\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
+\usepackage{color}
\newcommand{\si}{Si$_{\text{i}}${}}
\newcommand{\ci}{C$_{\text{i}}${}}
% additional stuff
\usepackage{miller}
+\newcommand{\prune}[1]{{\color{red} #1}}
+\newcommand{\possprune}[1]{{\color{blue} #1}}
+
\begin{document}
\title{Combined {\em ab initio} and classical potential simulation study on the silicon carbide precipitation in silicon}
\subsection{Carbon and silicon defect configurations}
\label{subsection:sep_def}
+%./visualize_cc_bonds -w 640 -h 480 -d results/c_100_2333_nosym_sp -nll -0.20 -0.20 -0.20 -fur 1.20 1.20 1.20 -b 0.0 0.0 0.0 1.0 1.0 1.0 -c 0.3 -1.7 1.1 -L 0.5 -1.0 0.5 -r 0.6 -A 2 109 217 1.9
\begin{figure}
\begin{minipage}[t]{0.32\columnwidth}
\underline{Si$_{\text{i}}$ \hkl<1 1 0> DB}\\
-\includegraphics[width=\columnwidth]{si110.eps}
+\includegraphics[width=\columnwidth]{si110_bonds.eps}
\end{minipage}
\begin{minipage}[t]{0.32\columnwidth}
\underline{Si$_{\text{i}}$ hexagonal}\\
-\includegraphics[width=\columnwidth]{sihex.eps}
+\includegraphics[width=\columnwidth]{sihex_bonds.eps}
\end{minipage}
\begin{minipage}[t]{0.32\columnwidth}
\underline{Si$_{\text{i}}$ tetrahedral}\\
-\includegraphics[width=\columnwidth]{sitet.eps}
+\includegraphics[width=\columnwidth]{sitet_bonds.eps}
\end{minipage}\\
\begin{minipage}[t]{0.32\columnwidth}
\underline{Si$_{\text{i}}$ \hkl<1 0 0> DB}\\
-\includegraphics[width=\columnwidth]{si100.eps}
+\includegraphics[width=\columnwidth]{si100_bonds.eps}
\end{minipage}
\begin{minipage}[t]{0.32\columnwidth}
\underline{Vacancy}\\
\end{minipage}
\begin{minipage}[t]{0.32\columnwidth}
\underline{C$_{\text{s}}$}\\
-\includegraphics[width=\columnwidth]{csub.eps}
+\includegraphics[width=\columnwidth]{csub_bonds.eps}
\end{minipage}\\
\begin{minipage}[t]{0.32\columnwidth}
\underline{C$_{\text{i}}$ \hkl<1 0 0> DB}\\
-\includegraphics[width=\columnwidth]{c100.eps}
+\includegraphics[width=\columnwidth]{c100_bonds.eps}
\end{minipage}
\begin{minipage}[t]{0.32\columnwidth}
\underline{C$_{\text{i}}$ \hkl<1 1 0> DB}\\
-\includegraphics[width=\columnwidth]{c110.eps}
+\includegraphics[width=\columnwidth]{c110_bonds.eps}
\end{minipage}
\begin{minipage}[t]{0.32\columnwidth}
\underline{C$_{\text{i}}$ bond-centered}\\
-\includegraphics[width=\columnwidth]{cbc.eps}
+\includegraphics[width=\columnwidth]{cbc_bonds.eps}
\end{minipage}
-\caption{Configurations of Si and C point defects in Si. Si and C atoms are illustrated by yellow and gray spheres respectively. Bonds are drawn whenever considered appropriate to ease identifying defect structures for the reader. Dumbbell configurations are abbreviated by DB.}
+\caption{Configurations of Si and C point defects in Si. Si and C atoms are illustrated by yellow and gray spheres respectively. Bonds of the defect atoms are drawn in red color. Dumbbell configurations are abbreviated by DB.}
\label{fig:sep_def}
\end{figure}
Table~\ref{table:sep_eof} summarizes the formation energies of relevant defect structures for the EA and DFT calculations.
\subsection{Pairs of C$_{\text{i}}$}
+% prune next
+\prune{
C$_{\text{i}}$ pairs of the \hkl<1 0 0> type have been investigated in the first part.
