\articlemag{1}
+\special{landscape}
+
\begin{document}
\extraslideheight{10in}
\newcommand{\foo}{\mathcal{U}}
\newcommand{\vir}{\mathcal{W}}
+% itemize level ii
+\renewcommand\labelitemii{{\color{gray}$\bullet$}}
+
% topic
\begin{slide}
\end{itemize}
\item Results gained by simulation
\begin{itemize}
- \item Carbon interstitials in silicon
- \item Existence of $SiC$-precipitates
+ \item Interstitials in silicon
+ \item SiC-precipitation experiments
\end{itemize}
\item Conclusion / Outlook
\end{itemize}
% start of contents
+\begin{slide}
+
+ {\large\bf
+ Motivation / Introduction
+ }
+
+ \small
+ \vspace{6pt}
+
+ Supposed mechanism of the conversion of heavily carbon doped Si into SiC:
+
+ \vspace{8pt}
+
+ \begin{minipage}{3.8cm}
+ \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
+ \end{minipage}
+
+ \vspace{8pt}
+
+ \begin{minipage}{3.8cm}
+ Formation of C-Si dumbbells on regular c-Si lattice sites
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ Agglomeration into large clusters (embryos)\\
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ 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}
+
+ Experimentally observed minimal diameter of precipitation: 4 - 5 nm
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Simulation details
+ }
+
+ 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
+ \item Observables obtained by time average
+ \end{itemize}
+
+ \vspace{4pt}
+
+ Application details:
+ \begin{itemize}
+ \item Integrator: velocity verlet, timestep: $1\, fs$
+ \item Ensemble control: NVT, Berendsen thermostat, $\tau=100.0$
+ \item Potential: Tersoff-like bond order potential\\
+ \[
+ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
+ \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
+ \]
+ \begin{center}
+ {\scriptsize P. Erhart und K. Albe. Phys. Rev. B 71 (2005) 035211}
+ \end{center}
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ 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 $(0,0,0)$ $\rightarrow$ {\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,-85)
+ \includegraphics[width=6cm]{unit_cell.eps}
+ \end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Simulation details
+ }
+
+ \small
+
+ SiC precipitation experiments:
+ \begin{itemize}
+ \item Initial configuration: $31\times31\times31$ unit cells Si
+ \item Periodic boundary conditions
+ \item $T=450\, ^{\circ}C$
+ \item Steady state time: $600\, fs$
+ \item C insertion steps:
+ \begin{itemize}
+ \item If $T=450\pm 1\, ^{\circ}C$:\\
+ Insertion of 10 atoms at random positions within $V_{ins}$
+ \item Otherwise: Annealing for another $100\, fs$
+ \end{itemize}
+ \item Annealing: ($T_a: 450\rightarrow 20 \, ^{\circ}C$)
+ \begin{itemize}
+ \item If $T=T_a$: Decrease $T_a$ by $1\, ^{\circ}C$
+ \item Otherwise: Annealing for another $50\, fs$
+ \end{itemize}
+ \end{itemize}
+
+ 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 $E_F^{\star}=4.48\, eV$
+ \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}
+
+\begin{slide}
+
+ {\large\bf
+ Results
+ }
+
+ \vspace{8pt}
+
+ Si self-interstitial \underline{random insertion} experiments:
+
+ \vspace{8pt}
+
+ foo
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ 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 $E_F\sim5.6\, eV$
+ \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}
+
+ {\large\bf
+ Results
+ }
+
+ \vspace{8pt}
+
+ Carbon \underline{random insertion} experiments:
+
+ \vspace{8pt}
+
+ bar
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Results
+ }
+
+ SiC-precipitation experiments:
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Conclusion / Outlook
+ }
+
+\end{slide}
+
\end{document}
projects / lectures / latex.git / blobdiff