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1 \pdfoutput=0
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3 \documentclass[landscape,semhelv]{seminar}
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6 \usepackage[greek,german]{babel}
7 \usepackage[latin1]{inputenc}
8 \usepackage[T1]{fontenc}
9 \usepackage{amsmath}
10 \usepackage{latexsym}
11 \usepackage{ae}
12
13 \usepackage{calc}               % Simple computations with LaTeX variables
14 \usepackage{caption}            % Improved captions
15 \usepackage{fancybox}           % To have several backgrounds
16
17 \usepackage{fancyhdr}           % Headers and footers definitions
18 \usepackage{fancyvrb}           % Fancy verbatim environments
19 \usepackage{pstricks}           % PSTricks with the standard color package
20
21 \usepackage{pstricks}
22 \usepackage{pst-node}
23
24 %\usepackage{epic}
25 %\usepackage{eepic}
26
27 \usepackage{graphicx}
28 \graphicspath{{../img/}}
29
30 \usepackage{miller}
31
32 \usepackage[setpagesize=false]{hyperref}
33
34 \usepackage{semcolor}
35 \usepackage{semlayer}           % Seminar overlays
36 \usepackage{slidesec}           % Seminar sections and list of slides
37
38 \input{seminar.bug}             % Official bugs corrections
39 \input{seminar.bg2}             % Unofficial bugs corrections
40
41 \articlemag{1}
42
43 \special{landscape}
44
45 % font
46 %\usepackage{cmbright}
47 %\renewcommand{\familydefault}{\sfdefault}
48 %\usepackage{mathptmx}
49
50 \usepackage{upgreek}
51
52 \begin{document}
53
54 \extraslideheight{10in}
55 \slideframe{none}
56
57 \pagestyle{empty}
58
59 % specify width and height
60 \slidewidth 27.7cm 
61 \slideheight 19.1cm 
62
63 % shift it into visual area properly
64 \def\slideleftmargin{3.3cm}
65 \def\slidetopmargin{0.6cm}
66
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68 \newcommand{\pot}{\mathcal{V}}
69 \newcommand{\foo}{\mathcal{U}}
70 \newcommand{\vir}{\mathcal{W}}
71
72 % itemize level ii
73 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
74
75 % nice phi
76 \renewcommand{\phi}{\varphi}
77
78 % roman letters
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80
81 % colors
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85 \newrgbcolor{hlbb}{0.825 0.88 0.968}
86 \newrgbcolor{lachs}{1.0 .93 .81}
87
88 % topic
89
90 \begin{slide}
91 \begin{center}
92
93  \vspace{16pt}
94
95  {\LARGE\bf
96   Atomistic simulation study of the silicon carbide precipitation
97   in silicon
98  }
99
100  \vspace{48pt}
101
102  \textsc{F. Zirkelbach}
103
104  \vspace{48pt}
105
106 Gruppenseminar
107
108  \vspace{08pt}
109
110  Paderborn am 7. Juli 2010
111
112 \end{center}
113 \end{slide}
114
115 % motivation / properties / applications of silicon carbide
116 \begin{slide}
117
118 \small
119
120 \begin{pspicture}(0,0)(13.5,5)
121
122
123
124  \psframe*[linecolor=hb](0,0)(13.5,5)
125
126  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.5,1)(7,1)(7,3)(5.5,3)
127  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.75,0.5)(8,2)(8,2)(6.75,3.5)
128
129  \rput[lt](0.2,4.6){\color{gray}PROPERTIES}
130
131  \rput[lt](0.5,4){wide band gap}
132  \rput[lt](0.5,3.5){high electric breakdown field}
133  \rput[lt](0.5,3){good electron mobility}
134  \rput[lt](0.5,2.5){high electron saturation drift velocity}
135  \rput[lt](0.5,2){high thermal conductivity}
136
137  \rput[lt](0.5,1.5){hard and mechanically stable}
138  \rput[lt](0.5,1){chemically inert}
139
140  \rput[lt](0.5,0.5){radiation hardness}
141
142  \rput[rt](13.3,4.6){\color{gray}APPLICATIONS}
143
144  \rput[rt](13,3.85){high-temperature, high power}
145  \rput[rt](13,3.5){and high-frequency}
146  \rput[rt](13,3.15){electronic and optoelectronic devices}
147
148  \rput[rt](13,2.35){material suitable for extreme conditions}
149  \rput[rt](13,2){microelectromechanical systems}
150  \rput[rt](13,1.65){abrasives, cutting tools, heating elements}
151
152  \rput[rt](13,0.85){first wall reactor material, detectors}
153  \rput[rt](13,0.5){and electronic devices for space}
154
155 \end{pspicture}
156
157 \begin{picture}(0,0)(-3,68)
158 \includegraphics[width=2.6cm]{wide_band_gap.eps}
159 \end{picture}
160 \begin{picture}(0,0)(-285,-162)
161 \includegraphics[width=3.38cm]{sic_led.eps}
162 \end{picture}
163 \begin{picture}(0,0)(-195,-162)
164 \includegraphics[width=2.8cm]{6h-sic_3c-sic.eps}
165 \end{picture}
166 \begin{picture}(0,0)(-313,65)
167 \includegraphics[width=2.2cm]{infineon_schottky.eps}
168 \end{picture}
169 \begin{picture}(0,0)(-220,65)
170 \includegraphics[width=2.9cm]{sic_wechselrichter_ise.eps}
171 \end{picture}
172 \begin{picture}(0,0)(0,-160)
173 \includegraphics[width=3.0cm]{sic_proton.eps}
174 \end{picture}
175 \begin{picture}(0,0)(-60,65)
176 \includegraphics[width=3.4cm]{sic_switch.eps}
177 \end{picture}
178
179 \end{slide}
180
181 % start of contents
182
183 \begin{slide}
184
185  {\large\bf
186   Polytypes of SiC
187  }
188
189  \vspace{4cm}
190
191  \small
