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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
15 \usepackage{caption}            % Improved captions
16 \usepackage{fancybox}           % To have several backgrounds
17
18 \usepackage{fancyhdr}           % Headers and footers definitions
19 \usepackage{fancyvrb}           % Fancy verbatim environments
20 \usepackage{pstricks}           % PSTricks with the standard color package
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
53 %\usepackage{cmbright}
54 %\renewcommand{\familydefault}{\sfdefault}
55 %\usepackage{mathptmx}
56
57 \usepackage{upgreek}
58
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64 \begin{document}
65
66 \extraslideheight{10in}
67 \slideframe{plain}
68
69 \pagestyle{empty}
70
71 % specify width and height
72 \slidewidth 26.3cm 
73 \slideheight 19.9cm 
74
75 % margin
76 \def\slidetopmargin{-0.15cm}
77
78 \newcommand{\ham}{\mathcal{H}}
79 \newcommand{\pot}{\mathcal{V}}
80 \newcommand{\foo}{\mathcal{U}}
81 \newcommand{\vir}{\mathcal{W}}
82
83 % itemize level ii
84 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
85
86 % nice phi
87 \renewcommand{\phi}{\varphi}
88
89 % roman letters
90 \newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
91
92 % colors
93 \newrgbcolor{si-yellow}{.6 .6 0}
94 \newrgbcolor{hb}{0.75 0.77 0.89}
95 \newrgbcolor{lbb}{0.75 0.8 0.88}
96 \newrgbcolor{hlbb}{0.825 0.88 0.968}
97 \newrgbcolor{lachs}{1.0 .93 .81}
98
99 % head
100 \newcommand{\headphd}{
101 \begin{pspicture}(0,0)(0,0)
102 \rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=hb,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{
103 \begin{minipage}{14cm}
104 \hfill
105 \vspace{0.7cm}
106 \end{minipage}
107 }}
108 \end{pspicture}
109 }
110
111 % shortcuts
112 \newcommand{\si}{Si$_{\text{i}}${}}
113 \newcommand{\ci}{C$_{\text{i}}${}}
114 \newcommand{\cs}{C$_{\text{sub}}${}}
115 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
116 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
117 \newcommand{\dista}[1]{\unit[#1]{\AA}{}}
118 \newcommand{\perc}[1]{\unit[#1]{\%}{}}
119
120 % no vertical centering
121 %\centerslidesfalse
122
123 % layout check
124 %\layout
125 \ifnum1=0
126 \begin{slide}
127 \center
128 {\Huge
129 E\\
130 F\\
131 G\\
132 A B C D E F G H G F E D C B A
133 G\\
134 F\\
135 E\\
136 }
137 \end{slide}
138 \fi
139
140 % topic
141
142 \begin{slide}
143
144  \small
145
146  \vspace{16pt}
147
148  {\LARGE\bf
149   %\hrule
150   %\vspace{5pt}
151   First-principles and empirical\\[0.2cm]
152   potential simulation study of intrinsic\\[0.2cm]
153   and carbon-related defects in silicon
154   %\vspace{10pt}
155   %\hrule
156  }
157
158  \vspace{30pt}
159
160  {\bf\small
161   \underline{F. Zirkelbach} $\color{gray}\bullet$ B. Stritzker\\
162  }
163  {\color{gray}
164   Experimentalphysik IV, Universit\"at Augsburg, 86135 Augsburg, Germany
165  }\\[0.3cm]
166  {\bf\small
167   K. Nordlund\\
168  }
169  {\color{gray}
170   Department of Physics, University of Helsinki, 00014 Helsinki, Finland
171  }\\[0.3cm]
172  {\bf\small
173   W. G. Schmidt $\color{gray}\bullet$ E. Rauls $\color{gray}\bullet$
174   J. K. N. Lindner\\
175  }
176  {\color{gray}
177   Department Physik, Universit\"at Paderborn, 33095 Paderborn, Germany
178  }
179
180  \vspace{30pt}
181
182  {
183   E-MRS Spring Meeting, Strasbourg, 17.05.2012
184  }
185
186 \end{slide}
187
188 % no vertical centering
189 \centerslidesfalse
190
191 % skip for preparation
192 %\ifnum1=0
193
194 % intro
195
196 \begin{slide}
197
198 \headphd
199 {\large\bf
200   Motivation \& Outline
201 }
202
203 \vspace{0.1cm}
204
205 {\bf
206  Ion beam synthesis (IBS) of epitaxial single crystalline 3C-SiC
207 }
208
209 \vspace{0.1cm}
210
211 \begin{minipage}{7.0cm}
212 \small
213 \begin{itemize}
214  \item \underline{Implantation}\\[0.1cm]
215         Stoichiometric dose | \unit[180]{keV} | \degc{500}\\
216         $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
217         {\color{blue}precipitates}
218  \item \underline{Annealing}\\[0.1cm]
219        \unit[10]{h} at \degc{1250}\\
220        $\Rightarrow$ Homogeneous 3C-SiC layer
221 \end{itemize}
222 \begin{center}
223 \psframebox[linecolor=blue,linewidth=0.05cm]{
224 \begin{minipage}{4.5cm}
225  \color{black}
226  \centering
227  3C-SiC precipitation\\
228  not yet fully understood
229 \end{minipage}
230 }
231 \end{center}
232 \end{minipage}
233 \begin{minipage}{5.0cm}
234 \includegraphics[width=5.5cm]{ibs_3c-sic.eps}\\[-0.4cm]
235 \begin{center}
236 {\tiny
237  XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
238 }
239 \end{center}
240 \end{minipage}\\[0.3cm]
241
242 \psframebox[fillstyle=solid,fillcolor=hb]{
243 \begin{minipage}{12.1cm}
244 {\bf
245  Outline
246 }
247
248 \begin{itemize}
249  \item Assumed SiC precipitation mechanisms / Controversy
250  \item Utilized simulation techniques
251  \item C and Si self-interstitial point defects in silicon
252  \item Silicon carbide precipitation simulations
253 \end{itemize}
254 \end{minipage}
255 }
256
257 \end{slide}
258
259 \begin{slide}
260
261 \headphd
262 {\large\bf
263   Supposed precipitation mechanism of SiC in Si
264 }
265
266  \scriptsize
267
268  \vspace{0.1cm}
269
270  \framebox{
271  \begin{minipage}{3.6cm}
272  \begin{center}
273  Si \& SiC lattice structure\\[0.1cm]
274  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
275  \end{center}
276 {\tiny
277  \begin{minipage}{1.7cm}
278 \underline{Silicon}\\
279 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
280 $a=\unit[5.429]{\\A}$\\
281 $\rho^*_{\text{Si}}=\unit[100]{\%}$
282  \end{minipage}
283  \begin{minipage}{1.7cm}
284 \underline{Silicon carbide}\\
285 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
286 $a=\unit[4.359]{\\A}$\\
287 $\rho^*_{\text{Si}}=\unit[97]{\%}$
288  \end{minipage}
289 }
290  \end{minipage}
291  }
292  \hspace{0.1cm}
293  \begin{minipage}{4.1cm}
294  \begin{center}
295  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
296  \end{center}
297  \end{minipage}
298  \hspace{0.1cm}
299  \begin{minipage}{4.0cm}
300  \begin{center}
301  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
302  \end{center}
303  \end{minipage}
304
305  \vspace{0.1cm}
306
307  \begin{minipage}{4.0cm}
308  \begin{center}
309  C-Si dimers (dumbbells)\\[-0.1cm]
310  on Si lattice sites
311  \end{center}
312  \end{minipage}
313  \hspace{0.1cm}
314  \begin{minipage}{4.1cm}
315  \begin{center}
316  Agglomeration of C-Si dumbbells\\[-0.1cm]
317  $\Rightarrow$ dark contrasts
318  \end{center}
319  \end{minipage}
320  \hspace{0.1cm}
321  \begin{minipage}{4.0cm}
322  \begin{center}
323  Precipitation of 3C-SiC in Si\\[-0.1cm]
324  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
325  \& release of Si self-interstitials
326  \end{center}
327  \end{minipage}
328
329  \vspace{0.1cm}
330
331  \begin{minipage}{4.0cm}
332  \begin{center}
333  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
334  \end{center}
335  \end{minipage}
336  \hspace{0.1cm}
337  \begin{minipage}{4.1cm}
338  \begin{center}
339  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
340  \end{center}
341  \end{minipage}
342  \hspace{0.1cm}
343  \begin{minipage}{4.0cm}
344  \begin{center}
345  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
346  \end{center}
347  \end{minipage}
348
349 \begin{pspicture}(0,0)(0,0)
350 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
351 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
352 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
353 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
354 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
355  $4a_{\text{Si}}=5a_{\text{SiC}}$
356  }}}
357 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
358 \hkl(h k l) planes match
359  }}}
360 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
361 r = \unit[2--4]{nm}
362  }}}
363 \end{pspicture}
364
365 \end{slide}
366
367 \begin{slide}
368
369 \headphd
370 {\large\bf
371  Supposed precipitation mechanism of SiC in Si
372 }
373
374  \scriptsize
375
376  \vspace{0.1cm}
377
378  \framebox{
379  \begin{minipage}{3.6cm}
380  \begin{center}
381  Si \& SiC lattice structure\\[0.1cm]
