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\begin{document}

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% header
\vspace{-1cm}
\begin{header}
  \begin{minipage} {.13\textwidth}
	\includegraphics[height=11cm]{uni-logo.eps}
  \end{minipage} \hfill
  \begin{minipage}   {.73\textwidth}
     \centerline{{\Huge \bfseries Monte Carlo simulation study of a selforganisation}}
     \centerline{{\Huge \bfseries process leading to ordered precipitate structures}}
     \vspace*{1cm}
     \centerline{\huge\textsc {\underline{F.~Zirkelbach}}, M.~H"aberlen,
                               J.~K.~N.~Lindner, B.~Stritzker}
     \vspace*{1cm}
     \centerline{\Large Institut f"ur Physik, Universit"at Augsburg,
                        D-86135 Augsburg, Germany}
  \end{minipage} \hfill
  \begin{minipage} {.13\textwidth}
      \includegraphics[height=10cm]{Lehrstuhl-Logo.eps}
  \end{minipage} \hfill
\end{header}

\begin{poster}

\vspace{-1cm}
\begin{pcolumn}
  \begin{pbox}
    \section*{Motivation}
	{\bf
	Experimentally observerd seflorganisation process at high-dose carbon
	implantations under certain implantation conditions.}
	\begin{itemize}
		\item Spherical and lamellar amorphous inclusions at the upper
		      a/c interface
		\begin{center}
			\includegraphics[width=20cm]{k393abild1_e.eps}
		\end{center}
		Cross section TEM image:\\
		$180 \, keV$ $C^+ \rightarrow Si$,
		$T=150 \, ^{\circ} \mathrm{C}$,
		Dose: $4.3 \times 10^{17} \, cm^{-2}$\\
		black/white: crystalline/amorphous material\\
		L: amorphous lamellae, S: spherical amorphous inclusions
		\item Carbon accumulation in amorphous volumes
		\begin{center}
			\includegraphics[width=20cm]{eftem.eps}
		\end{center}
		Brightfield TEM and respective EFTEM image:\\
		$180 \, keV$ $C^+ \rightarrow Si$,
		$T=200 \, ^{\circ} \mathrm{C}$,
		Dose: $4.3 \times 10^{17} \, cm^{-2}$\\
		yellow/blue: high/low concentrations of carbon
	\end{itemize}
	{\bf
	Observed for a number of ion/target combinations for which the
	material undergoes drastic density change upon amorphisation.}\\
	{\scriptsize
	A. H. van Ommen, Nucl. Instr. and Meth. B 39 (1989) 194.\\
	E. D. Specht et al., Nucl. Instr. and Meth. B 84 (1994) 323.\\
	M. Ishimaru et al., Nucl. Instr. and Meth. B 166-167 (2000) 390.}
  \end{pbox}
  \vspace{-1cm}
  \begin{pbox}
    \section*{Model}
	{\bf
	Model schematically displaying the formation of ordered lamellae
	with increasing dose.}
	\vspace{1cm}
	\begin{center}
		\includegraphics[width=20cm]{modell_ng_e.eps}
	\end{center}
	\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 amourphous} 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 ralaxation} 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 induced} lateral amorphisation
	\end{itemize}
  \end{pbox}
  \vspace{-1cm}
  \begin{pbox}
    \section*{Simulation}
	\begin{minipage}[t]{0.5\textwidth}
		{\bf Discretisation of the target}
		\begin{center}
			\includegraphics[width=12cm]{gitter_e.eps}
		\end{center}
		\vspace{2cm}
		\begin{itemize}
			\item divided into cells with a cube length of $3 \, nm$
			\item periodic boundary conditions in $x$,$y$-direction
		\end{itemize}
	\end{minipage}
	\begin{minipage}[t]{0.5\textwidth}
		{\bf TRIM collsion statstics}
		\begin{center}
			\includegraphics[width=12cm]{trim_coll_e.eps}
		\end{center}
		\begin{itemize}
			\item[] $\Rightarrow$ identical depth profiles for
				 number of
			        collisions per depth and nuclear stopping power
			\item[] $\Rightarrow$ mean constant energy loss per
				 collision
		\end{itemize}
	\end{minipage}
  \end{pbox}


\end{pcolumn}
\begin{pcolumn}

  \begin{pbox}
    \section*{Simulation algorithm}
    {\bf
    The simulation algorithm consists of the following three parts looped 
    $s$ times corresponding to a dose $D=s/(64\times64\times(3 \, nm)^2)$:}
	\subsection*{1. Amorphisation/Recrystallisation}
	\begin{itemize}
		\item random numbers distributed according to
		      the nuclear energy loss to determine the
		      volume in which a collision occurs
		\item compute local probability for amorphisation:\\
		      %\vspace{0.1cm}

		      \centerline{\fcolorbox[rgb]{0.,0.,0.}{1.,1.,.8}{
		      \begin{minipage}{20cm}
\[
 p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
\]
		      \end{minipage}
		      }}
		      \vspace{1cm}
		      and recrystallisation:\\
		      %\vspace{0.1cm}

