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1 \pdfoutput=0
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3 \documentclass[landscape,semhelv]{seminar}
4
5 \usepackage{verbatim}
6 \usepackage[greek,german]{babel}
7 \usepackage[latin1]{inputenc}
8 \usepackage[T1]{fontenc}
9 \usepackage{amsmath}
10 \usepackage{stmaryrd}
11 \usepackage{latexsym}
12 \usepackage{ae}
13
14 \usepackage{calc}               % Simple computations with LaTeX variables
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16 \usepackage{fancybox}           % To have several backgrounds
17
18 \usepackage{fancyhdr}           % Headers and footers definitions
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21
22 \usepackage{pstricks}
23 \usepackage{pst-node}
24 \usepackage{pst-grad}
25
26 %\usepackage{epic}
27 %\usepackage{eepic}
28
29 \usepackage{layout}
30
31 \usepackage{graphicx}
32 \graphicspath{{../img/}}
33
34 \usepackage{miller}
35
36 \usepackage[setpagesize=false]{hyperref}
37
38 % units
39 \usepackage{units}
40
41 \usepackage{semcolor}
42 \usepackage{semlayer}           % Seminar overlays
43 \usepackage{slidesec}           % Seminar sections and list of slides
44
45 \input{seminar.bug}             % Official bugs corrections
46 \input{seminar.bg2}             % Unofficial bugs corrections
47
48 \articlemag{1}
49
50 \special{landscape}
51
52 % font
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54 %\renewcommand{\familydefault}{\sfdefault}
55 %\usepackage{mathptmx}
56
57 \usepackage{upgreek}
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84 }
85
86 \begin{document}
87
88 \extraslideheight{10in}
89 \slideframe{plain}
90
91 \pagestyle{empty}
92
93 % specify width and height
94 \slidewidth 26.3cm 
95 \slideheight 19.9cm 
96
97 % margin
98 \def\slidetopmargin{-0.15cm}
99
100 \newcommand{\ham}{\mathcal{H}}
101 \newcommand{\pot}{\mathcal{V}}
102 \newcommand{\foo}{\mathcal{U}}
103 \newcommand{\vir}{\mathcal{W}}
104
105 % itemize level ii
106 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
107
108 % nice phi
109 \renewcommand{\phi}{\varphi}
110
111 % roman letters
112 \newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
113
114 % colors
115 \newrgbcolor{si-yellow}{.6 .6 0}
116 \newrgbcolor{hb}{0.75 0.77 0.89}
117 \newrgbcolor{lbb}{0.75 0.8 0.88}
118 \newrgbcolor{hlbb}{0.825 0.88 0.968}
119 \newrgbcolor{lachs}{1.0 .93 .81}
120
121 % shortcuts
122 \newcommand{\si}{Si$_{\text{i}}${}}
123 \newcommand{\ci}{C$_{\text{i}}${}}
124 \newcommand{\cs}{C$_{\text{sub}}${}}
125 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
126 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
127 \newcommand{\dista}[1]{\unit[#1]{\AA}{}}
128 \newcommand{\perc}[1]{\unit[#1]{\%}{}}
129
130 % no vertical centering
131 %\centerslidesfalse
132
133 % layout check
134 %\layout
135 \begin{slide}
136 \center
137 {\Huge
138 E\\
139 F\\
140 G\\
141 A B C D E F G H G F E D C B A
142 G\\
143 F\\
144 E\\
145 }
146 \end{slide}
147
148 % topic
149
150 \begin{slide}
151 \begin{center}
152
153  \vspace{16pt}
154
155  {\LARGE\bf
156   Atomistic simulation studies\\[0.2cm]
157   in the C/Si system
158  }
159
160  \vspace{48pt}
161
162  \textsc{Frank Zirkelbach}
163
164  \vspace{48pt}
165
166  Application talk at the Max Planck Institute for Solid State Research
167
168  \vspace{08pt}
169
170  Stuttgart, November 2011
171
172 \end{center}
173 \end{slide}
174
175 % no vertical centering
176 \centerslidesfalse
177
178 % intro
179
180 \begin{slide}
181
182 %{\large\bf
183 % Phase diagram of the C/Si system\\
184 %}
185
186 \vspace*{0.2cm}
187
188 \begin{minipage}{6.5cm}
189 \includegraphics[width=6.5cm]{si-c_phase.eps}
190 \begin{center}
191 {\tiny
192 R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959)
193 }
194 \end{center}
195 \begin{pspicture}(0,0)(0,0)
196 \psellipse[linecolor=blue,linewidth=0.1cm](3.55,4.0)(0.5,2.9)
197 \end{pspicture}
198 \end{minipage}
199 \begin{minipage}{6cm}
200 {\bf Phase diagram of the C/Si system}\\[0.2cm]
201 {\color{blue}Stoichiometric composition}
202 \begin{itemize}
203 \item only chemical stable compound
204 \item wide band gap semiconductor\\
205       \underline{silicon carbide}, SiC
206 \end{itemize}
207 \end{minipage}
208
209 \end{slide}
210
211 % motivation / properties / applications of silicon carbide
212
213 \begin{slide}
214
215 \vspace*{1.8cm}
216
217 \small
218
219 \begin{pspicture}(0,0)(13.5,5)
220
221  \psframe*[linecolor=hb](-0.2,0)(12.9,5)
222
223  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.2,1)(6.5,1)(6.5,3)(5.2,3)
224  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.4,0.5)(7.7,2)(7.7,2)(6.4,3.5)
225
226  \rput[lt](0,4.6){\color{gray}PROPERTIES}
227
228  \rput[lt](0.3,4){wide band gap}
229  \rput[lt](0.3,3.5){high electric breakdown field}
230  \rput[lt](0.3,3){good electron mobility}
231  \rput[lt](0.3,2.5){high electron saturation drift velocity}
232  \rput[lt](0.3,2){high thermal conductivity}
233
234  \rput[lt](0.3,1.5){hard and mechanically stable}
235  \rput[lt](0.3,1){chemically inert}
236
237  \rput[lt](0.3,0.5){radiation hardness}
238
239  \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
240
241  \rput[rt](12.5,3.85){high-temperature, high power}
242  \rput[rt](12.5,3.5){and high-frequency}
243  \rput[rt](12.5,3.15){electronic and optoelectronic devices}
244
245  \rput[rt](12.5,2.35){material suitable for extreme conditions}
246  \rput[rt](12.5,2){microelectromechanical systems}
247  \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
248
249  \rput[rt](12.5,0.85){first wall reactor material, detectors}
250  \rput[rt](12.5,0.5){and electronic devices for space}
251
252 \end{pspicture}
253
254 \begin{picture}(0,0)(5,-162)
255 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
256 \end{picture}
257 \begin{picture}(0,0)(-120,-162)
258 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
259 \end{picture}
260 \begin{picture}(0,0)(-270,-162)
261 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
262 \end{picture}
263 %%%%
264 \begin{picture}(0,0)(10,65)
265 \includegraphics[height=2.8cm]{sic_switch.eps}
266 \end{picture}
267 %\begin{picture}(0,0)(-243,65)
268 \begin{picture}(0,0)(-110,65)
269 \includegraphics[height=2.8cm]{ise_99.eps}
270 \end{picture}
271 %\begin{picture}(0,0)(-135,65)
272 \begin{picture}(0,0)(-100,65)
273 \includegraphics[height=1.2cm]{infineon_schottky.eps}
274 \end{picture}
275 \begin{picture}(0,0)(-233,65)
276 \includegraphics[height=2.8cm]{solar_car.eps}
277 \end{picture}
278
279 \end{slide}
280
281 % motivation
282
283 \begin{slide}
284
285  {\large\bf
286   Polytypes of SiC\\[0.4cm]
287  }
288
289 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
290 \begin{minipage}{1.9cm}
291 {\tiny cubic (twist)}
292 \end{minipage}
293 \begin{minipage}{2.9cm}
294 {\tiny hexagonal (no twist)}
295 \end{minipage}
296
297 \begin{picture}(0,0)(-150,0)
298  \includegraphics[width=7cm]{polytypes.eps}
299 \end{picture}
300
301 \vspace{0.6cm}
302
303 \footnotesize
304
305 \begin{tabular}{l c c c c c c}
306 \hline
307  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
308 \hline
309 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
310 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
311 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
312 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
313 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
314 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
315 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
316 \hline
317 \end{tabular}
318
319 \begin{pspicture}(0,0)(0,0)
320 \psellipse[linecolor=green](5.7,2.10)(0.4,0.5)
321 \end{pspicture}
322 \begin{pspicture}(0,0)(0,0)
323 \psellipse[linecolor=green](5.6,0.92)(0.4,0.2)
324 \end{pspicture}
325 \begin{pspicture}(0,0)(0,0)
326 \psellipse[linecolor=red](10.45,0.45)(0.4,0.2)
327 \end{pspicture}
328
329 \end{slide}
330
331 % fabrication
332
333 \begin{slide}
334
335  {\large\bf
336   Fabrication of silicon carbide
337  }
338
339  \small
340  
341  \vspace{2pt}
342
343 \begin{center}
344  {\color{gray}
345  \emph{Silicon carbide --- Born from the stars, perfected on earth.}
346  }
347 \end{center}
348
349 \vspace{2pt}
350
351 SiC thin films by MBE \& CVD
352 \begin{itemize}
353  \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
354  \item \underline{Commercially available} semiconductor power devices based on
355        \underline{\foreignlanguage{greek}{a}-SiC}
356  \item Production of favored \underline{3C-SiC} material
