\chapter{Point defects in silicon}
+\label{chapter:defects}
Given the conversion mechnism of SiC in crystalline silicon introduced in section \ref{section:assumed_prec} the understanding of carbon and silicon interstitial point defects in c-Si is of great interest.
Both types of defects are examined in the following both by classical potential as well as density functional theory calculations.
The method without updating the constraints but still applying them to all atoms shows a delayed crossing of the saddle point.
This is understandable since the update results in a more aggressive advance towards the final configuration.
In any case the barrier obtained is slightly higher, which means that it does not constitute an energetically more favorable pathway.
-The method in which the constraints are only applied to the diffusing C atom and two Si atoms, ... {\color{red}in progress} ...
+The method in which the constraints are only applied to the diffusing C atom and two Si atoms, ... {\color{red}Todo: does not work!} ...
\subsection{Migration barriers obtained by classical potential calculations}
\label{subsection:defects:mig_classical}
In the first migration path it is the configuration resulting from further relaxation of the rather unstable bond-centered configuration, which is fixed to be a transition point in the migration calculations.
The last two pathways show configurations almost identical to the \hkl<1 1 0> configuration, which constitute a local minimum within the pathway.
Thus, migration pathways with the \hkl<1 1 0> C-Si dumbbell interstitial configuration as a starting or final configuration are further investigated.
-\begin{figure}[ht!]
+\begin{figure}[!ht]
\begin{center}
\includegraphics[width=13cm]{110_mig.ps}
\end{center}
As expected by the initialization conditions the two carbon atoms form a bond.
This bond has a length of 1.38 \AA{} close to the nex neighbour distance in diamond or graphite, which is approximately 1.54 \AA.
The minimum of binding energy observed for this configuration suggests prefered C clustering as a competing mechnism to the C-Si dumbbell interstitial agglomeration inevitable for the SiC precipitation.
-{\color{red}Todo: Activation energies to obtain separated C confs currently in progress - could be added in the combined defect migration chapter and mentioned here, too!}
+{\color{red}Todo: Activation energies to obtain separated C confs FAILED (again?) - could be added in the combined defect migration chapter and mentioned here, too!}
However, for the second most favorable configuration, presented in figure \ref{fig:defects:comb_db_01} a), the amount of possibilities for this configuration is twice as high.
In this configuration the initial Si (I) and C (I) dumbbell atoms are displaced along \hkl<1 0 0> and \hkl<-1 0 0> in such a way that the Si atom is forming tetrahedral bonds with two silicon and two carbon atoms.
The carbon and silicon atom constituting the second defect are as well displaced in such a way, that the carbon atom forms tetrahedral bonds with four silicon neighbours, a configuration expected in silicon carbide.
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{table}[!ht]
\begin{center}
\begin{tabular}{l c c c c c c}
\hline
\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{table}[!ht]
\begin{center}
\begin{tabular}{l c c c c c c c c c c}
\hline
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.
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