192
193 \begin{tabular}{l c c c c c c}
194 \hline
195  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
196 \hline
197 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
198 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
199 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
200 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
201 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
202 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
203 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
204 \hline
205 \end{tabular}
206
207 {\tiny
208  Values for $T=300$ K
209 }
210
211 \begin{picture}(0,0)(-160,-155)
212  \includegraphics[width=7cm]{polytypes.eps}
213 \end{picture}
214 \begin{picture}(0,0)(-10,-185)
215  \includegraphics[width=3.8cm]{cubic_hex.eps}\\
216 \end{picture}
217 \begin{picture}(0,0)(-10,-175)
218  {\tiny cubic (twist)}
219 \end{picture}
220 \begin{picture}(0,0)(-60,-175)
221  {\tiny hexagonal (no twist)}
222 \end{picture}
223 \begin{pspicture}(0,0)(0,0)
224 \psellipse[linecolor=green](5.7,3.03)(0.4,0.5)
225 \end{pspicture}
226 \begin{pspicture}(0,0)(0,0)
227 \psellipse[linecolor=green](5.6,1.68)(0.4,0.2)
228 \end{pspicture}
229 \begin{pspicture}(0,0)(0,0)
230 \psellipse[linecolor=red](10.7,1.13)(0.4,0.2)
231 \end{pspicture}
232
233 \end{slide}
234
235 \begin{slide}
236
237  {\large\bf
238   Fabrication of silicon carbide
239  }
240
241  \small
242  
243  \vspace{4pt}
244
245  SiC - \emph{Born from the stars, perfected on earth.}
246  
247  \vspace{4pt}
248
249  Conventional thin film SiC growth:
250  \begin{itemize}
251   \item \underline{Sublimation growth using the modified Lely method}
252         \begin{itemize}
253          \item SiC single-crystalline seed at $T=1800 \, ^{\circ} \text{C}$
254          \item Surrounded by polycrystalline SiC in a graphite crucible\\
255                at $T=2100-2400 \, ^{\circ} \text{C}$
256          \item Deposition of supersaturated vapor on cooler seed crystal
257         \end{itemize}
258   \item \underline{Homoepitaxial growth using CVD}
259         \begin{itemize}
260          \item Step-controlled epitaxy on off-oriented 6H-SiC substrates
261          \item C$_3$H$_8$/SiH$_4$/H$_2$ at $1100-1500 \, ^{\circ} \text{C}$
262          \item Angle, temperature $\rightarrow$ 3C/6H/4H-SiC
263         \end{itemize}
264   \item \underline{Heteroepitaxial growth of 3C-SiC on Si using CVD/MBE}
265         \begin{itemize}
266          \item Two steps: carbonization and growth
267          \item $T=650-1050 \, ^{\circ} \text{C}$
268          \item SiC/Si lattice mismatch $\approx$ 20 \%
269          \item Quality and size not yet sufficient
270         \end{itemize}
271  \end{itemize}
272
273  \begin{picture}(0,0)(-280,-65)
274   \includegraphics[width=3.8cm]{6h-sic_3c-sic.eps}
275  \end{picture}
276  \begin{picture}(0,0)(-280,-55)
277   \begin{minipage}{5cm}
278   {\tiny
279    NASA: 6H-SiC and 3C-SiC LED\\[-7pt]
280    on 6H-SiC substrate
281   }
282   \end{minipage}
283  \end{picture}
284  \begin{picture}(0,0)(-265,-150)
285   \includegraphics[width=2.4cm]{m_lely.eps}
286  \end{picture}
287  \begin{picture}(0,0)(-333,-175)
288   \begin{minipage}{5cm}
289   {\tiny
290    1. Lid\\[-7pt]
291    2. Heating\\[-7pt]
292    3. Source\\[-7pt]
293    4. Crucible\\[-7pt]
294    5. Insulation\\[-7pt]
295    6. Seed crystal
296   }
297   \end{minipage}
298  \end{picture}
299  \begin{picture}(0,0)(-230,-35)
300  \framebox{
301  {\footnotesize\color{blue}\bf Hex: micropipes along c-axis}
302  }
303  \end{picture}
304  \begin{picture}(0,0)(-230,-10)
305  \framebox{
306  \begin{minipage}{3cm}
307  {\footnotesize\color{blue}\bf 3C-SiC fabrication\\
308                                less advanced}
309  \end{minipage}
310  }
311  \end{picture}
312
313 \end{slide}
314
315 \begin{slide}
316
317  {\large\bf
318   Fabrication of silicon carbide
319  }
320
321  \small
322
323  Alternative approach:
324  Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
325  \begin{itemize}
326   \item \underline{Implantation step 1}\\
327         180 keV C$^+$, $D=7.9\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=500\,^{\circ}\mathrm{C}$\\
328         $\Rightarrow$ box-like distribution of equally sized
329                        and epitactically oriented SiC precipitates
330                        
331   \item \underline{Implantation step 2}\\
332         180 keV C$^+$, $D=0.6\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=250\,^{\circ}\mathrm{C}$\\
333         $\Rightarrow$ destruction of SiC nanocrystals
334                       in growing amorphous interface layers
335   \item \underline{Annealing}\\
336         $T=1250\,^{\circ}\mathrm{C}$, $t=10\,\text{h}$\\
337         $\Rightarrow$ homogeneous, stoichiometric SiC layer
338                       with sharp interfaces
339  \end{itemize}
340
341  \begin{minipage}{6.3cm}
342  \includegraphics[width=6cm]{ibs_3c-sic.eps}\\[-0.2cm]