357        \underline{less advanced}
358  \item Quality and size not yet sufficient
359 \end{itemize}
360 \begin{picture}(0,0)(-310,-20)
361   \includegraphics[width=2.0cm]{cree.eps}
362 \end{picture}
363
364 \vspace{-0.2cm}
365
366 Alternative approach:
367 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
368
369 \vspace{0.2cm}
370
371 \scriptsize
372
373 \framebox{
374 \begin{minipage}{3.15cm}
375  \begin{center}
376 \includegraphics[width=3cm]{imp.eps}\\
377  {\tiny
378   Carbon implantation
379  }
380  \end{center}
381 \end{minipage}
382 \begin{minipage}{3.15cm}
383  \begin{center}
384 \includegraphics[width=3cm]{annealing.eps}\\
385  {\tiny
386   \unit[12]{h} annealing at \degc{1200}
387  }
388  \end{center}
389 \end{minipage}
390 }
391 \begin{minipage}{5.5cm}
392  \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
393  \begin{center}
394  {\tiny
395   XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
396  }
397  \end{center}
398 \end{minipage}
399
400 \end{slide}
401
402 % contents
403
404 \begin{slide}
405
406 {\large\bf
407  Systematic investigation of C implantations into Si
408 }
409
410 \vspace{1.7cm}
411 \begin{center}
412 \hspace{-1.0cm}
413 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
414 \end{center}
415
416 \end{slide}
417
418 % outline
419
420 \begin{slide}
421
422 {\large\bf
423  Outline
424 }
425
426 \vspace{1.7cm}
427 \begin{center}
428 \hspace{-1.0cm}
429 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
430 \end{center}
431
432 \begin{pspicture}(0,0)(0,0)
433 \rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=hred,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
434 \begin{minipage}{11cm}
435 {\color{black}Diploma thesis}\\
436  \underline{Monte Carlo} simulation modeling the selforganization process\\
437  leading to periodic arrays of nanometric amorphous SiC precipitates
438 \end{minipage}
439 }}}
440 \end{pspicture}
441 \begin{pspicture}(0,0)(0,0)
442 \rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=hblue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
443 \begin{minipage}{11cm}
444 {\color{black}Doctoral studies}\\
445  Classical potential \underline{molecular dynamics} simulations \ldots\\
446  \underline{Density functional theory} calculations \ldots\\[0.2cm]
447  \ldots on defect formation and SiC precipitation in Si
448 \end{minipage}
449 }}}
450 \end{pspicture}
451 \begin{pspicture}(0,0)(0,0)
452 \psellipse[linecolor=red,linewidth=0.05cm](5,3.0)(0.8,1.0)
453 \end{pspicture}
454 \begin{pspicture}(0,0)(0,0)
455 \psellipse[linecolor=blue,linewidth=0.05cm](8.2,3.2)(1.5,1.6)
456 \end{pspicture}
457
458 \end{slide}
459
460 \begin{slide}
461
462 \headdiplom
463 {\large\bf
464  Selforganization of nanometric amorphous SiC lamellae
465 }
466
467 \small
468
469 \vspace{0.2cm}
470
471 \begin{itemize}
472  \item Regularly spaced, nanometric spherical\\
473        and lamellar amorphous inclusions\\
474        at the upper a/c interface
475  \item Carbon accumulation\\
476        in amorphous volumes
477 \end{itemize}
478
479 \vspace{0.4cm}
480
481 \begin{minipage}{12cm}
482 \includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\
483 {\scriptsize
484 XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si,
485 {\color{red}\underline{\degc{150}}},
486 Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$}
487 }
488 \end{minipage}
489
490 \begin{picture}(0,0)(-182,-215)
491 \begin{minipage}{6.5cm}
492 \begin{center}
493 \includegraphics[width=6.5cm]{../../nlsop/img/eftem.eps}\\[-0.2cm]
494 {\scriptsize
495 XTEM bright-field and respective EFTEM C map
496 }
497 \end{center}
498 \end{minipage}
499 \end{picture}
500
501 \end{slide}
502
503 \begin{slide}
504
505 \headdiplom
506 {\large\bf
507  Model displaying the formation of ordered lamellae
508 }
509
510 \vspace{0.1cm}
511
512 \begin{center}
513  \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps}
514 \end{center}
515
516 \footnotesize
517
518 \begin{itemize}
519 \item Supersaturation of C in c-Si\\
520       $\rightarrow$ {\bf Carbon induced} nucleation of spherical
521       SiC$_x$-precipitates
522 \item High interfacial energy between 3C-SiC and c-Si\\
523       $\rightarrow$ {\bf Amorphous} precipitates
524 \item \unit[20-- 30]{\%} lower silicon density of a-SiC$_x$ compared to c-Si\\
525       $\rightarrow$ {\bf Lateral strain} (black arrows)
526 \item Implantation range near surface\\
527       $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component}
528 \item Reduction of the carbon supersaturation in c-Si\\
529       $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina
530       (white arrows)
531 \item Remaining lateral strain\\
532       $\rightarrow$ {\bf Strain enhanced} lateral amorphisation
533 \item Absence of crystalline neighbours (structural information)\\
534       $\rightarrow$ {\bf Stabilization} of amorphous inclusions 
535       {\bf against recrystallization}
536 \end{itemize}
537
538 \end{slide}
539
540 \begin{slide}
541
542 \headdiplom
543 {\large\bf
544  Implementation of the Monte Carlo code
545 }
546
547 \small
548
549 \begin{enumerate}
550  \item \underline{Amorphization / Recrystallization}\\
551        Ion collision in discretized target determined by random numbers
552        distributed according to nuclear energy loss.
553        Amorphization/recrystallization probability:
554 \[
555 p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
556 \]
557 \begin{itemize}
558  \item {\color{green} $p_b$} normal `ballistic' amorphization
559  \item {\color{blue} $p_c$} carbon induced amorphization
560  \item {\color{red} $p_s$} stress enhanced amorphization
561 \end{itemize}
562 \[
563 p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
564 \]
565 \[
566 \delta (\vec r) = \left\{
567 \begin{array}{ll}
568         1 & \textrm{if volume at position $\vec r$ is amorphous} \\
569         0 & \textrm{otherwise} \\
570 \end{array}
571 \right.
572 \]
573  \item \underline{Carbon incorporation}\\
574        Incorporation volume determined according to implantation profile
575  \item \underline{Diffusion / Sputtering}
576        \begin{itemize}
577         \item Transfer fraction of C atoms
578               of crystalline into neighbored amorphous volumes
579         \item Remove surface layer
580        \end{itemize}
581 \end{enumerate}
582
583 \end{slide}
584
585 \begin{slide}
586
587 \begin{minipage}{3.7cm}
588 \begin{pspicture}(0,0)(0,0)
589 \rput(1.7,0.2){\psframebox[fillstyle=gradient,gradbegin=hred,gradend=white,gradlines=1000,gradangle=10,gradmidpoint=1,linestyle=none]{
590 \begin{minipage}{3.7cm}
591 \hfill
592 \vspace{0.7cm}
593 \end{minipage}
594 }}
595 \end{pspicture}
596 {\large\bf
597  Results
598 }
599
600 \footnotesize
601
602 \vspace{1.2cm}
603
604 Evolution of the \ldots
605 \begin{itemize}
606  \item continuous\\
607        amorphous layer
608  \item a/c interface
609  \item lamellar precipitates
610 \end{itemize}
611 \ldots reproduced!\\[1.4cm]
612
613 {\color{blue}
614 \begin{center}
615 Experiment \& simulation\\
616 in good agreement\\[1.0cm]
617
618 Simulation is able to model the whole depth region\\[1.2cm]
619 \end{center}
620 }
621
622 \end{minipage}
623 \begin{minipage}{0.5cm}
624 \vfill
625 \end{minipage}
626 \begin{minipage}{8.0cm}
627  \vspace{-0.3cm}
628  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\
629  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps}
630 \end{minipage}
631
632 \end{slide}
633
634 \begin{slide}
635
636 \headdiplom
637 {\large\bf
638  Structural \& compositional details
639 }
640
641 \begin{minipage}[t]{7.5cm}
642 \includegraphics[height=6.5cm]{../../nlsop/img/ac_cconc_ver2_e.eps}\\
643 \end{minipage}
644 \begin{minipage}[t]{5.0cm}
645 \includegraphics[height=6.5cm]{../../nlsop/img/97_98_e.eps}
646 \end{minipage}
647
648 \footnotesize
649
650 \vspace{-0.1cm}
651
652 \begin{itemize}
653  \item Fluctuation of C concentration in lamellae region
654  \item \unit[8--10]{at.\%} C saturation limit
655        within the respective conditions
656  \item Complementarily arranged and alternating sequence of layers\\
657        with a high and low amount of amorphous regions
658  \item C accumulation in the amorphous phase / Origin of stress
659 \end{itemize}
660
661 \begin{picture}(0,0)(-260,-50)
662 \framebox{
663 \begin{minipage}{3cm}
664 \begin{center}
665 {\color{blue}
666 Precipitation process\\
667 gets traceable\\
668 by simulation!
