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\begin{document}

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% header
\vfill
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\psshadowbox{\makebox[0.95\textwidth]{%
	\hfill
	\parbox[c]{0.1\linewidth}{\includegraphics[height=4.5cm]{uni-logo.eps}}
	\parbox[c]{0.7\linewidth}{%
		\begin{center}
			\textbf{\Huge{Monte Carlo simulation study of a
			              selforganization process\\
			              leading to ordered precipitate structures}
			}\\[0.7em]
        		\textsc{\LARGE \underline{F. Zirkelbach}, M. H"aberlen,
			               J. K. N. Lindner, B. Stritzker
			}\\[0.7em]
        		{\large Institut f"ur Physik, Universit"at Augsburg,
			 D-86135 Augsburg, Germany
			}
		\end{center}
	}
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		\includegraphics[height=4.1cm]{Lehrstuhl-Logo.eps}
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\hfill\mbox{}\\[1.cm]

%\vspace*{1.3cm}

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% first column
%\begin{spalte}
%	\begin{kasten}
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%			{\large{\color{blue}\underline{ABSTRACT}}}
%		\end{center}
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% abstract ... skip it
%High-dose ion implantation into solids usually leads to a disordered distribution of defects or precipitates with variable sizes.
%However materials exist for which high-dose ion irradiation at certain conditions results in periodically arranged, self-organized, nanometric amorphous inclusions.
%This has been observed for a number of ion/target combinations \cite{ommen,specht,ishimaru} which all have in common a largely reduced density of host atoms of the amorphous phase compared to the crystalline host lattice.
%A simple model explaining the phenomenon is introduced and realized in a Monte Carlo simulation code, which focuses on high dose carbon implantation into silicon.
%The simulation is able to reproduce the depth distribution observed by TEM and RBS.
%While first versions of the simulation \cite{me1,me2} just covered a limited depth region of the target in which the selforganization is observed, the new version of this simulation code presented here is able to model the whole depth region affected by the irradiation process, as can be seen in chapter 4.
%Based on simulation results a recipe is proposed for producing broad distributions of lamellar, ordered structures which, according to recent studies \cite{wong}, are the starting point for materials with high photoluminescence.
%	\end{kasten}
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\begin{spalte}
	\begin{kasten}

        \section*{1 \hspace{0.1cm} {\color{blue}Experimental observations}}

		\subsection*{1.1 {\color{blue} Amorphous inclusions}}
			\begin{center}              
				\includegraphics[width=11cm]{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

		\subsection*{1.2 {\color{blue} Carbon distribution}}
			\begin{center}
				\includegraphics[width=11cm]{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{kasten}

	\begin{kasten}
        	\section*{2 \hspace{0.1cm} {\color{blue}Model}}

			\begin{center}
				\includegraphics[width=11cm]{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 reduction of the carbon supersaturation in $c-Si$\\
      $\rightarrow$ {\bf carbon diffusion} into amorphous volumina
      (white arrows)
\item lateral strain (vertical component relaxating)\\
      $\rightarrow$ {\bf strain induced} lateral amorphization
			\end{itemize}
	\end{kasten}
\end{spalte}
\begin{spalte}
	\begin{kasten}
		\section*{3 \hspace{0.1cm} {\color{blue}Simulation}}

		\subsection*{3.1 {\color{blue} Discretization of the target}}
	    		\begin{center}
            			\includegraphics[width=6cm]{gitter_e.eps}
			\end{center}

