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\begin{document}

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% itemize level ii
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% topic

\begin{slide}
\begin{center}

 \vspace{16pt}

 {\LARGE\bf
  Molecular dynamics simulation study\\
  of the silicon carbide precipitation process
 }

 \vspace{24pt}

 \textsc{\small \underline{F. Zirkelbach}$^1$, J. K. N. Lindner$^1$,
         K. Nordlund$^2$, B. Stritzker$^1$}\\

 \vspace{32pt}

 \begin{minipage}{2.0cm}
  \begin{center}
  \includegraphics[height=1.6cm]{uni-logo.eps}
  \end{center}
 \end{minipage}
 \begin{minipage}{8.0cm}
  \begin{center}
   {\footnotesize
    $^1$ Experimentalphysik IV, Institut f"ur Physik,\\
         Universit"at Augsburg, Universit"atsstr. 1,\\
         D-86135 Augsburg, Germany
   }
  \end{center}
 \end{minipage}
 \begin{minipage}{2.3cm}
  \begin{center}
  \includegraphics[height=1.5cm]{Lehrstuhl-Logo.eps}
  \end{center}
 \end{minipage}

 \vspace{16pt}

 \begin{minipage}{4.0cm}
  \begin{center}
  \includegraphics[height=1.6cm]{logo_eng.eps}
  \end{center}
 \end{minipage}
 \begin{minipage}{8.0cm}
  \begin{center}
  {\footnotesize
   $^2$ Accelerator Laboratory, Department of Physical Sciences,\\
   University of Helsinki, Pietari Kalmink. 2,\\
   00014 Helsinki, Finland
  }
  \end{center}
 \end{minipage}
\end{center}
\end{slide}

% contents

% no contents for such a short talk!

% start of contents

\begin{slide}

 {\large\bf
  Motivation / Introduction
 }

 \vspace{16pt}

 Reasons for understanding the SiC precipitation process:

 \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{orange}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
  Motivation / Introduction
 }

 \small
 \vspace{6pt}

 Supposed conversion mechanism 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}

 \vspace{12pt}

 Experimentally observed:
 \begin{itemize}
  \item Minimal diameter of precipitation: 4 - 5 nm
  \item (hkl)-planes identical for Si and SiC
 \end{itemize}

\end{slide}

\begin{slide}

 {\large\bf
  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-dimensional phase space
  \item Observables obtained by time average
 \end{itemize}

 \vspace{12pt}

 Application details:
 \begin{itemize}
  \item Integrator: Velocity Verlet, timestep: $1\, fs$
  \item Ensemble: 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 and K. Albe. Phys. Rev. B 71 (2005) 035211}
	\end{center}
 \end{itemize}

 \begin{picture}(0,0)(-240,-70)
  \includegraphics[width=5cm]{tersoff_angle.eps} 
 \end{picture}

\end{slide}

\begin{slide}

 {\large\bf
  Simulation details
 }

 \vspace{8pt}

 Interstitial experiments:

 \vspace{8pt}

 \begin{pspicture}(0,0)(7,8)
  \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
   \parbox{7cm}{
   \begin{itemize}
    \item Initial configuration: $9\times9\times9$ unit cells Si
    \item Periodic boundary conditions
    \item $T=0 \, K$
   \end{itemize}
  }}}}
\rput(3.5,3.5){\rnode{insert}{\psframebox{
 \parbox{7cm}{
  Insertion of C / Si atom:
  \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{magenta}110 dumbbell}
   \item random positions (critical distance check)
  \end{itemize}
  }}}}
  \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
   \parbox{3.5cm}{
   Relaxation time: $2\, ps$
  }}}}
  \ncline[]{->}{init}{insert}
  \ncline[]{->}{insert}{cool}
 \end{pspicture}

 \begin{picture}(0,0)(-210,-45)
  \includegraphics[width=6cm]{unit_cell.eps}
 \end{picture}

\end{slide}

\begin{slide}

 {\large\bf
  Results
 } - Si self-interstitial experiments

 \small

 \begin{minipage}[t]{4.3cm}
 \underline{Tetrahedral}\\
 $E_f=3.41\, eV$\\
 \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
 \end{minipage}
 \begin{minipage}[t]{4.3cm}
 \underline{110 dumbbell}\\
 $E_f=4.39\, eV$\\
 \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
 \end{minipage}
 \begin{minipage}[t]{4.3cm}
 \underline{Hexagonal} \hspace{4pt}
 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
 $E_f^{\star}\approx4.48\, eV$ (unstable!)\\
 \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
 \end{minipage}

