0> direction the bond of the dumbbell silicon atom to the silicon atom on the top left breaks and instead forms a bond to the silicon atom located in \hkl<1 -1 1> direction which is not shown in the figure.
-A binding energy of -3.14 eV is obtained for this structure composing another energetically favorable configuration.
-
-Vacancies created at positions 2 and 4 have similar
-
-Vac at position 2 and 4 have similar results.
-Less strain is reduced, since the displacement of the bottom silicon atom, whcih would be directly bond to the silicon atom replaced by the vacancy, is less.
-In the second case, there is even less strain reduction since the second next neighbour is replaced by the vacancy.
-A symmetric configuration is expected, but it is not!
-jahn-Teller distortion ... check this!
-In both cases the db is tilted in such a way, that the carbon atom moves towards the vacancy.
-At position 5 the silicon dumbbell atom moves in \hkl<1 1 0> direction, the same direction where the vacancy is located.
-Strain reducde by this is partialy absorbed by strain originating from the fact that si atom bound to and pulled by the carbon atom is also pulled by the vacancy.
-
-CHECK C-C DIST AND SI-C DIST !!! of all!!!
-
-{\color{red}Todo: Jahn-Teller distortion (vacancy) $\rightarrow$ actually three possibilities? Due to the initial defect symmetries are broken. It should have relaxed into the minumum energy configuration!?}
-Once a vacancy exists the minimal e conf is the c sub conf and ofcourse necessary for formation of SiC.
-The question is whether the migration into this conf is possible.
-Due to low e of conf at pos 3, this might constitute a trap.
-Thats why we havt to look at migration barriers into the configurations beneficial for SiC prec.
-Fig shows the migration of the 2 and 3 conf into the c sub conf.
-Low migration barriers, which means that SiC will modt probably form ... and so on ...
-
-{\color{red}Todo: Si int and C sub ...}
-The existance of a vacancy is most often accompanied by an interstitial.
-The silicon interstitital might diffuse to the surface or recombine with other vacancy defects and tus is out of the interested simulation region.
-However, investigation of near by vacancy, Si and C interstititla is necessary, too.
-As for the ground state of the single Si self-int a 110 this is also assumed as the lowest possibility in combination with other defects, which is a cruel assumption!!!
-
-{\color{red}Todo: Model of kick-out and kick-in mechnism?}
-
-
-\section{Conclusions for SiC preciptation}
+Si atoms 1 and 2, which form the initial DB, occupy Si lattice sites in the final configuration while Si atom 3 is transferred from a regular lattice site into the interstitial lattice.
+These results support the above assumptions of an increased entropic contribution to structural formation involving C$_{\text{s}}$ to a greater extent.
+
+% 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.
+
+\section{Conclusions concerning the SiC conversion mechanism}
+
+The ground state configuration of a carbon interstitial in crystalline siliocn is found to be the C-Si \hkl<1 0 0> dumbbell interstitial configuration, in which the threefold coordinated carbon and silicon atom share a usual silicon lattice site.
+This supports the assumption of C-Si \hkl<1 0 0>-type dumbbel interstitial formation in the first steps of the IBS process as proposed by the precipitation model introduced in section \ref{section:assumed_prec}.
+
+Migration simulations reveal this carbon interstitial to be mobile at prevailing implantation temperatures requireing an activation energy of approximately 0.9 eV for migration as well as reorientation processes.
+This enables possible migration of the defects to form defect agglomerates as demanded by the model.
+Unfortunately classical potential simulations show tremendously overestimated migration barriers indicating a possible failure of the necessary agglomeration of such defects.
+
+Investigations of two carbon interstitials of the \hkl<1 0 0>-type and varying separations and orientations state an attractive interaction between these interstitials.
+Depending on orientation, energetically favorable configurations are found in which these two interstitials are located close together instead of the occurernce of largely separated and isolated defects.
+This is due to strain compensation enabled by the combination of such defects in certain orientations.