343  {\tiny
344   XTEM micrograph of single crystalline 3C-SiC in Si\hkl(1 0 0)
345  }
346  \end{minipage}
347 \framebox{
348  \begin{minipage}{6.3cm}
349  \begin{center}
350  {\color{blue}
351   Precipitation mechanism not yet fully understood!
352  }
353  \renewcommand\labelitemi{$\Rightarrow$}
354  \small
355  \underline{Understanding the SiC precipitation}
356  \begin{itemize}
357   \item significant technological progress in SiC thin film formation
358   \item perspectives for processes relying upon prevention of SiC precipitation
359  \end{itemize}
360  \end{center}
361  \end{minipage}
362 }
363  
364 \end{slide}
365
366 % contents
367
368 \begin{slide}
369
370 {\large\bf
371  Outline
372 }
373
374  \begin{itemize}
375   \item Supposed precipitation mechanism of SiC in Si
376   \item Utilized simulation techniques
377         \begin{itemize}
378          \item Molecular dynamics (MD) simulations
379          \item Density functional theory (DFT) calculations
380         \end{itemize}
381   \item C and Si self-interstitial point defects in silicon
382   \item Silicon carbide precipitation simulations
383   \item Summary / Conclusion / Outlook
384  \end{itemize}
385
386 \end{slide}
387
388 \begin{slide}
389
390  {\large\bf
391   Supposed precipitation mechanism of SiC in Si
392  }
393
394  \scriptsize
395
396  \vspace{0.1cm}
397
398  \begin{minipage}{3.8cm}
399  Si \& SiC lattice structure\\[0.2cm]
400  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
401  \hrule
402  \end{minipage}
403  \hspace{0.6cm}
404  \begin{minipage}{3.8cm}
405  \begin{center}
406  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
407  \end{center}
408  \end{minipage}
409  \hspace{0.6cm}
410  \begin{minipage}{3.8cm}
411  \begin{center}
412  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
413  \end{center}
414  \end{minipage}
415
416  \begin{minipage}{4cm}
417  \begin{center}
418  C-Si dimers (dumbbells)\\[-0.1cm]
419  on Si interstitial sites
420  \end{center}
421  \end{minipage}
422  \hspace{0.2cm}
423  \begin{minipage}{4.2cm}
424  \begin{center}
425  Agglomeration of C-Si dumbbells\\[-0.1cm]
426  $\Rightarrow$ dark contrasts
427  \end{center}
428  \end{minipage}
429  \hspace{0.2cm}
430  \begin{minipage}{4cm}
431  \begin{center}
432  Precipitation of 3C-SiC in Si\\[-0.1cm]
433  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
434  \& release of Si self-interstitials
435  \end{center}
436  \end{minipage}
437
438  \begin{minipage}{3.8cm}
439  \begin{center}
440  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
441  \end{center}
442  \end{minipage}
443  \hspace{0.6cm}
444  \begin{minipage}{3.8cm}
445  \begin{center}
446  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
447  \end{center}
448  \end{minipage}
449  \hspace{0.6cm}
450  \begin{minipage}{3.8cm}
451  \begin{center}
452  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
453  \end{center}
454  \end{minipage}
455
456 \begin{pspicture}(0,0)(0,0)
457 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
458 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
459 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
460 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
461 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
462  $4a_{\text{Si}}=5a_{\text{SiC}}$
463  }}}
464 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
465 \hkl(h k l) planes match
466  }}}
467 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
468 r = 2 - 4 nm
469  }}}
470 \end{pspicture}
471
472 \end{slide}
473
474 \begin{slide}
475
476  {\large\bf
477   Molecular dynamics (MD) simulations
478  }
479
480  \vspace{12pt}
481
482  \small
483
484  {\bf MD basics:}
485  \begin{itemize}
486   \item Microscopic description of N particle system
487   \item Analytical interaction potential
488   \item Numerical integration using Newtons equation of motion\\
489         as a propagation rule in 6N-dimensional phase space
490   \item Observables obtained by time and/or ensemble averages
491  \end{itemize}
492  {\bf Details of the simulation:}
493  \begin{itemize}
494   \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
495   \item Ensemble: NpT (isothermal-isobaric)
496         \begin{itemize}
497          \item Berendsen thermostat:
498                $\tau_{\text{T}}=100\text{ fs}$
499          \item Berendsen barostat:\\
500                $\tau_{\text{P}}=100\text{ fs}$,
501                $\beta^{-1}=100\text{ GPa}$
502         \end{itemize}
503   \item Erhart/Albe potential: Tersoff-like bond order potential
504   \vspace*{12pt}
505         \[
506         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
507         \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
508         \]
509  \end{itemize}
510
511  \begin{picture}(0,0)(-230,-30)
512   \includegraphics[width=5cm]{tersoff_angle.eps} 
513  \end{picture}
514  
515 \end{slide}
516
517 \begin{slide}
518
519  {\large\bf
520   Density functional theory (DFT) calculations
521  }
