\begin{document}
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+\slideframe{none}
+
+\pagestyle{empty}
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\item Integrator, potential, ensemble control
\item Simulation sequence
\end{itemize}
- \item Results gained by simulation
+ \item Simulation results
\begin{itemize}
\item Interstitials in silicon
\item SiC-precipitation experiments
Motivation / Introduction
}
- Why C in Si?
+ \vspace{16pt}
+
+ Reasons for investigating C in Si:
\begin{itemize}
\item 3C-SiC wide band gap semiconductor formation
- \item Strained Si
+ \item Strained Si (no precipitation wanted!)
\end{itemize}
-
+ \vspace{16pt}
+
+ Si / 3C-SiC facts:
+
+ \begin{minipage}{8cm}
+ \begin{itemize}
+ \item Unit cell:
+ \begin{itemize}
+ \item {\color{yellow}fcc} $+$
+ \item {\color{gray}fcc shifted $1/4$ of volume diagonal}
+ \end{itemize}
+ \item Lattice constants: $4a_{Si}\approx5a_{SiC}$
+ \item Silicon density:
+ \[
+ \frac{n_{SiC}}{n_{Si}}=
+ \frac{4/a_{SiC}^3}{8/a_{Si}^3}=
+ \frac{5^3}{2\cdot4^3}={\color{cyan}97,66}\,\%
+ \]
+ \end{itemize}
+ \end{minipage}
+ \hspace{8pt}
+ \begin{minipage}{4cm}
+ \includegraphics[width=4cm]{sic_unit_cell.eps}
+ \end{minipage}
\end{slide}
Precipitation of 3C-SiC + Creation of interstitials\\
\end{minipage}
- \begin{center}
- \[
- \textrm{Silicon density: } \quad
- 5a_{SiC}=4a_{Si} \quad \Rightarrow \quad
- \frac{n_{SiC}}{n_{Si}}=\frac{\frac{4}{a_{SiC}^3}}{\frac{8}{a_{Si}^3}}=
- \frac{5^3}{2\cdot4^3}={\color{cyan}97,66}\,\%
- \]
- \end{center}
+ \vspace{12pt}
- Experimentally observed minimal diameter of precipitation: 4 - 5 nm
+ Experimentally observed:
+ \begin{itemize}
+ \item Minimal diameter of precipitation: 4 - 5 nm
+ \item (hkl)-planes identical for Si and SiC
+ \end{itemize}
\end{slide}
Simulation details
}
+ \vspace{12pt}
+
MD basics:
\begin{itemize}
\item Microscopic description of N particle system
\item Analytical interaction potential
\item Hamilton's equations of motion as propagation rule\\
- in 6N-dimemnsional phase space
+ in 6N-dimensional phase space
\item Observables obtained by time average
\end{itemize}
- \vspace{4pt}
+ \vspace{12pt}
Application details:
\begin{itemize}
- \item Integrator: velocity verlet, timestep: $1\, fs$
+ \item Integrator: Velocity Verlet, timestep: $1\, fs$
\item Ensemble control: NVT, Berendsen thermostat, $\tau=100.0$
\item Potential: Tersoff-like bond order potential\\
\[
\end{center}
\end{itemize}
+ \begin{picture}(0,0)(-240,-70)
+ \includegraphics[width=5cm]{tersoff_angle.eps}
+ \end{picture}
+
\end{slide}
\begin{slide}
\begin{itemize}
\item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
\item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
- \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$
+ \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
$\rightarrow$ {\color{yellow}110 dumbbell}
\item random positions (critical distance check)
\end{itemize}
\item Optional heating-up
\end{itemize}
- \begin{picture}(0,0)(-210,-85)
+ \begin{picture}(0,0)(-210,-45)
\includegraphics[width=6cm]{unit_cell.eps}
\end{picture}