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<frank.zirkelbach@physik.uni-augsburg.de>}
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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.
-High resolution transmission electron microscopy indicates 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.
+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.
A newly parametrized Tersoff-like bond order potential is used to model the system appropriately.
First results gained by molecular dynamics simulations using this potential are presented.
-The influence of the amount and placement of inserted carbon atoms on the defect formation and structural changes is discussed.
-Furthermore a minimal carbon concentration necessary for precipitation is examined by simulation.
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-{\bf Keywords:} Silicon carbide, Nucleation, Molecular dynamics simulation.
+{\bf Keywords:} Silicon, Carbon, Silicon carbide, Nucleation, Diffusion, Defect formation.
\section*{Introduction}
Understanding the precipitation process of cubic silicon carbide (3C-SiC) in heavily carbon doped silicon will enable significant technological progress in thin film formation of an important wide band gap semiconductor material.
On the other hand it will likewise offer perspectives for processes which rely upon prevention of precipitation events, e.g. the fabrication of strained silicon.
-Epitaxial growth of 3C-SiC films is achieved either by ion implantation or chemical vapour deposition techniques.
-Surface effects dominate the CVD process while for the implantation process carbon is introduced into bulk silicon.
-This work tries to realize conditions which hold for the ion implantation process.
+Epitaxial growth of 3C-SiC films is achieved either by ion implantation or chemical vapour deposition (CVD) techniques.
+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 suitable model is considered.
-After that the realization by simulation is discussed.
-First results gained by simulation are presented in a next step.
-Finally these results are outlined and conclusions are infered.
+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.
\section*{Supposed conversion mechanism}
-Silicon (Si) nucleates in diamond structure.
-This structure is composed of two fcc lattices, which are displaced by one quarter of the volume diagonal.
-3C-SiC nucleates in zincblende structure, where the atoms of one fcc lattice are substituted by carbon atoms.
-The length of four lattice constants of Si is approximately equal to the length of five 3C-SiC lattice constants ($4a_{Si}\approx 5a_{3C-SiC}$), which means that there is a lattice misfit of almost 20\%.
+Silicon nucleates in diamond structure.
+This structure is composed of two fcc lattices which are displaced by one quarter of the volume diagonal.
+3C-SiC nucleates in zincblende structure in which atoms of one fcc lattice are substituted by carbon atoms.
+The length of four lattice constants of Si is approximately equal to the length of five 3C-SiC lattice constants ($4a_{\text{Si}}\approx 5a_{\text{3C-SiC}}$) resultings in a lattice misfit of almost 20\%.
Due to this the silicon density of 3C-SiC is slightly lower than the one of Si.
\begin{figure}[!h]
\begin{minipage}{5.5cm}
\includegraphics[width=5cm]{sic_prec_seq_03.eps}
\end{minipage}
- \caption{Schematic of the supposed conversion mechanism of highly C doped Si into SiC. C is represented by red dots, Si by black dots and residual Si atoms by white dots with black border. The figure shows the dumbbell formation (left), the agglomeration into clusters (middle) and the situation after precipitation (right).}
+ \caption{Schematic of the supposed conversion mechanism of highly C (${\color{red}\bullet}$) doped Si (${\color{black}\bullet}$) into SiC ($_{\color{black}\bullet}^{{\color{red}\bullet}}$) and residual Si atoms ($\circ$). The figure shows the dumbbell formation (left), the agglomeration into clusters (middle) and the situation after precipitation (right).}
\end{center}
\end{figure}
-There is a supposed conversion mechanism of heavily carbon doped Si into SiC.
+There is a supposed conversion mechanism of heavily carbon doped Si into SiC \cite{}.
Fig. 1 schematically displays the mechanism.
-As indicated by high resolution transmission microscopy \cite{} introduced carbon atoms (red dots) form C-Si dumbbells on regular Si (black dots) lattice sites.
+As indicated by high resolution transmission microscopy \cite{} introduced carbon atoms (${\color{red}\bullet}$) form C-Si (${\color{black}\bullet}\,{\color{red}\bullet}$) dumbbells on regular Si (${\color{black}\bullet}$) 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.
-Due to the slightly lower silicon density of 3C-SiC residual silicon atoms exist.
+Due to the slightly lower silicon density of 3C-SiC ($_{\color{black}\bullet}^{{\color{red}\bullet}}$) residual silicon atoms ($\circ$) exist.
The residual atoms will most probably end up as self interstitials in the silicon matrix since there is more space than in 3C-SiC.
-Taking this into account, it is important to understand both, the configuration and dynamics of carbon interstitials in silicon and silicon self interstitials.
+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}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=8cm]{unit_cell.eps}
- \caption{Insertion positions for the tetrahedral (red), hexagonal (green) and <110> dumbbell (purple) interstitial configuration.}
+ \caption{Insertion positions for the tetrahedral (${\color{red}\bullet}$), hexagonal (${\color{green}\bullet}$) and <110> dumbbell (${\color{purple}\bullet}$) interstitial configuration.}
\end{center}
\end{figure}
To investigate the intesrtitial 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 $(0,0,0)$ (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).
+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 $(-1/8,-1/8)$ (${\color{purple}\bullet}$) 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 $(-1/4,-1/4,-1/4)$ ($\circ$).
The introduced kinetic energy is scaled out by a relaxation time of $2\, ps$.
The same volume is used to investigate diffusion.
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