-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{blue}TODO: Explain why this might be important.}
+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 a C substitutional.
+
+\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 & F & 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}
+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.
+
+{\color{blue}TODO:
+Results of energies ...
+Thus ...
+}
+
+\section{Migration in systems of combined defects}
+
+During carbon implantation into crystalline silicon the energetic carbon atoms may kick out silicon atoms from their lattice sites.
+A vacancy accompanied by a silicon self-interstitial is generated.
+The silicon self-interstitial may migrate to the surface or recombine with other vacancies.
+Once a vacancy and a carbon interstitial defect exist 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 discussed in the last section and 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.
+
+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 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 mig along 110 (at the starting of this section)?}
+
+{\color{red}Todo: Migration of Si int + vac and C sub/int ...?}