382  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
383  \end{center}
384 {\tiny
385  \begin{minipage}{1.7cm}
386 \underline{Silicon}\\
387 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
388 $a=\unit[5.429]{\\A}$\\
389 $\rho^*_{\text{Si}}=\unit[100]{\%}$
390  \end{minipage}
391  \begin{minipage}{1.7cm}
392 \underline{Silicon carbide}\\
393 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
394 $a=\unit[4.359]{\\A}$\\
395 $\rho^*_{\text{Si}}=\unit[97]{\%}$
396  \end{minipage}
397 }
398  \end{minipage}
399  }
400  \hspace{0.1cm}
401  \begin{minipage}{4.1cm}
402  \begin{center}
403  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
404  \end{center}
405  \end{minipage}
406  \hspace{0.1cm}
407  \begin{minipage}{4.0cm}
408  \begin{center}
409  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
410  \end{center}
411  \end{minipage}
412
413  \vspace{0.1cm}
414
415  \begin{minipage}{4.0cm}
416  \begin{center}
417  C-Si dimers (dumbbells)\\[-0.1cm]
418  on Si interstitial sites
419  \end{center}
420  \end{minipage}
421  \hspace{0.1cm}
422  \begin{minipage}{4.1cm}
423  \begin{center}
424  Agglomeration of C-Si dumbbells\\[-0.1cm]
425  $\Rightarrow$ dark contrasts
426  \end{center}
427  \end{minipage}
428  \hspace{0.1cm}
429  \begin{minipage}{4.0cm}
430  \begin{center}
431  Precipitation of 3C-SiC in Si\\[-0.1cm]
432  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
433  \& release of Si self-interstitials
434  \end{center}
435  \end{minipage}
436
437  \vspace{0.1cm}
438
439  \begin{minipage}{4.0cm}
440  \begin{center}
441  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
442  \end{center}
443  \end{minipage}
444  \hspace{0.1cm}
445  \begin{minipage}{4.1cm}
446  \begin{center}
447  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
448  \end{center}
449  \end{minipage}
450  \hspace{0.1cm}
451  \begin{minipage}{4.0cm}
452  \begin{center}
453  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
454  \end{center}
455  \end{minipage}
456
457 \begin{pspicture}(0,0)(0,0)
458 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
459 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
460 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
461 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
462 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
463  $4a_{\text{Si}}=5a_{\text{SiC}}$
464  }}}
465 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
466 \hkl(h k l) planes match
467  }}}
468 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
469 r = \unit[2--4]{nm}
470  }}}
471 % controversial view!
472 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
473 \begin{minipage}{14cm}
474 \hfill
475 \vspace{12cm}
476 \end{minipage}
477 }}
478 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
479 \begin{minipage}{10cm}
480 \small
481 \vspace*{0.2cm}
482 \begin{center}
483 {\color{gray}\bf Controversial findings}
484 \end{center}
485 \begin{itemize}
486 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
487  \begin{itemize}
488   \item {\color{blue}Substitutionally} incorporated C on regular Si lattice sites
489   \item \si{} reacting with further C in cleared volume
490  \end{itemize}
491 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
492  \begin{itemize}
493   \item Room temperature implantation $\rightarrow$ high C diffusion
494   \item Elevated temperature implantation $\rightarrow$ no C redistribution
495  \end{itemize}
496  $\Rightarrow$ mobile {\color{red}\ci} opposed to
497  stable {\color{blue}\cs{}} configurations
498 \item Strained Si$_{1-y}$C$_y$/Si heterostructures
499       {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
500  \begin{itemize}
501   \item Initial {\color{blue}coherent} SiC structures (tensile strain)
502   \item Incoherent SiC nanocrystals (strain relaxation)
503  \end{itemize}
504 \end{itemize}
505 \vspace{0.1cm}
506 \begin{center}
507 {\Huge${\lightning}$} \hspace{0.3cm}
508 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
509 {\Huge${\lightning}$}
510 \end{center}
511 \vspace{0.2cm}
512 \end{minipage}
513  }}}
514 \end{pspicture}
515
516 \end{slide}
517
518 \begin{slide}
519
520 \headphd
521 {\large\bf
522  Utilized computational methods
523 }
524
525 \vspace{0.3cm}
526
527 \small
528
529 {\bf Molecular dynamics (MD)}\\[0.1cm]
530 \scriptsize
531 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
532 \hline
533 System of $N$ particles &
534 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
535 Phase space propagation &
536 Velocity Verlet | timestep: \unit[1]{fs} \\
537 Analytical interaction potential &
538 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
539 (Erhart/Albe)
540 $\displaystyle
541 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
542     \pot_{ij} = {\color{red}f_C(r_{ij})}
543     \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
544 $\\
545 Observables: time/ensemble averages &
546 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
547 \hline
548 \end{tabular}
549
550 \small
551
552 \vspace{0.3cm}
553
554 {\bf Density functional theory (DFT)}
555
556 \scriptsize
557
558 \begin{minipage}[t]{6cm}
559 \begin{itemize}
560  \item Hohenberg-Kohn theorem:\\
561        $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
562  \item Kohn-Sham approach:\\
563        Single-particle effective theory
564 \end{itemize}
565 \hrule
566 \begin{itemize}
567 \item Code: \textsc{vasp}
568 \item Plane wave basis set | $E_{\text{cut}}=\unit[300]{eV}$
569 %$\displaystyle
570 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
571 %$\\
572 %$\displaystyle
573 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
574 %$
575 \item Ultrasoft pseudopotential
576 \item Exchange \& correlation: GGA
577 \item Brillouin zone sampling: $\Gamma$-point
578 \item Supercell: $N=216\pm2$
579 \end{itemize}
580 \end{minipage}
581 \begin{minipage}{6cm}
582 \begin{pspicture}(0,0)(0,0)
583 \pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
584 \rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
585 $\displaystyle
586 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
587 $
588 }}
589 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
590 $\displaystyle
591 n(r)=\sum_i^N|\Phi_i(r)|^2
592 $
593 }}
594 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
595 $\displaystyle
596 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
597                  +V_{\text{XC}}[n(r)]
598 $
599 }}
600 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
601 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
602 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
603
604 \end{pspicture}
605 \end{minipage}
606
607 \end{slide}
608
609 \begin{slide}
610
611 \headphd
612  {\large\bf
613   Point defects \& defect migration
614  }
615
616  \small
617
618  \vspace{0.2cm}
619
620 \begin{minipage}[b]{7.5cm}
621 {\bf Defect structure}\\
622   \begin{pspicture}(0,0)(7,4.4)
623   \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
624    \parbox{7cm}{
625    \begin{itemize}
626     \item Creation of c-Si simulation volume
627     \item Periodic boundary conditions
628     \item $T=0\text{ K}$, $p=0\text{ bar}$
629    \end{itemize}
630   }}}}
631 \rput(3.5,1.3){\rnode{insert}{\psframebox{
632  \parbox{7cm}{
633   \begin{center}
634   Insertion of interstitial C/Si atoms
635   \end{center}
636   }}}}
637   \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
638    \parbox{7cm}{
639    \begin{center}
640    Relaxation / structural energy minimization
641    \end{center}
642   }}}}
643   \ncline[]{->}{init}{insert}
644   \ncline[]{->}{insert}{cool}
645  \end{pspicture}
646 \end{minipage}
647 \begin{minipage}[b]{4.5cm}
648 \begin{center}
649 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
650 \end{center}
651 \begin{minipage}{2.21cm}
652 {\scriptsize
653 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
654 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
655 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
656 }
657 \end{minipage}
658 \begin{minipage}{2.21cm}
659 {\scriptsize
660 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
661 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
662 {\color{black}$\bullet$} Vac. / Sub.