+}
Fig.~\ref{fig:combos_ci} schematically displays the initial C$_{\text{i}}$ \hkl[0 0 -1] DB structure and various positions for the second defect (1-5) that have been used for investigating defect pairs.
Table~\ref{table:dc_c-c} summarizes resulting binding energies for the combination with a second C-Si \hkl<1 0 0> DB obtained for different orientations at positions 1 to 5.
\begin{figure}
The atomic arrangement is shown in the bottom right of Fig.~\ref{fig:036-239}.
The two C$_{\text{i}}$ atoms form a strong C-C bond, which is responsible for the large gain in energy resulting in a binding energy of \unit[-2.39]{eV}.
+% possibly prune next
+\possprune{
Investigating migration barriers allows to predict the probability of formation of defect complexes by thermally activated diffusion processes.
+}
% ground state configuration, C cluster
Based on the lowest energy migration path of a single C$_{\text{i}}$ DB, the configuration, in which the second C$_{\text{i}}$ DB is oriented along \hkl[0 1 0] at position 2, is assumed to constitute an ideal starting point for a transition into the ground state.
In addition, the starting configuration exhibits a low binding energy (\unit[-1.90]{eV}) and is, thus, very likely to occur.
However, a barrier height of more than \unit[4]{eV} was detected resulting in a low probability for the transition.
+% possibly prune next
+\possprune{
The high activation energy is attributed to the stability of such a low energy configuration, in which the C atom of the second DB is located close to the initial DB.
+}
Low barriers have only been identified for transitions starting from energetically less favorable configurations, e.g. the configuration of a \hkl[-1 0 0] DB located at position 2 (\unit[-0.36]{eV}).
Starting from this configuration, an activation energy of only \unit[1.2]{eV} is necessary for the transition into the ground-state configuration.
The corresponding migration energies and atomic configurations are displayed in Fig.~\ref{fig:036-239}.
% should possibly be transfered to discussion section
Since thermally activated C clustering is, thus, only possible by traversing energetically unfavored configurations, extensive C clustering is not expected.
Furthermore, the migration barrier of \unit[1.2]{eV} is still higher than the activation energy of \unit[0.9]{eV} observed for a single C$_{\text{i}}$ \hkl<1 0 0> DB in c-Si.
+% possibly prune next until EOP
+\possprune{
The migration barrier of a C$_{\text{i}}$ DB in a complex system is assumed to approximate the barrier of a DB in a separated system with increasing defect separation.
Accordingly, lower migration barriers are expected for pathways resulting in larger separations of the C$_{\text{i}}$ DBs.
% acknowledged by 188-225 (reverse order) calc
However, if the increase of separation is accompanied by an increase in binding energy, this difference is needed in addition to the activation energy for the respective migration process.
Configurations, which exhibit both, a low binding energy as well as afferent transitions with low activation energies are, thus, most probable C$_{\text{i}}$ complex structures.
On the other hand, if elevated temperatures enable migrations with huge activation energies, comparably small differences in configurational energy can be neglected resulting in an almost equal occupation of such configurations.
-In both cases, the configuration yielding a binding energy of \unit[-2.25]{eV} is promising.
+% EOP
+In both cases,} the configuration yielding a binding energy of \unit[-2.25]{eV} is promising.
First of all, it constitutes the second most energetically favorable structure.
Secondly, a migration path with a barrier as low as \unit[0.47]{eV} exists starting from a configuration of largely separated defects exhibiting a low binding energy (\unit[-1.88]{eV}).
The migration barrier and corresponding structures are shown in Fig.~\ref{fig:188-225}.
% 2 more migs: 051 -> 128 and 026! forgot why ... probably it's about probability of C clustering
Obviously agglomeration of C$_{\text{i}}$ and C$_{\text{s}}$ is energetically favorable except for separations along one of the \hkl<1 1 0> directions.
The energetically most favorable configuration (configuration b) forms a strong but compressively strained C-C bond with a separation distance of \unit[0.142]{nm} sharing a Si lattice site.
+\possprune{
Again, conclusions concerning the probability of formation are drawn by investigating migration paths.
+}
Since C$_{\text{s}}$ is unlikely to exhibit a low activation energy for migration the focus is on C$_{\text{i}}$.
