The blue torus, reinforcing the assumption of the p orbital, illustrates the resulting spin up electron density.
In addition, the energy level diagram shows a net amount of two spin up electrons.
-\section[Migration of the carbon \hkl<1 0 0> interstitial]{\boldmath Migration of the carbon \hkl<1 0 0> interstitial}
+\section[Migration of the carbon \hkl<1 0 0> interstitial]{Migration of the carbon \boldmath\hkl<1 0 0> interstitial}
\label{subsection:100mig}
In the following the problem of interstitial carbon migration in silicon is considered.
The theoretical description performed in this work is improved compared to a former study \cite{capaz94}, which underestimates the experimental value by 35 \%.
In addition the bond-ceneterd configuration, for which spin polarized calculations are necessary, is found to be a real local minimum instead of a saddle point configuration.
-\section{Combination of point defects}
+\section{Combination of adjacent 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 structural and energetic properties of combinations of point defects are examined in the following.
+Investigations are restricted to quantum-mechanical calculations.
+
+\subsection[Combinations with a C-Si \hkl<1 0 0>-type interstitial]{\boldmath Combinations with a C-Si \hkl<1 0 0>-type interstitial}
+
+This section focuses 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}[th]
\begin{center}
A binding energy of -0.50 eV is observed.
{\color{red}Todo: Jahn-Teller distortion (vacancy) $\rightarrow$ actually three possibilities. Due to the initial defect, symmetries are broken. The system should have relaxed into the minumum energy configuration!?}
-{\color{blue}Todo: Si int + vac and C sub/int ...?
-Investigation of vacancy, Si and C interstitital.
-As for the ground state of the single Si self-int, a 110 is also assumed as the lowest possibility in combination with other defects (which is a cruel assumption)!
+\subsection{Combinations of Si self-interstitials and substitutional carbon}
+
+{\color{blue}TODO: Explain why this might be important.}
+The ground state of a single Si self-interstitial was found to be the Si \hkl<1 1 0> self-interstitial configuration.
+For the follwoing study the same type of self-interstitial is assumed to provide the energetically most favorable configuration in combination with a C substitutional.
+
+\begin{table}[ht!]
+\begin{center}
+\begin{tabular}{l c c c c c c}
+\hline
+\hline
+C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
+ \hkl<1 0 1> & \hkl<-1 0 1> \\
+\hline
+1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
+2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
+3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
+4 & \RM{4} & B & D & E & F & D \\
+5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption{Equivalent configurations of \hkl<1 1 0>-type Si self-interstitials created at position I of figure \ref{fig:defects:pos_of_comb} and substitutional C created at positions 1 to 5.}
+\label{tab:defects:comb_csub_si110}
+\end{table}
+Table \ref{tab:defects:comb_csub_si110} shows equivalent configurations of \hkl<1 1 0>-type Si self-interstitials and substitutional C.
+The notation of figure \ref{fig:defects:pos_of_comb} is used with the six possible Si self-interstitials created at the usual C-Si dumbbell position.
+Substitutional C is created at positions 1 to 5.
+
+{\color{blue}TODO:
+Results of energies ...
+Thus ...
}
\section{Migration in systems of combined defects}
\subsection{Constructed 3C-SiC precipitate in crystalline silicon}
-Before proceeding with simulations at temperatrures exceeding the silicon melting point a spherical 3C-SiC precipitate enclosed in a c-Si surrounding is constructed as it is expected from IBS experiments and from simulations that finally succeed in simulating the precipitation event.
+Before proceeding with simulations at temperatrures around the silicon melting point a spherical 3C-SiC precipitate enclosed in a c-Si surrounding is constructed as it is expected from IBS experiments and from simulations that finally succeed in simulating the precipitation event.
On the one hand this sheds light on characteristic values like the radial distribution function or the total amount of free energy for such a configuration that is aimed to be reproduced by simulation.
On the other hand, assuming a correct alignment of the precipitate with the c-Si matrix, properties of such precipitates and the surrounding as well as the interface can be investiagted.
Furthermore these investigations might establish the prediction of conditions necessary for the simulation of the precipitation process.
To play safe the precipitate configuration at 100 \% of the Si melting temperature is chosen and cooled down to $20\,^{\circ}\mathrm{C}$ with a cooling rate of $1\,^{\circ}\mathrm{C}/\text{ps}$.
{\color{blue}TODO: Wait for results and then compare structure (PC) and interface energy, maybe a energetically more favorable configuration arises.}
{\color{red}TODO: Mention the fact, that the precipitate is stable for eleveated temperatures, even for temperatures where the Si matrix is melting.}
+{\color{red}TODO: Si starts to melt at the interface, show pictures and explain, it is due to the defective interface region.}
-\subsection{Simulations at temperatures exceeding the silicon melting point}
+\subsection{Simulations at temperatures around the silicon melting point}
As discussed in section \ref{subsection:md:limit} and \ref{subsection:md:inct} a further increase of the system temperature might help to overcome limitations of the short range potential and accelerate the dynamics involved in structural evolution.
A maximum temperature to avoid melting was determined in section \ref{subsection:md:tval}, which is 120 \% of the Si melting point.
In the following simulations the system volume, the amount of C atoms inserted and the shape of the insertion volume are modified from the values used in the first MD simulations to now match the conditions given in the simulations of the self-constructed precipitate configuration for reasons of comparability.
To quantify, the initial simulation volume now consists of 21 Si unit cells in each direction and 5500 C atoms are inserted in either the whole volume or in a sphere with a radius of 3 nm.
Since the investigated temperatures exceed the Si melting point the initial Si bulk material is heated up slowly by $1\,^{\circ}\mathrm{C}/\text{ps}$ starting from $1650\,^{\circ}\mathrm{C}$ before the C insertion sequence is started.
+The 100 ps sequence at the respective temperature intended for the structural evolution is exchanged by a 10 ns sequence, which will hopefully result in the occurence of infrequent processes.
+The return to lower temperatures is considered seperately.
\begin{figure}[!ht]
\begin{center}
\label{fig:md:exceed120}
\end{figure}
Figure \ref{fig:md:exceed100} and \ref{fig:md:exceed120} show the evolution of the free energy per atom and the quality at 100 \% and 120 \% of the Si melting temperature.
-
+{\color{red}TODO: Melting occurs, show and explain it and that it's due to the defects created.}
+
+{\color{red}TODO: Due to melting, after insertion, simulation is continued NVE, so melting hopefully will not occur, before it will be cooled down later on.}
+
+{\color{red}TODO: In additions simulations at 95 \% of the Si melting temperature are started again for longer times.}
\subsection{Further accelerated dynamics approaches}
{\color{red}TODO: self-guided MD!}
-{\color{red}TODO: other approaches!}
+{\color{red}TODO: other approaches?}
-{\color{red}TODO: ART MD?}
+{\color{red}
+TODO: ART MD?
+Also, how about forcing a migration of a $V_2$ configuration to a constructed prec configuration, detrmine the maximum saddle point and let the simulation run.
+}
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