+Figure \ref{fig:defects:comb_db_02} c) displays the results of another \hkl<0 0 1> dumbbell inserted at position 3.
+The binding energy is -2.05 eV.
+Both dumbbells are tilted along the same direction remaining parallely aligned and the second dumbbell is pushed downwards in such a way, that the four dumbbell atoms form a rhomboid.
+Both carbon atoms form tetrahedral bonds to four silicon atoms.
+However, silicon atom 1 and 3, which are bound to the second carbon dumbbell interstitial are also bound to the initial carbon atom.
+These four atoms of the rhomboid reside in a plane and, thus, do not match the situation in silicon carbide.
+The carbon atoms have a distance of 2.75 \AA.
+In figure \ref{fig:defects:comb_db_02} b) a second \hkl<0 1 0> dumbbell is constructed at position 2.
+An energy of -1.90 eV is observed.
+The initial dumbbell and especially the carbon atom is pushed towards the silicon atom of the second dumbbell forming an additional fourth bond.
+Silicon atom number 1 is pulled towards the carbon atoms of the dumbbells accompanied by the disappearance of its bond to silicon number 5 as well as the bond of silicon number 5 to its next neighboured silicon atom in \hkl<1 1 -1> direction.
+The carbon atom of the second dumbbell forms threefold coordinated bonds to its silicon neighbours.
+A distance of 2.80 \AA{} is observed for the two carbon atoms.
+Again, the two carbon atoms and its two interconnecting silicon atoms form a rhomboid.
+C-C distances of 2.70 to 2.80 \AA{} seem to be characteristic for such configurations, in which the carbon atoms and the two interconnecting silicon atoms reside in a plane.
+
+Configurations obtained by adding a second dumbbell interstitial at position 4 are characterized by minimal changes from their initial creation condition during relaxation.
+There is a low interaction of the dumbbells, which seem to exist independent of each other.
+This, on the one hand, becomes evident by investigating the final structure, in which both of the dumbbells essentially retain the structure expected for a single dumbbell and on the other hand is supported by the observed binding energies which vary only slightly around zero.
+This low interaction is due to the larger distance and a missing direct connection by bonds along a crystallographic direction.
+Both carbon and silicon atoms of the dumbbells form threefold coordinated bonds to their next neighbours.
+The energetically most unfavorable configuration ($E_{\text{b}}=0.26\text{ eV}$) is obtained for the \hkl<0 0 1> interstitial oppositely orientated to the initial one.
+A dumbbell taking the same orientation as the initial one is less unfavorble ($E_{\text{b}}=0.04\text{ eV}$).
+Both configurations are unfavorable compared to far-off isolated dumbbells.
+Nonparallel orientations, that is the \hkl<0 1 0>, \hkl<0 -1 0> and its equivalents, result in binding energies of -0.12 eV and -0.27 eV, thus, constituting energetically favorable configurations.
+The reduction of strain energy is higher in the second case where the carbon atom of the second dumbbell is placed in the direction pointing away from the initial carbon atom.
+
+\begin{figure}[t!h!]
+\begin{center}
+\begin{minipage}[t]{7cm}
+a) \underline{$E_{\text{b}}=-1.53\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/1-53.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{7cm}
+b) \underline{$E_{\text{b}}=-1.66\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/1-66.eps}
+\end{center}
+\end{minipage}\\[0.2cm]
+\begin{minipage}[t]{7cm}
+c) \underline{$E_{\text{b}}=-1.88\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/1-88.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{7cm}
+d) \underline{$E_{\text{b}}=-1.38\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/1-38.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Relaxed structures of defect complexes obtained by creating a a) \hkl<0 0 1>, a b) \hkl<0 0 -1>, a c) \hkl<0 -1 0> and a d) \hkl<1 0 0> dumbbell at position 5.}
+\label{fig:defects:comb_db_03}
+\end{figure}
+Energetically beneficial configurations of defect complexes are observed for second interstititals of all orientations placed at position 5, a position two bonds away from the initial interstitial along the \hkl<1 1 0> direction.
+Relaxed structures of these complexes are displayed in figure \ref{fig:defects:comb_db_03}.
+Figure \ref{fig:defects:comb_db_03} a) and b) show the relaxed structures of \hkl<0 0 1> and \hkl<0 0 -1> dumbbells.
+The upper dumbbell atoms are pushed towards each other forming fourfold coordinated bonds.
+While the displacements of the silicon atoms in case b) are symmetric to the \hkl(1 1 0) plane, in case a) the silicon atom of the initial dumbbel is pushed a little further in the direction of the carbon atom of the second dumbbell than the carbon atom is pushed towards the silicon atom.
