From: hackbard Date: Tue, 16 Feb 2010 10:05:24 +0000 (+0100) Subject: e table for defect combos X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=eb509e5b5ef4ede50aea14682fe1d6519be9340e;p=lectures%2Flatex.git e table for defect combos --- diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex index b421b3d..17fd7bc 100644 --- a/posic/thesis/defects.tex +++ b/posic/thesis/defects.tex @@ -652,6 +652,11 @@ In addition the bond-ceneterd configuration, for which spin polarized calculatio \section{Combination of 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 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}[h] \begin{center} \begin{minipage}{7.5cm} @@ -680,12 +685,38 @@ Relative silicon neighbour positions: \caption[\hkl<0 0 -1> dumbbell interstitial defect and positions of next neighboured silicon atoms used for the second defect.]{\hkl<0 0 -1> dumbbell interstitial defect and positions of next neighboured silicon atoms used for the second defect. Two possibilities exist for red numbered atoms and four possibilities exist for blue numbered atoms.} \label{fig:defects:pos_of_comb} \end{figure} -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 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. -Figure \ref{fig:defects:pos_of_comb} shows the initial \hkl<0 0 -1> dumbbell interstitial defect and the positions of the next neighboured silicon atoms used for the second defect. - +\begin{table}[h] +\begin{center} +\begin{tabular}{l c c c c c} +\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 +\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}.} +\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. +Table \ref{tab:defects:e_of_comb} summarizes energetic results obtained after relaxation of the defect combinations. +The energy of interest $E$ is defined to be +\begin{equation} +E= +E_{\text{f}}^{\text{defect combination}}- +E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}- +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.