		\subsection*{3.2 {\color{blue} Simulation algorithm}}

		\subsubsection*{3.2.1 Amorphization/Recrystallization}
			\begin{itemize}
				\item random numbers according to the nuclear
				      energy loss to determine the volume hit
				      by an impinging ion
				\item compute local probability for
				      amorphization:\\
\[
 p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
\]
				      and recrystallization:
\[
 p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
\]
\[
\delta (\vec r) = \left\{
\begin{array}{ll}
	1 & \textrm{volume at position $\vec r$ amorphous} \\
	0 & \textrm{otherwise} \\
\end{array}
\right.
\]
				\item loop for the mean amount of hits by the
				      ion
			\end{itemize}
Three contributions to the amorphization process controlled by:
\begin{itemize}
	\item {\color{green} $p_b$} normal 'ballistic' amorphization
	\item {\color{blue} $p_c$} carbon induced amorphization
	\item {\color{red} $p_s$} stress enhanced amorphization
\end{itemize}

		\subsubsection*{3.2.2 Carbon incorporation}
			\begin{itemize}
				\item random numbers according to the
				      implantation profile to determine the
				      incorporation volume
				\item increase the amount of carbon atoms in
				      that volume
			\end{itemize}
		\subsubsection*{3.2.3 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}
	\end{kasten}
\end{spalte}
\begin{spalte}
	\begin{kasten}
		\section*{4 \hspace{0.1cm} {\color{blue}Simulation results}}

		\subsection*{4.1 {\color{blue} Comparison with experiments}}
			\begin{center}              
			\includegraphics[width=11cm]{dosis_entwicklung_ng_e_1-2.eps}
			\end{center}
			\begin{center}              
			\includegraphics[width=11cm]{dosis_entwicklung_ng_e_2-2.eps}
			\end{center}

		\subsection*{4.1 {\color{blue} Carbon distribution}}
			\begin{center}              
			\includegraphics[width=11cm]{ac_cconc_ver2_e.eps}
			\end{center}
			
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% fourth column
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	\begin{kasten}
		\section*{5 \hspace{0.1cm} {\color{blue}Broad distribution of
		                                        lamellar structure}}
			\begin{mbox}
			\begin{itemize}
				\item $10 \, at.\%$ constant carbon plateau
				      by multiple implantation steps at
				      energies between $180$ and $10 \, keV$
			\end{itemize}
			\begin{center}              
				\includegraphics[width=6cm]{multiple_impl_cp.eps}
			\end{center}
			\begin{itemize}
				\item foloowed by $2 \, MeV$ $C^+$ implantation
			\end{itemize}
			\begin{center}              
				\includegraphics[width=10cm]{multiple_impl.eps}
			\end{center}

	\end{kasten}

\vspace{0.5cm}
      \begin{kasten}
         \section*{6 \hspace{0.1cm} {\color{red} \underline{Conclusions}}}
             \begin{itemize}
             \item
             
             \item
             
             \item
             
             \item
             
             \end{itemize}
      \end{kasten}

\vspace{0.5cm}
      \begin{kasten}

           {\small
           \begin{thebibliography}{9}
           \bibitem{ommen} A. H. van Ommen,
                           Nucl. Instr. and Meth. B 39 (1989) 194.
           \bibitem{specht} E. D. Specht, D. A. Walko, S. J. Zinkle,
                           Nucl. Instr. and Meth. B 84 (2000) 390.
           \bibitem{ishimaru} M. Ishimaru,  R. M. Dickerson, K. E. Sickafus,
                              Nucl. Instr. and Meth. B 166-167 (2000) 390.
	\bibitem{me1} F. Zirkelbach, M. H"aberlen, J. K. N. Lindner,
	              B. Stritzker,
	              Comp. Mater. Sci. 33 (2005) 310.
	\bibitem{me2} F. Zirkelbach, M. H"aberlen, J. K. N. Lindner,
	              B. Stritzker,
	              Nucl. Instr. and Meth. B 242 (2006) 679.
           \bibitem{wong} Dihu Chen, Z. M. Liao, L. Wang, H. Z. Wang, Fuli Zhao,
                          W. Y. Cheung, S. P. Wong,
                          Opt. Mater. 23 (2003) 65. Opt. Mater. 23 (2003) 65.
           \end{thebibliography}
           }
   \end{kasten}
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    }
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