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140 \parbox[c]{0.1\linewidth}{\includegraphics[height=4.5cm]{uni-logo.eps}}
141 \parbox[c]{0.7\linewidth}{%
143 \textbf{\Huge{Monte Carlo simulation study of a
144 selforganization process\\
145 leading to ordered precipitate structures}
147 \textsc{\LARGE \underline{F. Zirkelbach}, M. H"aberlen,
148 J. K. N. Lindner, B. Stritzker
150 {\large Institut f"ur Physik, Universit"at Augsburg,
151 D-86135 Augsburg, Germany
155 \parbox[c]{0.1\linewidth}{%
156 \includegraphics[height=4.1cm]{Lehrstuhl-Logo.eps}
160 \hfill\mbox{}\\[0.5cm]
164 % content, let's rock the columns
165 \begin{lrbox}{\spalten}
166 \parbox[t][\textheight]{1.3\textwidth}{%
173 \section*{1 \hspace{0.1cm} {\color{blue}Experimental observations}}
175 \subsection*{1.1 {\color{blue} Amorphous inclusions}}
177 \includegraphics[width=11cm]{k393abild1_e.eps}
179 Cross section TEM image:\\
180 $180 \, keV$ $C^+ \rightarrow Si$,
181 $T=150 \, ^{\circ} \mathrm{C}$,
182 Dose: $4.3 \times 10^{17} \, cm^{-2}$\\
183 black/white: crystalline/amorphous material\\
184 L: amorphous lamellae, S: spherical amorphous inclusions
186 \subsection*{1.2 {\color{blue} Carbon distribution}}
188 \includegraphics[width=11cm]{eftem.eps}
190 Brightfield TEM and respective EFTEM image:\\
191 $180 \, keV$ $C^+ \rightarrow Si$,
192 $T=200 \, ^{\circ} \mathrm{C}$,
193 Dose: $4.3 \times 10^{17} \, cm^{-2}$\\
194 yellow/blue: high/low concentrations of carbon
199 \section*{2 \hspace{0.1cm} {\color{blue}Model}}
202 \includegraphics[width=11cm]{modell_ng_e.eps}
205 \item supersaturation of $C$ in $c-Si$\\
206 $\rightarrow$ {\bf carbon induced} nucleation of spherical
208 \item high interfacial energy between $3C-SiC$ and $c-Si$\\
209 $\rightarrow$ {\bf amourphous} precipitates
210 \item $20 - 30\,\%$ lower silicon density of $a-SiC_x$ compared to $c-Si$\\
211 $\rightarrow$ {\bf lateral strain} (black arrows)
212 \item reduction of the carbon supersaturation in $c-Si$\\
213 $\rightarrow$ {\bf carbon diffusion} into amorphous volumina
215 \item lateral strain (vertical component relaxating)\\
216 $\rightarrow$ {\bf strain induced} lateral amorphization
222 \section*{3 \hspace{0.1cm} {\color{blue}Simulation}}
224 \subsection*{3.1 {\color{blue} Discretization of the target}}
226 \includegraphics[width=6cm]{gitter_e.eps}
229 \subsection*{3.2 {\color{blue} Simulation algorithm}}
231 \subsubsection*{3.2.1 Amorphization/Recrystallization}
233 \item random numbers according to the nuclear
234 energy loss to determine the volume hit
236 \item compute local probability for
239 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}}
241 and recrystallization:
243 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{,}
246 \delta (\vec r) = \left\{
248 1 & \textrm{volume at position $\vec r$ amorphous} \\
249 0 & \textrm{otherwise} \\
253 \item loop for the mean amount of hits by the
256 Three contributions to the amorphization process controlled by:
258 \item {\color{green} $p_b$} normal 'ballistic' amorphization
259 \item {\color{blue} $p_c$} carbon induced amorphization
260 \item {\color{red} $p_s$} stress enhanced amorphization
263 \subsubsection*{3.2.2 Carbon incorporation}
265 \item random numbers according to the
266 implantation profile to determine the
268 \item increase the amount of carbon atoms in
271 \subsubsection*{3.2.3 Diffusion/Sputtering}
273 \item every $d_v$ steps transfer $d_r$ of the
274 carbon atoms of crystalline volumina to
275 an amorphous neighbour volume
276 \item do the sputter routine after $n$ steps
277 corresponding to $3 \, nm$ of substrat
284 \section*{4 \hspace{0.1cm} {\color{blue}Simulation results}}
286 \subsection*{4.1 {\color{blue} Comparison with experiments}}
288 \includegraphics[width=11cm]{dosis_entwicklung_ng_e_1-2.eps}
291 \includegraphics[width=11cm]{dosis_entwicklung_ng_e_2-2.eps}
295 \subsection*{4.2 {\color{blue} Carbon distribution}}
297 \includegraphics[width=11cm]{ac_cconc_ver2_e.eps}
305 \subsection*{4.3 {\color{blue} More structural/compositional
308 \includegraphics[width=8cm]{97_98_ng_e.eps} \\
309 Plane view of consecutive target layers $z$ and $z+1$
313 \subsection*{4.4 \hspace{0.1cm} {\color{blue} Broad distribution
314 of lamellar structure - the recipe}}
315 \subsubsection*{4.4.1 Constant carbon concentration}
318 \includegraphics[width=6cm]{multiple_impl_cp_e.eps}
322 \item multiple implantation \\ steps
323 \item energies: $180$ - $10 \, keV$
325 $\Rightarrow$ nearly constant carbon distribution
329 \subsubsection*{4.4.2 2 MeV C$^+$ implantation
332 \includegraphics[width=10cm]{multiple_impl_e.eps}
337 \section*{5 \hspace{0.1cm} {\color{red} Conclusions}}
339 \item selforganized nanometric precipitates by ion irradiation
340 \item model describing the seoforganization process
341 \item precipitate structures traceable by simulation
342 \item detailed structural/compositional information
343 \item recipe for broad distributions of lamellar structure
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