663 }
664 \end{minipage}
665 \end{minipage}
666
667 \vspace{0.3cm}
668
669 \begin{minipage}[t]{6cm}
670 {\bf Defect formation energy}\\
671 \framebox{
672 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.5cm]
673 %Particle reservoir: Si \& SiC\\[0.2cm]
674 {\bf Binding energy}\\
675 \framebox{
676 $
677 E_{\text{b}}=
678 E_{\text{f}}^{\text{comb}}-
679 E_{\text{f}}^{1^{\text{st}}}-
680 E_{\text{f}}^{2^{\text{nd}}}
681 $
682 }\\[0.1cm]
683 \footnotesize
684 $E_{\text{b}}<0$: energetically favorable configuration\\
685 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
686 \end{minipage}
687 \begin{minipage}[t]{6cm}
688 \vspace{1.4cm}
689 {\bf Migration barrier}
690 \footnotesize
691 \begin{itemize}
692  \item Displace diffusing atom
693  \item Constrain relaxation of (diffusing) atoms
694  \item Record configurational energy
695 \end{itemize}
696 \begin{picture}(0,0)(-60,-33)
697 \includegraphics[width=4.5cm]{crt_mod.eps}
698 \end{picture}
699 \end{minipage}
700
701 \end{slide}
702
703 \begin{slide}
704
705 \footnotesize
706
707 \headphd
708 {\large\bf
709  C interstitial point defects in silicon\\
710 }
711
712 \begin{tabular}{l c c c c c c r}
713 \hline
714  $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
715  {\color{black} \cs{} \& \si}\\
716 \hline
717  \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
718  Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
719 \hline
720 \end{tabular}\\[0.1cm]
721
722 \framebox{
723 \begin{minipage}{2.8cm}
724 \underline{Hexagonal} \hspace{2pt}
725 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
726 $E_{\text{f}}^*=9.05\text{ eV}$\\
727 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
728 \end{minipage}
729 \begin{minipage}{0.4cm}
730 \begin{center}
731 $\Rightarrow$
732 \end{center}
733 \end{minipage}
734 \begin{minipage}{2.8cm}
735 \underline{\hkl<1 0 0>}\\
736 $E_{\text{f}}=3.88\text{ eV}$\\
737 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
738 \end{minipage}
739 }
740 \begin{minipage}{1.4cm}
741 \hfill
742 \end{minipage}
743 \begin{minipage}{3.0cm}
744 \begin{flushright}
745 \underline{Tetrahedral}\\
746 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
747 \end{flushright}
748 \end{minipage}
749
750 \framebox{
751 \begin{minipage}{2.8cm}
752 \underline{Bond-centered}\\
753 $E_{\text{f}}^*=5.59\text{ eV}$\\
754 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
755 \end{minipage}
756 \begin{minipage}{0.4cm}
757 \begin{center}
758 $\Rightarrow$
759 \end{center}
760 \end{minipage}
761 \begin{minipage}{2.8cm}
762 \underline{\hkl<1 1 0> dumbbell}\\
763 $E_{\text{f}}=5.18\text{ eV}$\\
764 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
765 \end{minipage}
766 }
767 \begin{minipage}{1.4cm}
768 \hfill
769 \end{minipage}
770 \begin{minipage}{3.0cm}
771 \begin{flushright}
772 \underline{Substitutional}\\
773 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
774 \end{flushright}
775 \end{minipage}
776
777 \end{slide}
778
779 \begin{slide}
780
781 \headphd
782 {\large\bf\boldmath
783  C interstitial migration
784 }
785
786 \scriptsize
787
788 \vspace{0.3cm}
789
790 \begin{minipage}{6.8cm}
791 {\bf\underline{First-principles}} $\quad$ \hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]\\
792 \begin{minipage}{2.0cm}
793 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
794 \end{minipage}
795 \begin{minipage}{0.2cm}
796 $\rightarrow$
797 \end{minipage}
798 \begin{minipage}{2.0cm}
799 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
800 \end{minipage}
801 \begin{minipage}{0.2cm}
802 $\rightarrow$
803 \end{minipage}
804 \begin{minipage}{2.0cm}
805 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
806 \end{minipage}\\[0.1cm]
807 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
808 $\Rightarrow$ {\color{blue}Migration mechanism identified!}\\
809 Note: Change in orientation\\
810 \end{minipage}
811 \begin{minipage}{5.4cm}
812 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
813 \end{minipage}\\[0.5cm]
814 \begin{minipage}{6.8cm}
815 {\bf\underline{Empirical potential}} $\quad$
816 \hkl[0 0 -1] $\rightarrow$ \hkl[1 1 0] $\rightarrow$ \hkl[0 -1 0]\\[-0.1cm]
817 \begin{itemize}
818  \item Transition involving \hkl[1 1 0] DB\\
819        (instability of BC configuration)
820  \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
821  \item 2.4 -- 3.4 times higher than ab initio result
822  \item After all: Change of the DB orientation
823 \end{itemize}
824 \vspace{0.2cm}
825 \begin{center}
826 {\color{red}Drastically overestimated diffusion barrier}
827 \end{center}
828 \vspace{0.4cm}
829 \end{minipage}
830 \begin{minipage}{5.4cm}
831 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
832 \end{minipage}
833
834 \end{slide}
835
836 \begin{slide}
837
838 \headphd
839 {\large\bf\boldmath
840  Defect combinations --- ab inito
841 }
842
843 \footnotesize
844
845 \vspace{0.3cm}
846
847 \begin{minipage}{9cm}
848 {\bf
849  Summary of combinations}\\[0.1cm]
850 {\scriptsize
851 \begin{tabular}{l c c c c c c}
852 \hline
853  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
854  \hline
855  \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
856  \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
857  \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}\\
858  \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}\\
859  \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}\\
860  \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}\\
861  \hline
862  C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
863  Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
864 \hline
865 \end{tabular}
866 }
867 \end{minipage}
868 \begin{minipage}{3cm}
869 \includegraphics[width=3.5cm]{comb_pos.eps}
870 \end{minipage}
871
872 \vspace{0.7cm}
873
874 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
875 \begin{minipage}{6.1cm}
876 \begin{itemize}
877  \item \ci{} agglomeration energetically favorable
878  \item Reduction of strain
879  \item Capture radius exceeding \unit[1]{nm}
880  \item Disappearance of attractive forces\\
881        between two lowest separations.
