From: hackbard Date: Thu, 28 Jan 2010 17:54:12 +0000 (+0100) Subject: more 100 db X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=dd13f356dd8a24480bc6e633ac9c94cd1f1e07b7;p=lectures%2Flatex.git more 100 db --- diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex index 2a4dcb2..c286426 100644 --- a/posic/thesis/defects.tex +++ b/posic/thesis/defects.tex @@ -328,12 +328,13 @@ In calculations performed in this work the bond-centered configuration in fact i As the \hkl<1 0 0> dumbbell interstitial is the lowest configuration in energy it is the most probable hence important interstitial configuration of carbon in silicon. It was first identified by infra-red (IR) spectroscopy \cite{bean70} and later on by electron paramagnetic resonance (EPR) spectroscopy \cite{watkins76}. -Figure \ref{fig:defects:100db_cmp} schematically shows the \hkl<1 0 0> dumbbell structure and table \ref{tab:defects:100db_cmp} lists the details of displacements obtained by analytical potential and quantum-mechanical calculations. +Figure \ref{fig:defects:100db_cmp} schematically shows the \hkl<1 0 0> dumbbell structure and table \ref{tab:defects:100db_cmp} lists the details of the atomic displacements, distances and bond angles obtained by analytical potential and quantum-mechanical calculations. +For comparison, the obtained structures for both methods visualized out of the atomic position data are presented in figure \ref{fig:defects:100db_vis_cmp}. \begin{figure}[h] \begin{center} \includegraphics[width=12cm]{100-c-si-db_cmp.eps} \end{center} -\caption[Sketch of the \hkl<1 0 0> dumbbell structure.]{Sketch of the \hkl<1 0 0> dumbbell structure. Atomic displacements and distances are listed in table \ref{tab:defects:100db_cmp}.} +\caption[Sketch of the \hkl<1 0 0> dumbbell structure.]{Sketch of the \hkl<1 0 0> dumbbell structure. Atomic displacements, distances and bond angles are listed in table \ref{tab:defects:100db_cmp}.} \label{fig:defects:100db_cmp} \end{figure} % @@ -344,7 +345,7 @@ Displacements\\ \hline \hline & & & & \multicolumn{3}{c}{Atom 2} & \multicolumn{3}{c}{Atom 3} \\ - & $a$ & $b$ & $|a|+|b|$ & $\Delta x$ & $\Delta y$ & $\Delta z$ & $\Delta x$ & $\Delta y$ & $\Delta z$ \\ +and bond angles & $a$ & $b$ & $|a|+|b|$ & $\Delta x$ & $\Delta y$ & $\Delta z$ & $\Delta x$ & $\Delta y$ & $\Delta z$ \\ \hline Erhard/Albe & 0.084 & -0.091 & 0.175 & -0.015 & -0.015 & -0.031 & -0.014 & 0.014 & 0.020 \\ VASP & 0.109 & -0.065 & 0.174 & -0.011 & -0.011 & -0.024 & -0.014 & 0.014 & 0.025 \\ @@ -372,23 +373,44 @@ Angles\\ \hline & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\ \hline -Erhard/Albe & 0.175 & 0.329 & 0.186 & 0.226 \\ -VASP & 0.174 & 0.341 & 0.182 & 0.229 \\ +Erhard/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\ +VASP & 130.7 & 114.4 & 146.0 & 107.0 \\ \hline \hline \end{tabular}\\[0.5cm] \end{center} -\caption[Atomic displacements and distances of the \hkl<1 0 0> dumbbell structure obtained by the Erhard/Albe potential and VASP calculations.]{Atomic displacements and distances of the \hkl<1 0 0> dumbbell structure obtained by the Erhard/Albe potential and VASP calculations. The displacements and distances are given in nm and schematically displayed in figure \ref{fig:defects:100db_cmp}. In addition, the equilibrium lattice constant for crystalline silicon is listed.} +\caption[Atomic displacements, distances and bond angles of the \hkl<1 0 0> dumbbell structure obtained by the Erhard/Albe potential and VASP calculations.]{Atomic displacements, distances and bond angles of the \hkl<1 0 0> dumbbell structure obtained by the Erhard/Albe potential and VASP calculations. The displacements and distances are given in nm and the angles are given in degrees. Displacements, distances and angles are schematically displayed in figure \ref{fig:defects:100db_cmp}. In addition, the equilibrium lattice constant for crystalline silicon is listed.} \label{tab:defects:100db_cmp} \end{table} +\begin{figure}[h] +\begin{center} +\begin{minipage}{6cm} +\begin{center} +\underline{Erhard/Albe} +\includegraphics[width=5cm]{c_pd_albe/100_cmp.eps} +\end{center} +\end{minipage} +\begin{minipage}{6cm} +\begin{center} +\underline{VASP} +\includegraphics[width=5cm]{c_pd_vasp/100_cmp.eps} +\end{center} +\end{minipage} +\end{center} +\caption{Comparison of the visualized \hkl<1 0 0> dumbbel structures obtained by Erhard/Albe potential and VASP calculations.} +\label{fig:defects:100db_vis_cmp} +\end{figure} The silicon atom numbered '1' and the C atom compose the dumbbell structure. They share the lattice site which is indicated by the dashed red circle and which they are displaced from by length $a$ and $b$ respectively. The atoms no longer have four tetrahedral bonds to the silicon atoms located on the alternating opposite edges of the cube. -Instead, each of the dumbbell atoms forms threefold coordinated bonds, whcih are located in a plane. +Instead, each of the dumbbell atoms forms threefold coordinated bonds, which are located in a plane. One bond is formed to the other dumbbell atom. The other two bonds are bonds to the two silicon edge atoms located in the opposite direction of the dumbbell atom. -Angles ... The distance of the two dumbbell atoms is almost the same for both types of calculations. +However, in the case of the VASP calculation, the dumbbell structure is pushed upwards compared to the Erhard/Albe results. +Thus, the angles of bonds of the silicon dumbbell atom are clos to $120^{\circ}$ signifying the predominance of $sp^2$ hybridization. +On the other hand, the carbon atom forms an almost colinear bond with the two silicon edge atoms implying the predominance of $p$ and $sp$ bonding. +This is in figure \ref{fig:defects:100db_vis_cmp} as well as by the ... \subsection{Bond-centered interstitial configuration} \label{subsection:bc}