+\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}
+
+{\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}
+\begin{table}[ht!]
+\begin{center}
+\begin{tabular}{l c 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 &F\\
+\hline
+$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.56 & 5.32 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 & 5.32 \\
+$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.03 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 & -0.03 \\
+\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.
+
+{\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}