522
523  \small
524
525  Basic ingredients necessary for DFT
526
527  \begin{itemize}
528   \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
529         \begin{itemize}
530          \item ... uniquely determines the ground state potential
531                / wavefunctions
532          \item ... minimizes the systems total energy
533         \end{itemize}
534   \item \underline{Born-Oppenheimer}
535         - $N$ moving electrons in an external potential of static nuclei
536 \[
537 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
538               +\sum_i^N V_{\text{ext}}(r_i)
539               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
540 \]
541   \item \underline{Effective potential}
542         - averaged electrostatic potential \& exchange and correlation
543 \[
544 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
545                  +V_{\text{XC}}[n(r)]
546 \]
547   \item \underline{Kohn-Sham system}
548         - Schr\"odinger equation of N non-interacting particles
549 \[
550 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
551 =\epsilon_i\Phi_i(r)
552 \quad
553 \Rightarrow
554 \quad
555 n(r)=\sum_i^N|\Phi_i(r)|^2
556 \]
557   \item \underline{Self-consistent solution}\\
558 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
559 which in turn depends on $n(r)$
560   \item \underline{Variational principle}
561         - minimize total energy with respect to $n(r)$
562  \end{itemize}
563
564 \end{slide}
565
566 \begin{slide}
567
568  {\large\bf
569   Density functional theory (DFT) calculations
570  }
571
572  \small
573
574  \vspace*{0.2cm}
575
576  Details of applied DFT calculations in this work
577
578  \begin{itemize}
579   \item \underline{Exchange correlation functional}
580         - approximations for the inhomogeneous electron gas
581         \begin{itemize}
582          \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
583          \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
584         \end{itemize}
585   \item \underline{Plane wave basis set}
586         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
587 \[
588 \rightarrow
589 \text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
590 \qquad ({\color{blue}300\text{ eV}})
591 \]
592   \item \underline{Brillouin zone sampling} -
593         {\color{blue}$\Gamma$-point only} calculations
594   \item \underline{Pseudo potential} 
595         - consider only the valence electrons
596   \item \underline{Code} - VASP 4.6
597  \end{itemize}
598
599  \vspace*{0.2cm}
600
601  MD and structural optimization
602
603  \begin{itemize}
604   \item MD integration: Gear predictor corrector algorithm
605   \item Pressure control: Parrinello-Rahman pressure control
606   \item Structural optimization: Conjugate gradient method
607  \end{itemize}
608
609 \begin{pspicture}(0,0)(0,0)
610 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
611 \end{pspicture}
612
613 \end{slide}
614
615 \begin{slide}
616
617  {\large\bf
618   C and Si self-interstitial point defects in silicon
619  }
620
621  \small
622
623  \vspace*{0.3cm}
624
625 \begin{minipage}{8cm}
626 Procedure:\\[0.3cm]
627   \begin{pspicture}(0,0)(7,5)
628   \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
629    \parbox{7cm}{
630    \begin{itemize}
631     \item Creation of c-Si simulation volume
632     \item Periodic boundary conditions
633     \item $T=0\text{ K}$, $p=0\text{ bar}$
634    \end{itemize}
635   }}}}
636 \rput(3.5,2.1){\rnode{insert}{\psframebox{
637  \parbox{7cm}{
638   \begin{center}
639   Insertion of interstitial C/Si atoms
640   \end{center}
641   }}}}
642   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
643    \parbox{7cm}{
644    \begin{center}
645    Relaxation / structural energy minimization
646    \end{center}
647   }}}}
648   \ncline[]{->}{init}{insert}
649   \ncline[]{->}{insert}{cool}
650  \end{pspicture}
651 \end{minipage}
652 \begin{minipage}{5cm}
653   \includegraphics[width=5cm]{unit_cell_e.eps}\\
654 \end{minipage}
655
656 \begin{minipage}{9cm}
657  \begin{tabular}{l c c}
658  \hline
659  & size [unit cells] & \# atoms\\
660 \hline
661 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
662 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
663 \hline
664  \end{tabular}
665 \end{minipage}
666 \begin{minipage}{4cm}
667 {\color{red}$\bullet$} Tetrahedral\\
668 {\color{green}$\bullet$} Hexagonal\\
669 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
670 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
671 {\color{cyan}$\bullet$} Bond-centered\\
672 {\color{black}$\bullet$} Vacancy / Substitutional
673 \end{minipage}
674
675 \end{slide}
676
677 \begin{slide}
678
679  \footnotesize
680
681 \begin{minipage}{9.5cm}
682
683  {\large\bf
684   Si self-interstitial point defects in silicon\\
685  }
686
687 \begin{tabular}{l c c c c c}
688 \hline
689  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
690 \hline
691  VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
