\documentclass[semhelv]{seminar}

\usepackage{verbatim}
\usepackage[german]{babel}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{ae}

\usepackage{calc}               % Simple computations with LaTeX variables
\usepackage[hang]{caption2}     % Improved captions
\usepackage{fancybox}           % To have several backgrounds

\usepackage{fancyhdr}           % Headers and footers definitions
\usepackage{fancyvrb}           % Fancy verbatim environments
\usepackage{pstcol}             % PSTricks with the standard color package

\usepackage{graphicx}
\graphicspath{{./img/}}

\usepackage{semcolor}
\usepackage{semlayer}           % Seminar overlays
\usepackage{slidesec}           % Seminar sections and list of slides

\input{seminar.bug}             % Official bugs corrections
\input{seminar.bg2}             % Unofficial bugs corrections

\articlemag{1}

\begin{document}

\extraslideheight{10in}
\slideframe{none}

\def\slideleftmargin{.0in}
\def\sliderightmargin{0in}
\def\slidetopmargin{0in}
\def\slidebottommargin{.2in} % fucking slide number gone now :)

% topic

\begin{slide}
\begin{figure}[t]
 \begin{center}
  \includegraphics[height=1cm]{ifp.eps}
  \\
  \includegraphics[height=2cm]{Lehrstuhl-Logo.eps}
 \end{center}
\end{figure}
\begin{center}
 \large\bf
 Monte Carlo simulation study of a selforganization process leading
 to ordered precipitate structures
\end{center}
\begin{center}
 F. Zirkelbach, M. H"aberlen, J. K. N. Lindner und B. Stritzker
\end{center}
\end{slide}

% start of content
\ptsize{8}

\begin{slide}
{\large\bf
 Outline
}
\begin{picture}(300,30)
\end{picture}
\begin{itemize}
 \item Cross-section TEM: selforganized $SiC_x$-precipitates
 \item Model describing the selforganization process
 \item Monte Carlo simulation
 \item Comparison of experiment and simulation
 \item Recipe for thick films of ordered laemllae
 \item Summary
\end{itemize}
\end{slide}

\begin{slide}
{\large\bf
 Cross-Section TEM image showing selforganized amorphous lamellar inclusions
}
\begin{figure}
 \begin{center}
  \includegraphics[width=10cm]{k393abild1_e.eps}
  $180 keV \textrm{ } C^+ \rightarrow Si(100)$, $150 \, ^{\circ} \mathrm{C}$, $4.3 \times 10^{17} cm^{-2}$
 \end{center}
\end{figure}
\end{slide}

\begin{slide}
{\large\bf
 Model
}
\begin{figure}
 \begin{center}
  \includegraphics[width=8cm]{modell_ng_e.eps}
 \end{center}
\end{figure}
 \scriptsize
\begin{itemize}
 \item Supersaturation of $C$ in $c-Si$ \\
       $\rightarrow$ {\bf Carbon induced} nucleation of spherical $SiC_x$-precipitates
 \item High interfacial energy between $3C-SiC$ and $c-Si$\\
       $\rightarrow$ {\bf Amorphous} precipitates
 \item $20 - 30\,\%$ lower silicon density of $a-SiC_x$ compared to $c-Si$\\
       $\rightarrow$ {\bf Lateral strain} (black arrows)
 \item Implantation range near surface\\
       $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component}
 \item Reduction of the carbon supersaturation in $c-Si$\\
       $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina (white arrows)
 \item Remaining lateral strain\\
       $\rightarrow$ {\bf Strain enhanced} lateral amorphization
 \item Absence of crystalline neighbours (structural information)\\
       $\rightarrow$ {\bf Stabilization} of amorphous inclusions {\bf against recrystallization}
\end{itemize}
\end{slide}

\begin{slide}
{\large\bf
 Simulation\\
}
\\
{\bf Discretization of the target}
\begin{center}
  \includegraphics[width=8cm]{gitter_e.eps}
\end{center}
\begin{itemize}
  \item divided into cells with a cube length of $3 \, nm$
  \item periodic boundary conditions in $x$,$y$-direction
\end{itemize}
\end{slide}

