\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_05}
+\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_05}.
-Figure \ref{fig:defects:comb_db_05} a) and b) show the relaxed structures of \hkl<0 0 1> and \hkl<0 0 -1> dumbbells.
+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_05} c) and d) the nonparallel orientations, namely the \hkl<0 -1 0> and \hkl<1 0 0> dumbbells are shown.
+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.
This behavior is no longer valid for the immediate vicinity revealed by the saturating binding energy of a second dumbbell at position 1, which is ignored in the fitting procedure.
{\color{red}Todo: DB mig along 110?}
+\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 5 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 th etransition of the carbon dumbbell atom into another substitutional atom occupying the dumbbell lattice site.
-Figure ...
-c-sub:
-position 5: the sub and the db both pull the the bottom si atoms in concerning \hkl<1 1 0> direction.
-Tensile strain which explains the binding energy.
-lowest energy observed at position 3.
-sub is located in top of the initial db.
-in contrast to the latter case, strain compensation occurs.
-position 2 and 4 the sub is (zwar) located (unter) db but due to the configuration not that much strain arises, since ...
-at position 1, c-c bond is formed, like in graphit or diamond.
-both c atoms are pushed towards each other resulting in high displacements and high strain energy in the near surrounding of the si crystal, which perfectly explains the high energy of ... eV.
-
+\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 vacancies at positions 2 (a)), 3 (b)), 4 (c)) and 5 (d)).}
+\label{fig:defects:comb_db_03}
+\end{figure}
The creation of the vacancy at position 1 ... c interstitital moves to acancy position ending up in a configuration of a substitutional carbon which explains the highbinding energy.
At position 3 a great amount of strain energy is reduced, since the the vacancy replaces a silicon atom usually bond to and thus starined by the silicon dumbbell atom.
db moves towards the vacancy in \hkl<1 -1 0> direction.
projects / lectures / latex.git / commitdiff