669 }
670 \end{center}
671 \end{minipage}
672 }
673 \end{picture}
674
675 \end{slide}
676
677 \begin{slide}
678
679 \headphd
680 {\large\bf
681  Formation of epitaxial single crystalline 3C-SiC
682 }
683
684 \footnotesize
685
686 \vspace{0.2cm}
687
688 \begin{center}
689 \begin{itemize}
690  \item \underline{Implantation step 1}\\[0.1cm]
691         Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
692         $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
693         {\color{blue}precipitates}
694  \item \underline{Implantation step 2}\\[0.1cm]
695         Little remaining dose | \unit[180]{keV} | \degc{250}\\
696         $\Rightarrow$
697         Destruction/Amorphization of precipitates at layer interface
698  \item \underline{Annealing}\\[0.1cm]
699        \unit[10]{h} at \degc{1250}\\
700        $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
701 \end{itemize}
702 \end{center}
703
704 \begin{minipage}{7cm}
705 \includegraphics[width=7cm]{ibs_3c-sic.eps}
706 \end{minipage}
707 \begin{minipage}{5cm}
708 \begin{pspicture}(0,0)(0,0)
709 \rnode{box}{
710 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
711 \begin{minipage}{5.3cm}
712  \begin{center}
713  {\color{blue}
714   3C-SiC precipitation\\
715   not yet fully understood
716  }
717  \end{center}
718  \vspace*{0.1cm}
719  \renewcommand\labelitemi{$\Rightarrow$}
720  Details of the SiC precipitation
721  \begin{itemize}
722   \item significant technological progress\\
723         in SiC thin film formation
724   \item perspectives for processes relying\\
725         upon prevention of SiC precipitation
726  \end{itemize}
727 \end{minipage}
728 }}
729 \rput(-6.8,5.4){\pnode{h0}}
730 \rput(-3.0,5.4){\pnode{h1}}
731 \ncline[linecolor=blue]{-}{h0}{h1}
732 \ncline[linecolor=blue]{->}{h1}{box}
733 \end{pspicture}
734 \end{minipage}
735
736 \end{slide}
737
738 \begin{slide}
739
740 \headphd
741 {\large\bf
742   Supposed precipitation mechanism of SiC in Si
743 }
744
745  \scriptsize
746
747  \vspace{0.1cm}
748
749  \framebox{
750  \begin{minipage}{3.6cm}
751  \begin{center}
752  Si \& SiC lattice structure\\[0.1cm]
753  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
754  \end{center}
755 {\tiny
756  \begin{minipage}{1.7cm}
757 \underline{Silicon}\\
758 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
759 $a=\unit[5.429]{\\A}$\\
760 $\rho^*_{\text{Si}}=\unit[100]{\%}$
761  \end{minipage}
762  \begin{minipage}{1.7cm}
763 \underline{Silicon carbide}\\
764 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
765 $a=\unit[4.359]{\\A}$\\
766 $\rho^*_{\text{Si}}=\unit[97]{\%}$
767  \end{minipage}
768 }
769  \end{minipage}
770  }
771  \hspace{0.1cm}
772  \begin{minipage}{4.1cm}
773  \begin{center}
774  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
775  \end{center}
776  \end{minipage}
777  \hspace{0.1cm}
778  \begin{minipage}{4.0cm}
779  \begin{center}
780  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
781  \end{center}
782  \end{minipage}
783
784  \vspace{0.1cm}
785
786  \begin{minipage}{4.0cm}
787  \begin{center}
788  C-Si dimers (dumbbells)\\[-0.1cm]
789  on Si interstitial sites
790  \end{center}
791  \end{minipage}
792  \hspace{0.1cm}
793  \begin{minipage}{4.1cm}
794  \begin{center}
795  Agglomeration of C-Si dumbbells\\[-0.1cm]
796  $\Rightarrow$ dark contrasts
797  \end{center}
798  \end{minipage}
799  \hspace{0.1cm}
800  \begin{minipage}{4.0cm}
801  \begin{center}
802  Precipitation of 3C-SiC in Si\\[-0.1cm]
803  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
804  \& release of Si self-interstitials
805  \end{center}
806  \end{minipage}
807
808  \vspace{0.1cm}
809
810  \begin{minipage}{4.0cm}
811  \begin{center}
812  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
813  \end{center}
814  \end{minipage}
815  \hspace{0.1cm}
816  \begin{minipage}{4.1cm}
817  \begin{center}
818  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
819  \end{center}
820  \end{minipage}
821  \hspace{0.1cm}
822  \begin{minipage}{4.0cm}
823  \begin{center}
824  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
825  \end{center}
826  \end{minipage}
827
828 \begin{pspicture}(0,0)(0,0)
829 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
830 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
831 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
832 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
833 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
834  $4a_{\text{Si}}=5a_{\text{SiC}}$
835  }}}
836 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
837 \hkl(h k l) planes match
838  }}}
839 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
840 r = \unit[2--4]{nm}
841  }}}
842 \end{pspicture}
843
844 \end{slide}
845
846 \begin{slide}
847
848 \headphd
849 {\large\bf
850  Supposed precipitation mechanism of SiC in Si
851 }
852
853  \scriptsize
854
855  \vspace{0.1cm}
856
857  \framebox{
858  \begin{minipage}{3.6cm}
859  \begin{center}
860  Si \& SiC lattice structure\\[0.1cm]
861  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
862  \end{center}
863 {\tiny
864  \begin{minipage}{1.7cm}
865 \underline{Silicon}\\
866 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
867 $a=\unit[5.429]{\\A}$\\
868 $\rho^*_{\text{Si}}=\unit[100]{\%}$
869  \end{minipage}
870  \begin{minipage}{1.7cm}
871 \underline{Silicon carbide}\\
872 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
873 $a=\unit[4.359]{\\A}$\\
874 $\rho^*_{\text{Si}}=\unit[97]{\%}$
875  \end{minipage}
876 }
877  \end{minipage}
878  }
879  \hspace{0.1cm}
880  \begin{minipage}{4.1cm}
881  \begin{center}
882  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
883  \end{center}
884  \end{minipage}
885  \hspace{0.1cm}
886  \begin{minipage}{4.0cm}
887  \begin{center}
888  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
889  \end{center}
890  \end{minipage}
891
892  \vspace{0.1cm}
893
894  \begin{minipage}{4.0cm}
895  \begin{center}
896  C-Si dimers (dumbbells)\\[-0.1cm]
897  on Si interstitial sites
898  \end{center}
899  \end{minipage}
900  \hspace{0.1cm}
901  \begin{minipage}{4.1cm}
902  \begin{center}
903  Agglomeration of C-Si dumbbells\\[-0.1cm]
904  $\Rightarrow$ dark contrasts
905  \end{center}
906  \end{minipage}
907  \hspace{0.1cm}
908  \begin{minipage}{4.0cm}
909  \begin{center}
910  Precipitation of 3C-SiC in Si\\[-0.1cm]
911  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
912  \& release of Si self-interstitials
913  \end{center}
914  \end{minipage}
915
916  \vspace{0.1cm}
917
918  \begin{minipage}{4.0cm}
919  \begin{center}
920  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
921  \end{center}
922  \end{minipage}
923  \hspace{0.1cm}
924  \begin{minipage}{4.1cm}
925  \begin{center}
926  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
927  \end{center}
928  \end{minipage}
929  \hspace{0.1cm}
930  \begin{minipage}{4.0cm}
931  \begin{center}
932  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
933  \end{center}
934  \end{minipage}
935
936 \begin{pspicture}(0,0)(0,0)
937 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
938 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
939 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
940 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
941 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
942  $4a_{\text{Si}}=5a_{\text{SiC}}$
943  }}}
944 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
945 \hkl(h k l) planes match
946  }}}
947 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
948 r = \unit[2--4]{nm}
949  }}}
950 % controversial view!
