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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}
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 implantation range near surface\\
228 $\rightarrow$ {\bf ralaxation} of {\bf vertical strain component}
229 \item reduction of the carbon supersaturation in $c-Si$\\
230 $\rightarrow$ {\bf carbon diffusion} into amorphous volumina
232 \item remaining lateral strain\\
233 $\rightarrow$ {\bf strain induced} lateral amorphization
237 \section*{3 \hspace{0.1cm} {\color{blue}Simulation}}
239 \subsection*{3.1 {\color{blue} Discretization of the target}}
241 \includegraphics[width=6cm]{gitter_e.eps}
243 Periodic boundary conditions in $x,y$-direction.\\
244 Start conditions: All volumes crystalline, zero carbon
247 \subsection*{3.3 {\color{blue} TRIM collision statistics}}
249 \includegraphics[width=8cm]{trim_coll_e.eps}
252 $\Rightarrow$ mean constant energy loss per collision of an ion
258 \subsection*{3.2 {\color{blue} Simulation algorithm}}
260 \subsubsection*{3.2.1 Amorphization/Recrystallization}
262 \item random numbers distributed according to
263 the nuclear energy loss to determine the
264 volume hit by an impinging ion
265 \item compute local probability for
268 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}}
270 and recrystallization:
272 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{,}
275 \delta (\vec r) = \left\{
277 1 & \textrm{volume at position $\vec r$ amorphous} \\
278 0 & \textrm{otherwise} \\
282 \item loop for the mean amount of hits by the
285 Three contributions to the amorphization process controlled by:
287 \item {\color{green} $p_b$} normal 'ballistic' amorphization
288 \item {\color{blue} $p_c$} carbon induced amorphization
289 \item {\color{red} $p_s$} stress enhanced amorphization
292 \subsubsection*{3.2.2 Carbon incorporation}
294 \item random numbers distributed according to
295 the implantation profile to determine the
297 \item increase the amount of carbon atoms in
300 \subsubsection*{3.2.3 Diffusion/Sputtering}
302 \item every $d_v$ steps transfer $d_r$ of the
303 carbon atoms of crystalline volumina to
304 an amorphous neighbour volume
305 \item do the sputter routine after $n$ steps
306 corresponding to $3 \, nm$ of substrat
312 \section*{4 \hspace{0.1cm} {\color{blue}Simulation results}}
314 \subsection*{4.1 {\color{blue} Comparison with experiments}}
316 \includegraphics[width=11cm]{dosis_entwicklung_ng_e_1-2.eps}
319 \includegraphics[width=11cm]{dosis_entwicklung_ng_e_2-2.eps}
321 Simulation parameters:\\
322 $p_b=0.01$, $p_c=0.001$, $p_s=0.0001$, $d_r=0.05$,
326 \subsection*{4.2 {\color{blue} Variation of the simulation parameters}}
328 \includegraphics[width=11cm]{var_sim_paramters_en.eps}
330 Parameters of initial situation:\\
331 $p_b=0.01$, $p_c=0.001$, $p_s=0.0001$, $d_r=0.05$,
337 \subsection*{4.3 {\color{blue} Carbon distribution}}
339 \includegraphics[width=11cm]{ac_cconc_ver2_e.eps}
344 \subsection*{4.4 {\color{blue} More structural/compositional
347 \includegraphics[width=8cm]{97_98_ng_e.eps} \\
348 Plane view of consecutive target layers $z$ and $z+1$
352 \subsection*{4.5 \hspace{0.1cm} {\color{blue} Broad distribution
353 of lamellar structure - the recipe}}
354 \subsubsection*{4.5.1 Constant carbon concentration}
358 \item multiple implantation\\
360 \item energies: $180$ - $10 \, keV$
361 \item temeprature: $500 ^{\circ} \mathrm{C}$\\
362 $\rightarrow$ prevent amorphization
364 $\Rightarrow$ nearly constant carbon distribution
368 \includegraphics[width=6cm]{multiple_impl_cp_e.eps}
371 \subsubsection*{4.5.2 2 MeV C$^+$ implantation
374 \includegraphics[width=10cm]{multiple_impl_e.eps}
376 Starting point for materials with high photoluminescence.\\
377 Dihu Chen et al. Opt. Mater. 23 (2003) 65.
381 \section*{5 \hspace{0.1cm} {\color{red} Conclusion}}
383 \item selforganized nanometric precipitates by ion irradiation
384 \item model describing the seoforganization process
385 \item set of parameters reproducing the experimental observations
386 \item precipitation process traceable by simulation
387 \item detailed structural/compositional information
388 \item recipe for broad distributions of lamellar structure
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