692  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
693 \hline
694 \end{tabular}\\[0.2cm]
695
696 \begin{minipage}{4.7cm}
697 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
698 \end{minipage}
699 \begin{minipage}{4.7cm}
700 \begin{center}
701 {\tiny nearly T $\rightarrow$ T}\\
702 \end{center}
703 \includegraphics[width=4.7cm]{nhex_tet.ps}
704 \end{minipage}\\
705
706 \underline{Hexagonal} \hspace{2pt}
707 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
708 \framebox{
709 \begin{minipage}{2.7cm}
710 $E_{\text{f}}^*=4.48\text{ eV}$\\
711 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
712 \end{minipage}
713 \begin{minipage}{0.4cm}
714 \begin{center}
715 $\Rightarrow$
716 \end{center}
717 \end{minipage}
718 \begin{minipage}{2.7cm}
719 $E_{\text{f}}=3.96\text{ eV}$\\
720 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
721 \end{minipage}
722 }
723 \begin{minipage}{2.9cm}
724 \begin{flushright}
725 \underline{Vacancy}\\
726 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
727 \end{flushright}
728 \end{minipage}
729
730 \end{minipage}
731 \begin{minipage}{3.5cm}
732
733 \begin{flushright}
734 \underline{\hkl<1 1 0> dumbbell}\\
735 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
736 \underline{Tetrahedral}\\
737 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
738 \underline{\hkl<1 0 0> dumbbell}\\
739 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
740 \end{flushright}
741
742 \end{minipage}
743
744 \end{slide}
745
746 \begin{slide}
747
748 \footnotesize
749
750  {\large\bf
751   C interstitial point defects in silicon\\[-0.1cm]
752  }
753
754 \begin{tabular}{l c c c c c c}
755 \hline
756  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B \\
757 \hline
758  VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 \\
759  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & 0.75 & 5.59$^*$ \\
760 \hline
761 \end{tabular}\\[0.1cm]
762
763 \framebox{
764 \begin{minipage}{2.7cm}
765 \underline{Hexagonal} \hspace{2pt}
766 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
767 $E_{\text{f}}^*=9.05\text{ eV}$\\
768 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
769 \end{minipage}
770 \begin{minipage}{0.4cm}
771 \begin{center}
772 $\Rightarrow$
773 \end{center}
774 \end{minipage}
775 \begin{minipage}{2.7cm}
776 \underline{\hkl<1 0 0>}\\
777 $E_{\text{f}}=3.88\text{ eV}$\\
778 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
779 \end{minipage}
780 }
781 \begin{minipage}{2cm}
782 \hfill
783 \end{minipage}
784 \begin{minipage}{3cm}
785 \begin{flushright}
786 \underline{Tetrahedral}\\
787 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
788 \end{flushright}
789 \end{minipage}
790
791 \framebox{
792 \begin{minipage}{2.7cm}
793 \underline{Bond-centered}\\
794 $E_{\text{f}}^*=5.59\text{ eV}$\\
795 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
796 \end{minipage}
797 \begin{minipage}{0.4cm}
798 \begin{center}
799 $\Rightarrow$
800 \end{center}
801 \end{minipage}
802 \begin{minipage}{2.7cm}
803 \underline{\hkl<1 1 0> dumbbell}\\
804 $E_{\text{f}}=5.18\text{ eV}$\\
805 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
806 \end{minipage}
807 }
808 \begin{minipage}{2cm}
809 \hfill
810 \end{minipage}
811 \begin{minipage}{3cm}
812 \begin{flushright}
813 \underline{Substitutional}\\
814 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
815 \end{flushright}
816 \end{minipage}
817
818 \end{slide}
819
820 \begin{slide}
821
822 \footnotesize
823
824  {\large\bf\boldmath
825   C \hkl<1 0 0> dumbbell interstitial configuration\\
826  }
827
828 {\tiny
829 \begin{tabular}{l c c c c c c c c}
830 \hline
831  Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
832 \hline
833 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
834 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
835 \hline
836 \end{tabular}\\[0.2cm]
837 \begin{tabular}{l c c c c }
838 \hline
839  Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
840 \hline
841 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
842 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
843 \hline
844 \end{tabular}\\[0.2cm]
845 \begin{tabular}{l c c c}
846 \hline
847  Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
848 \hline
849 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
850 VASP & 0.109 & -0.065 & 0.174 \\
851 \hline
852 \end{tabular}\\[0.6cm]
853 }
854
855 \begin{minipage}{3.0cm}
856 \begin{center}
857 \underline{Erhart/Albe}
858 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
859 \end{center}
860 \end{minipage}
861 \begin{minipage}{3.0cm}
862 \begin{center}
863 \underline{VASP}
864 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
865 \end{center}
866 \end{minipage}\\
867
868 \begin{picture}(0,0)(-185,10)
869 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
870 \end{picture}
871 \begin{picture}(0,0)(-280,-150)
872 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
873 \end{picture}
874
875 \begin{pspicture}(0,0)(0,0)