951 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
952 \begin{minipage}{14cm}
953 \hfill
954 \vspace{12cm}
955 \end{minipage}
956 }}
957 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
958 \begin{minipage}{10cm}
959 \small
960 \vspace*{0.2cm}
961 \begin{center}
962 {\color{gray}\bf Controversial findings}
963 \end{center}
964 \begin{itemize}
965 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
966  \begin{itemize}
967   \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
968   \item \si{} reacting with further C in cleared volume
969  \end{itemize}
970 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
971  \begin{itemize}
972   \item Room temperature implantation $\rightarrow$ high C diffusion
973   \item Elevated temperature implantation $\rightarrow$ no C redistribution
974  \end{itemize}
975  $\Rightarrow$ mobile {\color{red}\ci} opposed to
976  stable {\color{blue}\cs{}} configurations
977 \item Strained silicon \& Si/SiC heterostructures
978       {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
979  \begin{itemize}
980   \item {\color{blue}Coherent} SiC precipitates (tensile strain)
981   \item Incoherent SiC (strain relaxation)
982  \end{itemize}
983 \end{itemize}
984 \vspace{0.1cm}
985 \begin{center}
986 {\Huge${\lightning}$} \hspace{0.3cm}
987 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
988 {\Huge${\lightning}$}
989 \end{center}
990 \vspace{0.2cm}
991 \end{minipage}
992  }}}
993 \end{pspicture}
994
995 \end{slide}
996
997 \begin{slide}
998
999 \headphd
1000 {\large\bf
1001  Utilized computational methods
1002 }
1003
1004 \vspace{0.3cm}
1005
1006 \small
1007
1008 {\bf Molecular dynamics (MD)}\\[0.1cm]
1009 \scriptsize
1010 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
1011 \hline
1012 System of $N$ particles &
1013 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
1014 Phase space propagation &
1015 Velocity Verlet | timestep: \unit[1]{fs} \\
1016 Analytical interaction potential &
1017 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
1018 (Erhart/Albe)
1019 $\displaystyle
1020 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
1021     \pot_{ij} = {\color{red}f_C(r_{ij})}
1022     \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
1023 $\\
1024 Observables: time/ensemble averages &
1025 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
1026 \hline
1027 \end{tabular}
1028
1029 \small
1030
1031 \vspace{0.3cm}
1032
1033 {\bf Density functional theory (DFT)}
1034
1035 \scriptsize
1036
1037 \begin{minipage}[t]{6cm}
1038 \begin{itemize}
1039  \item Hohenberg-Kohn theorem:\\
1040        $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
1041  \item Kohn-Sham approach:\\
1042        Single-particle effective theory
1043 \end{itemize}
1044 \hrule
1045 \begin{itemize}
1046 \item Code: \textsc{vasp}
1047 \item Plane wave basis set
1048 %$\displaystyle
1049 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
1050 %$\\
1051 %$\displaystyle
1052 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
1053 %$
1054 \item Ultrasoft pseudopotential
1055 \item Exchange \& correlation: GGA
1056 \item Brillouin zone sampling: $\Gamma$-point
1057 \item Supercell: $N=216\pm2$
1058 \end{itemize}
1059 \end{minipage}
1060 \begin{minipage}{6cm}
1061 \begin{pspicture}(0,0)(0,0)
1062 \pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
1063 \rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
1064 $\displaystyle
1065 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
1066 $
1067 }}
1068 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
1069 $\displaystyle
1070 n(r)=\sum_i^N|\Phi_i(r)|^2
1071 $
1072 }}
1073 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
1074 $\displaystyle
1075 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1076                  +V_{\text{XC}}[n(r)]
1077 $
1078 }}
1079 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
1080 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
1081 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
1082
1083 \end{pspicture}
1084 \end{minipage}
1085
1086 \end{slide}
1087
1088 \begin{slide}
1089
1090 \headphd
1091  {\large\bf
1092   Point defects \& defect migration
1093  }
1094
1095  \small
1096
1097  \vspace{0.2cm}
1098
1099 \begin{minipage}[b]{7.5cm}
1100 {\bf Defect structure}\\
1101   \begin{pspicture}(0,0)(7,4.4)
1102   \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1103    \parbox{7cm}{
1104    \begin{itemize}
1105     \item Creation of c-Si simulation volume
1106     \item Periodic boundary conditions
1107     \item $T=0\text{ K}$, $p=0\text{ bar}$
1108    \end{itemize}
1109   }}}}
1110 \rput(3.5,1.3){\rnode{insert}{\psframebox{
1111  \parbox{7cm}{
1112   \begin{center}
1113   Insertion of interstitial C/Si atoms
1114   \end{center}
1115   }}}}
1116   \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1117    \parbox{7cm}{
1118    \begin{center}
1119    Relaxation / structural energy minimization
1120    \end{center}
1121   }}}}
1122   \ncline[]{->}{init}{insert}
1123   \ncline[]{->}{insert}{cool}
1124  \end{pspicture}
1125 \end{minipage}
1126 \begin{minipage}[b]{4.5cm}
1127 \begin{center}
1128 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
1129 \end{center}
1130 \begin{minipage}{2.21cm}
1131 {\scriptsize
1132 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
1133 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
1134 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
1135 }
1136 \end{minipage}
1137 \begin{minipage}{2.21cm}
1138 {\scriptsize
1139 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
1140 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
1141 {\color{black}$\bullet$} Vac. / Sub.
1142 }
1143 \end{minipage}
1144 \end{minipage}
1145
1146 \vspace{0.2cm}
1147
1148 \begin{minipage}[b]{6cm}
1149 {\bf Defect formation energy}\\
1150 \framebox{
1151 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
1152 Particle reservoir: Si \& SiC\\[0.2cm]
1153 {\bf Binding energy}\\
1154 \framebox{
1155 $
1156 E_{\text{b}}=
1157 E_{\text{f}}^{\text{comb}}-
1158 E_{\text{f}}^{1^{\text{st}}}-
1159 E_{\text{f}}^{2^{\text{nd}}}
1160 $
1161 }\\[0.1cm]
1162 \footnotesize
1163 $E_{\text{b}}<0$: energetically favorable configuration\\
1164 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
1165 \end{minipage}
1166 \begin{minipage}[b]{6cm}
1167 {\bf Migration barrier}
1168 \footnotesize
1169 \begin{itemize}
1170  \item Displace diffusing atom
1171  \item Constrain relaxation of (diffusing) atoms
1172  \item Record configurational energy
1173 \end{itemize}
1174 \begin{picture}(0,0)(-60,-33)
1175 \includegraphics[width=4.5cm]{crt_mod.eps}
1176 \end{picture}
1177 \end{minipage}
1178
1179 \end{slide}
1180
1181 \begin{slide}
1182
1183 \footnotesize
1184
1185 \headphd
1186 {\large\bf
1187  Si self-interstitial point defects in silicon\\[0.1cm]
1188 }
1189
1190 \begin{center}
1191 \begin{tabular}{l c c c c c}
1192 \hline
1193  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1194 \hline
1195  \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1196  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1197 \hline
1198 \end{tabular}\\[0.4cm]
1199 \end{center}
1200
1201 \begin{minipage}{3cm}
1202 \begin{center}
1203 \underline{Vacancy}\\
1204 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
1205 \end{center}
1206 \end{minipage}
1207 \begin{minipage}{3cm}
1208 \begin{center}
1209 \underline{\hkl<1 1 0> DB}\\
1210 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
1211 \end{center}
1212 \end{minipage}
1213 \begin{minipage}{3cm}
1214 \begin{center}
1215 \underline{\hkl<1 0 0> DB}\\
1216 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
1217 \end{center}
1218 \end{minipage}
1219 \begin{minipage}{3cm}
1220 \begin{center}
1221 \underline{Tetrahedral}\\
1222 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
1223 \end{center}
1224 \end{minipage}\\
1225
1226 \underline{Hexagonal} \hspace{2pt}
1227 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1228 \framebox{
1229 \begin{minipage}{2.7cm}
1230 $E_{\text{f}}^*=4.48\text{ eV}$\\
1231 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
1232 \end{minipage}
1233 \begin{minipage}{0.4cm}
1234 \begin{center}
1235 $\Rightarrow$
1236 \end{center}
1237 \end{minipage}
1238 \begin{minipage}{2.7cm}
1239 $E_{\text{f}}=3.96\text{ eV}$\\
1240 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
1241 \end{minipage}
1242 }
1243 \begin{minipage}{5.5cm}
1244 \begin{center}
1245 {\tiny nearly T $\rightarrow$ T}\\
1246 \end{center}
1247 \includegraphics[width=6.0cm]{nhex_tet.ps}
1248 \end{minipage}
1249
1250 \end{slide}
1251
1252 \begin{slide}
1253
1254 \footnotesize
1255
1256 \headphd
1257 {\large\bf
1258  C interstitial point defects in silicon\\
1259 }
1260
1261 \begin{tabular}{l c c c c c c r}
1262 \hline
1263  $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
1264  {\color{black} \cs{} \& \si}\\
1265 \hline
1266  \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1267  Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1268 \hline
1269 \end{tabular}\\[0.1cm]
1270
1271 \framebox{
1272 \begin{minipage}{2.8cm}
1273 \underline{Hexagonal} \hspace{2pt}
1274 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1275 $E_{\text{f}}^*=9.05\text{ eV}$\\
1276 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
1277 \end{minipage}
1278 \begin{minipage}{0.4cm}
1279 \begin{center}
1280 $\Rightarrow$
1281 \end{center}
1282 \end{minipage}
1283 \begin{minipage}{2.8cm}
1284 \underline{\hkl<1 0 0>}\\
1285 $E_{\text{f}}=3.88\text{ eV}$\\
1286 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
1287 \end{minipage}
1288 }
1289 \begin{minipage}{1.4cm}
1290 \hfill
1291 \end{minipage}
1292 \begin{minipage}{3.0cm}
1293 \begin{flushright}
1294 \underline{Tetrahedral}\\
1295 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
1296 \end{flushright}
1297 \end{minipage}
1298
1299 \framebox{
1300 \begin{minipage}{2.8cm}
1301 \underline{Bond-centered}\\
1302 $E_{\text{f}}^*=5.59\text{ eV}$\\
1303 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
1304 \end{minipage}
1305 \begin{minipage}{0.4cm}
1306 \begin{center}
1307 $\Rightarrow$
1308 \end{center}
1309 \end{minipage}
1310 \begin{minipage}{2.8cm}
1311 \underline{\hkl<1 1 0> dumbbell}\\
1312 $E_{\text{f}}=5.18\text{ eV}$\\
1313 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
1314 \end{minipage}
1315 }
1316 \begin{minipage}{1.4cm}
1317 \hfill
1318 \end{minipage}
1319 \begin{minipage}{3.0cm}
1320 \begin{flushright}
1321 \underline{Substitutional}\\
1322 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
1323 \end{flushright}
1324 \end{minipage}
1325
1326 \end{slide}
1327
1328 \begin{slide}
1329
1330 \headphd
1331 {\large\bf\boldmath
1332  C-Si dimer \& bond-centered interstitial configuration
1333 }
1334
1335 \footnotesize
1336
1337 \vspace{0.1cm}
1338
1339 \begin{minipage}[t]{4.1cm}
1340 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
1341 \begin{minipage}{2.0cm}
1342 \begin{center}
1343 \underline{Erhart/Albe}
1344 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
1345 \end{center}
1346 \end{minipage}
1347 \begin{minipage}{2.0cm}
1348 \begin{center}
1349 \underline{\textsc{vasp}}
1350 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
1351 \end{center}
1352 \end{minipage}\\[0.2cm]
1353 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
1354 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
1355 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
1356 $\Rightarrow$ $sp^2$ hybridization
1357 \begin{center}
1358 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
1359 {\tiny Charge density isosurface}
1360 \end{center}
1361 \end{minipage}
1362 \begin{minipage}{0.2cm}
1363 \hfill
1364 \end{minipage}
1365 \begin{minipage}[t]{8.1cm}
1366 \begin{flushright}
1367 {\bf Bond-centered interstitial}\\[0.1cm]
