Experimentally measured activation energies for reorientation range from 0.77 eV to 0.88 eV \cite{watkins76,song90}.
Thus, this pathway is more likely to be composed of two consecutive steps of the second path.
-{\color{red}TODO: Stress out that this is a promising result excellently matching experimental observations.}
+{\color{red}Todo: Stress out that this is a promising result excellently matching experimental observations.}
Since the activation energy of the first and last migration path is much greater than the experimental value, the second path is identified to be responsible as a migration path for the most likely carbon interstitial in silicon explaining both, annealing and reorientation experiments.
The activation energy of roughly 0.9 eV nicely compares to experimental values.
The theoretical description performed in this work is improved compared to a former study \cite{capaz94}, which underestimates the experimental value by 35 \%.
Since the bond-centered configuration is unstable relaxing into the \hkl<1 1 0> C-Si dumbbell interstitial configuration within this potential the low kinetic energy state is used as a starting configuration.
Depending on the time constant activation energies of 2.4 eV and 2.2 eV respectively are obtained.
The migration path obtained by simulations with a time constant of 1 fs remains in the \hkl(1 1 0) plane.
-Using 100 fs as a time constant the C atom breaks out of the \hkl(1 0 0) plane already at the beginning of the migration accompanied by a reduction in energy.
+Using 100 fs as a time constant the C atom breaks out of the \hkl(1 1 0) plane already at the beginning of the migration accompanied by a reduction in energy.
The energy barrier of this path is 0.2 eV lower in energy than the direct migration within the \hkl(1 1 0) plane.
However, the investigated pathways cover an activation energy approximately twice as high as the one obtained by quantum-mechanical calculations.
For the entire transition of the \hkl<0 0 -1> into the \hkl<0 0 1> configuration by passing the bond-centered configuration an additional activation energy of 0.5 eV is necessary to escape from the bond-centered and reach the \hkl<0 0 1> configuration.
An activation energy of 2.2 eV is necessary to reorientate the \hkl<0 0 -1> dumbbell configuration into the \hkl<1 1 0> configuration, which is 1.3 eV higher in energy.
Residing in this state another 0.9 eV is enough to make the C atom form a \hkl<0 0 -1> dumbbell configuration with the Si atom of the neighboured lattice site.
In contrast to quantum-mechanical calculations, in which the direct transition is the energetically most favorable transition and the transition composed of the intermmediate migration steps is very unlikely to occur the just presented pathway is much more supposable in classical potential simulations, since the energetically most favorable transition found so far is also composed of two migration steps with activation energies of 2.2 eV and 0.5 eV.
-{\color{red}TODO: 00-1 to 001 transition, does it pass the bc conf?}
Although classical potential simulations reproduce the order in energy of the \hkl<1 0 0> and \hkl<1 1 0> C-Si dumbbell interstitial configurations as obtained by more accurate quantum-mechanical calculations the obtained migration pathways and resulting activation energies differ to a great extent.
On the one hand the most favorable pathways differ.
\subsection{Combinations of Si self-interstitials and substitutional carbon}
-{\color{blue}TODO: Explain why this might be important.}
+So far the C-Si \hkl<1 0 0> interstitial was found to be the energetically most favorable configuration.
+In fact substitutional C exhibits a configuration more than 3 eV lower in formation energy, however, the configuration does not account for the accompanying Si self-interstitial that is generated once a C atom occupies the site of a Si atom.
+With regard to the IBS process, in which highly energetic C atoms enter the Si target being able to kick out Si atoms from their lattice sites, such configurations are absolutely conceivable and a significant role for the precipitation process might be attributed to them.
+Thus, combinations of substitutional C and an additional Si self-interstitial are examined in the following.
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.
+For the follwoing study the same type of self-interstitial is assumed to provide the energetically most favorable configuration in combination with substitutional C.
\begin{table}[ht!]
\begin{center}
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 \\
+4 & \RM{4} & B & D & E & E & D \\
5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
\hline
\hline
\end{table}
\begin{table}[ht!]
\begin{center}
-\begin{tabular}{l c c c c c c c c c c c}
+\begin{tabular}{l c c c c c c c c c c}
\hline
\hline
-Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E &F\\
+Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
\hline
-$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.56 & 5.32 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 & 5.32 \\
-$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.03 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 & -0.03 \\
+$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
+$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
+$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
\hline
\hline
\end{tabular}
\caption{Formation $E_{\text{f}}$ and binding $E_{\text{b}}$ energies in eV of the combinational substitutional C and Si self-interstitial configurations as defined in table \ref{tab:defects:comb_csub_si110}.}
\label{tab:defects:comb_csub_si110_energy}
\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.
+Resulting formation and binding energies of the relaxed structures are listed in table \ref{tab:defects:comb_csub_si110_energy}.
+In addition the separation distance of the ssubstitutional C atom and the Si \hkl<1 1 0> dumbbell interstitial, which is defined to reside at $\frac{a_{\text{Si}}}{4} \hkl<1 1 1>$ is given.