\begin{slide}
{\large\bf
 Simulation\\
}
{\bf TRIM collision statistics}
\begin{center}
  \includegraphics[width=8cm]{trim_coll_e.eps}
\end{center}
\begin{itemize}
  \item identical depth profiles for
        number of
        collisions per depth and nuclear stopping power
  \item mean constant energy loss per
        collision
\end{itemize}
\end{slide}

\begin{slide}
{\large\bf
 Simulation algorithm\\
}
\\
The simulation algorithm consists of the following three parts looped 
$s$ times corresponding to a dose $D=s/(64\times64\times(3 \, nm)^2)$:\\
\begin{itemize}
  \item Amorphization / Recrystallization
  \item Carbon incorporation
  \item Diffusion / Sputtering
\end{itemize}
\end{slide}

\begin{slide}
{\large\bf
 Amorphization / Recrystallization \\
}
\begin{itemize}
  \item random numbers distributed according to the nuclear energy loss\\
        $\rightarrow$ determine the volume in which a collision occurs
  \item compute local probability for amorphization / recyrstallization
  \item let another random number decide ...
\end{itemize}
\vspace{12pt}
\[
  \displaystyle p_{c \rightarrow a}(\vec r) = \textcolor[rgb]{0,1,1}{p_{b}} \qquad + \qquad \textcolor{red}{p_{c} \, c_{Carbon}(\vec r)} \qquad + \textcolor[rgb]{0.5,0.25,0.12}{\sum_{amorphous \, neighbours} \frac{p_{s} \, c_{Carbon}(\vec{r'})}{(\vec r - \vec{r'})^2}} \\
\]
\begin{picture}(70,15)(-10,0)
 \bf \textcolor[rgb]{0,1,1}{normal (ballistic)}
\end{picture}
\begin{picture}(100,15)(-15,0)
 \bf \textcolor{red}{carbon inuced}
\end{picture}
\begin{picture}(120,15)(-40,0)
 \bf \textcolor[rgb]{0.5,0.25,0.12}{stress enhanced}
\end{picture}
\begin{picture}(300,40)
$
  p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \displaystyle \Big( 1 - \frac{\sum_{direct\, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{, }
$
\end{picture}
\vspace{6pt}
\begin{displaymath}
 \delta (\vec r) = \left\{ \begin{array}{ll}
  1 & \textrm{if volume $\vec r$ is amorphous} \\
  0 & \textrm{else} \\
 \end{array} \right.
\end{displaymath}
\end{slide}

\begin{slide}
{\large\bf
 Carbon incorporation
}
\begin{itemize}
   \item random numbers distributed according to
         the implantation profile to determine the
         incorporation volume
   \item increase the amount of carbon atoms in
         that volume
\end{itemize}
\begin{picture}(50,20)(0,0)\end{picture}\\
{\large\bf
Diffusion/Sputtering
}
\begin{itemize}
  \item every $d_v$ steps transfer of a fraction $d_r$
        of carbon atoms from crystalline volumina to
        an amorphous neighbour volume
  \item remove $3 \, nm$ surface layer after $n$ loops,
        shift remaining cells $3 \, nm$ up and insert
        an empty, crystalline $3 \, nm$ bottom layer
\end{itemize}
\end{slide}

\begin{slide}
{\large\bf
 Comparison of experiment and simulation \\
}
\begin{center}
  \includegraphics[width=10cm]{dosis_entwicklung_ng_e_1-2.eps}
\end{center}
Simulation parameters:\\
$p_b=0.01$, $p_c=0.001 \times (3 \, nm)^3$,
$p_s=0.0001 \times (3 \, nm)^5$, $d_r=0.05$, $d_v=1 \times 10^6$.
\end{slide}

\begin{slide}
{\large\bf
 Comparison of experiment and simulation \\
}
\begin{center}
  \includegraphics[width=10cm]{dosis_entwicklung_ng_e_2-2.eps}
\end{center}
Simulation parameters:\\
$p_b=0.01$, $p_c=0.001 \times (3 \, nm)^3$,
$p_s=0.0001 \times (3 \, nm)^5$, $d_r=0.05$, $d_v=1 \times 10^6$.
\end{slide}