+The bottom atoms of the dumbbells remain in threefold coordination.
+The symmetric configuration is energetically more favorable ($E_{\text{b}}=-1.66\text{ eV}$) since the displacements of the atoms is less than in the antiparallel case ($E_{\text{b}}=-1.53\text{ eV}$).
+In figure \ref{fig:defects:comb_db_03} c) and d) the nonparallel orientations, namely the \hkl<0 -1 0> and \hkl<1 0 0> dumbbells are shown.
+Binding energies of -1.88 eV and -1.38 eV are obtained for the relaxed structures.
+In both cases the silicon atom of the initial interstitial is pulled towards the near by atom of the second dumbbell so that both atoms form fourfold coordinated bonds to their next neighbours.
+In case c) it is the carbon and in case d) the silicon atom of the second interstitial which forms the additional bond with the silicon atom of the initial interstitial.
+The atom of the second dumbbell, the carbon atom of the initial dumbbell and the two interconnecting silicon atoms again reside in a plane.
+A typical C-C distance of 2.79 \AA{} is, thus, observed for case c).
+The far-off atom of the second dumbbell resides in threefold coordination.
+
+Assuming that it is possible for the system to minimize free energy by an in place reorientation of the dumbbell at any position the minimum energy orientation of dumbbells along the \hkl<1 1 0> direction and the resulting C-C distance is shown in table \ref{tab:defects:comb_db110}.
+\begin{table}[t!h!]
+\begin{center}
+\begin{tabular}{l c c c c c c}
+\hline
+\hline
+ & 1 & 2 & 3 & 4 & 5 & 6\\
+\hline
+$E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
+C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
+Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption{Binding energy and type of the minimum energy configuration of an additional dumbbell with respect to the separation distance in bonds along the \hkl<1 1 0> direction and the C-C distance.}
+\label{tab:defects:comb_db110}
+\end{table}
+\begin{figure}[t!h!]
+\begin{center}
+\includegraphics[width=12.5cm]{db_along_110.ps}\\
+\includegraphics[width=12.5cm]{db_along_110_cc.ps}
+\end{center}
+\caption{Minimum binding energy of dumbbell combinations with respect to the separation distance in bonds along \hkl<1 1 0> and C-C distance.}
+\label{fig:defects:comb_db110}
+\end{figure}
+Figure \ref{fig:defects:comb_db110} shows the corresponding plot of the data including a cubic spline interplation and a suitable fitting curve.
+The funtion found most suitable for curve fitting is $f(x)=a/x^3$ comprising the single fit parameter $a$.
+Thus, far-off located dumbbells show an interaction proportional to the reciprocal cube of the distance and the amount of bonds along \hkl<1 1 0> respectively.
+This behavior is no longer valid for the immediate vicinity revealed by the saturating binding energy of a second dumbbell at position 1, which is ignored in the fitting procedure.
+
+\begin{figure}[t!h!]
+\begin{center}
+\begin{minipage}[t]{5cm}
+a) \underline{Pos: 1, $E_{\text{b}}=0.26\text{ eV}$}
+\begin{center}
+\includegraphics[width=4.8cm]{00-1dc/0-26.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{5cm}
+b) \underline{Pos: 3, $E_{\text{b}}=-0.93\text{ eV}$}
+\begin{center}
+\includegraphics[width=4.8cm]{00-1dc/0-93.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{5cm}
+c) \underline{Pos: 5, $E_{\text{b}}=0.49\text{ eV}$}
+\begin{center}
+\includegraphics[width=4.8cm]{00-1dc/0-49.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Relaxed structures of defect complexes obtained by creating a carbon substitutional at position 1 (a)), 3 (b)) and 5 (c)).}
+\label{fig:defects:comb_db_04}
+\end{figure}
+\begin{figure}[t!h!]
+\begin{center}
+\begin{minipage}[t]{7cm}
+a) \underline{Pos: 2, $E_{\text{b}}=-0.51\text{ eV}$}
+\begin{center}
+\includegraphics[width=6cm]{00-1dc/0-51.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{7cm}
+b) \underline{Pos: 4, $E_{\text{b}}=-0.15\text{ eV}$}
+\begin{center}
+\includegraphics[width=6cm]{00-1dc/0-15.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Relaxed structures of defect complexes obtained by creating a carbon substitutional at position 2 (a)) and 4 (b)).}
+\label{fig:defects:comb_db_05}
+\end{figure}
+The second part of table \ref{tab:defects:e_of_comb} lists the energetic results of substitutional carbon and vacancy combinations with the initial \hkl<0 0 -1> dumbbell.
+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.
+
+\begin{figure}[t!h!]
