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154 \parbox[c]{0.15\linewidth}{\includegraphics[height=4.5cm]{uni-logo.eps}}
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157 \textbf{\Huge{Monte Carlo simulation study \\
158 of a selforganization process \\
159 leading to ordered precipitate structures}
161 \textsc{\LARGE \underline{F. Zirkelbach}, M. H"aberlen,
162 J. K. N. Lindner, B. Stritzker
164 {\large Institut f"ur Physik, Universit"at Augsburg,
165 D-86135 Augsburg, Germany
169 \parbox[c]{0.15\linewidth}{%
170 \includegraphics[height=4.1cm]{Lehrstuhl-Logo.eps}
174 \hfill\mbox{}\\[0.1cm]
178 % content, let's rock the columns
179 \begin{lrbox}{\spalten}
180 \parbox[t][\textheight]{1.3\textwidth}{%
188 \section*{1 \hspace{0.1cm} {\color{blue}Experimental observations}}
190 \subsection*{1.1 {\color{blue} Amorphous inclusions}}
192 \includegraphics[width=11cm]{k393abild1_e.eps}
194 Cross section TEM image:\\
195 $180 \, keV$ $C^+ \rightarrow Si$,
196 $T=150 \, ^{\circ} \mathrm{C}$,
197 Dose: $4.3 \times 10^{17} \, cm^{-2}$\\
198 black/white: crystalline/amorphous material\\
199 L: amorphous lamellae, S: spherical amorphous inclusions
201 \subsection*{1.2 {\color{blue} Carbon distribution}}
203 \includegraphics[width=11cm]{eftem.eps}
205 Brightfield TEM and respective EFTEM image:\\
206 $180 \, keV$ $C^+ \rightarrow Si$,
207 $T=200 \, ^{\circ} \mathrm{C}$,
208 Dose: $4.3 \times 10^{17} \, cm^{-2}$\\
209 yellow/blue: high/low concentrations of carbon
214 \section*{2 \hspace{0.1cm} {\color{blue}Model}}
217 \includegraphics[width=11cm]{modell_ng_e.eps}
220 \item supersaturation of $C$ in $c-Si$\\
221 $\rightarrow$ {\bf carbon induced} nucleation of spherical
223 \item high interfacial energy between $3C-SiC$ and $c-Si$\\
224 $\rightarrow$ {\bf amourphous} precipitates
225 \item $20 - 30\,\%$ lower silicon density of $a-SiC_x$ compared to $c-Si$\\
226 $\rightarrow$ {\bf lateral strain} (black arrows)
227 \item reduction of the carbon supersaturation in $c-Si$\\
228 $\rightarrow$ {\bf carbon diffusion} into amorphous volumina
230 \item lateral strain (vertical component relaxating)\\
231 $\rightarrow$ {\bf strain induced} lateral amorphization
235 \section*{3 \hspace{0.1cm} {\color{blue}Simulation}}
237 \subsection*{3.1 {\color{blue} Discretization of the target}}
239 \includegraphics[width=6cm]{gitter_e.eps}
241 Periodic boundary conditions in $x,y$-direction.\\
242 Start conditions: All volumes crystalline, zero carbon
245 \subsection*{3.3 {\color{blue} TRIM collision statistics}}
247 \includegraphics[width=8cm]{trim_coll_e.eps}
250 $\Rightarrow$ mean constant energy loss per collision of an ion
256 \subsection*{3.2 {\color{blue} Simulation algorithm}}
258 \subsubsection*{3.2.1 Amorphization/Recrystallization}
260 \item random numbers according to the nuclear
261 energy loss to determine the volume hit
263 \item compute local probability for
266 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}}
268 and recrystallization:
270 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{,}
273 \delta (\vec r) = \left\{
275 1 & \textrm{volume at position $\vec r$ amorphous} \\
276 0 & \textrm{otherwise} \\
280 \item loop for the mean amount of hits by the
283 Three contributions to the amorphization process controlled by:
285 \item {\color{green} $p_b$} normal 'ballistic' amorphization
286 \item {\color{blue} $p_c$} carbon induced amorphization
287 \item {\color{red} $p_s$} stress enhanced amorphization
290 \subsubsection*{3.2.2 Carbon incorporation}
292 \item random numbers according to the
293 implantation profile to determine the
295 \item increase the amount of carbon atoms in
298 \subsubsection*{3.2.3 Diffusion/Sputtering}
300 \item every $d_v$ steps transfer $d_r$ of the
301 carbon atoms of crystalline volumina to
302 an amorphous neighbour volume
303 \item do the sputter routine after $n$ steps
304 corresponding to $3 \, nm$ of substrat
310 \section*{4 \hspace{0.1cm} {\color{blue}Simulation results}}
312 \subsection*{4.1 {\color{blue} Comparison with experiments}}
314 \includegraphics[width=11cm]{dosis_entwicklung_ng_e_1-2.eps}
317 \includegraphics[width=11cm]{dosis_entwicklung_ng_e_2-2.eps}
319 Simulation parameters:\\
320 $p_b=0.01$, $p_c=0.001$, $p_s=0.0001$, $d_r=0.05$,
324 \subsection*{4.2 {\color{blue} Variation of the simulation parameters}}
326 \includegraphics[width=11cm]{var_sim_paramters_en.eps}
328 Parameters of initial situation:\\
329 $p_b=0.01$, $p_c=0.001$, $p_s=0.0001$, $d_r=0.05$,
335 \subsection*{4.3 {\color{blue} Carbon distribution}}
337 \includegraphics[width=11cm]{ac_cconc_ver2_e.eps}
342 \subsection*{4.4 {\color{blue} More structural/compositional
345 \includegraphics[width=8cm]{97_98_ng_e.eps} \\
346 Plane view of consecutive target layers $z$ and $z+1$
350 \subsection*{4.5 \hspace{0.1cm} {\color{blue} Broad distribution
351 of lamellar structure - the recipe}}
352 \subsubsection*{4.5.1 Constant carbon concentration}
356 \item multiple implantation \\ steps
357 \item energies: $180$ - $10 \, keV$
358 \item higher temeprature\\
359 $\rightarrow$ prevent amorphization
361 $\Rightarrow$ nearly constant carbon distribution
365 \includegraphics[width=6cm]{multiple_impl_cp_e.eps}
368 \subsubsection*{4.5.2 2 MeV C$^+$ implantation
371 \includegraphics[width=10cm]{multiple_impl_e.eps}
376 \section*{5 \hspace{0.1cm} {\color{red} Conclusions}}
378 \item selforganized nanometric precipitates by ion irradiation
379 \item model describing the seoforganization process
380 \item precipitate structures traceable by simulation
381 \item detailed structural/compositional information
382 \item recipe for broad distributions of lamellar structure
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