882 \end{itemize}
883 \vspace{0.1cm}
884 \begin{center}
885 {\color{blue}\ci{} agglomeration / no C clustering}
886 \end{center}
887 \end{minipage}
888
889 \begin{picture}(0,0)(-180,-50)
890 \begin{minipage}{6.0cm}
891 \scriptsize\centering
892 Interaction along \hkl[1 1 0]\\
893 \includegraphics[width=6.2cm]{db_along_110_cc.ps}
894 \end{minipage}
895 \end{picture}
896
897 \end{slide}
898
899 \begin{slide}
900
901 \headphd
902 {\large\bf
903  Defect combinations of C-Si dimers and vacancies
904 }
905 \footnotesize
906
907 \vspace{0.2cm}
908
909 \begin{minipage}[b]{2.6cm}
910 \begin{flushleft}
911 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
912 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
913 \end{flushleft}
914 \end{minipage}
915 \begin{minipage}[b]{7cm}
916 \hfill
917 \end{minipage}
918 \begin{minipage}[b]{2.6cm}
919 \begin{flushright}
920 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
921 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
922 \end{flushright}
923 \end{minipage}\\[0.2cm]
924
925 \begin{minipage}{6.5cm}
926 \includegraphics[width=6.0cm]{059-539.ps}
927 \end{minipage}
928 \begin{minipage}{5.7cm}
929 \includegraphics[width=6.0cm]{314-539.ps}
930 \end{minipage}
931
932 \begin{pspicture}(0,0)(0,0)
933 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
934
935 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
936 \begin{minipage}{6.5cm}
937 \begin{center}
938 IBS: Impinging C creates V \& far away \si\\[0.3cm]
939 Low migration barrier towards C$_{\text{sub}}$\\
940 \&\\
941 High barrier for reverse process\\[0.3cm]
942 {\color{blue}
943 High probability of stable C$_{\text{sub}}$ configuration
944 }
945 \end{center}
946 \end{minipage}
947 }}}
948 \end{pspicture}
949
950 \end{slide}
951
952 \begin{slide}
953
954 \headphd
955 {\large\bf
956  Combinations of substitutional C and Si self-interstitials
957 }
958
959 \scriptsize
960
961 \vspace{0.3cm}
962
963 \begin{minipage}{6.2cm}
964 \begin{center}
965 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
966 \begin{itemize}
967  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
968  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
969  \item Interaction drops quickly to zero\\
970        $\rightarrow$ low capture radius
971 \end{itemize}
972 \end{center}
973 \end{minipage}
974 \begin{minipage}{0.2cm}
975 \hfill
976 \end{minipage}
977 \begin{minipage}{6.0cm}
978 \begin{center}
979 {\bf Transition from the ground state}
980 \begin{itemize}
981  \item Low transition barrier
982  \item Barrier smaller than \ci{} migration barrier
983  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
984        $\rightarrow$ Separation of \cs{} \& \si{} most probable
985 \end{itemize}
986 \end{center}
987 \end{minipage}\\[0.3cm]
988
989 \begin{minipage}{6.0cm}
990 \includegraphics[width=6.0cm]{c_sub_si110.ps}
991 \end{minipage}
992 \begin{minipage}{0.4cm}
993 \hfill
994 \end{minipage}
995 \begin{minipage}{6.0cm}
996 \begin{flushright}
997 \includegraphics[width=6.0cm]{162-097.ps}
998 \end{flushright}
999 \end{minipage}
1000
1001 \begin{pspicture}(0,0)(0,0)
1002 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1003 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1004 \begin{minipage}{8cm}
1005 \begin{center}
1006 \vspace{0.1cm}
1007 {\color{black}
1008 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1009 IBS --- process far from equilibrium\\
1010 }
1011 \end{center}
1012 \end{minipage}
1013 }}}
1014 \end{pspicture}
1015
1016 \end{slide}
1017
1018 \begin{slide}
1019
1020 \headphd
1021 {\large\bf
1022  Combinations of substitutional C and Si self-interstitials
1023 }
1024
1025 \scriptsize
1026
1027 \vspace{0.3cm}
1028
1029 \begin{minipage}{6.2cm}
1030 \begin{center}
1031 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1032 \begin{itemize}
1033  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1034  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1035  \item Interaction drops quickly to zero\\
1036        $\rightarrow$ low capture radius
1037 \end{itemize}
1038 \end{center}
1039 \end{minipage}
1040 \begin{minipage}{0.2cm}
1041 \hfill
1042 \end{minipage}
1043 \begin{minipage}{6.0cm}
1044 \begin{center}
1045 {\bf Transition from the ground state}
1046 \begin{itemize}
1047  \item Low transition barrier
1048  \item Barrier smaller than \ci{} migration barrier
1049  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1050        $\rightarrow$ Separation of \cs{} \& \si{} most probable
1051 \end{itemize}
1052 \end{center}
1053 \end{minipage}\\[0.3cm]
1054
1055 \begin{minipage}{6.0cm}
1056 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1057 \end{minipage}
1058 \begin{minipage}{0.4cm}
1059 \hfill
1060 \end{minipage}
1061 \begin{minipage}{6.0cm}
1062 \begin{flushright}
1063 \includegraphics[width=6.0cm]{162-097.ps}
1064 \end{flushright}
1065 \end{minipage}
1066
1067 \begin{pspicture}(0,0)(0,0)
1068 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1069 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1070 \begin{minipage}{8cm}
1071 \begin{center}
1072 \vspace{0.1cm}
1073 {\color{black}
1074 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1075 IBS --- process far from equilibrium\\
1076 }
1077 \end{center}
1078 \end{minipage}
1079 }}}
1080 \end{pspicture}
1081
1082 % md support
1083 \begin{pspicture}(0,0)(0,0)
1084 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1085 \begin{minipage}{14cm}
1086 \hfill
1087 \vspace{14cm}
1088 \end{minipage}
1089 }}
1090 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1091 \begin{minipage}{11cm}
1092 \begin{center}
1093 \vspace{0.2cm}
1094 \scriptsize
1095 Ab initio MD at \degc{900}\\[0.4cm]
1096 \begin{minipage}{5.4cm}
1097 \centering
1098 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1099 $t=\unit[2230]{fs}$
1100 \end{minipage}
1101 \begin{minipage}{5.4cm}
1102 \centering
1103 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1104 $t=\unit[2900]{fs}$
1105 \end{minipage}\\[0.5cm]
1106 {\color{blue}
1107 Contribution of entropy to structural formation\\[0.1cm]
1108 }
1109 \end{center}
1110 \end{minipage}
1111 }}}
1112 \end{pspicture}
1113
1114 \end{slide}
1115
1116 \begin{slide}
1117
1118 \headphd
1119 {\large\bf
1120  Silicon carbide precipitation simulations
1121 }
1122
1123 \small
1124
1125 \vspace{0.2cm}
1126
1127 {\bf Procedure}
1128
1129 {\scriptsize
1130  \begin{pspicture}(0,0)(12,6.5)
1131   % nodes