\begin{slide}
{\large\bf
 Conclusion:\\
}
\begin{itemize}
  \item Simulation in good agreement with experimentally observed
        formation and growth of the continuous amorphous layer
  \item Lamellar precipitates and their evolution at the upper
        a/c interface with increasing dose is reproduced
\end{itemize}
\begin{picture}(50,20)(0,0)\end{picture}\\
{\bf\color{red} Simulation is able to model the whole
                depth region affected by the 
                irradiation process}
\end{slide}

\begin{slide}
{\large\bf
 Structural/compositional\\information \\
}
\begin{itemize}
  \item Fluctuation of the carbon\\
        concentration in the region\\
        of the lamellae
  \item Saturation limit of carbon\\
        in c-$Si$ under given\\
        implantation conditions\\
        between $8$ and $10 \, at. \%$
\end{itemize}
\begin{picture}(0,0)(-145,60)
\includegraphics[height=8cm=]{ac_cconc_ver2_e.eps}
\end{picture}
\end{slide}

\begin{slide}
{\large\bf
 Structural/compositional\\information \\
}
\begin{itemize}
  \item Complementarily arranged and\\
        alternating sequence of layers\\
        with high and low amount of\\
        amorphous regions
  \item Carbon accumulation in the\\
        amorphous phase
\end{itemize}
\begin{picture}(0,0)(-155,60)
\includegraphics[height=8cm]{97_98_ng_e.eps}
\end{picture}
\end{slide}

\begin{slide}
{\large\bf
 Recipe for thick films of ordered lamellae \\
}
\\
Prerequisites:\\
Crystalline silicon target with a nearly constant carbon
concentration at $10 \, at. \%$ in a $500 \, nm$ thick
surface layer   
\includegraphics[width=8cm]{multiple_impl_cp_e.eps}
\begin{itemize}
  \item Multiple energy ($180$-$10 \, keV$) $C^+$ $\rightarrow$ $Si$ implantation
  \item $T_i=500 \, ^{\circ} \mathrm{C}$, to prevent amorphization
\end{itemize}
\end{slide}

\begin{slide}
{\large\bf
 Recipe for thick films of ordered lamellae \\
}
\\
{\bf Stirring up:}
$2 \, MeV$ $C^+$ $\rightarrow$ $Si$ irradiation step at
$150 \, ^{\circ} \mathrm{C}$
\begin{itemize}
  \item This does not significantly change the carbon
        concentration in the top $500 \, nm$
  \item Nearly constant nuclear energy loss in the top $700 \, nm$
        region
\end{itemize}
\includegraphics[width=8cm]{multiple_impl_e_ver2.eps}\\
{\bf\color{blue} Starting point for materials showing strong photoluminescence}\\
{\scriptsize Dihu Chen et al. Opt. Mater. 23 (2003) 65.}
\end{slide}

\begin{slide}
{\large\bf
 Summary
}
\begin{itemize}
 \item Observation of selforganized nanometric precipitates by ion irradiation\\
  $C \rightarrow Si \qquad T_{i}: 150 - 350 \, ^{\circ} \mathrm{C} \qquad D \le 8 \times 10^{17} cm^{-2}$
 \item Model proposed describing the selforganization process
 \item Model implemented in a Monte Carlo simulation code
 \item Modelling of the complete depth region affected by the irradiation process
 \item Simulation is able to reproduce entire amorphous phase formation
 \item Precipitation process gets traceable by simulation
 \item Detailed structural/compositional information available by simulation
 \item Recipe proposed for the formation of thick films of lamellar structure
\end{itemize}
\end{slide}

\begin{slide}
{\large\bf
 Thank you for your attention!\\
 Thanks for accepting me as a guest!\\
}
\\
\ldots another recipe I propose:\\
\begin{itemize}
  \item {\color{blue} 06 cl vodka}
  \item {\color{blue} 03 cl peach liqueur}
  \item {\color{blue} 03 cl amaretto}
  \item {\color{red} 16 cl black currant juice}
  \item {\color{red} dash of citron}
  \item {\color{red} 3-4 ice cubes}
\end{itemize}
$\Rightarrow$ Killer Cool Aid
\end{slide}

\end{document}
