}
%\hfill
}}
-\hfill\mbox{}\\[0.1cm]
+\hfill\mbox{}\\[0cm]
%\vspace*{1.3cm}
$\rightarrow$ {\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 lateral strain (vertical component relaxating)\\
+\item remaining lateral strain\\
$\rightarrow$ {\bf strain induced} lateral amorphization
\end{itemize}
\end{kasten}
\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 random numbers distributed according to
+ the nuclear energy loss to determine the
+ volume hit by an impinging ion
\item compute local probability for
amorphization:\\
\[
\subsubsection*{3.2.2 Carbon incorporation}
\begin{itemize}
- \item random numbers according to the
- implantation profile to determine the
+ \item random numbers distributed according to
+ the implantation profile to determine the
incorporation volume
\item increase the amount of carbon atoms in
that volume
\makebox[11cm]{%
\parbox[c]{5cm}{%
\begin{itemize}
- \item multiple implantation \\ steps
+ \item multiple implantation\\
+ steps
\item energies: $180$ - $10 \, keV$
- \item higher temeprature\\
+ \item temeprature: $500 ^{\circ} \mathrm{C}$\\
$\rightarrow$ prevent amorphization
\end{itemize}
$\Rightarrow$ nearly constant carbon distribution
\begin{center}
\includegraphics[width=10cm]{multiple_impl_e.eps}
\end{center}
+ Starting point for materials with high photoluminescence.\\
+ Dihu Chen et al. Opt. Mater. 23 (2003) 65.
\end{kasten}
\begin{kasten}
- \section*{5 \hspace{0.1cm} {\color{red} Conclusions}}
+ \section*{5 \hspace{0.1cm} {\color{red} Conclusion}}
\begin{itemize}
\item selforganized nanometric precipitates by ion irradiation
\item model describing the seoforganization process
- \item precipitate structures traceable by simulation
+ \item set of parameters reproducing the experimental observations
+ \item precipitation process traceable by simulation
\item detailed structural/compositional information
\item recipe for broad distributions of lamellar structure
\end{itemize}
--- /dev/null
+\documentclass[portrait,a0b,final]{a0poster}
+\usepackage{epsf,psfig,pstricks,multicol,pst-grad,color}
+\usepackage{graphicx,amsmath,amssymb}
+\graphicspath{{../img/}}
+\usepackage[german]{babel}
+
+\begin{document}
+
+% Fliessenden Hintergrund von RGB-Farbe 1. .98 .98 nach 1. .85 .85
+% und wieder nach 1. .98 .98 (1. .85 .85 wird nach 0.1=10% des Hinter-
+% grunds angenommen)
+% Achtung Werte unter .8 verbrauchen zu viel Tinte!!!
+
+%\background{.95 .95 1.}{.78 .78 1.}{0.05}
+\background{.50 .50 .50}{.85 .85 .85}{0.5}
+%\newrgbcolor{blue1}{.9 .9 1.}
+
+% Groesse der einzelnen Spalten als Anteil der Gesamt-Textbreite
+\renewcommand{\columnfrac}{.31}
+
+% 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}
+
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