1132   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1133    \parbox{7cm}{
1134    \begin{itemize}
1135     \item Create c-Si volume
1136     \item Periodc boundary conditions
1137     \item Set requested $T$ and $p=0\text{ bar}$
1138     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1139    \end{itemize}
1140   }}}}
1141   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1142    \parbox{7cm}{
1143    Insertion of C atoms at constant T
1144    \begin{itemize}
1145     \item total simulation volume {\pnode{in1}}
1146     \item volume of minimal SiC precipitate size {\pnode{in2}}
1147     %\item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1148     \item volume containing Si atoms to form a minimal {\pnode{in3}}\\
1149           precipitate
1150    \end{itemize} 
1151   }}}}
1152   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1153    \parbox{7.0cm}{
1154    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1155   }}}}
1156   \ncline[]{->}{init}{insert}
1157   \ncline[]{->}{insert}{cool}
1158   \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
1159   \rput(7.6,6){\footnotesize $V_1$}
1160   \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
1161   \rput(8.9,4.85){\tiny $V_2$}
1162   \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
1163   \rput(9.25,4.45){\footnotesize $V_3$}
1164   \rput(7.9,3.2){\pnode{ins1}}
1165   \rput(8.92,2.8){\pnode{ins2}}
1166   \rput(10.8,2.4){\pnode{ins3}}
1167   \ncline[]{->}{in1}{ins1}
1168   \ncline[]{->}{in2}{ins2}
1169   \ncline[]{->}{in3}{ins3}
1170  \end{pspicture}
1171 }
1172
1173 \vspace{-0.5cm}
1174
1175 {\bf Note}
1176
1177 \footnotesize
1178
1179 \begin{minipage}{5.7cm}
1180 \begin{itemize}
1181  \item Amount of C atoms: 6000\\
1182        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
1183  \item Simulation volume: $31^3$ Si unit cells\\
1184        (238328 Si atoms)
1185 \end{itemize}
1186 \end{minipage}
1187 \begin{minipage}{0.3cm}
1188 \hfill
1189 \end{minipage}
1190 \framebox{
1191 \begin{minipage}{6.0cm}
1192 Restricted to classical potential caclulations\\
1193 $\rightarrow$ Low C diffusion / overestimated barrier\\
1194 $\rightarrow$ Consider $V_2$ and $V_3$
1195 %\begin{itemize}
1196 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
1197 %\end{itemize}
1198 \end{minipage}
1199 }
1200
1201 \end{slide}
1202
1203 \begin{slide}
1204
1205 \headphd
1206 {\large\bf
1207  Silicon carbide precipitation simulations
1208 }
1209
1210 \small
1211
1212 \begin{minipage}{6.3cm}
1213 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1214 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1215 \hfill
1216 \end{minipage} 
1217 \begin{minipage}{6.1cm}
1218 \scriptsize
1219 \underline{Temperature as used in IBS (\degc{450})}\\[0.2cm]
1220 \ci{} \hkl<1 0 0> dumbbell dominated structure\\
1221 \begin{pspicture}(0,0)(6.0,1.0)
1222 \rput(2.75,0.4){\psframebox[linewidth=0.05cm,linecolor=black]{
1223 \begin{minipage}{5cm}
1224 \vspace{0.1cm}
1225 \centering
1226 {\color{blue}Formation of \ci{} DBs}\\
1227 {\color{red}No agllomeration / precipitation}
1228 \end{minipage}
1229 }}
1230 \end{pspicture}\\[0.1cm]
1231 Limitations:
1232 \begin{itemize}
1233  \item Time scale problem of MD\\
1234        $\Rightarrow$ slow phase space propagation
1235  \item Short range potential\\
1236        $\Rightarrow$ overestimated diffusion barrier
1237 \end{itemize}
1238 \vspace{0.7cm}
1239 \underline{Increased temperatures}\\[0.2cm]
1240 \cs{} dominated structure\\
1241 \begin{pspicture}(0,0)(6.0,1.0)
1242 \rput(2.75,0.4){\psframebox[linewidth=0.05cm,linecolor=black]{
1243 \begin{minipage}{5cm}
1244 \vspace{0.1cm}
1245 \centering
1246 Si-{\color{blue}C$_{\text{sub}}$}-Si along \hkl<1 1 0>\\
1247 {\color{blue}\cs}-Si-{\color{blue}\cs} \& nearby \si
1248 \end{minipage}
1249 }}
1250 \end{pspicture}\\[0.1cm]
1251 Conclusions:
1252 \begin{itemize}
1253  \item Stretched coherent SiC structures\\
1254        $\Rightarrow$ \cs{} involved in precipitation mechanism
1255  \item Reduction in strain by \si{} 
1256 \end{itemize}
1257 \vspace{0.4cm}
1258
1259 \end{minipage} 
1260
1261 \end{slide}
1262
1263 \begin{slide}
1264
1265 \headphd
1266 {\large\bf
1267  Summary and Conclusions
1268 }
1269
1270 Summary
1271
1272 \begin{itemize}
1273  \item First-principles investigation of defect combinations
1274        and mobilities in Si
1275  \item Empirical potential MD simulations on SiC precipitation in Si
1276 \end{itemize}
1277
1278 \vspace{0.2cm}
1279
1280 \psframebox[linecolor=hb,fillstyle=solid,fillcolor=hb]{
1281 \begin{minipage}{12cm}
1282 Conclusions on SiC precipitation $\qquad$
1283 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}
1284
1285 \begin{itemize}
1286 \item \cs{} involved in the precipitation mechanism
1287 \item Role of the \si{}
1288       \begin{itemize}
1289        \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
1290        \item Building block for surrounding Si host \& further SiC
1291        \item Strain compensation \ldots\\
1292              \ldots Si/SiC interface\\
1293              \ldots within stretched coherent SiC structure
1294       \end{itemize}
1295 \end{itemize}
1296 \end{minipage}
1297 }
1298
1299 \vspace{0.2cm}
1300
1301 Further conclusions
1302
1303 \begin{itemize}
1304  \item High T $\leftrightarrow$ IBS conditions far from equilibrium
1305 \end{itemize}
1306
1307 \end{slide}
1308
1309 \begin{slide}
1310
1311 \headphd
1312 {\large\bf
1313  Acknowledgements
1314 }
1315
1316  \vspace{0.1cm}
1317
1318  \small
1319
1320  Thanks to \ldots
1321
1322 \begin{minipage}[t]{6cm}
1323  \underline{Augsburg}
1324  \begin{itemize}
1325   \item Prof. B. Stritzker
1326  \end{itemize}
1327  
1328  \underline{Helsinki}
1329  \begin{itemize}
1330   \item Prof. K. Nordlund
1331  \end{itemize}
1332
1333  \underline{Munich}
1334  \begin{itemize}
1335   \item Bayerische Forschungsstiftung
1336  \end{itemize}
1337 \end{minipage}
1338 \begin{minipage}[t]{6cm}
1339  \underline{Paderborn}
1340  \begin{itemize}
1341   \item Prof. J. Lindner
1342   \item Prof. G. Schmidt
1343   \item Dr. E. Rauls
1344  \end{itemize}
1345 \end{minipage}
1346
1347 \vspace{2.5cm}
1348
1349 \begin{center}
1350 \framebox{
1351 \LARGE\bf Thank you for your attention!
1352 }
1353 \end{center}
1354
1355 \end{slide}
1356
1357
1358
1359
1360
1361
1362 \begin{slide}
1363
1364 \headphd
1365  {\large\bf
1366   Polytypes of SiC\\[0.6cm]
1367  }
1368