1368 \begin{minipage}{4.4cm}
1369 %\scriptsize
1370 \begin{itemize}
1371  \item Linear Si-C-Si bond
1372  \item Si: one C \& 3 Si neighbours
1373  \item Spin polarized calculations
1374  \item No saddle point!\\
1375        Real local minimum!
1376 \end{itemize}
1377 \end{minipage}
1378 \begin{minipage}{2.7cm}
1379 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1380 \vspace{0.2cm}
1381 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
1382 \end{minipage}
1383
1384 \framebox{
1385  \tiny
1386  \begin{minipage}[t]{6.5cm}
1387   \begin{minipage}[t]{1.2cm}
1388   {\color{red}Si}\\
1389   {\tiny sp$^3$}\\[0.8cm]
1390   \underline{${\color{black}\uparrow}$}
1391   \underline{${\color{black}\uparrow}$}
1392   \underline{${\color{black}\uparrow}$}
1393   \underline{${\color{red}\uparrow}$}\\
1394   sp$^3$
1395   \end{minipage}
1396   \begin{minipage}[t]{1.4cm}
1397   \begin{center}
1398   {\color{red}M}{\color{blue}O}\\[0.8cm]
1399   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1400   $\sigma_{\text{ab}}$\\[0.5cm]
1401   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1402   $\sigma_{\text{b}}$
1403   \end{center}
1404   \end{minipage}
1405   \begin{minipage}[t]{1.0cm}
1406   \begin{center}
1407   {\color{blue}C}\\
1408   {\tiny sp}\\[0.2cm]
1409   \underline{${\color{white}\uparrow\uparrow}$}
1410   \underline{${\color{white}\uparrow\uparrow}$}\\
1411   2p\\[0.4cm]
1412   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1413   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1414   sp
1415   \end{center}
1416   \end{minipage}
1417   \begin{minipage}[t]{1.4cm}
1418   \begin{center}
1419   {\color{blue}M}{\color{green}O}\\[0.8cm]
1420   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1421   $\sigma_{\text{ab}}$\\[0.5cm]
1422   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1423   $\sigma_{\text{b}}$
1424   \end{center}
1425   \end{minipage}
1426   \begin{minipage}[t]{1.2cm}
1427   \begin{flushright}
1428   {\color{green}Si}\\
1429   {\tiny sp$^3$}\\[0.8cm]
1430   \underline{${\color{green}\uparrow}$}
1431   \underline{${\color{black}\uparrow}$}
1432   \underline{${\color{black}\uparrow}$}
1433   \underline{${\color{black}\uparrow}$}\\
1434   sp$^3$
1435   \end{flushright}
1436   \end{minipage}
1437  \end{minipage}
1438 }\\[0.4cm]
1439
1440 %\framebox{
1441 \begin{minipage}{3.0cm}
1442 %\scriptsize
1443 \underline{Charge density}\\
1444 {\color{gray}$\bullet$} Spin up\\
1445 {\color{green}$\bullet$} Spin down\\
1446 {\color{blue}$\bullet$} Resulting spin up\\
1447 {\color{yellow}$\bullet$} Si atoms\\
1448 {\color{red}$\bullet$} C atom
1449 \end{minipage}
1450 \begin{minipage}{3.6cm}
1451 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
1452 \end{minipage}
1453 %}
1454
1455 \end{flushright}
1456
1457 \end{minipage}
1458 \begin{pspicture}(0,0)(0,0)
1459 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
1460 \end{pspicture}
1461
1462 \end{slide}
1463
1464 \begin{slide}
1465
1466 \headphd
1467 {\large\bf\boldmath
1468  C interstitial migration --- ab initio
1469 }
1470
1471 \scriptsize
1472
1473 \vspace{0.1cm}
1474
1475 \begin{minipage}{6.8cm}
1476 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
1477 \begin{minipage}{2.0cm}
1478 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1479 \end{minipage}
1480 \begin{minipage}{0.2cm}
1481 $\rightarrow$
1482 \end{minipage}
1483 \begin{minipage}{2.0cm}
1484 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
1485 \end{minipage}
1486 \begin{minipage}{0.2cm}
1487 $\rightarrow$
1488 \end{minipage}
1489 \begin{minipage}{2.0cm}
1490 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
1491 \end{minipage}\\[0.1cm]
1492 Spin polarization\\
1493 $\Rightarrow$ BC configuration constitutes local minimum\\
1494 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
1495 \end{minipage}
1496 \begin{minipage}{5.4cm}
1497 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
1498 \end{minipage}\\[0.2cm]
1499 %\hrule
1500 %
1501 \begin{minipage}{6.8cm}
1502 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
1503 \begin{minipage}{2.0cm}
1504 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1505 \end{minipage}
1506 \begin{minipage}{0.2cm}
1507 $\rightarrow$
1508 \end{minipage}
1509 \begin{minipage}{2.0cm}
1510 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
1511 \end{minipage}
1512 \begin{minipage}{0.2cm}
1513 $\rightarrow$
1514 \end{minipage}
1515 \begin{minipage}{2.0cm}
1516 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
1517 \end{minipage}\\[0.1cm]
1518 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
1519 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
1520 Note: Change in orientation
1521 \end{minipage}
1522 \begin{minipage}{5.4cm}
1523 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
1524 \end{minipage}\\[0.1cm]
1525 %
1526 \begin{center}
1527 Reorientation pathway composed of two consecutive processes of the above type
1528 \end{center}
1529
1530 \end{slide}
1531
1532 \begin{slide}
1533
1534 \headphd
1535 {\large\bf\boldmath
1536  C interstitial migration --- analytical potential
1537 }
1538
1539 \scriptsize
1540
1541 \vspace{0.3cm}
1542
1543 \begin{minipage}[t]{6.0cm}
1544 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
1545 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
1546 \begin{itemize}
1547  \item Lowermost migration barrier
1548  \item $\Delta E \approx \unit[2.2]{eV}$
1549  \item 2.4 times higher than ab initio result
1550  \item Different pathway
1551 \end{itemize}
1552 \end{minipage}
1553 \begin{minipage}[t]{0.2cm}
1554 \hfill
1555 \end{minipage}
1556 \begin{minipage}[t]{6.0cm}
1557 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
1558 \vspace{0.1cm}
1559 \begin{itemize}
1560  \item Bond-centered configuration unstable\\
1561        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1562  \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
1563        $\rightarrow$ \ci{} \hkl<1 1 0> DB
1564 \end{itemize}
1565 \vspace{0.1cm}
1566 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
1567 \begin{itemize}
1568  \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
1569  \item 2.4 -- 3.4 times higher than ab initio result
1570  \item After all: Change of the DB orientation
1571 \end{itemize}
1572 \end{minipage}
1573
1574 \vspace{0.5cm}
1575 \begin{center}
1576 {\color{red}\bf Drastically overestimated diffusion barrier}
1577 \end{center}
1578
1579 \begin{pspicture}(0,0)(0,0)
1580 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
1581 \end{pspicture}
1582
1583 \end{slide}
1584
1585 \begin{slide}
1586
1587 \headphd
1588 {\large\bf\boldmath
1589  Defect combinations
1590 }
1591
1592 \footnotesize
1593
1594 \vspace{0.3cm}
1595
1596 \begin{minipage}{9cm}
1597 {\bf
1598  Summary of combinations}\\[0.1cm]
1599 {\scriptsize
1600 \begin{tabular}{l c c c c c c}
1601 \hline
1602  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1603  \hline
1604  \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1605  \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1606  \hkl[0 -1 0] & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
1607  \hkl[0 1 0] & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
1608  \hkl[-1 0 0] & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
1609  \hkl[1 0 0] & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
1610  \hline
1611  C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1612  Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1613 \hline
1614 \end{tabular}
1615 }
1616 \vspace{0.2cm}
1617 \begin{center}
1618 {\color{blue}
1619  $E_{\text{b}}$ explainable by stress compensation / increase
1620 }
1621 \end{center}
1622 \end{minipage}
1623 \begin{minipage}{3cm}
1624 \includegraphics[width=3.5cm]{comb_pos.eps}
1625 \end{minipage}
1626
1627 \vspace{0.2cm}
1628
1629 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1630 \begin{minipage}[t]{3.2cm}
1631 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1632 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1633 \end{minipage}
1634 \begin{minipage}[t]{3.0cm}
1635 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1636 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1637 \end{minipage}
1638 \begin{minipage}[t]{6.1cm}
1639 \vspace{0.7cm}
1640 \begin{itemize}
1641  \item \ci{} agglomeration energetically favorable
1642  \item Most favorable: C clustering\\
1643        {\color{red}However \ldots}\\
1644         \ldots high migration barrier ($>4\,\text{eV}$)\\
1645         \ldots entropy:
1646         $4\times{\color{cyan}[-2.25]}$ versus
1647         $2\times{\color{orange}[-2.39]}$
1648 \end{itemize}
1649 \begin{center}
1650 {\color{blue}\ci{} agglomeration / no C clustering}
1651 \end{center}
1652 \end{minipage}
1653
1654 \end{slide}
1655
1656 \begin{slide}
1657
1658 \headphd
1659 {\large\bf\boldmath
1660  Defect combinations
1661 }
1662
1663 \footnotesize
1664
1665 \vspace{0.3cm}
1666
1667 \begin{minipage}{9cm}
1668 {\bf
1669  Summary of combinations}\\[0.1cm]
1670 {\scriptsize
1671 \begin{tabular}{l c c c c c c}
1672 \hline
1673  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1674  \hline
1675  \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1676  \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1677  \hkl[0 -1 0] & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
1678  \hkl[0 1 0] & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
1679  \hkl[-1 0 0] & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
1680  \hkl[1 0 0] & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
1681  \hline
1682  C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1683  Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1684 \hline
1685 \end{tabular}
1686 }
1687 \vspace{0.2cm}
1688 \begin{center}
1689 {\color{blue}
1690  $E_{\text{b}}$ explainable by stress compensation / increase
1691 }
1692 \end{center}
1693 \end{minipage}
1694 \begin{minipage}{3cm}
1695 \includegraphics[width=3.5cm]{comb_pos.eps}
1696 \end{minipage}
1697
1698 \vspace{0.2cm}
1699
1700 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1701 \begin{minipage}[t]{3.2cm}
1702 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1703 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1704 \end{minipage}
1705 \begin{minipage}[t]{3.0cm}
1706 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1707 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1708 \end{minipage}
1709 \begin{minipage}[t]{6.1cm}
1710 \vspace{0.7cm}
1711 \begin{itemize}
1712  \item \ci{} agglomeration energetically favorable
1713  \item Most favorable: C clustering\\
1714        {\color{red}However \ldots}\\
1715         \ldots high migration barrier ($>4\,\text{eV}$)\\
1716         \ldots entropy:
1717         $4\times{\color{cyan}[-2.25]}$ versus
1718         $2\times{\color{orange}[-2.39]}$
1719 \end{itemize}
1720 \begin{center}
1721 {\color{blue}\ci{} agglomeration / no C clustering}
1722 \end{center}
1723 \end{minipage}
1724
1725 % insert graph ...