876 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
877 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
878 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
879 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
880 \end{pspicture}
881
882 \end{slide}
883
884 \begin{slide}
885
886 \small
887
888 \begin{minipage}{8.5cm}
889
890  {\large\bf
891   Bond-centered interstitial configuration\\[-0.1cm]
892  }
893
894 \begin{minipage}{3.0cm}
895 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
896 \end{minipage}
897 \begin{minipage}{5.2cm}
898 \begin{itemize}
899  \item Linear Si-C-Si bond
900  \item Si: one C \& 3 Si neighbours
901  \item Spin polarized calculations
902  \item No saddle point!\\
903        Real local minimum!
904 \end{itemize}
905 \end{minipage}
906
907 \framebox{
908  \tiny
909  \begin{minipage}[t]{6.5cm}
910   \begin{minipage}[t]{1.2cm}
911   {\color{red}Si}\\
912   {\tiny sp$^3$}\\[0.8cm]
913   \underline{${\color{black}\uparrow}$}
914   \underline{${\color{black}\uparrow}$}
915   \underline{${\color{black}\uparrow}$}
916   \underline{${\color{red}\uparrow}$}\\
917   sp$^3$
918   \end{minipage}
919   \begin{minipage}[t]{1.4cm}
920   \begin{center}
921   {\color{red}M}{\color{blue}O}\\[0.8cm]
922   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
923   $\sigma_{\text{ab}}$\\[0.5cm]
924   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
925   $\sigma_{\text{b}}$
926   \end{center}
927   \end{minipage}
928   \begin{minipage}[t]{1.0cm}
929   \begin{center}
930   {\color{blue}C}\\
931   {\tiny sp}\\[0.2cm]
932   \underline{${\color{white}\uparrow\uparrow}$}
933   \underline{${\color{white}\uparrow\uparrow}$}\\
934   2p\\[0.4cm]
935   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
936   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
937   sp
938   \end{center}
939   \end{minipage}
940   \begin{minipage}[t]{1.4cm}
941   \begin{center}
942   {\color{blue}M}{\color{green}O}\\[0.8cm]
943   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
944   $\sigma_{\text{ab}}$\\[0.5cm]
945   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
946   $\sigma_{\text{b}}$
947   \end{center}
948   \end{minipage}
949   \begin{minipage}[t]{1.2cm}
950   \begin{flushright}
951   {\color{green}Si}\\
952   {\tiny sp$^3$}\\[0.8cm]
953   \underline{${\color{green}\uparrow}$}
954   \underline{${\color{black}\uparrow}$}
955   \underline{${\color{black}\uparrow}$}
956   \underline{${\color{black}\uparrow}$}\\
957   sp$^3$
958   \end{flushright}
959   \end{minipage}
960  \end{minipage}
961 }\\[0.1cm]
962
963 \framebox{
964 \begin{minipage}{4.5cm}
965 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
966 \end{minipage}
967 \begin{minipage}{3.5cm}
968 {\color{gray}$\bullet$} Spin up\\
969 {\color{green}$\bullet$} Spin down\\
970 {\color{blue}$\bullet$} Resulting spin up\\
971 {\color{yellow}$\bullet$} Si atoms\\
972 {\color{red}$\bullet$} C atom
973 \end{minipage}
974 }
975
976 \end{minipage}
977 \begin{minipage}{4.2cm}
978 \begin{flushright}
979 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
980 {\color{green}$\Box$} {\tiny unoccupied}\\
981 {\color{red}$\bullet$} {\tiny occupied}
982 \end{flushright}
983 \end{minipage}
984
985 \end{slide}
986
987 \begin{slide}
988
989  {\large\bf\boldmath
990   Migration of the C \hkl<1 0 0> dumbbell interstitial
991  }
992
993 \scriptsize
994
995  {\small Investigated pathways}
996
997 \begin{minipage}{8.5cm}
998 \begin{minipage}{8.3cm}
999 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1000 \begin{minipage}{2.4cm}
1001 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1002 \end{minipage}
1003 \begin{minipage}{0.4cm}
1004 $\rightarrow$
1005 \end{minipage}
1006 \begin{minipage}{2.4cm}
1007 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1008 \end{minipage}
1009 \begin{minipage}{0.4cm}
1010 $\rightarrow$
1011 \end{minipage}
1012 \begin{minipage}{2.4cm}
1013 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1014 \end{minipage}
1015 \end{minipage}\\
1016 \begin{minipage}{8.3cm}
1017 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1018 \begin{minipage}{2.4cm}
1019 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1020 \end{minipage}
1021 \begin{minipage}{0.4cm}
1022 $\rightarrow$
1023 \end{minipage}
1024 \begin{minipage}{2.4cm}
1025 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1026 \end{minipage}
1027 \begin{minipage}{0.4cm}
1028 $\rightarrow$
1029 \end{minipage}
1030 \begin{minipage}{2.4cm}
1031 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1032 \end{minipage}
1033 \end{minipage}\\
1034 \begin{minipage}{8.3cm}
1035 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1036 \begin{minipage}{2.4cm}
1037 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1038 \end{minipage}
1039 \begin{minipage}{0.4cm}
1040 $\rightarrow$
1041 \end{minipage}
1042 \begin{minipage}{2.4cm}
1043 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1044 \end{minipage}
1045 \begin{minipage}{0.4cm}
1046 $\rightarrow$
1047 \end{minipage}
1048 \begin{minipage}{2.4cm}
1049 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1050 \end{minipage}
1051 \end{minipage}
1052 \end{minipage}
1053 \framebox{
1054 \begin{minipage}{4.2cm}
1055  {\small Constrained relaxation\\