Pathways starting from the two next most favored configurations were investigated, which show activation energies above \unit[2.2]{eV} and \unit[3.5]{eV} respectively.
Although lower than the barriers for obtaining the ground state of two C$_{\text{i}}$ defects, the activation energies are yet considered too high.
+\possprune{
For the same reasons as in the last subsection, structures other than the ground-state configuration are, thus, assumed to arise more likely due to much lower activation energies necessary for their formation and still comparatively low binding energies.
+}
\subsection{C$_{\text{i}}$ next to V}
+\prune{
In the last subsection configurations of a C$_{\text{i}}$ DB with C$_{\text{s}}$ occupying a vacant site have been investigated.
+}
+\possprune{
Additionally, configurations might arise in IBS, in which the impinging C atom creates a vacant site near a C$_{\text{i}}$ DB, but does not occupy it.
+}
Resulting binding energies of a C$_{\text{i}}$ DB and a nearby vacancy are listed in the second row of Table~\ref{table:dc_c-sv}.
All investigated structures are preferred compared to isolated, largely separated defects.
In contrast to C$_{\text{s}}$, this is also valid for positions along \hkl[1 1 0] resulting in an entirely attractive interaction between defects of these types.
As shown in section~\ref{subsection:sep_def}, C$_{\text{s}}$ exhibits the lowest energy of formation.
Considering a perfect Si crystal and conservation of particles, however, the occupation of a Si lattice site by a slowed down implanted C atom is necessarily accompanied by the formation of a Si self-interstitial.
+\prune{
There are good reasons for the existence of regions exhibiting such configurations with regard to the IBS process.
Highly energetic C atoms are able to kick out a Si atom from its lattice site, resulting in a Si self-interstitial accompanied by a vacant site, which might get occupied by another C atom that lost almost all of its kinetic energy.
%Thus, configurations of C$_{\text{s}}$ and Si self-interstitials are investigated in the following.
Provided that the first C atom, which created the V and Si$_{\text{i}}$ pair has enough kinetic energy to escape the affected region, the C$_{\text{s}}$-Si$_{\text{i}}$ pair can be described as a separated defect complex.
+}
The Si$_{\text{i}}$ \hkl<1 1 0> DB, which was found to exhibit the lowest energy of formation within the investigated self-interstitial configurations, is assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$.
\begin{table}
Si atoms 1 and 2, which form the initial DB, occupy Si lattice sites in the final configuration while Si atom 3 is transferred from a regular lattice site into the interstitial lattice.
\begin{figure}
\begin{minipage}{0.49\columnwidth}
-\includegraphics[width=\columnwidth]{md01.eps}
+\includegraphics[width=\columnwidth]{md01_bonds.eps}
\end{minipage}
\begin{minipage}{0.49\columnwidth}
-\includegraphics[width=\columnwidth]{md02.eps}\\
+\includegraphics[width=\columnwidth]{md02_bonds.eps}\\
\end{minipage}\\
\begin{minipage}{0.49\columnwidth}
\begin{center}
$t=\unit[2900]{fs}$
\end{center}
\end{minipage}
-\caption{Atomic configurations of an {\em ab initio} molecular dynamics run at \unit[900]{$^{\circ}$C} starting from a configuration of C$_{\text{s}}$ located next to a Si$_{\text{i}}$ \hkl[1 1 0] DB (atoms 1 and 2). Equal atoms are marked by equal numbers. Bonds are drawn for substantial atoms only.}
+\caption{Atomic configurations of an {\em ab initio} molecular dynamics run at \unit[900]{$^{\circ}$C} starting from a configuration of C$_{\text{s}}$ located next to a Si$_{\text{i}}$ \hkl[1 1 0] DB (atoms 1 and 2). Equal atoms are marked by equal numbers.}
\label{fig:md}
\end{figure}
\newblock Phys. Rev. Lett. {\bf 70}, 2435 (1993).
\bibitem{tang97}
-M.~Tang, L.~Colombo, J.~Zhu, and T.~D. de~la Rubia,
+M.~Tang, L.~Colombo, J.~Zhu, and T.~Diaz de~la Rubia,
\newblock Phys. Rev. B {\bf 55}, 14279 (1997).
\bibitem{leung99}
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