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<frank.zirkelbach@physik.uni-augsburg.de>}
\end{center}
+\selectlanguage{english}
+
\vspace{24pt}
\section*{Abstract}
There is a supposed conversion mechanism of heavily carbon doped Si into SiC.
Fig. 1 schematically displays the mechanism.
+\begin{figure}
+ \begin{center}
+ \begin{minipage}{5.5cm}
+ \includegraphics[width=5cm]{sic_prec_seq_01.eps}
+ \end{minipage}
+ \begin{minipage}{5.5cm}
+ \includegraphics[width=5cm]{sic_prec_seq_02.eps}
+ \end{minipage}
+ \begin{minipage}{5.5cm}
+ \includegraphics[width=5cm]{sic_prec_seq_03.eps}
+ \end{minipage}
+ \caption{foo}
+ \end{center}
+\end{figure}
As indicated by high resolution transmission microscopy \ref{hrem_ind} introduced carbon atoms (red dots) form C-Si dumbbells on regular Si (black dots) lattice sites.
The dumbbells agglomerate int large clusters, so called embryos.
Finally, when the cluster size reaches a critical radius of 2 to 4 nm, the high interfacial energy due to the lattice misfit is overcome and the precipitation occurs.
Coupling to the heat bath is achieved by the Berendsen thermostat \ref{} with a time constant $\tau_T=100\, fs$.
The pressure is scaled by the Berendsen barostat \ref{} again using a timeconstant of $\tau_P=100\, fs$ and a bulk modulus of $100\, GPa$ for silicon.
To exclude surface effects periodic boundary conditions are applied.
-\\\\
+
To investigate the intesrtitial configurations of C and Si in Si, a simulation volume of 9 silicon unit cells is each direction 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 $(0,0,0)$ (red), hexagonal $(-1/8,-1/8,1/8)$ (green), supposed dumbbell $(-1/8,-1/8)$ (purple) and at random positions (in units of the silicon lattice constant) where the origin is located in the middle of the unit cell.
In order to avoid too high kinetic energies in the case of the dumbbell configuration the nearest silicon neighbour atom is shifted to $(-1/4,-1/4,-1/4)$ (dashed border).
The introduced kinetic energy is scaled out by a relaxation time of $2\, ps$.
-\\\\
+
The same volume is used to investigate diffusion.
-A certain amount of silicon atoms are inserted at random positions in a centered region of $11 \, \AA$ in each direction.
+A certain amount of silicon atoms are inserted at random positions in a centered region of $11 \,\textrm{\AA}$ in each direction.
The insertion is taking place step by step in order to maintain a constant system temeprature.
Finally a carbon atom is inserted at a random position in the unit cell located in the middle of the simulation volume.
The simulation continues for another $30\, ps$.
-\\\\
-Simulation runs /unt
-
+The sequence of the simulations aiming to reproduce a precipitation process is indicated in Fig 3.
+The size of the simulation 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 minimal 3C-SiC precipitation) 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 a minimal SiC precipitation volume and the volume containing the necessary amount of silicon to form such a precipitation.
+After the insertion procedure the system is cooled down to $20\, ^{\circ} \textrm{C}$.
\section*{Results}
+The tetrahedral and the <110> dumbbell self interstitial configurations can be reproduced as observed in \ref{}.
+The formation energies are $3.4\, eV$ and $4.4\, eV$ respectively.
+However the hexagonal one is not stable opposed to what is presented in \ref{}.
+The atom moves towards a energetically more favorable position very close to the tetrahedral one but slightly displaced along the three coordinate axes.
+The formation energy of $4.0\, eV$ of this type of interstitial equals the result obtained in the reference for the hexagonal one.
+The same type of interstitial is observed within the random insertion runs.
+Variations exist where the displacement is along two axes ($E_f=3.8\, eV$) or along one axis ($E_f=3.6\, eV$) succesively approximating the tetrahedral configuration and formation energy.
+
+The tetrahedral and <110> dumbbel carbon interstitial configurations are stable.
+The formation energies are $2.7\, eV$ and $1.8\, eV$ respectively.
+Again the hexagonal one is found to be not stable.
+The interstitial atom moves to the more favorable <100> dumbbell position, which has a formation energy of $0.5\, eV$.
+There is experimental evidence \ref{} of the existence of this configuration.
+This type of configuration is frequently observed for the random insertion runs.
+
+
+
\section*{Conclusion}
\end{document}