1056          technique (CRT) method}\\
1057 \includegraphics[width=4cm]{crt_orig.eps}
1058 \begin{itemize}
1059  \item Constrain diffusing atom
1060  \item Static constraints 
1061 \end{itemize}
1062 \vspace*{0.3cm}
1063  {\small Modifications}\\
1064 \includegraphics[width=4cm]{crt_mod.eps}
1065 \begin{itemize}
1066  \item Constrain all atoms
1067  \item Update individual\\
1068        constraints
1069 \end{itemize}
1070 \end{minipage}
1071 }
1072
1073 \end{slide}
1074
1075 \begin{slide}
1076
1077  {\large\bf\boldmath
1078   Migration of the C \hkl<1 0 0> dumbbell interstitial
1079  }
1080
1081 \scriptsize
1082
1083 \framebox{
1084 \begin{minipage}{5.9cm}
1085 \begin{flushleft}
1086 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1087 \end{flushleft}
1088 \begin{center}
1089 \begin{picture}(0,0)(60,0)
1090 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1091 \end{picture}
1092 \begin{picture}(0,0)(-5,0)
1093 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1094 \end{picture}
1095 \begin{picture}(0,0)(-55,0)
1096 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1097 \end{picture}
1098 \begin{picture}(0,0)(12.5,10)
1099 \includegraphics[width=1cm]{110_arrow.eps}
1100 \end{picture}
1101 \begin{picture}(0,0)(90,0)
1102 \includegraphics[height=0.9cm]{001_arrow.eps}
1103 \end{picture}
1104 \end{center}
1105 \vspace*{0.35cm}
1106 \end{minipage}
1107 }
1108 \begin{minipage}{0.3cm}
1109 \hfill
1110 \end{minipage}
1111 \framebox{
1112 \begin{minipage}{5.9cm}
1113 \begin{flushright}
1114 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1115 \end{flushright}
1116 \begin{center}
1117 \begin{picture}(0,0)(60,0)
1118 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
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1131 \end{picture}
1132 \end{center}
1133 \vspace*{0.3cm}
1134 \end{minipage}\\
1135 }
1136
1137 \vspace*{0.05cm}
1138
1139 \framebox{
1140 \begin{minipage}{5.9cm}
1141 \begin{flushleft}
1142 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1143 \end{flushleft}
1144 \begin{center}
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1159 \end{picture}
1160 \end{center}
1161 \vspace*{0.3cm}
1162 \end{minipage}
1163 }
1164 \begin{minipage}{0.3cm}
1165 \hfill
1166 \end{minipage}
1167 \begin{minipage}{6.5cm}
1168 VASP results
1169 \begin{itemize}
1170  \item Energetically most favorable path
1171        \begin{itemize}
1172         \item Path 2
1173         \item Activation energy: $\approx$ 0.9 eV 
1174         \item Experimental values: 0.73 ... 0.87 eV
1175        \end{itemize}
1176        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1177  \item Reorientation (path 3)
1178        \begin{itemize}
1179         \item More likely composed of two consecutive steps of type 2
1180         \item Experimental values: 0.77 ... 0.88 eV
1181        \end{itemize}
1182        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1183 \end{itemize}
1184 \end{minipage}
1185
1186 \end{slide}
1187
1188 \begin{slide}
1189
1190  {\large\bf\boldmath
1191   Migration of the C \hkl<1 0 0> dumbbell interstitial
1192  }
1193
1194 \scriptsize
1195
1196 \begin{minipage}{6.5cm}
1197
1198 \framebox{
1199 \begin{minipage}{5.9cm}
1200 \begin{flushleft}
1201 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1202 \end{flushleft}
1203 \begin{center}
1204 \begin{pspicture}(0,0)(0,0)
1205 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1206 \end{pspicture}
1207 \begin{picture}(0,0)(60,-50)
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1209 \end{picture}
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1227 \end{picture}
1228 \begin{picture}(0,0)(35,-15)
1229 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1230 \end{picture}
1231 \begin{picture}(0,0)(-5,-15)
1232 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1233 \end{picture}
1234 \begin{picture}(0,0)(-55,-15)
1235 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1236 \end{picture}
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1239 \end{picture}
1240 \begin{picture}(0,0)(90,-15)
1241 \includegraphics[height=0.9cm]{010_arrow.eps}
1242 \end{picture}
1243 \end{center}
1244 \end{minipage}
1245 }\\[0.1cm]
1246
1247 \begin{minipage}{5.9cm}
1248 Erhart/Albe results
1249 \begin{itemize}
1250  \item Lowest activation energy: $\approx$ 2.2 eV
1251  \item 2.4 times higher than VASP
1252  \item Different pathway
1253  \item Transition minima ($\rightarrow$ \hkl<1 1 0> dumbbell)
1254 \end{itemize}
1255 \end{minipage}
1256
1257 \end{minipage}
1258 \begin{minipage}{6.5cm}
1259
1260 \framebox{
1261 \begin{minipage}{5.9cm}
1262 \begin{flushright}
1263 \includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1264 \end{flushright}
1265 \begin{center}
1266 \begin{pspicture}(0,0)(0,0)
1267 \psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1268 \end{pspicture}
1269 \begin{picture}(0,0)(60,-5)
1270 \includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
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1272 \begin{picture}(0,0)(0,-5)
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1283 \end{picture}
1284 \end{center}
1285 \vspace{0.2cm}
1286 \end{minipage}
1287 }\\[0.2cm]
1288
1289 \framebox{
1290 \begin{minipage}{5.9cm}
1291 \includegraphics[width=5.9cm]{00-1_ip0-10.ps}
