added image of si self int relaxations

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index 3e3d8d2ae39a22874445768f332c98228883e5c6..459b7f4d055b755e67ed7e5593643eaa837e9eb6 100644 (file)
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -20,7 +20,7 @@ All point defects are calculated for the neutral charge state.
 \begin{center}
 \includegraphics[width=9cm]{unit_cell_e.eps}
 \end{center}
-\caption{Insertion positions for the tetrahedral ({\color{red}$\bullet$}), hexagonal  ({\color{green}$\bullet$}), \hkl<1 0 0> dumbbell ({\color{yellow}$\bullet$}), \hkl<1 1 0> dumbbell ({\color{magenta}$\bullet$}) and bond-centered ({\color{cyan}$\bullet$}) interstitial configuration.}
+\caption[Insertion positions for the tetrahedral ({\color{red}$\bullet$}), hexagonal  ({\color{green}$\bullet$}), \hkl<1 0 0> dumbbell ({\color{yellow}$\bullet$}), \hkl<1 1 0> dumbbell ({\color{magenta}$\bullet$}) and bond-centered ({\color{cyan}$\bullet$}) interstitial configuration.]{Insertion positions for the tetrahedral ({\color{red}$\bullet$}), hexagonal  ({\color{green}$\bullet$}), \hkl<1 0 0> dumbbell ({\color{yellow}$\bullet$}), \hkl<1 1 0> dumbbell ({\color{magenta}$\bullet$}) and bond-centered ({\color{cyan}$\bullet$}) interstitial configuration. The black dots ({\color{black}$\bullet$}) correspond to the silicon atoms and the blue lines ({\color{blue}-}) indicate the covalent bonds of the perfect c-Si structure.}
 \label{fig:defects:ins_pos}
 \end{figure}
 
@@ -78,6 +78,84 @@ The formation energies of some of the silicon self-interstitial configurations a
 \caption[Formation energies of silicon self-interstitials in crystalline silicon determined by classical potential molecular dynamics and density functional calculations.]{Formation energies of silicon self-interstitials in crystalline silicon determined by classical potential molecular dynamics and density functional calculations. The formation energies are given in eV. T denotes the tetrahedral, H the hexagonal, B the bond-centered and V the vacancy interstitial configuration. The dumbbell configurations are abbreviated by DB.}
 \label{tab:defects:si_self}
 \end{table}
+The final configurations obtained after relaxation are presented in figure \ref{fig:defects:conf}.
+\begin{figure}[h]
+\begin{center}
+\hrule
+\vspace*{0.2cm}
+\begin{flushleft}
+\begin{minipage}{5cm}
+\underline{\hkl<1 1 0> dumbbell}\\
+$E_{\text{f}}=3.39\text{ eV}$\\
+\includegraphics[width=4.0cm]{si_pd_vasp/110_2333.eps}
+\end{minipage}
+\begin{minipage}{5cm}
+\underline{Hexagonal}\\
+$E_{\text{f}}=3.42\text{ eV}$\\
+\includegraphics[width=4.0cm]{si_pd_vasp/hex_2333.eps}
+\end{minipage}
+\begin{minipage}{5cm}
+\underline{Tetrahedral}\\
+$E_{\text{f}}=3.77\text{ eV}$\\
+\includegraphics[width=4.0cm]{si_pd_vasp/tet_2333.eps}
+\end{minipage}\\[0.2cm]
+\begin{minipage}{5cm}
+\underline{\hkl<1 0 0> dumbbell}\\
+$E_{\text{f}}=4.41\text{ eV}$\\
+\includegraphics[width=4.0cm]{si_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{5cm}
+\underline{Vacancy}\\
+$E_{\text{f}}=3.63\text{ eV}$\\
+\includegraphics[width=4.0cm]{si_pd_vasp/vac_2333.eps}
+\end{minipage}
+\begin{minipage}{5cm}
+\begin{center}
+VASP\\
+calculations\\
+\end{center}
+\end{minipage}
+\end{flushleft}
+\vspace*{0.2cm}
+\hrule
+\begin{flushleft}
+\begin{minipage}{5cm}
+\underline{\hkl<1 1 0> dumbbell}\\
+$E_{\text{f}}=3.39\text{ eV}$\\
+\includegraphics[width=4.0cm]{si_pd_albe/110.eps}
+\end{minipage}
+\begin{minipage}{5cm}
+\underline{Hexagonal}\\
+$E_{\text{f}}=3.42\text{ eV}$\\
+\includegraphics[width=4.0cm]{si_pd_albe/hex.eps}
+\end{minipage}
+\begin{minipage}{5cm}
+\underline{Tetrahedral}\\
+$E_{\text{f}}=3.77\text{ eV}$\\
+\includegraphics[width=4.0cm]{si_pd_albe/tet.eps}
+\end{minipage}\\[0.2cm]
+\begin{minipage}{5cm}
+\underline{\hkl<1 0 0> dumbbell}\\
+$E_{\text{f}}=4.41\text{ eV}$\\
+\includegraphics[width=4.0cm]{si_pd_albe/100.eps}
+\end{minipage}
+\begin{minipage}{5cm}
+\underline{Vacancy}\\
+$E_{\text{f}}=3.63\text{ eV}$\\
+\includegraphics[width=4.0cm]{si_pd_albe/vac.eps}
+\end{minipage}
+\begin{minipage}{5cm}
+\begin{center}
+Erhard/Albe potential\\
+calculations\\
+\end{center}
+\end{minipage}
+\end{flushleft}
+\hrule
+\end{center}
+\caption[Relaxed silicon self-interstitial defect configurations.]{Relaxed silicon self-interstitial defect configurations. The silicon atoms and the bonds (only for the interstitial atom) are illustrated by yellow spheres and blue lines.}
+\label{fig:defects:conf}
+\end{figure}
 
 There are differences between the various results of the quantum-mechanical calculations but the consesus view is that the \hkl<1 1 0> dumbbell followed by the hexagonal and tetrahedral defect is the lowest in energy.
 This is nicely reproduced by the DFT calculations performed in this work.
@@ -91,12 +169,19 @@ The Si interstitial atom moves towards an energetically more favorable position
 The formation energy of 3.96 eV for this type of interstitial is equal to the result for the hexagonal one in the original work \cite{}.
 Obviously the authors did not carefully check the relaxed results assuming a hexagonal configuration.
 To exclude failures in the implementation of the potential or the MD code itself the hexagonal defect structure was double-checked with the PARCAS MD code \cite{}.
+The same type of interstitial arises using random insertions.
+In addition, variations exist in which the displacement is only along two \hkl<1 0 0> axes ($E_\text{f}=3.8\text{ eV}$) or along a single \hkl<1 0 0> axes ($E_\text{f}=3.6\text{ eV}$) successively approximating the tetdrahedral configuration and formation energy.
+The existence of these local minima located near the tetrahedral configuration seems to be an artefact of the analytical potential without physical authenticity revealing basic problems of analytical potential models for describing defect structures.
+However, the energy barrier is small (DAS MAL DURCHRECHNEN).
+Hence these artefacts should have a negligent influence in finite temperature simulations.
 
-The bond-centered configuration is unstable for both, the Erhard/Albe and VASP calculations.
+The bond-centered configuration is unstable and the \hkl<1 0 0> dumbbell interstitial is the most unfavorable configuration for both, the Erhard/Albe and VASP calculations.
 
 
 \section{Carbon related point defects}
 
+
+
 \section[Migration of the carbon \hkl<1 0 0> interstitial]{\boldmath Migration of the carbon \hkl<1 0 0> interstitial}
 
 \section{Combination of point defects}