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\begin{document}
As concluded from high resolution transmission electron microscopy (HREM) carbon atoms introduced into c-Si 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/c-Si lattice misfit is overcome and precipitation occurs.
-In HREM this transformation manifestsitself by the disappearance of patches with dark background in favour of high resolution Moir\'e fringes due to 3C-SiC precipitates embedded in c-Si \cite{3,4}.
+In HREM this transformation manifests itself by the disappearance of patches with dark background in favour of high resolution Moir\'e fringes due to 3C-SiC precipitates embedded in c-Si \cite{3,4}.
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 c-Si matrix since there is more space than in 3C-SiC.
Thus, in addition to the precipitation event itself, knowledge of C and Si interstitials in Si are of great interest in order to investigate the precipitation of 3C-SiC in heavily C doped c-Si.
The interaction of the silicon and carbon atoms is realized by a newly parametrized Tersoff-like bond order potential \cite{6}.
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{7} with a time constant of 100 fs.
-The pressure is scaled by the Berendsen barostat \cite{7} again using a timeconstant of 100 fs and a bulk modulus of 100 GPa for silicon.
+The pressure is controlled by the Berendsen barostat \cite{7} again using a time constant of 100 fs and a bulk modulus of 100 GPa for silicon.
To exclude surface effects periodic boundary conditions are applied.
In order to study the behaviour of carbon in c-Si, two different simulation sequences are used.
For the simulations aiming to reproduce a precipitation process the simulation volume is 31 silicon lattice constants in each direction.
The system temperature is set to $450\, ^{\circ} \textrm{C}$ like in IBS \cite{3}.
$6000$ carbon atoms (the number necessary to form a 3C-SiC precipitate with a radius of $\sim 3$ nm) are consecutively inserted in a way to keep the system temperature constant.
-Carbon is inserted statistically distributed over either the whole simulation volme (insertion volume $V_1$), an insertion volume $V_2$ corresponding to the minimum size of a 3C-SiC precipitate or the volume $V_3$ containing the number of Si atoms necessary for the formation of such a minimum precipitate.
+Carbon is inserted statistically distributed over either the whole simulation volume (insertion volume $V_1$), an insertion volume $V_2$ corresponding to the minimum size of a 3C-SiC precipitate or the volume $V_3$ containing the number of Si atoms necessary for the formation of such a minimum precipitate.
The two latter insertion volumes are considered since no diffusion of carbon atoms is observed at this temperature.
Following the insertion procedure the system is cooled down to $20\, ^{\circ} \textrm{C}$.
After insertion of C atoms the Si-Si pair correlation function in fact shows non-zero g(r) values around distance values of 0.31 nm while the amount of Si pairs at the regular distances of 0.24 and 0.38 nm decreases.
However, no clear peak is observed but the interval of enhanced g(r) values corresponds to the width of the C-C g(r) peak.
Analyses of randomly chosen configurations in which distances around 0.3 nm appear, identify <100> C-Si dumbbells to be responsible for stretching the Si-Si next neighbour distance for low C concentrations, i.e. for the $V_1$ and early stages of $V_2$ and $V_3$ simulation runs.
-This excellently agrees with the calculation for a single <100> dumbbell ($r(13)$ in Fig. 3).
+This excellently agrees with the calculation for a single <100> dumbbell (r(13) in Fig. 3).
For higher C concentrations the defect concentration is likewise increased and a considerable amount of damage is introduced into the insertion volume.
Damage and superposition of defects generate new displacement arrangements which become hard to categorize and trace and obviously lead to a broader distribution of pair distances.
The step-like increase of Si-Si pairs at 0.29 nm is probably due to the Si-Si cut-off radius of 0.296 nm in the used bond order potential \cite{6}.
First results of the simulations suggest that in the precipitation process C atoms introduced as differently oriented C-Si dumbbells into the c-Si matrix are the first elements properly arranged for the 3C-SiC formation.
Furthermore, the observation of high amounts of damage particularly for high carbon concentrations demands for elevated system temperatures to achieve the precipitation event.
-%\bibliography{../../bibdb/bibdb}
\begin{thebibliography}{8}
\bibitem{1} J. H. Edgar, J. Mater. Res. 7 (1992) 235.
\bibitem{2} J. W. Strane, S. R. Lee, H. J. Stein, S. T. Picraux,
\begin{figure}[!h]
\begin{center}
- \includegraphics[width=8cm]{unit_cell_s.eps}
+ \includegraphics[width=8cm]{fig1.eps}
\caption{Insertion positions for the tetrahedral (${\color{red}\triangleleft}$), hexagonal (${\color{green}\triangleright}$) and <110> dumbbell (${\color{magenta}\Box}$) interstitial configuration.}
\end{center}
\end{figure}
\begin{figure}[!h]
\begin{center}
- \includegraphics[width=6cm]{c_in_si_int_001db_0.eps}
+ \includegraphics[width=6cm]{fig2.eps}
\caption{Position of a <100> dumbbell carbon interstitial in silicon.
Only bonds of the carbon interstitial atom are shown.}
\end{center}
\begin{figure}[!h]
\begin{center}
- \includegraphics[width=15cm]{100-c-si-db_s.eps}
+ \includegraphics[width=15cm]{fig3.eps}
\caption{Schematic of the <100> C-Si dumbbell configuration.
Displacements of the atoms relative to their initial position are given.
The displacement of the carbon atom is relative to the initial position of atom 1.
\begin{figure}[!h]
\begin{center}
- \includegraphics[]{pc_si-c_c-c.eps}
+ \includegraphics[]{fig4.eps}
\caption{Pair correlation functions for Si-C and C-C bonds.
The three curves represent results for the three different insertion volumes $V_1$, $V_2$ and $V_3$, as explained in the text.
The dashed vertical lines mark further calculated C-Si atom pair distances appearing in the <100> C-Si dumbbell interstitial configuration, which are not displayed in Fig. 3.}
\begin{figure}[!h]
\begin{center}
- \includegraphics[]{pc_si-si.eps}
+ \includegraphics[]{fig5.eps}
\caption{Si-Si pair correlation function for pure Si and Si with 3000 inserted C atoms.
The inset shows a magnified region between 0.28 and 0.36 nm.}
\end{center}
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