X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Fthesis%2Fdefects.tex;h=709343c2790e2e1048b6576fccecdc762e01b13f;hp=5465ef8fc6abc2ffe4829c8ee79df2a6abcde47c;hb=21dd9359e717a7a1b4f8f5afa288434ec29e0ba6;hpb=0d60ebb25d9eeb2169a5ce8fcc43da927d7e0df5

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index 5465ef8..709343c 100644
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -464,7 +464,7 @@ This is supported by the charge density isosurface and the Kohn-Sham levels in f
 The blue torus, reinforcing the assumption of the p orbital, illustrates the resulting spin up electron density.
 In addition, the energy level diagram shows a net amount of two spin up electrons.
 
-\section[Migration of the carbon \hkl<1 0 0> interstitial]{\boldmath Migration of the carbon \hkl<1 0 0> interstitial}
+\section[Migration of the carbon \hkl<1 0 0> interstitial]{Migration of the carbon \boldmath\hkl<1 0 0> interstitial}
 \label{subsection:100mig}
 
 In the following the problem of interstitial carbon migration in silicon is considered.
@@ -648,13 +648,16 @@ The activation energy of roughly 0.9 eV nicely compares to experimental values.
 The theoretical description performed in this work is improved compared to a former study \cite{capaz94}, which underestimates the experimental value by 35 \%.
 In addition the bond-ceneterd configuration, for which spin polarized calculations are necessary, is found to be a real local minimum instead of a saddle point configuration.
 
-\section{Combination of point defects}
+\section{Combination of adjacent point defects}
 
-The structural and energetic properties of combinations of point defects are investigated in the following.
-The focus is on combinations of the \hkl<0 0 -1> dumbbell interstitial with a second defect.
+The structural and energetic properties of combinations of point defects are examined in the following.
+Investigations are restricted to quantum-mechanical calculations.
+
+\subsection[Combinations with a C-Si \hkl<1 0 0>-type interstitial]{\boldmath Combinations with a C-Si \hkl<1 0 0>-type interstitial}
+
+This section focuses on combinations of the \hkl<0 0 -1> dumbbell interstitial with a second defect.
 The second defect is either another \hkl<1 0 0>-type interstitial occupying different orientations, a vacany or a substitutional carbon atom.
 Several distances of the two defects are examined.
-Investigations are restricted to quantum-mechanical calculations.
 
 \begin{figure}[th]
 \begin{center}
@@ -1021,9 +1024,39 @@ Strain reduced by this huge displacement is partially absorbed by tensile strain
 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!?}
 
-{\color{blue}Todo: Si int + vac and C sub/int ...?
-Investigation of vacancy, Si and C interstitital.
-As for the ground state of the single Si self-int, a 110 is also assumed as the lowest possibility in combination with other defects (which is a cruel assumption)!
+\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}
+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}