1369 \vspace{0.6cm}
1370
1371 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
1372 \begin{minipage}{1.9cm}
1373 {\tiny cubic (twist)}
1374 \end{minipage}
1375 \begin{minipage}{2.9cm}
1376 {\tiny hexagonal (no twist)}
1377 \end{minipage}
1378
1379 \begin{picture}(0,0)(-150,0)
1380  \includegraphics[width=7cm]{polytypes.eps}
1381 \end{picture}
1382
1383 \vspace{0.6cm}
1384
1385 \footnotesize
1386
1387 \begin{tabular}{l c c c c c c}
1388 \hline
1389  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
1390 \hline
1391 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
1392 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
1393 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
1394 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
1395 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
1396 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
1397 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
1398 \hline
1399 \end{tabular}
1400
1401 \begin{pspicture}(0,0)(0,0)
1402 \psellipse[linecolor=green](5.7,2.05)(0.4,0.50)
1403 \end{pspicture}
1404 \begin{pspicture}(0,0)(0,0)
1405 \psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
1406 \end{pspicture}
1407 \begin{pspicture}(0,0)(0,0)
1408 \psellipse[linecolor=red](10.45,0.42)(0.4,0.20)
1409 \end{pspicture}
1410
1411 \end{slide}
1412
1413 \begin{slide}
1414
1415 \headphd
1416 {\large\bf
1417  IBS of epitaxial single crystalline 3C-SiC
1418 }
1419
1420 \footnotesize
1421
1422 \vspace{0.2cm}
1423
1424 \begin{center}
1425 \begin{itemize}
1426  \item \underline{Implantation step 1}\\[0.1cm]
1427         Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
1428         $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
1429         {\color{blue}precipitates}
1430  \item \underline{Implantation step 2}\\[0.1cm]
1431         Low remaining amount of dose | \unit[180]{keV} | \degc{250}\\
1432         $\Rightarrow$
1433         Destruction/Amorphization of precipitates at layer interface
1434  \item \underline{Annealing}\\[0.1cm]
1435        \unit[10]{h} at \degc{1250}\\
1436        $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
1437 \end{itemize}
1438 \end{center}
1439
1440 \begin{minipage}{6.9cm}
1441 \includegraphics[width=7cm]{ibs_3c-sic.eps}\\[-0.4cm]
1442 \begin{center}
1443 {\tiny
1444  XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
1445 }
1446 \end{center}
1447 \end{minipage}
1448 \begin{minipage}{5cm}
1449 \begin{center}
1450 \begin{pspicture}(0,0)(0,0)
1451 \rnode{box}{
1452 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
1453 \begin{minipage}{3.3cm}
1454  \begin{center}
1455  {\color{blue}
1456   3C-SiC precipitation\\
1457   not yet fully understood
1458  }
1459  \end{center}
1460 % \vspace*{0.1cm}
1461 % \renewcommand\labelitemi{$\Rightarrow$}
1462 % Details of the SiC precipitation
1463 % \begin{itemize}
1464 %  \item significant technological progress\\
1465 %        in SiC thin film formation
1466 %  \item perspectives for processes relying\\
1467 %        upon prevention of SiC precipitation
1468 % \end{itemize}
1469 \end{minipage}
1470 }}
1471 \rput(-5.3,5.5){\pnode{h0}}
1472 \rput(-1.95,5.5){\pnode{h1}}
1473 \ncline[linecolor=blue]{-}{h0}{h1}
1474 \ncline[linecolor=blue]{->}{h1}{box}
1475 \end{pspicture}
1476 \end{center}
1477 \end{minipage}
1478
1479 \end{slide}
1480
1481 \begin{slide}
1482
1483 \footnotesize
1484
1485 \headphd
1486 {\large\bf
1487  Si self-interstitial point defects in silicon\\[0.1cm]
1488 }
1489
1490 \begin{center}
1491 \begin{tabular}{l c c c c c}
1492 \hline
1493  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1494 \hline
1495  \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1496  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1497 \hline
1498 \end{tabular}\\[0.4cm]
1499 \end{center}
1500
1501 \begin{minipage}{3cm}
1502 \begin{center}
1503 \underline{Vacancy}\\
1504 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
1505 \end{center}
1506 \end{minipage}
1507 \begin{minipage}{3cm}
1508 \begin{center}
1509 \underline{\hkl<1 1 0> DB}\\
1510 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
1511 \end{center}
1512 \end{minipage}
1513 \begin{minipage}{3cm}
1514 \begin{center}
1515 \underline{\hkl<1 0 0> DB}\\
1516 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
1517 \end{center}
1518 \end{minipage}
1519 \begin{minipage}{3cm}
1520 \begin{center}
1521 \underline{Tetrahedral}\\
1522 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
1523 \end{center}
1524 \end{minipage}\\
1525
1526 \underline{Hexagonal} \hspace{2pt}
1527 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1528 \framebox{
1529 \begin{minipage}{2.7cm}
1530 $E_{\text{f}}^*=4.48\text{ eV}$\\
1531 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
1532 \end{minipage}
1533 \begin{minipage}{0.4cm}
1534 \begin{center}
1535 $\Rightarrow$
1536 \end{center}
1537 \end{minipage}
1538 \begin{minipage}{2.7cm}
1539 $E_{\text{f}}=3.96\text{ eV}$\\
1540 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
1541 \end{minipage}
1542 }
1543 \begin{minipage}{5.5cm}
1544 \begin{center}
1545 {\tiny nearly T $\rightarrow$ T}\\
1546 \end{center}
1547 \includegraphics[width=6.0cm]{nhex_tet.ps}
1548 \end{minipage}
1549
1550 \end{slide}
1551
1552 \begin{slide}
1553
1554 \headphd
1555 {\large\bf\boldmath
1556  C-Si dimer \& bond-centered interstitial configuration
1557 }
1558
1559 \footnotesize
1560
1561 \vspace{0.1cm}
1562
1563 \begin{minipage}[t]{4.1cm}
1564 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
1565 \begin{minipage}{2.0cm}
1566 \begin{center}
1567 \underline{Erhart/Albe}
1568 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
1569 \end{center}
1570 \end{minipage}
1571 \begin{minipage}{2.0cm}
1572 \begin{center}
1573 \underline{\textsc{vasp}}
1574 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
1575 \end{center}
1576 \end{minipage}\\[0.2cm]
1577 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
1578 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
1579 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
1580 $\Rightarrow$ $sp^2$ hybridization
1581 \begin{center}
1582 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
1583 {\tiny Charge density isosurface}
1584 \end{center}
1585 \end{minipage}
1586 \begin{minipage}{0.2cm}
1587 \hfill
1588 \end{minipage}
1589 \begin{minipage}[t]{8.1cm}
1590 \begin{flushright}
1591 {\bf Bond-centered interstitial}\\[0.1cm]