1726 \begin{pspicture}(0,0)(0,0)
1727 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1728 \begin{minipage}{14cm}
1729 \hfill
1730 \vspace{12cm}
1731 \end{minipage}
1732 }}
1733 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1734 \begin{minipage}{8cm}
1735 \begin{center}
1736 \vspace{0.2cm}
1737 \scriptsize
1738 Interaction along \hkl[1 1 0]
1739 \includegraphics[width=7cm]{db_along_110_cc.ps}
1740 \end{center}
1741 \end{minipage}
1742 }}}
1743 \end{pspicture}
1744
1745 \end{slide}
1746
1747 \begin{slide}
1748
1749 \headphd
1750 {\large\bf
1751  Defect combinations of C-Si dimers and vacancies
1752 }
1753 \footnotesize
1754
1755 \vspace{0.2cm}
1756
1757 \begin{minipage}[b]{2.6cm}
1758 \begin{flushleft}
1759 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1760 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1761 \end{flushleft}
1762 \end{minipage}
1763 \begin{minipage}[b]{7cm}
1764 \hfill
1765 \end{minipage}
1766 \begin{minipage}[b]{2.6cm}
1767 \begin{flushright}
1768 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1769 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1770 \end{flushright}
1771 \end{minipage}\\[0.2cm]
1772
1773 \begin{minipage}{6.5cm}
1774 \includegraphics[width=6.0cm]{059-539.ps}
1775 \end{minipage}
1776 \begin{minipage}{5.7cm}
1777 \includegraphics[width=6.0cm]{314-539.ps}
1778 \end{minipage}
1779
1780 \begin{pspicture}(0,0)(0,0)
1781 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1782
1783 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1784 \begin{minipage}{6.5cm}
1785 \begin{center}
1786 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1787 Low migration barrier towards C$_{\text{sub}}$\\
1788 \&\\
1789 High barrier for reverse process\\[0.3cm]
1790 {\color{blue}
1791 High probability of stable C$_{\text{sub}}$ configuration
1792 }
1793 \end{center}
1794 \end{minipage}
1795 }}}
1796 \end{pspicture}
1797
1798 \end{slide}
1799
1800 \begin{slide}
1801
1802 \headphd
1803 {\large\bf
1804  Combinations of substitutional C and Si self-interstitials
1805 }
1806
1807 \scriptsize
1808
1809 \vspace{0.3cm}
1810
1811 \begin{minipage}{6.2cm}
1812 \begin{center}
1813 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1814 \begin{itemize}
1815  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1816  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1817  \item Interaction drops quickly to zero\\
1818        $\rightarrow$ low capture radius
1819 \end{itemize}
1820 \end{center}
1821 \end{minipage}
1822 \begin{minipage}{0.2cm}
1823 \hfill
1824 \end{minipage}
1825 \begin{minipage}{6.0cm}
1826 \begin{center}
1827 {\bf Transition from the ground state}
1828 \begin{itemize}
1829  \item Low transition barrier
1830  \item Barrier smaller than \ci{} migration barrier
1831  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1832        $\rightarrow$ Separation of \cs{} \& \si{} most probable
1833 \end{itemize}
1834 \end{center}
1835 \end{minipage}\\[0.3cm]
1836
1837 \begin{minipage}{6.0cm}
1838 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1839 \end{minipage}
1840 \begin{minipage}{0.4cm}
1841 \hfill
1842 \end{minipage}
1843 \begin{minipage}{6.0cm}
1844 \begin{flushright}
1845 \includegraphics[width=6.0cm]{162-097.ps}
1846 \end{flushright}
1847 \end{minipage}
1848
1849 \begin{pspicture}(0,0)(0,0)
1850 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1851 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1852 \begin{minipage}{8cm}
1853 \begin{center}
1854 \vspace{0.1cm}
1855 {\color{black}
1856 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1857 IBS --- process far from equilibrium\\
1858 }
1859 \end{center}
1860 \end{minipage}
1861 }}}
1862 \end{pspicture}
1863
1864 \end{slide}
1865
1866 \begin{slide}
1867
1868 \headphd
1869 {\large\bf
1870  Combinations of substitutional C and Si self-interstitials
1871 }
1872
1873 \scriptsize
1874
1875 \vspace{0.3cm}
1876
1877 \begin{minipage}{6.2cm}
1878 \begin{center}
1879 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1880 \begin{itemize}
1881  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1882  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1883  \item Interaction drops quickly to zero\\
1884        $\rightarrow$ low capture radius
1885 \end{itemize}
1886 \end{center}
1887 \end{minipage}
1888 \begin{minipage}{0.2cm}
1889 \hfill
1890 \end{minipage}
1891 \begin{minipage}{6.0cm}
1892 \begin{center}
1893 {\bf Transition from the ground state}
1894 \begin{itemize}
1895  \item Low transition barrier
1896  \item Barrier smaller than \ci{} migration barrier
1897  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1898        $\rightarrow$ Separation of \cs{} \& \si{} most probable
1899 \end{itemize}
1900 \end{center}
1901 \end{minipage}\\[0.3cm]
1902
1903 \begin{minipage}{6.0cm}
1904 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1905 \end{minipage}
1906 \begin{minipage}{0.4cm}
1907 \hfill
1908 \end{minipage}
1909 \begin{minipage}{6.0cm}
1910 \begin{flushright}
1911 \includegraphics[width=6.0cm]{162-097.ps}
1912 \end{flushright}
1913 \end{minipage}
1914
1915 \begin{pspicture}(0,0)(0,0)
1916 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1917 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1918 \begin{minipage}{8cm}
1919 \begin{center}
1920 \vspace{0.1cm}
1921 {\color{black}
1922 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1923 IBS --- process far from equilibrium\\
1924 }
1925 \end{center}
1926 \end{minipage}
1927 }}}
1928 \end{pspicture}
1929
1930 % md support
1931 \begin{pspicture}(0,0)(0,0)
1932 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1933 \begin{minipage}{14cm}
1934 \hfill
1935 \vspace{14cm}
1936 \end{minipage}
1937 }}
1938 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1939 \begin{minipage}{11cm}
1940 \begin{center}
1941 \vspace{0.2cm}
1942 \scriptsize
1943 Ab initio MD at \degc{900}\\[0.4cm]
1944 \begin{minipage}{5.4cm}
1945 \centering
1946 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1947 $t=\unit[2230]{fs}$
1948 \end{minipage}
1949 \begin{minipage}{5.4cm}
1950 \centering
1951 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1952 $t=\unit[2900]{fs}$
1953 \end{minipage}\\[0.5cm]
1954 {\color{blue}
1955 Contribution of entropy to structural formation\\[0.1cm]
1956 }
1957 \end{center}
1958 \end{minipage}
1959 }}}
1960 \end{pspicture}
1961
1962 \end{slide}
1963
1964 \begin{slide}
1965
1966 \headphd
1967 {\large\bf
1968  Silicon carbide precipitation simulations
1969 }
1970
1971 \small
1972
1973 \vspace{0.2cm}
1974
1975 {\bf Procedure}
1976
1977 {\scriptsize
1978  \begin{pspicture}(0,0)(12,6.5)
1979   % nodes
1980   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1981    \parbox{7cm}{
1982    \begin{itemize}
1983     \item Create c-Si volume
1984     \item Periodc boundary conditions
1985     \item Set requested $T$ and $p=0\text{ bar}$
1986     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1987    \end{itemize}
1988   }}}}
1989   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1990    \parbox{7cm}{
1991    Insertion of C atoms at constant T
1992    \begin{itemize}
