% \end{center}
%\end{figure}
There is a supposed conversion mechanism of heavily carbon doped Si into SiC \cite{werner97}.
-As concluded by high resolution transmission electron microscopy \cite{werber97,} introduced carbon atoms form C-Si dumbbells on regular Si lattice sites.
+As concluded by high resolution transmission electron microscopy introduced carbon atoms form C-Si dumbbells on regular Si lattice sites.
The dumbbells agglomerate into large clusters, called embryos.
Finally, when the cluster size reaches a critical radius of 2 to 4 nm, the high interfacial energy due to the 3C-SiC/Si lattice misfit is overcome and precipitation occurs.
Due to the slightly lower silicon density of 3C-SiC excessive silicon atoms exist which will most probably end up as self-interstitials in the silicon matrix since there is more space than in 3C-SiC.
To investigate the interstitial configurations of C and Si in Si, a simulation volume of 9 silicon unit cells in each direction is used.
The temperature is set to $T=0\, K$.
The insertion positions are illustrated in Fig. 2.
-In separated simulation runs a carbon and a silicon atom respectively is inserted at the tetrahedral $(0,0,0)$ (${\color{red}\triangleleft}$), hexagonal $(-1/8,-1/8,1/8)$ (${\color{green}\triangleright}$), supposed dumbbell $(-1/8,-1/8,-1/4)$ (${\color{magenta}\bullet}$) and at random positions (in units of the silicon lattice constant) where the origin is located in the centre of the unit cell.
+In separated simulation runs a carbon and a silicon atom respectively is inserted at the tetrahedral $(0,0,0)$ (${\color{red}\triangleleft}$), hexagonal $(-1/8,-1/8,1/8)$ (${\color{green}\triangleright}$), nearby dumbbell $(-1/8,-1/8,-1/4)$ (${\color{magenta}\bullet}$) and at random positions (in units of the silicon lattice constant) where the origin is located in the centre of the unit cell.
In order to avoid too high potential energies in the case of the dumbbell configuration the nearest silicon neighbour atom is shifted to $(-3/8,-3/8,-1/4)$ ($\circ$).
The energy introduced into the system is scaled out within a relaxation phase of $2\, ps$.
-The same volume is used to investigate diffusion.
-Different amounts of silicon atoms are inserted at random positions within a centered region of $11 \,\textrm{\AA}$ in each direction.
-Insertion events are carried out step by step maintaining a constant system temperature of $450\, ^{\circ} \textrm{C}$.
-Finally a single carbon atom is inserted at a random position within the unit cell located in the middle of the simulation volume.
-The simulation is proceeded for another $30\, ps$.
+%The same volume is used to investigate diffusion.
+%Different amounts of silicon atoms are inserted at random positions within a centered region of $11 \,\textrm{\AA}$ in each direction.
+%Insertion events are carried out step by step maintaining a constant system temperature of $450\, ^{\circ} \textrm{C}$.
+%Finally a single carbon atom is inserted at a random position within the unit cell located in the middle of the simulation volume.
+%The simulation is proceeded for another $30\, ps$.
For the simulations aiming to reproduce a precipitation process the volume is 31 silicon lattice constants in each direction.
The system temperature is set to $450\, ^{\circ} \textrm{C}$.
$6000$ carbon atoms (the amount necessary to form a 3C-SiC precipitate with a radius of 3 nm) are consecutively inserted in a way to keep constant the system temperature.
Precipitation is examined for three insertion volumes which differ in size.
The whole simulation volume, the volume corresponding to the size of a minimal SiC precipitate and the volume containing the amount of silicon necessary for the formation of such a minimal precipitate.
+The two latter ones are accomplished since no long range diffusion of the carbon atoms is expected at this temperature.
Following the insertion procedure the system is cooled down to $20\, ^{\circ} \textrm{C}$.
\section*{Results}
The formation energies are $2.7\, eV$ and $1.8\, eV$ respectively.
Again the hexagonal one is found to be unstable.
The interstitial atom moves to the more favorable <100> dumbbell position which has a formation energy of $0.5\, eV$.
+The interstitial configuration is shown in Fig. 2.
There is experimental evidence \cite{watkins76} of the existence of this configuration.
-This type of configuration is frequently observed for the random insertion runs and is assumed to be the lowest in energy.
+It is frequently generated and has the lowest formation energy of all the defects observed in all the simulation runs in which carbon is inserted at random positions.
\begin{figure}[!h]
\begin{center}
- \includegraphics[width=12cm]{../plot/diff_dep.ps}
- \caption{Diffusion coefficients of a single carbon atom for different amount of Si selft interstitials}
+ \includegraphics[width=8cm]{c_in_si_int_001db_0.eps}
+ \caption{Position of a <100> dumbbell carbon interstitial in silicon.
+ Only bonds of the carbon interstitial atom are shown.}
\end{center}
\end{figure}
-The influence of Si self-interstitials on the diffusion of a single carbon atom is displayed in Fig. 3.
-Diffusion coefficients for different amount of Si self-interstitials are shown.
-A slight increase is first observed in the case of 30 interstitial atoms.
-Further increasing the amount of interstitials leads to a tremendous decay of the diffusion coeeficient.
-Generally there is no long range diffusion of the carbon atom for a temperature of $450\, ^{\circ} \textrm{C}$.
-The maximal displacement of the carbon atom relativ to its insertion position is between 0.5 and 0.7 \AA.
+
+%\begin{figure}[!h]
+% \begin{center}
+% \includegraphics[width=12cm]{../plot/diff_dep.ps}
+% \caption{Diffusion coefficients of a single carbon atom for different amount of Si selft interstitials}
+% \end{center}
+%\end{figure}
+%The influence of Si self-interstitials on the diffusion of a single carbon atom is displayed in Fig. 3.
+%Diffusion coefficients for different amount of Si self-interstitials are shown.
+%A slight increase is first observed in the case of 30 interstitial atoms.
+%Further increasing the amount of interstitials leads to a tremendous decay of the diffusion coeeficient.
+%Generally there is no long range diffusion of the carbon atom for a temperature of $450\, ^{\circ} \textrm{C}$.
+%The maximal displacement of the carbon atom relativ to its insertion position is between 0.5 and 0.7 \AA.
\begin{figure}[!h]
\begin{center}
\section*{Summary}
The supposed conversion mechanism of heavily carbon doped silicon into silicon carbide is presented.
-Molecular dynamics simulation sequences to investigate interstitial configurations, the influence of interstitials on the atomic diffusion and the precipitation of SiC are proposed.
-The <100> C-Si dumbbel is reproducable by simulation and is the energetically most favorable configuration.
-The influence of silicon self-interstitials on the diffusion of a single carbon atom is demonstrated.
+Molecular dynamics simulation sequences to investigate interstitial configurations
+%, the influence of interstitials on the atomic diffusion
+and the precipitation of SiC are explained.
+The <100> C-Si dumbbel is reproduced and is the energetically most favorable configuration observed by simulation.
+%The influence of silicon self-interstitials on the diffusion of a single carbon atom is demonstrated.
Two competing bond formations, either Si-C or C-C, seem to coexist, where the strength of either of them depends on the size of the region in which carbon is introduced.
\bibliography{../../bibdb/bibdb}
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