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\begin{document}

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% header
\vspace{-1.2cm}
\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{-0.35cm}
\begin{pcolumn}
  \begin{pbox}
    \section*{Motivation}
	{\bf
	Experimentally observed selforganisation process at high-dose carbon
	implantations under certain implantation conditions.}
	\begin{itemize}
		\item Regularly spaced, nanometric spherical and lamellar
                      amorphous inclusions at the upper a/c interface
		\begin{center}
			\includegraphics[width=20cm]{k393abild1_e.eps}
		\end{center}
		Cross-section TEM bright-field images:\\
		$180 \, keV$ $C^+ \rightarrow Si$,
		$T_i=150 \, ^{\circ} \mathrm{C}$,
		Dose: $4.3 \times 10^{17} \, cm^{-2}$\\
		Amorphous inclusions appear white on darker backgrounds\\
		L: amorphous lamellae, S: spherical amorphous inclusions
		\item Carbon accumulation in amorphous volumes
		\begin{center}
			\includegraphics[width=20cm]{eftem.eps}
		\end{center}
		Bright-field TEM image and respective EFTEM $C$ map:\\
		$180 \, keV$ $C^+ \rightarrow Si$,
		$T_i=200 \, ^{\circ} \mathrm{C}$,
		Dose: $4.3 \times 10^{17} \, cm^{-2}$\\
		yellow/blue: high/low concentrations of carbon
	\end{itemize}
	{\bf
	Similarly ordered precipitate nanostructures also
	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{-1.4cm}
  \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 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 amorphisation
\item Absence of crystalline neighbours (structural information)\\
      $\rightarrow$ {\bf Stabilisation} of amorphous inclusions 
      {\bf against recrystallisation}
	\end{itemize}
  \end{pbox}
  \vspace{-1.5cm}
  \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 collision statistics}
		\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
    $D=s/(64\times64\times(3 \, nm)^2)$:}\\
\begin{minipage}{0.10\textwidth}
	\begin{picture}(0,0)(0,600)
		\includegraphics[height=40.0cm]{loop-arrow_ver2.eps}
	\end{picture}%
\end{minipage}
\begin{minipage}{0.90\textwidth}
	\vspace{1cm}
	\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}
		{\bf
		Simulation parameters $d_v$, $d_r$ and $n$ control the
		diffusion and sputtering process.}
		\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{minipage}%
  \end{pbox}
  \vspace{-0.7cm}
  \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:\\
	$p_b=0.01$, $p_c=0.001 \times (3 \, nm)^3$,
        $p_s=0.0001 \times (3 \, nm)^5$, $d_r=0.05$, $d_v=1 \times 10^6$.
	\\[0.7cm]{\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}
	{\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{minipage}[t]{0.9\textwidth}
		\vspace{-0.45cm}
		\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}%
	\end{minipage}%
	\begin{minipage}[t]{0.43\textwidth}
		\includegraphics[height=15cm]{97_98_ng_e.eps}
		%\includegraphics[height=13cm]{gitter_e.eps}
		%\includegraphics[height=15cm=]{test_foo.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{-1.4cm}
  \begin{pbox}
	\section*{Recipe for thick films of ordered lamellae}
	\begin{minipage}{0.33\textwidth}
		{\bf Prerequisites:}\\
		Crystalline silicon target with a nearly constant carbon
		concentration at $10 \, at. \%$ in a $500 \, nm$ thick
		surface layer	
	\end{minipage}
	\begin{minipage}{0.65\textwidth}
		\begin{center}
			\includegraphics[width=15cm]{multiple_impl_cp_e.eps}
		\end{center}
	\end{minipage}
	{\bf Creation:}
	\begin{itemize}
		\item Multiple energy ($180$-$10 \, keV$) $C^+$ $\rightarrow$
		      $Si$ implantation
		\item $T_i=500 \, ^{\circ} \mathrm{C}$, to prevent amorphisation
	\end{itemize}
	\vspace{1cm}
	{\bf Stirring up:}\\[0.5cm]
	$2 \, MeV$ $C^+$ $\rightarrow$ $Si$ 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}
	\vspace{1cm}
	{\bf Result:}
	\vspace{0.7cm}
	\begin{center}
		\includegraphics[width=25cm]{multiple_impl_e_ver2.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{-1.4cm}
  \begin{pbox}
	\section*{Conclusions}
		\begin{itemize}
			\item Observation of selforganised nanometric
			      precipitates by ion irradiation
			\item Model proposed describing the selforganisation
			      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{pbox}
  \vspace{-1.4cm}
  \begin{pbox}
	%\section*{Literature}
        {\bf Literature}\\
	 	{\scriptsize
                F. Zirkelbach, M. H"aberlen, J. K. N. Lindner,
                B. Stritzker. Comp. Mater. Sci. 33 (2005) 310.\\
	        F. Zirkelbach, M. H"aberlen, J. K. N. Lindner,
                B. Stritzker. Nucl. Instr. and Meth. B 242 (2006) 679.}
  \end{pbox}

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

