From dd8959739ad96c93d2b0e735417c4dcaf97da263 Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 17 Feb 2010 16:43:19 +0100 Subject: [PATCH] more defect combo --- posic/thesis/defects.tex | 41 +++++++++++++++++++++++++++++----------- 1 file changed, 30 insertions(+), 11 deletions(-) diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex index 17fd7bc..5bec37f 100644 --- 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. + + + + -- 2.20.1