\begin{document}
\extraslideheight{10in}
-\slideframe{plain}
+\slideframe{none}
+
+\pagestyle{empty}
% specify width and height
\slidewidth 27.7cm
% shift it into visual area properly
\def\slideleftmargin{3.3cm}
-\def\slidetopmargin{0.0cm}
+\def\slidetopmargin{0.6cm}
\newcommand{\ham}{\mathcal{H}}
\newcommand{\pot}{\mathcal{V}}
\newcommand{\foo}{\mathcal{U}}
\newcommand{\vir}{\mathcal{W}}
+% itemize level ii
+\renewcommand\labelitemii{{\color{gray}$\bullet$}}
+
% topic
\begin{slide}
\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
+ \item SiC-precipitation experiments
\end{itemize}
\item Conclusion / Outlook
\end{itemize}
% start of contents
+\begin{slide}
+
+ {\large\bf
+ Motivation / Introduction
+ }
+
+ \vspace{16pt}
+
+ Reasons for investigating C in Si:
+
+ \begin{itemize}
+ \item 3C-SiC wide band gap semiconductor formation
+ \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}
+
+ \small
\begin{slide}
{\large\bf
Precipitation of 3C-SiC + Creation of interstitials\\
\end{minipage}
- \begin{center}
- \[5a_{SiC}=4a_{Si} \quad \Rightarrow \quad
- \frac{n_{SiC}}{n_{Si}}=\frac{\frac{4}{a_{SiC}^3}}{\frac{8}{a_{Si}^3}}=
- \frac{5^3}{2\cdot4^3}=97,66\%
- \]
- \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}
Simulation details
}
+ \vspace{20pt}
+
Interstitial experiments:
+
+ \vspace{12pt}
+
\begin{itemize}
\item Initial configuration: $9\times9\times9$ unit cells Si
\item Periodic boundary conditions
\item $T=0 \, K$
\item Insertion of Si / C atom at
\begin{itemize}
- \item $(0,0,0)$ (tetrahedral)
- \item $(-1/8,-1/8,1/8)$ (hexagonal)
- \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$ (110 dumbbell)
+ \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
+ \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
+ \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
+ $\rightarrow$ {\color{yellow}110 dumbbell}
\item random positions (critical distance check)
\end{itemize}
\item Relaxation time: $2\, ps$
+ \item Optional heating-up
\end{itemize}
+ \begin{picture}(0,0)(-210,-45)
+ \includegraphics[width=6cm]{unit_cell.eps}
+ \end{picture}
+
\end{slide}
\begin{slide}
Simulation details
}
+ \small
+
SiC precipitation experiments:
\begin{itemize}
\item Initial configuration: $31\times31\times31$ unit cells Si
\end{itemize}
\end{itemize}
- 3 szenarios
+ Szenarios:
+ \begin{enumerate}
+ \item $V_{ins}$: total simulation volume $V$
+ \item $V_{ins}$: $12\times12\times12$ SiC unit cells
+ ($\sim$ volume of minimal SiC precipitation)
+ \item $V_{ins}$: $9\times9\times9$ SiC unit cells
+ ($\sim$ volume of necessary amount of Si)
+ \end{enumerate}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Results
+ }
+
+ Si self-interstitial experiments:
+
+ {\footnotesize
+ {\bf Note:}
+ \begin{itemize}
+ \item $r_{cutoff}^{Si-Si}=2.96>\frac{5.43}{2}$
+ \item Bond length near $r_{cutoff} \Rightarrow$ small bond strength
+ \end{itemize}
+ }
+
+ \vspace{8pt}
+
+ \small
+
+ \begin{minipage}[t]{4.0cm}
+ \underline{Tetrahedral}
+ \begin{itemize}
+ \item $E_F=3.41\, eV$
+ \item essentialy tetrahedral\\
+ bonds
+ \end{itemize}
+ \end{minipage}
+ \hspace{0.3cm}
+ \begin{minipage}[t]{4.0cm}
+ \underline{110 dumbbell}
+ \begin{itemize}
+ \item $E_F=4.39\, eV$
+ \item essentially 4 bonds
+ \end{itemize}
+ \end{minipage}
+ \hspace{0.3cm}
+ \begin{minipage}[t]{4.0cm}
+ \underline{Hexagonal}
\begin{itemize}
- \item $V_ins$: total volume $V$
- \item $V_ins$:
+ \item $E_F^{\star}\approx4.48\, eV$
+ \item unstable!
\end{itemize}
+ \end{minipage}
+
+ \vspace{8pt}
+
+ \begin{minipage}{4.3cm}
+ \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+ \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+ \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
+ \end{minipage}
\end{slide}
Results
}
+ \vspace{8pt}
+
+ Si self-interstitial \underline{random insertion} experiments:
+
+ \vspace{8pt}
+
+ foo
+
\end{slide}
\begin{slide}
Results
}
+ Carbon interstitial experiments:
+
+ \vspace{8pt}
+
+ \small
+
+ \begin{minipage}[t]{4.0cm}
+ \underline{Tetrahedral}
+ \begin{itemize}
+ \item $E_F=2.67\, eV$
+ \item tetrahedral bond
+ \end{itemize}
+ \end{minipage}
+ \hspace{0.3cm}
+ \begin{minipage}[t]{4.0cm}
+ \underline{110 dumbbell}
+ \begin{itemize}
+ \item $E_F=1.76\, eV$
+ \item C forms 3 bonds
+ \end{itemize}
+ \end{minipage}
+ \hspace{0.3cm}
+ \begin{minipage}[t]{4.0cm}
+ \underline{Hexagonal}
+ \begin{itemize}
+ \item $E_F^{\star}\approx5.6\, eV$
+ \item unstable!
+ \end{itemize}
+ \end{minipage}
+
+ \vspace{8pt}
+
+ \begin{minipage}{4.3cm}
+ \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+ \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+ \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
+ \end{minipage}
+
\end{slide}
\begin{slide}
Results
}
+ \vspace{8pt}
+
+ Carbon \underline{random insertion} experiments:
+
+ \vspace{8pt}
+
+ bar
+
\end{slide}
\begin{slide}
Results
}
+ SiC-precipitation experiments:
+
\end{slide}
\begin{slide}
\end{slide}
-
\end{document}
projects / lectures / latex.git / blobdiff