more defect combo

[lectures/latex.git] / posic / thesis / defects.tex

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index 17fd7bc..5bec37f 100644 (file)
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -667,7 +667,7 @@ Investigations are restricted to quantum-mechanical calculations.
 Initial interstitial: $\frac{1}{4}\hkl<1 1 1>$\\
 Relative silicon neighbour positions:
 \begin{enumerate}
- \item $\frac{1}{4}\hkl<1 1 -1>$, $\frac{1}{4}\hkl<-1 -1 -1>$ ()
+ \item $\frac{1}{4}\hkl<1 1 -1>$, $\frac{1}{4}\hkl<-1 -1 -1>$
  \item $\frac{1}{2}\hkl<1 0 1>$, $\frac{1}{2}\hkl<0 1 -1>$,\\[0.2cm]
        $\frac{1}{2}\hkl<0 -1 -1>$, $\frac{1}{2}\hkl<-1 0 -1>$
  \item $\frac{1}{4}\hkl<1 -1 1>$, $\frac{1}{4}\hkl<-1 1 1>$
@@ -691,20 +691,21 @@ Relative silicon neighbour positions:
 \hline
 \hline
  & 1 & 2 & 3 & 4 & 5 \\
-\hline
- \hkl<0 0 -1> & & & & & \\
- \hkl<0 0 1> & & & & & \\
- \hkl<0 -1 0> & & & & & \\
- \hkl<0 1 0> & & & & & \\
- \hkl<-1 0 0> & & & & & \\
- \hkl<1 0 0> & & & & & \\
- C substitutional & & & & & \\
- Vacancy & & & & & \\
+ \hline
+ \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66\\
+ \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53\\
+ \hkl<0 -1 0> & {\color{orange}-2.39} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88}\\
+ \hkl<0 1 0> & {\color{cyan}-2.25} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38}\\
+ \hkl<-1 0 0> & {\color{orange}-2.39} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88}\\
+ \hkl<1 0 0> & {\color{cyan}-2.25} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} \\
+ \hline
+ C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 \\
+ Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 \\
 \hline
 \hline
 \end{tabular}
 \end{center}
-\caption[Energetic results of defect combinations.]{Energetic results of defect combinations. The given energies in eV are defined by equation \eqref{eq:defects:e_of_comb}.}
+\caption[Energetic results of defect combinations.]{Energetic results of defect combinations. The given energies in eV are defined by equation \eqref{eq:defects:e_of_comb}. Equivalent configurations are marked by identical colors. The first column lists the types of the second defect combined with the initial \hkl<0 0 -1> dumbbell interstitial. The position index of the second defect is given in the first row according to figure \ref{fig:defects:pos_of_comb}.}
 \label{tab:defects:e_of_comb}
 \end{table}
 Figure \ref{fig:defects:pos_of_comb} shows the initial \hkl<0 0 -1> dumbbell interstitial defect and the positions of next neighboured silicon atoms used for the second defect.
@@ -718,5 +719,23 @@ E_{\text{f}}^{\text{2nd defect}}
 \label{eq:defects:e_of_comb}
 \end{equation}
 with $E_{\text{f}}^{\text{defect combination}}$ being the formation energy of the defect combination, $E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}$ being the formation energy of the C \hkl<0 0 -1> dumbbell interstitial defect and $E_{\text{f}}^{\text{2nd defect}}$ being the formation energy of the second defect.
+For defects far away from each other the formation energy of the defect combination should approximately become the sum of the formation energies of the individual defects.
+The interaction of such defects is low resulting in $E=0$.
+In fact, for another \hkl<0 0 -1> dumbbell interstitial created at position $\frac{a_{\text{Si}}}{2}\hkl<3 2 3>$ relative to the initial one an energy of \ldots eV is obtained.
+Configurations wih energies greater than zero are energetically unfavorable and expose a repulsive interaction.
+These configurations are unlikely to arise or to persist for non-zero temperatures.
+Energies below zero indicate configurations favored compared to configurations in which these point defects are separated far away from each other.
+
+Investigating the first part of table \ref{tab:defects:e_of_comb}, namely the combinations with another \hkl<1 0 0>-type interstitial, most of the combinations result in energies below zero.
+Surprisingly the most favorable configurations are the ones with the second defect created at the very next silicon neighbour and a change in orientation compared to the initial one.
+\begin{figure}[h]
+\caption{}
+\label{fig:defects:comb_db_01}
+\end{figure}
+Figure \ref{} shows the structure of these two configurations.
+
+
+
+