1592 \begin{minipage}{4.4cm}
1593 %\scriptsize
1594 \begin{itemize}
1595  \item Linear Si-C-Si bond
1596  \item Si: one C \& 3 Si neighbours
1597  \item Spin polarized calculations
1598  \item No saddle point!\\
1599        Real local minimum!
1600 \end{itemize}
1601 \end{minipage}
1602 \begin{minipage}{2.7cm}
1603 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1604 \vspace{0.2cm}
1605 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
1606 \end{minipage}
1607
1608 \framebox{
1609  \tiny
1610  \begin{minipage}[t]{6.5cm}
1611   \begin{minipage}[t]{1.2cm}
1612   {\color{red}Si}\\
1613   {\tiny sp$^3$}\\[0.8cm]
1614   \underline{${\color{black}\uparrow}$}
1615   \underline{${\color{black}\uparrow}$}
1616   \underline{${\color{black}\uparrow}$}
1617   \underline{${\color{red}\uparrow}$}\\
1618   sp$^3$
1619   \end{minipage}
1620   \begin{minipage}[t]{1.4cm}
1621   \begin{center}
1622   {\color{red}M}{\color{blue}O}\\[0.8cm]
1623   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1624   $\sigma_{\text{ab}}$\\[0.5cm]
1625   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1626   $\sigma_{\text{b}}$
1627   \end{center}
1628   \end{minipage}
1629   \begin{minipage}[t]{1.0cm}
1630   \begin{center}
1631   {\color{blue}C}\\
1632   {\tiny sp}\\[0.2cm]
1633   \underline{${\color{white}\uparrow\uparrow}$}
1634   \underline{${\color{white}\uparrow\uparrow}$}\\
1635   2p\\[0.4cm]
1636   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1637   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1638   sp
1639   \end{center}
1640   \end{minipage}
1641   \begin{minipage}[t]{1.4cm}
1642   \begin{center}
1643   {\color{blue}M}{\color{green}O}\\[0.8cm]
1644   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1645   $\sigma_{\text{ab}}$\\[0.5cm]
1646   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1647   $\sigma_{\text{b}}$
1648   \end{center}
1649   \end{minipage}
1650   \begin{minipage}[t]{1.2cm}
1651   \begin{flushright}
1652   {\color{green}Si}\\
1653   {\tiny sp$^3$}\\[0.8cm]
1654   \underline{${\color{green}\uparrow}$}
1655   \underline{${\color{black}\uparrow}$}
1656   \underline{${\color{black}\uparrow}$}
1657   \underline{${\color{black}\uparrow}$}\\
1658   sp$^3$
1659   \end{flushright}
1660   \end{minipage}
1661  \end{minipage}
1662 }\\[0.4cm]
1663
1664 %\framebox{
1665 \begin{minipage}{3.0cm}
1666 %\scriptsize
1667 \underline{Charge density}\\
1668 {\color{gray}$\bullet$} Spin up\\
1669 {\color{green}$\bullet$} Spin down\\
1670 {\color{blue}$\bullet$} Resulting spin up\\
1671 {\color{yellow}$\bullet$} Si atoms\\
1672 {\color{red}$\bullet$} C atom
1673 \end{minipage}
1674 \begin{minipage}{3.6cm}
1675 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
1676 \end{minipage}
1677 %}
1678
1679 \end{flushright}
1680
1681 \end{minipage}
1682 \begin{pspicture}(0,0)(0,0)
1683 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
1684 \end{pspicture}
1685
1686 \end{slide}
1687
1688 \begin{slide}
1689
1690 \headphd
1691 {\large\bf\boldmath
1692  C interstitial migration --- ab initio
1693 }
1694
1695 \scriptsize
1696
1697 \vspace{0.3cm}
1698
1699 \begin{minipage}{6.8cm}
1700 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
1701 \begin{minipage}{2.0cm}
1702 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1703 \end{minipage}
1704 \begin{minipage}{0.2cm}
1705 $\rightarrow$
1706 \end{minipage}
1707 \begin{minipage}{2.0cm}
1708 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
1709 \end{minipage}
1710 \begin{minipage}{0.2cm}
1711 $\rightarrow$
1712 \end{minipage}
1713 \begin{minipage}{2.0cm}
1714 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
1715 \end{minipage}\\[0.1cm]
1716 Symmetry:\\
1717 $\Rightarrow$ Sufficient to consider \hkl[00-1] to BC transition\\
1718 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
1719 \end{minipage}
1720 \begin{minipage}{5.4cm}
1721 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
1722 %\end{minipage}\\[0.2cm]
1723 \end{minipage}\\[0.4cm]
1724 %\hrule
1725 %
1726 \begin{minipage}{6.8cm}
1727 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
1728 \begin{minipage}{2.0cm}
1729 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1730 \end{minipage}
1731 \begin{minipage}{0.2cm}
1732 $\rightarrow$
1733 \end{minipage}
1734 \begin{minipage}{2.0cm}
1735 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
1736 \end{minipage}
1737 \begin{minipage}{0.2cm}
1738 $\rightarrow$
1739 \end{minipage}
1740 \begin{minipage}{2.0cm}
1741 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
1742 \end{minipage}\\[0.1cm]
1743 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
1744 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
1745 Note: Change in orientation
1746 \end{minipage}
1747 \begin{minipage}{5.4cm}
1748 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
1749 \end{minipage}\\[0.1cm]
1750 %
1751 %\begin{center}
1752 %Reorientation pathway composed of two consecutive processes of the above type
1753 %\end{center}
1754
1755 \end{slide}
1756
1757 \begin{slide}
1758
1759 \headphd
1760 {\large\bf\boldmath
1761  C interstitial migration --- analytical potential
1762 }
1763 \scriptsize
1764
1765 \vspace{0.3cm}
1766
1767 \begin{minipage}[t]{6.0cm}
1768 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
1769 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
1770 \begin{itemize}
1771  \item Lowermost migration barrier
1772  \item $\Delta E \approx \unit[2.2]{eV}$
1773  \item 2.4 times higher than ab initio result
1774  \item Different pathway
1775 \end{itemize}
1776 \end{minipage}
1777 \begin{minipage}[t]{0.2cm}
1778 \hfill
1779 \end{minipage}
1780 \begin{minipage}[t]{6.0cm}
1781 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
1782 \vspace{0.1cm}
1783 \begin{itemize}
1784  \item Bond-centered configuration unstable\\
1785        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1786  \item Minimum of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
1787        $\rightarrow$ \ci{} \hkl<1 1 0> DB
1788 \end{itemize}
1789 \vspace{0.1cm}
1790 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
1791 \begin{itemize}
1792  \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
1793  \item 2.4 -- 3.4 times higher than ab initio result
1794  \item After all: Change of the DB orientation
1795 \end{itemize}
1796 \end{minipage}
1797
1798 \vspace{0.5cm}
1799 \begin{center}
1800 {\color{red}\bf Drastically overestimated diffusion barrier}
1801 \end{center}
1802
1803 \begin{pspicture}(0,0)(0,0)
1804 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
1805 \end{pspicture}
1806
1807 \end{slide}
1808
1809 \begin{slide}
1810
1811 \headphd
1812 {\large\bf\boldmath
1813  Silicon carbide precipitation simulations at \degc{450} as in IBS
1814 }
1815
1816 \small
1817
1818 \begin{minipage}{6.3cm}
1819 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1820 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1821 \hfill
1822 \end{minipage} 
1823 \begin{minipage}{6.1cm}
1824 \scriptsize
1825 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1826 \ci{} \hkl<1 0 0> dumbbell dominated structure
1827 \begin{itemize}
1828  \item Si-C bumbs around \unit[0.19]{nm}
1829  \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1830        concatenated differently oriented \ci{} DBs
1831  \item Si-Si NN distance stretched to \unit[0.3]{nm}
1832 \end{itemize}
1833 \begin{pspicture}(0,0)(6.0,1.0)
1834 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1835 \begin{minipage}{6cm}
1836 \centering
1837 Formation of \ci{} dumbbells\\
1838 C atoms separated as expected in 3C-SiC
1839 \end{minipage}
1840 }}
1841 \end{pspicture}\\[0.1cm]
1842 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1843 \begin{itemize}
1844 \item High amount of strongly bound C-C bonds
1845 \item Increased defect \& damage density\\
1846       $\rightarrow$ Arrangements hard to categorize and trace
1847 \item Only short range order observable
1848 \end{itemize}
1849 \begin{pspicture}(0,0)(6.0,0.8)
1850 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1851 \begin{minipage}{6cm}
1852 \centering
1853 Amorphous SiC-like phase
1854 \end{minipage}
1855 }}
1856 \end{pspicture}\\[0.3cm]
1857 \begin{pspicture}(0,0)(6.0,2.0)
1858 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
1859 \begin{minipage}{6cm}
1860 \vspace{0.1cm}
1861 \centering
1862 {\bf\color{red}Formation of 3C-SiC fails to appear}\\[0.3cm]
1863 \begin{minipage}{0.8cm}
1864 {\bf\boldmath $V_1$:}
1865 \end{minipage}
1866 \begin{minipage}{5.1cm}
1867 Formation of \ci{} indeed occurs\\
1868 Agllomeration not observed
1869 \end{minipage}\\[0.3cm]
1870 \begin{minipage}{0.8cm}
1871 {\bf\boldmath $V_{2,3}$:}
1872 \end{minipage}
1873 \begin{minipage}{5.1cm}
1874 Amorphous SiC-like structure\\
1875 (not expected at \degc{450})\\[0.05cm]
1876 No rearrangement/transition into 3C-SiC
1877 \end{minipage}\\[0.1cm]
1878 \end{minipage}
1879 }}
1880 \end{pspicture}
1881 \end{minipage}
1882
1883 \end{slide}
1884
1885 \begin{slide}
1886
1887 \headphd
1888 {\large\bf\boldmath
1889  Increased temperature simulations --- $V_1$
1890 }
1891
1892 \small
1893
1894 \begin{minipage}{6.2cm}
1895 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1896 \hfill
1897 \end{minipage}
1898 \begin{minipage}{6.2cm}
1899 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
1900 \end{minipage}
1901
1902 \begin{minipage}{6.2cm}
1903 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
1904 \hfill
1905 \end{minipage}
1906 \begin{minipage}{6.3cm}
1907 \scriptsize
1908  \underline{Si-C bonds:}
1909  \begin{itemize}
1910   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1911   \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$
1912         {\color{blue}\cs{}}
1913  \end{itemize}
1914  \underline{Si-Si bonds:}
1915  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1916  ($\rightarrow$ 0.325 nm)\\[0.1cm]
1917  \underline{C-C bonds:}
1918  \begin{itemize}
1919   \item C-C next neighbour pairs reduced (mandatory)
1920   \item Peak at 0.3 nm slightly shifted\\[0.05cm]
1921         $\searrow$ \ci{} combinations (dashed arrows)\\
1922         $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
1923         $\nearrow$ \ci{} pure \cs{} combinations ($\downarrow$)\\[0.05cm]
1924         Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
1925  \end{itemize}
1926 \end{minipage}
1927
1928 \end{slide}
1929
1930 \begin{slide}
1931
1932  {\large\bf
1933   Increased temperature simulations at high C concentration
1934  }
1935
1936 \footnotesize
1937
1938 \begin{minipage}{6.0cm}
1939 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
1940 \end{minipage}
1941 \begin{minipage}{6.0cm}
1942 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
1943 \end{minipage}
1944
1945 \vspace{0.1cm}
1946
1947 \scriptsize
1948
1949 \framebox{
1950 \begin{minipage}[t]{5.5cm}
1951 0.186 nm: Si-C pairs $\uparrow$\\
1952 (as expected in 3C-SiC)\\[0.2cm]
1953 0.282 nm: Si-C-C\\[0.2cm]
1954 $\approx$0.35 nm: C-Si-Si
1955 \end{minipage}
1956 }
1957 \begin{minipage}{0.1cm}
1958 \hfill
1959 \end{minipage}
1960 \framebox{
1961 \begin{minipage}[t]{5.9cm}
1962 0.15 nm: C-C pairs $\uparrow$\\
1963 (as expected in graphite/diamond)\\[0.2cm]