+In total 10 different configurations exist within the investigated range.
+
+According to the formation energies none of the investigated structures is energetically preferred over the C-Si \hkl<1 0 0> dumbbell interstitial, which exhibits a formation energy of 3.88 eV.
+Further separated defects are assumed to approximate the sum of the formation energies of the isolated single defects.
+This is affirmed by the plot of the binding energies with respect to the separation distance in figure \ref{fig:defects:csub_si110} approximating zero with increasing distance.
+Thus, the C-Si \hkl<1 0 0> dumbbell structure remains the ground state configuration of a C interstitial in c-Si with a constant number of Si atoms.
+\begin{figure}[th!]
+\begin{center}
+\includegraphics[width=12cm]{c_sub_si110.ps}
+\end{center}
+\caption{Binding energy of combinations of a substitutional C and a Si \hkl<1 1 0> dumbbell self-interstitial with respect to the separation distance.}
+\label{fig:defects:csub_si110}
+\end{figure}
-{\color{blue}TODO:
-Results of energies ...
-Thus ...
-}
+The energetically most favorable configuration of the combined structures is the one with the substitutional C atom located next to the \hkl<1 1 0> interstitial along the \hkl<1 1 0> direction (configuration \RM{1}).
+Compressive stress along the \hkl<1 1 0> direction originating from the Si \hkl<1 1 0> self-intesrtitial is partially compensated by tensile stress resulting from substitutional C occupying the neighboured Si lattice site.
+In the same way the energetically most unfavorable configuration can be explained, which is configuration \RM{3}.
+The substitutional C is located next to the lattice site shared by the \hkl<1 1 0> Si self-interstitial along the \hkl<1 -1 0> direction.
+Thus, the compressive stress along \hkl<1 1 0> of the Si \hkl<1 1 0> interstitial is not compensated but intensified by the tensile stress of the substitutional C atom, which is no longer loacted along the direction of stress.
+
+{\color{red}Todo: Mig of C-Si DB conf to or from C sub + Si 110 int conf.}
+{\color{red}Todo: Si \hkl<1 1 0> migration barriers. If Si can go away fast, formation of substitutional C (and thus formation of SiC) might be a more probable process than C-Si dumbbell agglomeration.}
+{\color{red}Todo: Attraction of defect pair for large separation distances might be very low and thus, substitutional C + Si, which is diffusing somewhere else remains (out of a reaction radius)?}
\section{Migration in systems of combined defects}
In fact, migration simulations yield a barrier as low as 0.1 eV.
This energy is needed to tilt the dumbbell as the displayed structure at 30 \% displacement shows.
Once this barrier is overcome, the carbon atom forms a bond to the top left silicon atom and the interstitial silicon atom capturing the vacant site is forming new tetrahedral bonds to its neighboured silicon atoms.
-These new bonds and the relaxation into the substitutional carbon configuration are responsible for the gain free energy.
+These new bonds and the relaxation into the substitutional carbon configuration are responsible for the gain in free energy.
For the reverse process approximately 2.4 eV are nedded, which is 24 times higher than the forward process.
Thus, substitutional carbon is assumed to be stable in contrast to the C-Si dumbbell interstitial located next to a vacancy.
-{\color{red}Todo: DB mig along 110 (at the starting of this section)?}
-
-{\color{red}Todo: Migration of Si int + vac and C sub/int ...?}
-
-{\color{red}Todo: Model of kick-out and kick-in mechnism?}
+{\color{red}Todo: DB migration calculations along 110 (at the starting of this section)?}
\section{Conclusions concerning the SiC conversion mechanism}
Thus, carbon interstitials and vacancies located close together are assumed to end up in such a configuration in which the carbon atom is tetrahedrally coordinated and bound to four silicon atoms as expected in silicon carbide.
In contrast to the above, this would suggest a silicon carbide precipitation by succesive creation of substitutional carbon instead of the agglomeration of C-Si dumbbell interstitials followed by an abrupt precipitation.
-{\color{red}Todo:
-C atoms in 100 DB tightend in 110 direction, which is important for stress compensation in some combined constellations.
-}
-{\color{red}Todo:
-Most of the combinations should only be thought of intermediate configurations, which need to be transformed in the later SiC precipitation process.
-}
{\color{red}Todo:
Better structure, better language, better methodology!
}
{\color{red}Todo:
-Fit of lennard-jones an other rep + attr potentials in 110 interaction data!
+Fit of lennard-jones and other rep + attr potentials in 110 interaction data!
}
Obviously the precipitate lowers the transition point of the surrounding c-Si matrix.
For the rearrangement simulations temperatures well below the transition point should be used since it is very unlikely to recrystallize the molten Si surrounding properly when cooling down.
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.}
+{\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 around the silicon melting point}
\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: 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: 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.}
+{\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: self-guided MD!}
-{\color{red}TODO: other approaches?}
+{\color{red}Todo: other approaches?}
{\color{red}
-TODO: ART MD?
+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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