		      \centerline{\fcolorbox[rgb]{0.,0.,0.}{1.,1.,.8}{
		      \begin{minipage}{20cm}
\[
p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
\]
\[
\delta (\vec r) = \left\{
\begin{array}{ll}
	1 & \textrm{if volume at position $\vec r$ is amorphous} \\
	0 & \textrm{otherwise} \\
\end{array}
\right.
\]
		      \end{minipage}
		      }}
		      \vspace{1cm}
		\item loop for the mean amount of hits by the ion
	\end{itemize}
	Three contributions to the amorphisation process controlled by:
	\begin{itemize}
		\item {\color{green} $p_b$} normal 'ballistic' amorphisation
		\item {\color{blue} $p_c$} carbon induced amorphisation
		\item {\color{red} $p_s$} stress enhanced amorphisation
	\end{itemize}
	\subsection*{2. 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}
	\subsection*{3. Diffusion/Sputtering}
		\begin{itemize}
			\item every $d_v$ steps transfer $d_r$ of the
			      carbon atoms of crystalline volumina to
			      an amorphous neighbour volume
			\item do the sputter routine after $n$ steps
			      corresponding to $3 \, nm$ of substrat
			      removal
		\end{itemize}
		{\bf
		Simulation parameters $d_v$, $d_r$ and $n$ control the
		diffusion and sputtering process.}
  \end{pbox}
  \vspace{-1cm}
  \begin{pbox}
	\section*{Comparison of experiment and simulation}
	 \begin{center}
		\includegraphics[width=25cm]{dosis_entwicklung_ng_e_1-2.eps}
	\end{center}
	\begin{center}
		\includegraphics[width=25cm]{dosis_entwicklung_ng_e_2-2.eps}
	\end{center}
	Simulation parameters:\\
	$p_b=0.01$, $p_c=0.001$, $p_s=0.0001$, $d_r=0.05$, $d_v=1 \times 10^6$.
	\\[0.7cm]{\bf Conclusion:}
	\begin{itemize}
		\item Essentially conforming 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}
	{\bf\color{red} Simulation is able to model the whole
	                depth region affected by the 
	                irradiation process}
  \end{pbox}
\end{pcolumn}
\begin{pcolumn}

  \begin{pbox}
	\section*{Structural/compositional information}
	\begin{minipage}[t]{0.57\textwidth}
		\includegraphics[height=15cm=]{ac_cconc_ver2_e.eps}
		\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}
	\end{minipage}
	\begin{minipage}[t]{0.43\textwidth}
		\includegraphics[height=15cm]{97_98_ng_e.eps}
		\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}
	\end{minipage}
  \end{pbox}
  \vspace{-1cm}
  \begin{pbox}
	\section*{Recipe:\\
	          Thick films of ordered lamellar structure}
	{\bf Prerequisites:}\\
		Crystalline silicon target with a nearly constant carbon
		concentration at $10 \, at. \%$ in a $500 \, nm$ thick
		surface layer	
	\begin{center}
		\includegraphics[width=18cm]{multiple_impl_cp_e.eps}
	\end{center}
	{\bf Creation:}
	\begin{itemize}
		\item multiple energy ($180$-$10 \, keV$) $C^+$ $\rightarrow$
		      $Si$ implantation
		\item $T=500 \, ^{\circ} \mathrm{C}$, to prevent amorphisation
	\end{itemize}
	{\bf Stiring up:}\\
	2nd $2 \, MeV$ $C^+$ $\rightarrow$ $Si$ implantation 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 energy loss in the affected depth region
	\end{itemize}
	{\bf Result:}
	\begin{center}
		\includegraphics[width=25cm]{multiple_impl_e.eps}
	\end{center}
	\begin{itemize}
		\item Already ordered structures after $100 \times 10^6$ steps
		      corresponding to a dose of $D=2.7 \times 10^{17} cm^{-2}$
		\item More defined structures with increasing dose
	\end{itemize}
	{\bf\color{blue} Starting point for materials showing strong\\
                        photoluminescence}\\
	{\scriptsize Dihu Chen et al. Opt. Mater. 23 (2003) 65.}
  \end{pbox}
  \vspace{-1cm}
  \begin{pbox}
	\section*{Conclusions}
		\begin{itemize}
			\item Observation of self-organised nanometric
			      precipitates by ion irradiation
			\item Model proposed describing the seoforganisation
			      process
			\item Model implemented to a Monte Carlo simulation code
			\item Simulation is able to reproduce experimenal
			      observations
			\item Precipitation process gets traceable by simulation
			\item Detailed structural/compositional information
			      available by simulation
			\item Recipe proposed for the formation of broad
			      distributions of lamellar structure
		\end{itemize}
  \end{pbox}

\end{pcolumn}
\end{poster}
\end{document}