1964 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
1965 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
1966 \end{minipage}
1967 }
1968
1969 \begin{itemize}
1970 \item Decreasing cut-off artifact
1971 \item {\color{red}Amorphous} SiC-like phase remains
1972 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
1973 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
1974 \end{itemize}
1975
1976 \begin{center}
1977 {\color{blue}
1978 \framebox{
1979 {\color{black}
1980 High C \& small $V$ \& short $t$
1981 $\Rightarrow$
1982 }
1983 \begin{minipage}{4cm}
1984 \begin{center}
1985 Slow structural evolution due to strong C-C bonds
1986 \end{center}
1987 \end{minipage}
1988 {\color{black}
1989 $\Leftarrow$
1990 High C \& low T implants
1991 }
1992 }
1993 }
1994 \end{center}
1995
1996 \end{slide}
1997
1998 \begin{slide}
1999
2000  {\large\bf
2001   Long time scale simulations at maximum temperature
2002  }
2003
2004 \small
2005
2006 \vspace{0.1cm}
2007  
2008 \underline{Differences}
2009 \begin{itemize}
2010  \item Temperature set to $0.95 \cdot T_{\text{m}}$
2011  \item Cubic insertion volume $\Rightarrow$ spherical insertion volume
2012  \item Amount of C atoms: 6000 $\rightarrow$ 5500
2013        $\Leftrightarrow r_{\text{prec}}=0.3\text{ nm}$
2014  \item Simulation volume: 21 unit cells of c-Si in each direction
2015 \end{itemize}
2016
2017 \footnotesize
2018
2019 \vspace{0.3cm}
2020
2021 \begin{minipage}[t]{4.3cm}
2022 \begin{center}
2023 \underline{Low C concentration, Si-C}
2024 \includegraphics[width=4.3cm]{c_in_si_95_v1_si-c.ps}\\
2025 Sharper peaks!
2026 \end{center}
2027 \end{minipage}
2028 \begin{minipage}[t]{4.3cm}
2029 \begin{center}
2030 \underline{Low C concentration, C-C}
2031 \includegraphics[width=4.3cm]{c_in_si_95_v1_c-c.ps}\\
2032 Sharper peaks!\\
2033 No C agglomeration!
2034 \end{center}
2035 \end{minipage}
2036 \begin{minipage}[t]{3.4cm}
2037 \begin{center}
2038 \underline{High C concentration}
2039 \includegraphics[width=4.3cm]{c_in_si_95_v2.ps}\\
2040 No significant changes\\
2041 iC-Si-Si $\uparrow$\\
2042 C-Si-C $\downarrow$
2043 \end{center}
2044 \end{minipage}
2045
2046 \begin{center}
2047 \framebox{
2048 Long time scales and high temperatures most probably not sufficient enough!
2049 }
2050 \end{center}
2051
2052 \end{slide}
2053
2054 \begin{slide}
2055
2056  {\large\bf
2057   Investigation of a silicon carbide precipitate in silicon
2058  }
2059
2060  \scriptsize
2061
2062 \vspace{0.2cm}
2063
2064 \framebox{
2065 \scriptsize
2066 \begin{minipage}{5.3cm}
2067 \[
2068 \frac{8}{a_{\text{Si}}^3}(
2069 \underbrace{21^3 a_{\text{Si}}^3}_{=V}
2070 -\frac{4}{3}\pi x^3)+
2071 \underbrace{\frac{4}{y^3}\frac{4}{3}\pi x^3}_{\stackrel{!}{=}5500}
2072 =21^3\cdot 8
2073 \]
2074 \[
2075 \Downarrow
2076 \]
2077 \[
2078 \frac{8}{a_{\text{Si}}^3}\frac{4}{3}\pi x^3=5500
2079 \Rightarrow x = \left(\frac{5500 \cdot 3}{32 \pi} \right)^{1/3}a_{\text{Si}}
2080 \]
2081 \[
2082 y=\left(\frac{1}{2} \right)^{1/3}a_{\text{Si}}
2083 \]
2084 \end{minipage}
2085 }
2086 \begin{minipage}{0.1cm}
2087 \hfill
2088 \end{minipage}
2089 \begin{minipage}{6.3cm}
2090 \underline{Construction}
2091 \begin{itemize}
2092  \item Simulation volume: 21$^3$ unit cells of c-Si
2093  \item Spherical topotactically aligned precipitate\\
2094        $r=3.0\text{ nm}$ $\Leftrightarrow$ $\approx$ 5500 C atoms
2095  \item Create c-Si but skipped inside sphere\\
2096        of radius $x$
2097  \item Create 3C-SiC inside sphere of radius $x$\\
2098        and lattice constant $y$
2099  \item Strong coupling to heat bath ($T=20\,^{\circ}\mathrm{C}$)
2100 \end{itemize}
2101 \end{minipage}
2102
2103 \vspace{0.3cm}
2104
2105 \begin{minipage}{6.0cm}
2106 \includegraphics[width=6cm]{pc_0.ps}
2107 \end{minipage}
2108 \begin{minipage}{6.1cm}
2109 \underline{Results}
2110 \begin{itemize}
2111  \item Slight increase of c-Si lattice constant!
2112  \item C-C peaks\\
2113        (imply same distanced Si-Si peaks)
2114        \begin{itemize}
2115         \item New peak at 0.307 nm: 2$^{\text{nd}}$ NN in 3C-SiC
2116         \item Bumps ({\color{green}$\downarrow$}):
2117               4$^{\text{th}}$ and 6$^{\text{th}}$ NN
2118        \end{itemize}
2119  \item 3C-SiC lattice constant: 4.34 \AA (bulk: 4.36 \AA)\\
2120        $\rightarrow$ compressed precipitate
2121  \item Interface tension:\\
2122        20.15 eV/nm$^2$ or $3.23 \times 10^{-4}$ J/cm$^2$\\
2123        (literature: $2 - 8 \times 10^{-4}$ J/cm$^2$)
2124 \end{itemize}
2125 \end{minipage}
2126
2127 \end{slide}
2128
2129 \begin{slide}
2130
2131  {\large\bf
2132   Investigation of a silicon carbide precipitate in silicon
2133  }
2134
2135  \footnotesize
2136
2137 \begin{minipage}{7cm}
2138 \underline{Appended annealing steps}
2139 \begin{itemize}
2140  \item artificially constructed interface\\
2141        $\rightarrow$ allow for rearrangement of interface atoms
2142  \item check SiC stability
2143 \end{itemize}
2144 \underline{Temperature schedule}
2145 \begin{itemize}
2146  \item rapidly heat up structure up to $2050\,^{\circ}\mathrm{C}$\\
2147        (75 K/ps)
2148  \item slow heating up to $1.2\cdot T_{\text{m}}=2940\text{ K}$
2149        by 1 K/ps\\
2150        $\rightarrow$ melting at around 2840 K
2151        (\href{../video/sic_prec_120.avi}{$\rhd$})
2152  \item cooling down structure at 100 \% $T_{\text{m}}$ (1 K/ps)\\
2153        $\rightarrow$ no energetically more favorable struture
2154 \end{itemize}
2155 \end{minipage}
2156 \begin{minipage}{5cm}
2157 \includegraphics[width=5.5cm]{fe_and_t_sic.ps}
2158 \end{minipage}
2159
2160 \begin{minipage}{4cm}
2161 \includegraphics[width=4cm]{sic_prec/melt_01.eps}
2162 \end{minipage}
2163 \begin{minipage}{0.2cm}
2164 $\rightarrow$
2165 \end{minipage}
2166 \begin{minipage}{4cm}
2167 \includegraphics[width=4cm]{sic_prec/melt_02.eps}
2168 \end{minipage}
2169 \begin{minipage}{0.2cm}
2170 $\rightarrow$
2171 \end{minipage}
2172 \begin{minipage}{3.7cm}
2173 \includegraphics[width=4cm]{sic_prec/melt_03.eps}
2174 \end{minipage}
2175
2176 \end{slide}
2177
2178 \begin{slide}
2179
2180  {\large\bf
2181   DFT parameters
2182  }
2183
2184 \scriptsize
2185
2186 \vspace{0.1cm}
2187
2188 Equilibrium lattice constants and cohesive energies
2189
2190 \begin{tabular}{l r c c c c c}
2191 \hline
2192 \hline
2193  & & USPP, LDA & USPP, GGA & PAW, LDA & PAW, GGA & Exp. \\
2194 \hline
2195 Si (dia) & $a$ [\AA] & 5.389 & 5.455 & - & - & 5.429 \\
2196          & $\Delta_a$ [\%] & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - & - & - \\
2197        & $E_{\text{coh}}$ [eV] & -5.277 & -4.591 & - & - & -4.63 \\
2198        & $\Delta_E$ [\%] & \unit[{\color{red}14.0}]{\%} & \unit[{\color{green}0.8}]{\%} & - & - & - \\
2199 \hline
2200 C (dia) & $a$ [\AA] & 3.527 & 3.567 & - & - & 3.567 \\
2201          & $\Delta_a$ [\%] & \unit[{\color{green}1.1}]{\%} & \unit[{\color{green}0.01}]{\%} & - & - & - \\
2202        & $E_{\text{coh}}$ [eV] & -8.812 & -7.703 & - & - & -7.374 \\
2203        & $\Delta_E$ [\%] & \unit[{\color{red}19.5}]{\%} & \unit[{\color{orange}4.5}]{\%} & - & - & - \\
2204 \hline
2205 3C-SiC & $a$ [\AA] & 4.319 & 4.370 & 4.330 & 4.379 & 4.359 \\
2206          & $\Delta_a$ [\%] & \unit[{\color{green}0.9}]{\%} & \unit[{\color{green}0.3}]{\%} & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - \\
2207        & $E_{\text{coh}}$ [eV] & -7.318 & -6.426 &  -7.371 & -6.491 & -6.340 \\
2208        & $\Delta_E$ [\%] & \unit[{\color{red}15.4}]{\%} & \unit[{\color{green}1.4}]{\%} & \unit[{\color{red}16.3}]{\%} & \unit[{\color{orange}2.4}]{\%} & - \\
2209 \hline
2210 \hline
2211 \end{tabular}
2212
2213 \vspace{0.3cm}
2214
2215 \begin{minipage}{7cm}
2216 \begin{center}
2217 \begin{tabular}{l c c c}
2218 \hline
2219 \hline
2220  & Si (dia) & C (dia) & 3C-SiC \\
2221 \hline
2222 $a$ [\AA] & 5.458 & 3.562 & 4.365 \\
2223 $\Delta_a$ [\%] & 0.5 & 0.1 & 0.1 \\
2224 \hline
2225 $E_{\text{coh}}$ [eV] & -4.577 & -7.695 & -6.419 \\
2226 $\Delta_E$ [\%] & 1.1 & 4.4 & 1.2 \\
2227 \hline
2228 \hline
2229 \end{tabular}
2230 \end{center}
2231 \end{minipage}
2232 \begin{minipage}{5cm}
2233 $\leftarrow$ entire parameter set
2234 \end{minipage}
2235
2236 \end{slide}
2237
2238 \begin{slide}
2239
2240  {\large\bf
2241   DFT parameters\\
2242  }
2243
2244 \footnotesize
2245
2246 \begin{minipage}{6cm}
2247 \begin{center}
2248 \includegraphics[width=6cm]{sic_32pc_gamma_cutoff_lc.ps}
2249 \end{center}
2250 \end{minipage}
2251 \begin{minipage}{6cm}
2252 \begin{center}
2253 Lattice constants with respect to the PW cut-off energy
2254 \end{center}
2255 \end{minipage}
2256
2257 \begin{minipage}{6cm}
2258 \begin{center}
2259 \includegraphics[width=6cm]{si_self_int_thesis.ps}
2260 \end{center}
2261 \end{minipage}
2262 \begin{minipage}{6cm}
2263 \begin{center}
2264 Defect formation energy with respect to the size of the supercell\\[0.1cm]
2265 \end{center}
2266
2267 \end{minipage}
2268
2269 \end{slide}
2270
2271 \end{document}
2272