1993     \item total simulation volume {\pnode{in1}}
1994     \item volume of minimal SiC precipitate size {\pnode{in2}}
1995     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1996           precipitate
1997    \end{itemize} 
1998   }}}}
1999   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2000    \parbox{7.0cm}{
2001    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2002   }}}}
2003   \ncline[]{->}{init}{insert}
2004   \ncline[]{->}{insert}{cool}
2005   \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
2006   \rput(7.6,6){\footnotesize $V_1$}
2007   \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
2008   \rput(8.9,4.85){\tiny $V_2$}
2009   \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
2010   \rput(9.25,4.45){\footnotesize $V_3$}
2011   \rput(7.9,3.2){\pnode{ins1}}
2012   \rput(8.92,2.8){\pnode{ins2}}
2013   \rput(10.8,2.4){\pnode{ins3}}
2014   \ncline[]{->}{in1}{ins1}
2015   \ncline[]{->}{in2}{ins2}
2016   \ncline[]{->}{in3}{ins3}
2017  \end{pspicture}
2018 }
2019
2020 \vspace{-0.5cm}
2021
2022 {\bf Note}
2023
2024 \footnotesize
2025
2026 \begin{minipage}{5.7cm}
2027 \begin{itemize}
2028  \item Amount of C atoms: 6000\\
2029        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
2030  \item Simulation volume: $31^3$ Si unit cells\\
2031        (238328 Si atoms)
2032 \end{itemize}
2033 \end{minipage}
2034 \begin{minipage}{0.3cm}
2035 \hfill
2036 \end{minipage}
2037 \framebox{
2038 \begin{minipage}{6.0cm}
2039 Restricted to classical potential caclulations\\
2040 $\rightarrow$ Low C diffusion / overestimated barrier\\
2041 $\rightarrow$ Consider $V_2$ and $V_3$
2042 %\begin{itemize}
2043 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
2044 %\end{itemize}
2045 \end{minipage}
2046 }
2047
2048 \end{slide}
2049
2050 \begin{slide}
2051
2052 \headphd
2053 {\large\bf\boldmath
2054  Silicon carbide precipitation simulations at \degc{450} as in IBS
2055 }
2056
2057 \small
2058
2059 \begin{minipage}{6.3cm}
2060 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
2061 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
2062 \hfill
2063 \end{minipage} 
2064 \begin{minipage}{6.1cm}
2065 \scriptsize
2066 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
2067 \hkl<1 0 0> C-Si dumbbell dominated structure
2068 \begin{itemize}
2069  \item Si-C bumbs around \unit[0.19]{nm}
2070  \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
2071        concatenated differently oriented \ci{} DBs
2072  \item Si-Si NN distance stretched to \unit[0.3]{nm}
2073 \end{itemize}
2074 \begin{pspicture}(0,0)(6.0,1.0)
2075 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2076 \begin{minipage}{6cm}
2077 \centering
2078 Formation of \ci{} dumbbells\\
2079 C atoms in proper 3C-SiC distance first
2080 \end{minipage}
2081 }}
2082 \end{pspicture}\\[0.1cm]
2083 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
2084 \begin{itemize}
2085 \item High amount of strongly bound C-C bonds
2086 \item Increased defect \& damage density\\
2087       $\rightarrow$ Arrangements hard to categorize and trace
2088 \item Only short range order observable
2089 \end{itemize}
2090 \begin{pspicture}(0,0)(6.0,0.8)
2091 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2092 \begin{minipage}{6cm}
2093 \centering
2094 Amorphous SiC-like phase
2095 \end{minipage}
2096 }}
2097 \end{pspicture}\\[0.3cm]
2098 \begin{pspicture}(0,0)(6.0,2.0)
2099 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
2100 \begin{minipage}{6cm}
2101 \hfill
2102 \vspace{2.5cm}
2103 \end{minipage}
2104 }}
2105 \end{pspicture}
2106 \end{minipage} 
2107
2108 \end{slide}
2109
2110 \begin{slide}
2111
2112 \headphd
2113 {\large\bf\boldmath
2114  Silicon carbide precipitation simulations at \degc{450} as in IBS
2115 }
2116
2117 \small
2118
2119 \begin{minipage}{6.3cm}
2120 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
2121 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
2122 \hfill
2123 \end{minipage} 
2124 \begin{minipage}{6.1cm}
2125 \scriptsize
2126 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
2127 \hkl<1 0 0> C-Si dumbbell dominated structure
2128 \begin{itemize}
2129  \item Si-C bumbs around \unit[0.19]{nm}
2130  \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
2131        concatenated differently oriented \ci{} DBs
2132  \item Si-Si NN distance stretched to \unit[0.3]{nm}
2133 \end{itemize}
2134 \begin{pspicture}(0,0)(6.0,1.0)
2135 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2136 \begin{minipage}{6cm}
2137 \centering
2138 Formation of \ci{} dumbbells\\
2139 C atoms in proper 3C-SiC distance first
2140 \end{minipage}
2141 }}
2142 \end{pspicture}\\[0.1cm]
2143 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
2144 \begin{itemize}
2145 \item High amount of strongly bound C-C bonds
2146 \item Increased defect \& damage density\\
2147       $\rightarrow$ Arrangements hard to categorize and trace
2148 \item Only short range order observable
2149 \end{itemize}
2150 \begin{pspicture}(0,0)(6.0,0.8)
2151 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2152 \begin{minipage}{6cm}
2153 \centering
2154 Amorphous SiC-like phase
2155 \end{minipage}
2156 }}
2157 \end{pspicture}\\[0.3cm]
2158 \begin{pspicture}(0,0)(6.0,2.0)
2159 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
2160 \begin{minipage}{6cm}
2161 \vspace{0.1cm}
2162 \centering
2163 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
2164 \begin{minipage}{0.8cm}
2165 {\bf\boldmath $V_1$:}
2166 \end{minipage}
2167 \begin{minipage}{5.1cm}
2168 Formation of \ci{} indeed occurs\\
2169 Agllomeration not observed
2170 \end{minipage}\\[0.3cm]
2171 \begin{minipage}{0.8cm}
2172 {\bf\boldmath $V_{2,3}$:}
2173 \end{minipage}
2174 \begin{minipage}{5.1cm}
2175 Amorphous SiC-like structure\\
2176 (not expected at \degc{450})\\[0.05cm]
2177 No rearrangement/transition into 3C-SiC
2178 \end{minipage}\\[0.1cm]
2179 \end{minipage}
2180 }}
2181 \end{pspicture}
2182 \end{minipage} 
2183
2184 \end{slide}
2185
2186 \begin{slide}
2187
2188 \headphd
2189 {\large\bf
2190  Limitations of MD and short range potentials
2191 }
2192
2193 \small
2194
2195 \vspace{0.2cm}
2196
2197 {\bf Time scale problem of MD}\\[0.2cm]
2198 Precise integration \& thermodynamic sampling\\
2199 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
2200               $\omega$: vibrational mode\\
2201 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
2202 Several local minima separated by large energy barriers\\
2203 $\Rightarrow$ Transition event corresponds to a multiple
2204               of vibrational periods\\
2205 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
2206               infrequent transition events\\[0.2cm]
2207 {\color{blue}Accelerated methods:}
2208 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2209
2210 \vspace{0.2cm}
2211
2212 {\bf Limitations related to the short range potential}\\[0.2cm]
2213 Cut-off function limits interaction to next neighbours\\
2214 $\Rightarrow$ Overestimated unphysical high forces of next neighbours
2215               (factor: 2.4--3.4)
2216
2217 \vspace{1.4cm}
2218
2219 {\bf Approach to the (twofold) problem}\\[0.2cm]