+\begin{center}
+\begin{minipage}[t]{7cm}
+a) \underline{Pos: 2, $E_{\text{b}}=-0.59\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/0-59.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{7cm}
+b) \underline{Pos: 3, $E_{\text{b}}=-3.14\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/3-14.eps}
+\end{center}
+\end{minipage}\\[0.2cm]
+\begin{minipage}[t]{7cm}
+c) \underline{Pos: 4, $E_{\text{b}}=-0.54\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/0-54.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{7cm}
+d) \underline{Pos: 5, $E_{\text{b}}=-0.50\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/0-50.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Relaxed structures of defect complexes obtained by creating vacancies 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} 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 bound 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.
+A vacancy ctreated at position 2 enables a relaxation of the silicon atom number 1 mainly in \hkl<0 0 -1> direction.
+The bond to silicon atom number 5 breaks.
+Hence, the silicon dumbbell atom is not only displaced along \hkl<0 0 -1> but also and to a greater extent in \hkl<1 1 0> direction.
+The carbon atom is slightly displaced in \hkl<0 1 -1> direction.
+A binding energy of -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 silicon atom number 1, which would be directly bound to the replaced silicon atom at position 2.
+In the case of a vacancy created at position 4, even a slightly higher binding energy of -0.54 eV is observed, while the silicon atom at the bottom left, which is bound to the carbon dumbbell atom, is vastly displaced along \hkl<1 0 -1>.
+However the displacement of the carbon atom along \hkl<0 0 -1> is less than it is in the preceding configuration.
+Although expected due to the symmetric initial configuration silicon atom number 1 is not displaced correspondingly and also the silicon dumbbell 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.
+Figure \ref{fig:defects:comb_db_06} d) shows the relaxed structure of a vacancy created at position 5.
+The silicon dumbbell atom is largely displaced along \hkl<1 1 0> and somewaht less along \hkl<0 0 -1>, which corresponds to the direction towards the vacancy.
+The silicon dumbbell atom approaches silicon number 1.
+Indeed a non-zero charge density is observed inbetween these two atoms exhibiting a cylinder-like shape superposed with the charge density known from the dumbbell itself.
+Strain reduced by this huge displacement is partially absorbed by tensile strain on silicon atom number 1 originating from attractive forces of the carbon atom and the vacancy.
+A binding energy of -0.50 eV is observed.
+{\color{red}Todo: Jahn-Teller distortion (vacancy) $\rightarrow$ actually three possibilities. Due to the initial defect, symmetries are broken. The system should have relaxed into the minumum energy configuration!?}
+
+\subsection{Combinations of Si self-interstitials and substitutional carbon}
+
+So far the C-Si \hkl<1 0 0> interstitial was found to be the energetically most favorable configuration.
+In fact substitutional C exhibits a configuration more than 3 eV lower in 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 role for the precipitation process might be attributed to them.
+Thus, combinations of substitutional C and an additional Si self-interstitial are examined in the following.
+The ground state of a single Si self-interstitial was found to be the Si \hkl<1 1 0> self-interstitial configuration.
+For the follwoing study the same type of self-interstitial is assumed to provide the energetically most favorable configuration in combination with substitutional C.
+
+\begin{table}[ht!]
+\begin{center}
+\begin{tabular}{l c c c c c c}
+\hline
+\hline
+C$_{\text{sub}}$ & \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} & A & A & \RM{2} & C & \RM{5} \\
+3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
+4 & \RM{4} & B & D & E & E & D \\
+5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption{Equivalent configurations of \hkl<1 1 0>-type Si self-interstitials created at position I of figure \ref{fig:defects:pos_of_comb} and substitutional C created at positions 1 to 5.}
+\label{tab:defects:comb_csub_si110}
+\end{table}
+\begin{table}[ht!]
+\begin{center}
+\begin{tabular}{l c c c c c c c c c c}
+\hline
+\hline
+Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
+\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 $E_{\text{f}}$ and binding $E_{\text{b}}$ energies in eV of the combinational substitutional C and Si self-interstitial configurations 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} shows equivalent configurations of \hkl<1 1 0>-type Si self-interstitials and substitutional C.
+The notation of figure \ref{fig:defects:pos_of_comb} is used with the six possible Si self-interstitials created at the usual C-Si dumbbell position.
+Substitutional C is created at positions 1 to 5.
+Resulting formation and binding energies of the relaxed structures are listed in table \ref{tab:defects:comb_csub_si110_energy}.
+In addition the separation distance of the ssubstitutional C atom and the Si \hkl<1 1 0> dumbbell interstitial, which is defined to reside at $\frac{a_{\text{Si}}}{4} \hkl<1 1 1>$ is given.
+In total 10 different configurations exist within the investigated range.