+For dumbbells oriented along the \hkl<1 1 0> direction and the assumption that there is the possibility of free orientation, an interaction energy proportional to the reciprocal cube of the distance in the far field regime is found.
+These findings support the assumption of the C-Si dumbbell agglomeration proposed by the precipitation model.
+
+Next to the C-Si \hkl<1 0 0> dumbbell interstitial configuration, in which the C atom is sharing a Si lattice site with the corresponding Si atom the C atom could occupy the site of the Si atom, which in turn forms a Si self-interstitial.
+Combinations of substitutional C and a \hkl<1 1 0> Si self-interstitial, which is the ground state configuration for a Si self-interstitial and, thus, assumed to be the energetically most favorable configuration for combined structures, show formation energies 0.5 eV to 1.5 eV greater than that of the C-Si \hkl<1 0 0> interstitial configuration, which remains the energetically most favorable configuration.
+However, the binding energy of substitutional C and the Si self-interstitial quickly drops to zero already for short separations indicating a low interaction capture radius.
+Thus, due to missing attractive interaction forces driving the system to form C-Si \hkl<1 0 0> dumbbell interstitial complexes substitutional C, while thermodynamically not stable, constitutes a most likely configuration occuring in IBS, a process far from equlibrium.
+
+Due to the low interaction capture radius substitutional C can be treated independently of the existence of separated Si self-interstitials.
+This should be also true for combinations of C-Si interstitials next to a vacancy and a further separated Si self-interstitial excluded from treatment, which again is a conveivable configuration in IBS.
+By combination of a \hkl<1 0 0> dumbbell with a vacancy in the absence of the Si self-interstitial it is found that the configuration of substitutional carbon occupying the vacant site is the energetically most favorable configuration.
+Low migration barriers are necessary to obtain this configuration and in contrast comparatively high activation energies necessary for the reverse process.
+Thus, carbon interstitials and vacancies located close together are assumed to end up in such a configuration in which the carbon atom is tetrahedrally coordinated and bound to four silicon atoms as expected in silicon carbide.
+
+While first results support the proposed precipitation model the latter suggest the formation of silicon carbide by succesive creation of substitutional carbon instead of the agglomeration of C-Si dumbbell interstitials followed by an abrupt transition.
+Prevailing conditions in the IBS process at elevated temperatures and the fact that IBS is a nonequilibrium process reinforce the possibility of formation of substitutional C instead of the thermodynamically stable C-Si dumbbell interstitials predicted by simulations at zero Kelvin.
+\label{section:defects:noneq_process_02}
+
+{\color{blue}
+In addition, there are experimental findings, which might be exploited to reinforce the non-validity of the proposed precipitation model.
+High resolution TEM shows equal orientation of \hkl(h k l) planes of the c-Si host matrix and the 3C-SiC precipitate.
+Formation of 3C-SiC realized by successive formation of substitutional C, in which the atoms belonging to one of the two fcc lattices are substituted by C atoms perfectly conserves the \hkl(h k l) planes of the initial c-Si diamond lattice.
+Silicon self-interstitials consecutively created to the same degree are able to diffuse into the c-Si host one after another.
+Investigated combinations of C interstitials, however, result in distorted configurations, in which C atoms, which at some point will form SiC, are no longer aligned to the host.
+It is easily understandable that the mismatch in alignement will increase with increasing defect density.
+In addition, the amount of Si self-interstitials equal to the amount of agglomerated C atoms would be released all of a sudden probably not being able to diffuse into the c-Si host matrix without damaging the Si surrounding or the precipitate itself.
+In addition, IBS results in the formation of the cubic polytype of SiC only.
+As this result conforms well with the model of precipitation by substitutional C there is no obvious reason why hexagonal polytypes should not be able to form or an equal alignement would be mandatory assuming the model of precipitation by C-Si dumbbell agglomeration.
+}
+
+{\color{red}Todo: C mobility higher than Si mobility? -> substitutional C is more likely to arise, since it migrates 'faster' to vacant sites?}