2220 Increased temperature simulations without TAD corrections\\
2221 Accelerated methods or higher time scales exclusively not sufficient!
2222
2223 \begin{pspicture}(0,0)(0,0)
2224 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
2225 \begin{minipage}{7.5cm}
2226 \centering
2227 \vspace{0.05cm}
2228 Potential enhanced slow phase space propagation
2229 \end{minipage}
2230 }}
2231 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2232 \begin{minipage}{2.7cm}
2233 \tiny
2234 \centering
2235 retain proper\\
2236 thermodynamic sampling
2237 \end{minipage}
2238 }}
2239 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
2240 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
2241 \begin{minipage}{3.6cm}
2242 \tiny
2243 \centering
2244 \underline{IBS}\\[0.1cm]
2245 3C-SiC also observed for higher T\\[0.1cm]
2246 Higher T inside sample\\[0.1cm]
2247 Structural evolution vs.\\
2248 equilibrium properties
2249 \end{minipage}
2250 }}
2251 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
2252 \end{pspicture}
2253
2254 \end{slide}
2255
2256 \begin{slide}
2257
2258 \headphd
2259 {\large\bf\boldmath
2260  Increased temperature simulations --- $V_1$
2261 }
2262
2263 \small
2264
2265 \begin{minipage}{6.2cm}
2266 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2267 \hfill
2268 \end{minipage}
2269 \begin{minipage}{6.2cm}
2270 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2271 \end{minipage}
2272
2273 \begin{minipage}{6.2cm}
2274 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2275 \hfill
2276 \end{minipage}
2277 \begin{minipage}{6.3cm}
2278 \scriptsize
2279  \underline{Si-C bonds:}
2280  \begin{itemize}
2281   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2282   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2283  \end{itemize}
2284  \underline{Si-Si bonds:}
2285  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2286  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2287  \underline{C-C bonds:}
2288  \begin{itemize}
2289   \item C-C next neighbour pairs reduced (mandatory)
2290   \item Peak at 0.3 nm slightly shifted
2291         \begin{itemize}
2292          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2293                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2294                combinations (|)\\
2295                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2296                ($\downarrow$)
2297          \item Range [|-$\downarrow$]:
2298                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2299                with nearby Si$_{\text{I}}$}
2300         \end{itemize}
2301  \end{itemize}
2302 \end{minipage}
2303
2304 \end{slide}
2305
2306 \begin{slide}
2307
2308 \headphd
2309 {\large\bf\boldmath
2310  Increased temperature simulations --- $V_1$
2311 }
2312
2313 \small
2314
2315 \begin{minipage}{6.2cm}
2316 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2317 \hfill
2318 \end{minipage}
2319 \begin{minipage}{6.2cm}
2320 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2321 \end{minipage}
2322
2323 \begin{minipage}{6.2cm}
2324 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2325 \hfill
2326 \end{minipage}
2327 \begin{minipage}{6.3cm}
2328 \scriptsize
2329  \underline{Si-C bonds:}
2330  \begin{itemize}
2331   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2332   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2333  \end{itemize}
2334  \underline{Si-Si bonds:}
2335  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2336  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2337  \underline{C-C bonds:}
2338  \begin{itemize}
2339   \item C-C next neighbour pairs reduced (mandatory)
2340   \item Peak at 0.3 nm slightly shifted
2341         \begin{itemize}
2342          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2343                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2344                combinations (|)\\
2345                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2346                ($\downarrow$)
2347          \item Range [|-$\downarrow$]:
2348                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2349                with nearby Si$_{\text{I}}$}
2350         \end{itemize}
2351  \end{itemize}
2352 \end{minipage}
2353
2354 % conclusions
2355 \begin{pspicture}(0,0)(0,0)
2356 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
2357 \begin{minipage}{14cm}
2358 \hfill
2359 \vspace{14cm}
2360 \end{minipage}
2361 }}
2362 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
2363 \begin{minipage}{9cm}
2364 \vspace{0.2cm}
2365 \small
2366 \begin{center}
2367 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
2368 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
2369 \end{center}
2370 \begin{itemize}
2371 \item Stretched coherent SiC structures\\
2372 $\Rightarrow$ Precipitation process involves {\color{blue}\cs}
2373 \item Explains annealing behavior of high/low T C implantations
2374       \begin{itemize}
2375        \item Low T: highly mobile {\color{red}\ci}
2376        \item High T: stable configurations of {\color{blue}\cs}
2377       \end{itemize}
2378 \item Role of \si{}
2379       \begin{itemize}
2380        \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
2381        \item Building block for surrounding Si host \& further SiC
2382        \item Strain compensation \ldots\\
2383              \ldots Si/SiC interface\\
2384              \ldots within stretched coherent SiC structure
2385       \end{itemize}
2386 \end{itemize}
2387 \vspace{0.2cm}
2388 \centering
2389 \psframebox[linecolor=blue,linewidth=0.05cm]{
2390 \begin{minipage}{7cm}
2391 \centering
2392 Precipitation mechanism involving \cs\\
2393 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2394 \end{minipage}
2395 }
2396 \end{minipage}
2397 \vspace{0.2cm}
2398 }}
2399 \end{pspicture}
2400
2401 \end{slide}
2402
2403 % skip high T / C conc ... only here!
2404 \ifnum1=0
2405
2406 \begin{slide}
2407
2408  {\large\bf
2409   Increased temperature simulations at high C concentration
2410  }
2411
2412 \footnotesize
2413
2414 \begin{minipage}{6.5cm}
2415 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2416 \end{minipage}
2417 \begin{minipage}{6.5cm}
2418 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2419 \end{minipage}
2420
2421 \vspace{0.1cm}
2422
2423 \scriptsize
2424
2425 \framebox{
2426 \begin{minipage}[t]{6.0cm}
2427 0.186 nm: Si-C pairs $\uparrow$\\
2428 (as expected in 3C-SiC)\\[0.2cm]
2429 0.282 nm: Si-C-C\\[0.2cm]
2430 $\approx$0.35 nm: C-Si-Si
2431 \end{minipage}
2432 }
2433 \begin{minipage}{0.2cm}
2434 \hfill
2435 \end{minipage}
2436 \framebox{
2437 \begin{minipage}[t]{6.0cm}
2438 0.15 nm: C-C pairs $\uparrow$\\
2439 (as expected in graphite/diamond)\\[0.2cm]
2440 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2441 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2442 \end{minipage}
2443 }
2444
2445 \begin{itemize}
2446 \item Decreasing cut-off artifact
2447 \item {\color{red}Amorphous} SiC-like phase remains
2448 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2449 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2450 \end{itemize}
2451
2452 \vspace{-0.1cm}
2453
2454 \begin{center}
2455 {\color{blue}
2456 \framebox{
2457 {\color{black}
2458 High C \& small $V$ \& short $t$
2459 $\Rightarrow$
2460 }
2461 Slow restructuring due to strong C-C bonds
2462 {\color{black}
2463 $\Leftarrow$
2464 High C \& low T implants
2465 }
2466 }
2467 }
2468 \end{center}
2469
2470 \end{slide}
2471
2472 % skipped high T / C conc
2473 \fi
2474
2475 \begin{slide}
2476
2477 {\large\bf
2478  Summary / Outlook
2479 }
2480
2481 \small
2482
2483 \begin{pspicture}(0,0)(12,1.0)
2484 \psframebox[fillstyle=gradient,gradbegin=hred,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
2485 \begin{minipage}{11cm}
2486 {\color{black}Diploma thesis}\\
2487  \underline{Monte Carlo} simulation modeling the selforganization process\\
2488  leading to periodic arrays of nanometric amorphous SiC precipitates
2489 \end{minipage}
2490 }
2491 \end{pspicture}\\[0.4cm]
2492 \begin{pspicture}(0,0)(12,2)
2493 \psframebox[fillstyle=gradient,gradbegin=hblue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
2494 \begin{minipage}{11cm}
2495 {\color{black}Doctoral studies}\\
2496  Classical potential \underline{molecular dynamics} simulations \ldots\\
2497  \underline{Density functional theory} calculations \ldots\\[0.2cm]
2498  \ldots on defect formation and SiC precipitation in Si
2499 \end{minipage}
2500 }
2501 \end{pspicture}\\[0.5cm]
2502 \begin{pspicture}(0,0)(12,3)
2503 \psframebox[fillstyle=solid,fillcolor=white,linestyle=solid]{
2504 \begin{minipage}{11cm}
2505 \vspace{0.2cm}
2506 {\color{black}\bf How to proceed \ldots}\\[0.1cm]
2507 MC $\rightarrow$ empirical potential MD $\rightarrow$ Ground-state DFT \ldots
2508 \begin{itemize}
2509  \renewcommand\labelitemi{$\ldots$}
2510  \item beyond LDA/GGA methods \& ground-state DFT
2511 \end{itemize}
2512 Investigation of structure \& structural evolution \ldots
2513 \begin{itemize}
2514  \renewcommand\labelitemi{$\ldots$}
2515  \item electronic/optical properties
2516  \item electronic correlations
2517  \item non-equilibrium systems
2518 \end{itemize}
2519 \end{minipage}
2520 }
2521 \end{pspicture}\\[0.5cm]
2522
2523 \end{slide}
2524
2525 \begin{slide}
2526
2527  {\large\bf
2528   Acknowledgements
2529  }
2530
2531  \vspace{0.1cm}
2532
2533  \small
2534
2535  Thanks to \ldots
2536
2537  \underline{Augsburg}
2538  \begin{itemize}
2539   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2540   \item Ralf Utermann (EDV)
2541  \end{itemize}
2542  
2543  \underline{Helsinki}
2544  \begin{itemize}
2545   \item Prof. K. Nordlund (MD)
2546  \end{itemize}
2547  
2548  \underline{Munich}
2549  \begin{itemize}
2550   \item Bayerische Forschungsstiftung (financial support)
2551  \end{itemize}
2552  
2553  \underline{Paderborn}
2554  \begin{itemize}
2555   \item Prof. J. Lindner (SiC)
2556   \item Prof. G. Schmidt (DFT + financial support)
2557   \item Dr. E. Rauls (DFT + SiC)
2558  \end{itemize}
2559
2560  \underline{Stuttgart}
2561 \begin{center}
2562 \framebox{
2563 \bf Thank you for your attention / invitation!
2564 }
2565 \end{center}
2566
2567 \end{slide}
2568
2569 \end{document}
2570