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\section*{Abstract}
-The precipitation process of silicon carbide in heavily carbon doped silicon is not yet understood for the most part.
+The precipitation process of silicon carbide in heavily carbon doped silicon is not yet fully understood.
High resolution transmission electron microscopy observations suggest that in a first step carbon atoms form C-Si dumbbells on regular Si lattice sites which agglomerate into large clusters.
In a second step, when the cluster size reaches a radius of a few $nm$, the high interfacial energy due to the SiC/Si lattice misfit of almost 20\% is overcome and the precipitation occurs.
By simulation details of the precipitation process can be obtained on the atomic level.
While CVD is governed by surface effects carbon is directly introduced into bulk silicon for the implantation process.
In the present work the simulation runs try to realize conditions which hold for the ion implantation process.
-First of all a picture of the supposed precipitation event is worked out.
-Afterwards the realization via simulation is discussed.
-In a next step first results gained by simulation are presented.
+First of all a picture of the supposed precipitation event is presented.
+Afterwards the applied simulation sequences are discussed.
+Finally first results gained by simulation are presented.
\section*{Supposed conversion mechanism}
Silicon nucleates in diamond structure.
Taking this into account it is important to understand both, the configuration and dynamics of carbon interstitials in silicon and silicon self interstitials.
Additionaly the influence of interstitials on atomic diffusion is investigated.
-\section*{Simulation}
+\section*{Simulation sequences}
A molecular dynamics simulation approach is used to examine the steps involved in the precipitation process.
-For integrating the equations of motion the velocity verlet algorithm \cite{verlet67} with a timestep of 1 fs is deployed.
+For integrating the equations of motion the velocity verlet algorithm \cite{verlet67} with a timestep of $1\, fs$ is adopted.
The interaction of the silicon and carbon atoms is realized by a newly parametrized Tersoff-like bond order potential \cite{albe_sic_pot}.
Since temperature and pressure of the system is kept constant in experiment the isothermal-isobaric NPT ensemble is chosen for the simulation.
Coupling to the heat bath is achieved by the Berendsen thermostat \cite{berendsen84} with a time constant $\tau_T=100\, fs$.
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 $(0,0,0)$ (${\color{red}\bullet}$), hexagonal $(-1/8,-1/8,1/8)$ (${\color{green}\bullet}$), 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 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 $(-3/8,-3/8,-1/4)$ ($\circ$).
-The introduced kinetic energy is scaled out by a relaxation time of $2\, ps$.
+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.
-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 $30\, ps$.
+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 temeprature.
+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 simulation is 31 silicon lattice constants in each direction.
+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 minimal 3C-SiC precipitation) are consecutively inserted in a way to keep constant the system temperature.
+$6000$ carbon atoms (the amount necessary to form a minimal 3C-SiC precipitate) 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 $20\, ^{\circ} \textrm{C}$.
+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.
+Following 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 \cite{albe_sic_pot}.
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 \cite{albe_sic_pot}.
-The atom moves towards a energetically more favorable position very close to the tetrahedral one but slightly displaced along the three coordinate axes.
+The atom moves towards an 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 same type of interstitial may arise using random insertions.
+In addition variations exist in which the displacement is only along two axes ($E_f=3.8\, eV$) or along a single 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 $0.5\, eV$.
+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 $0.5\, eV$.
There is experimental evidence \cite{watkins76} of the existence of this configuration.
-This type of configuration is frequently observed for the random insertion runs.
+This type of configuration is frequently observed for the random insertion runs and is assumed to be the lowest in energy.
\begin{figure}[!h]
\begin{center}
Carbon atoms are introduced into the whole simulation volume (red), the region which corresponds to the size of a minimal SiC precipitation (green) and the volume which contains the necessary amount of silicon for a minimal precipitation (blue).}
\end{center}
\end{figure}
-Fig. 4 shows results of the simulation runs targeting the observation of a precipitation event.
+Fig. 4 shows results of the simulation runs targeting the observation of precipitation events.
The C-C pair correlation function suggests carbon nucleation for the simulation runs where carbon was inserted into the two smaller regions.
The peak at $1.5\, \textrm{\AA}$ fits quite well the next neighbour distance of diamond.
On the other hand the Si-C pair correlation function indicates formation of SiC bonds with an increased crystallinity for the simulation in which carbon is inserted into the whole simulation volume.
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