 \underline{Random insertion}

 \begin{minipage}{4.3cm}
 $E_f=3.97\, eV$\\
 \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
 \end{minipage}
 \begin{minipage}{4.3cm}
 $E_f=3.75\, eV$\\
 \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
 \end{minipage}
 \begin{minipage}{4.3cm}
 $E_f=3.56\, eV$\\
 \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
 \end{minipage}

\end{slide}

\begin{slide}

 {\large\bf
  Results
 } - Carbon interstitial experiments

 \small

 \begin{minipage}[t]{4.3cm}
 \underline{Tetrahedral}\\
 $E_f=2.67\, eV$\\
 \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
 \end{minipage}
 \begin{minipage}[t]{4.3cm}
 \underline{110 dumbbell}\\
 $E_f=1.76\, eV$\\
 \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
 \end{minipage}
 \begin{minipage}[t]{4.3cm}
 \underline{Hexagonal} \hspace{4pt}
 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
 $E_f^{\star}\approx5.6\, eV$ (unstable!)\\
 \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
 \end{minipage}

 \underline{Random insertion}

 \footnotesize

\begin{minipage}[t]{3.3cm}
   $E_f=0.47\, eV$\\
   \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
   \begin{picture}(0,0)(-15,-3)
    001 dumbbell
   \end{picture}
\end{minipage}
\begin{minipage}[t]{3.3cm}
   $E_f=1.62\, eV$\\
   \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
\end{minipage}
\begin{minipage}[t]{3.3cm}
   $E_f=2.39\, eV$ \hspace{2pt}
   \href{../video/c_in_si_int_rand_239.avi}{$\rhd$}\\
   \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
\end{minipage}
\begin{minipage}[t]{3.0cm}
   $E_f=3.41\, eV$ \hspace{2pt}
   \href{../video/c_in_si_int_rand_341.avi}{$\rhd$}\\
   \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
\end{minipage}

\end{slide}

\begin{slide}

 {\large\bf
  Simulation details
 }

 \small

 \vspace{8pt}

 SiC precipitation experiments:

 \vspace{8pt}

 \begin{pspicture}(0,0)(12,8)
  % nodes
  \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
   \parbox{7cm}{
   \begin{itemize}
    \item Initial configuration: $31\times31\times31$ unit cells Si
    \item Periodic boundary conditions
    \item $T=450\, ^{\circ}C$
    \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
   \end{itemize}
  }}}}
  \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
   \parbox{7cm}{
   Insertion of $6000$ carbon atoms at constant\\
   temperature into:
   \begin{itemize}
    \item Total simulation volume {\pnode{in1}}
    \item Volume of minimal SiC precipitation {\pnode{in2}}
    \item Volume of necessary amount of Si {\pnode{in3}}
   \end{itemize} 
  }}}}
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   \parbox{3.5cm}{
   Cooling down to $20\, ^{\circ}C$
  }}}}
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  \ncline[]{->}{insert}{cool}
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  \ncline[]{->}{in1}{ins1}
  \ncline[]{->}{in2}{ins2}
  \ncline[]{->}{in3}{ins3}
 \end{pspicture}

\end{slide}

\begin{slide}

 {\large\bf
  Very first results of the SiC precipitation experiments
 }

 \begin{minipage}[t]{6.3cm}
  %\includegraphics[width=6.0cm]{../plot/sic_prec_energy.ps}
  %\includegraphics[width=6.0cm]{../plot/sic_prec_temp.ps}
 \end{minipage}
 \begin{minipage}[c]{12.5cm}
  \includegraphics[height=5.0cm]{../plot/sic_pc.ps}
  \includegraphics[height=4.0cm]{sic_si-c-n.eps}
 \end{minipage}

\end{slide}

\begin{slide}

 {\large\bf
  Summary / Outlook
 }

\vspace{24pt}

\begin{itemize}
 \item Importance of understanding C in Si
 \item Interstitial configurations in silicon using the Albe potential
 \item Indication of SiC precipitation
\end{itemize}

\vspace{16pt}

\begin{itemize}
 \item Displacement and stress calculations
 \item Diffusion dependence of temperature and carbon concentration
 \item Analyzing results of the precipitation simulation runs
 \item Analyzing self-designed Si/SiC interface
\end{itemize}

\end{slide}

\end{document}