+
+\begin{figure}[th!]
+\begin{center}
+\includegraphics[width=12cm]{c_sub_si110.ps}
+\end{center}
+\caption[Binding energy of combinations of a substitutional C and a Si \hkl<1 1 0> dumbbell self-interstitial with respect to the separation distance.]{Binding energy of combinations of a substitutional C and a Si \hkl<1 1 0> dumbbell self-interstitial with respect to the separation distance. The binding energy of the defect pair is well approximated by a Lennard-Jones 6-12 potential, which is used for curve fitting.}
+\label{fig:defects:csub_si110}
+\end{figure}
+According to the formation energies none of the investigated structures is energetically preferred over the C-Si \hkl<1 0 0> dumbbell interstitial, which exhibits a formation energy of 3.88 eV.
+Further separated defects are assumed to approximate the sum of the formation energies of the isolated single defects.
+This is affirmed by the plot of the binding energies with respect to the separation distance in figure \ref{fig:defects:csub_si110} approximating zero with increasing distance.
+Thus, the C-Si \hkl<1 0 0> dumbbell structure remains the ground state configuration of a C interstitial in c-Si with a constant number of Si atoms.
+
+{\color{blue}
+However the binding energy quickly drops to zero with respect to the distance, which is reinforced by the Lennard-Jones fit estimating almost zero interaction energy already at 0.6 nm.
+This indicates a possibly low interaction capture radius of the defect pair.
+Highly energetic collisions in the IBS process might result in separations of these defects exceeding the capture radius.
+For this reason situations most likely occur in which the configuration of substitutional C can be considered without a nearby interacting Si self-interstitial and, thus, unable to form a thermodynamically more stable C-Si \hkl<1 0 0> dumbbell configuration.
+}
+\label{section:defects:noneq_process_01}
+
+The energetically most favorable configuration of the combined structures is the one with the substitutional C atom located next to the \hkl<1 1 0> interstitial along the \hkl<1 1 0> direction (configuration \RM{1}).
+Compressive stress along the \hkl<1 1 0> direction originating from the Si \hkl<1 1 0> self-intesrtitial is partially compensated by tensile stress resulting from substitutional C occupying the neighboured Si lattice site.
+In the same way the energetically most unfavorable configuration can be explained, which is configuration \RM{3}.
+The substitutional C is located next to the lattice site shared by the \hkl<1 1 0> Si self-interstitial along the \hkl<1 -1 0> direction.
+Thus, the compressive stress along \hkl<1 1 0> of the Si \hkl<1 1 0> interstitial is not compensated but intensified by the tensile stress of the substitutional C atom, which is no longer loacted along the direction of stress.
+
+{\color{red}Todo: Erhart/Albe calc for most and less favorable configuration!}
+
+{\color{red}Todo: Mig of C-Si DB conf to or from C sub + Si 110 in progress.}
+
+{\color{red}Todo: Mig of Si DB located next to a C sub (also by MD!).}
+
+\section{Migration in systems of combined defects}
+
+As already pointed out in the previous section energetic carbon atoms may kick out silicon atoms from their lattice sites during carbon implantation into crystalline silicon.
+However configurations might arise in which C atoms do not already occupy the vacant site but instead form a C interstitial next to the vacancy.
+These combinations have been investigated shortly before in the very end of section \ref{subsection:defects:c-si_comb}.
+In the absence of the Si self-interstitial the energetically most favorable configuration is the configuration of a substitutional carbon atom, that is the carbon atom occupying the vacant site.
+In addition, it is a conceivable configuration the system might experience during the silicon carbide precipitation process.
+Energies needed to overcome the migration barrier of the transformation into this configuration enable predictions concerning the feasibility of a silicon carbide conversion mechanism derived from these microscopic processes.
+This is especially important for the case, in which the vacancy is created at position 3, as displayed in figure \ref{fig:defects:comb_db_06} b).
+Due to the low binding energy this configuration might constitute a trap, which it is hard to escape from.
+However, migration simulations show that only a low amount of energy is necessary to transform the system into the energetically most favorable configuration.
+\begin{figure}[!t!h]
+\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}[!t!h]
+\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}
+Figure \ref{fig:defects:comb_mig_01} and \ref{fig:defects:comb_mig_02} show the migration barriers and structures for transitions of the vacancy-interstitial configurations examined in figure \ref{fig:defects:comb_db_06} a) and b) into a configuration of substitutional carbon.
+If the vacancy is created at position 1 the system will end up in a configuration of substitutional C anyways.
+
+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.
+{\color{red}Todo: Direct migration of C in progress.}
+
+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 needed, 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.
+
+\section{Conclusions concerning the SiC conversion mechanism}