relation (uer), minimum range model (mrm)",
}
+@Article{balamane92,
+ title = "Comparative study of silicon empirical interatomic
+ potentials",
+ author = "H. Balamane and T. Halicioglu and W. A. Tiller",
+ journal = "Phys. Rev. B",
+ volume = "46",
+ number = "4",
+ pages = "2250--2279",
+ numpages = "29",
+ year = "1992",
+ month = jul,
+ doi = "10.1103/PhysRevB.46.2250",
+ publisher = "American Physical Society",
+ notes = "comparison of classical potentials for si",
+}
+
@Article{koster2002,
title = "Stress relaxation in $a-Si$ induced by ion
bombardment",
doi = "10.1103/PhysRevB.66.195214",
publisher = "American Physical Society",
notes = "c in c-si, diffusion, interstitial configuration +
- links",
+ links, interaction of carbon and silicon
+ interstitials",
}
@Article{leung99,
In fact the resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modified Tersoff potential \cite{gao02}.
So why is it amorphous?
+Experiments show crystalline 3C-SiC at the prevailing temperature.
Short range bond order potentials show overestimated interactions.
Indeed it is not only the C-C bonds which seem to be unbreakable.
Also the C-Si pairs, as observed in the low concentration simulations, are stuck.
Finally explain which methods will be applied in the following.
-\subsection{Constructed minimal 3C-SiC precipitate in crystalline silicon}
-
\subsection{Increased temperature simulations}
\subsection{Simulations at temperatures exceeding the silicon melting point}
LL Cool J is hot as hell!
+\subsection{Constructed 3C-SiC precipitate in crystalline silicon}
+
+In the following a spherical 3C-SiC precipitate enclosed in a c-Si surrounding is constructed as it is expected from IBS experiments and from simulations that finally succeed simulating the precipitation event.
+On the one hand this sheds light on characteristic values like the radial distribution function or the total amount of energy for configurations that are aimed to be reproduced by simulation possibly enabling the prediction of conditions necessary for the simulation of the precipitation process.
+On the other hand, assuming a correct alignment of the precipitate with the c-Si matrix, investigations of the behaviour of such precipitates and the surrounding can be made.
+
+To construct a spherical 3C-SiC precipitate in c-Si, the approach illustrated in the following is applied.
+A total simulation volume $V$ consisting of 21 unit cells of c-Si in each direction is used.
+To obtain a minimal and stable precipitate 5500 carbon atoms are considered necessary.
+The initial precipitate configuration is constructed in two steps.
+In the first step the surrounding silicon matrix is created.
+This is realized by just skipping the generation of silicon atoms inside a sphere of radius $x$, which is the first unknown variable.
+The silicon lattice constant $a_{\text{Si}}$ of the surrounding c-Si matrix is assumed to not alter dramatically and, thus, is used for the initial lattice creation.
+In a second step 3C-SiC is created inside the empty sphere of radius $x$.
+The lattice constant $y$, the second unknown variable, is chosen in such a way, that the necessary amount of carbon is generated.
+This is entirely described by the system of equations \eqref{eq:md:constr_sic_01}
+\begin{equation}
+\frac{8}{a_{\text{Si}}^3}(
+\underbrace{21^3 a_{\text{Si}}^3}_{=V}
+-\frac{4}{3}\pi x^3)+
+\underbrace{\frac{4}{y^3}\frac{4}{3}\pi x^3}_{\stackrel{!}{=}5500}
+=21^3\cdot 8
+\label{eq:md:constr_sic_01}
+\text{ ,}
+\end{equation}
+which can be simplified to read
+\begin{equation}
+\frac{8}{a_{\text{Si}}^3}\frac{4}{3}\pi x^3=5500
+\Rightarrow x = \left(\frac{5500 \cdot 3}{32 \pi} \right)^{1/3}a_{\text{Si}}
+\label{eq:md:constr_sic_02}
+\end{equation}
+and
+\begin{equation}
+%x^3=\frac{16\pi}{5500 \cdot 3}y^3=
+%\frac{16\pi}{5500 \cdot 3}\frac{5500 \cdot 3}{32 \pi}a_{\text{Si}}^3
+%\Rightarrow
+y=\left(\frac{1}{2} \right)^{1/3}a_{\text{Si}}
+\text{ .}
+\label{eq:md:constr_sic_03}
+\end{equation}
+By this means values of 2.973 nm and 4.309 \AA{} are obtained for the initial precipitate radius and lattice constant of 3C-SiC.
+Since the generation of atoms is a discrete process with regard to the size of the volume the expected amounts of atoms are not obtained.
+However, by applying these values the final configuration varies only slightly from the expected one by five carbon and eleven silicon atoms, as can be seen in table \ref{table:md:sic_prec}.
+\begin{table}[!ht]
+\begin{center}
+\begin{tabular}{l c c c c}
+\hline
+\hline
+ & C in 3C-SiC & Si in 3C-SiC & Si in c-Si surrounding & total amount of Si\\
+\hline
+Expected & 5500 & 5500 & 68588 & 74088\\
+Obtained & 5495 & 5486 & 68591 & 74077\\
+Difference & 5 & 14 & -3 & 11\\
+\hline
+\hline
+\end{tabular}
+\caption{Comparison of the expected and obtained amounts of Si and C atoms by applying the values from equations \eqref{eq:md:constr_sic_02} and \eqref{eq:md:constr_sic_03} in the 3C-SiC precipitate construction approach.}
+\label{table:md:sic_prec}
+\end{center}
+\end{table}
+
+After the initial configuration is constructed some of the atoms located at the 3C-SiC/c-Si interface show small distances, which results in high repulsive forces acting on the atoms.
+Thus, the system is equilibrated using strong coupling to the heat bath, which is set to be $20\,^{\circ}\mathrm{C}$.
+Once the main part of th excess energy is carried out previous settings for the Berendsen thermostat are restored and the system is relaxed for another 10 ps.
+
+PC and energy of that one.
+
+Now let's see, whether annealing will lead to some energetically more favorable configurations.
+
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