1292 \end{minipage}
1293 }
1294
1295 \end{minipage}
1296
1297 \end{slide}
1298
1299 \begin{slide}
1300
1301  {\large\bf\boldmath
1302   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1303  }
1304
1305 \small
1306
1307 \vspace*{0.1cm}
1308
1309 Binding energy: 
1310 $
1311 E_{\text{b}}=
1312 E_{\text{f}}^{\text{defect combination}}-
1313 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1314 E_{\text{f}}^{\text{2nd defect}}
1315 $
1316
1317 \vspace*{0.1cm}
1318
1319 {\scriptsize
1320 \begin{tabular}{l c c c c c c}
1321 \hline
1322  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1323  \hline
1324  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1325  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1326  \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}\\
1327  \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}\\
1328  \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}\\
1329  \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}\\
1330  \hline
1331  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1332  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1333 \hline
1334 \end{tabular}
1335 }
1336
1337 \vspace*{0.3cm}
1338
1339 \footnotesize
1340
1341 \begin{minipage}[t]{3.8cm}
1342 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1343 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1344 \end{minipage}
1345 \begin{minipage}[t]{3.5cm}
1346 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1347 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1348 \end{minipage}
1349 \begin{minipage}[t]{5.5cm}
1350 \begin{itemize}
1351  \item Restricted to VASP simulations
1352  \item $E_{\text{b}}=0$ for isolated non-interacting defects
1353  \item $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1354  \item Stress compensation / increase
1355  \item Most favorable: C clustering
1356  \item Unfavored: antiparallel orientations
1357  \item Indication of energetically favored\\
1358        agglomeration
1359 \end{itemize}
1360 \end{minipage}
1361
1362 \begin{picture}(0,0)(-295,-130)
1363 \includegraphics[width=3.5cm]{comb_pos.eps}
1364 \end{picture}
1365
1366 \end{slide}
1367
1368 \begin{slide}
1369
1370  {\large\bf\boldmath
1371   Combinations of C-Si \hkl<1 0 0>-type interstitials
1372  }
1373
1374 \small
1375
1376 \vspace*{0.1cm}
1377
1378 Energetically most favorable combinations along \hkl<1 1 0>
1379
1380 \vspace*{0.1cm}
1381
1382 {\scriptsize
1383 \begin{tabular}{l c c c c c c}
1384 \hline
1385  & 1 & 2 & 3 & 4 & 5 & 6\\
1386 \hline
1387 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1388 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1389 Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\
1390 \hline
1391 \end{tabular}
1392 }
1393
1394 \vspace*{0.3cm}
1395
1396 \begin{minipage}{7.0cm}
1397 \includegraphics[width=7cm]{db_along_110_cc.ps}
1398 \end{minipage}
1399 \begin{minipage}{6.0cm}
1400 \begin{center}
1401 {\color{blue}
1402  Interaction proportional to reciprocal cube of C-C distance
1403 }\\[0.2cm]
1404  Saturation in the immediate vicinity
1405 \end{center}
1406 \end{minipage}
1407
1408 \vspace{0.2cm}
1409
1410 \end{slide}
1411
1412 \begin{slide}
1413
1414  {\large\bf\boldmath
1415   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1416  }
1417
1418  \scriptsize
1419
1420 \begin{center}
1421 \begin{minipage}{3.2cm}
1422 \includegraphics[width=3cm]{sub_110_combo.eps}
1423 \end{minipage}
1424 \begin{minipage}{7.8cm}
1425 \begin{tabular}{l c c c c c c}
1426 \hline
1427 C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
1428                    \hkl<1 0 1> & \hkl<-1 0 1> \\
1429 \hline
1430 1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
1431 2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
1432 3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
1433 4 & \RM{4} & B & D & E & E & D \\
1434 5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
1435 \hline
1436 \end{tabular}
1437 \end{minipage}
1438 \end{center}
1439
1440 \begin{center}
1441 \begin{tabular}{l c c c c c c c c c c}
1442 \hline
1443 Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
1444 \hline
1445 $E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
1446 $E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
1447 $r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
1448 \hline
1449 \end{tabular}
1450 \end{center}
1451
1452 \begin{minipage}{6.0cm}
1453 \includegraphics[width=5.8cm]{c_sub_si110.ps}
1454 \end{minipage}
1455 \begin{minipage}{7cm}
1456 \small
1457 \begin{itemize}
1458  \item IBS: C may displace Si\\
1459        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
1460  \item Assumption:\\
1461        \hkl<1 1 0>-type $\rightarrow$ favored combination
1462  \renewcommand\labelitemi{$\Rightarrow$}
1463  \item Less favorable than C-Si \hkl<1 0 0> dumbbell\\
1464        ($E_{\text{f}}=3.88\text{ eV}$)
1465  \item Interaction drops quickly to zero\\
1466        (low interaction capture radius)
1467 \end{itemize}
1468 \end{minipage}
1469
1470 \end{slide}
1471
1472 \begin{slide}
1473
1474  {\large\bf\boldmath
1475   Migration in C-Si \hkl<1 0 0> and vacancy combinations
1476  }
1477
1478  \footnotesize
1479
1480 \vspace{0.1cm}
1481
1482 \begin{minipage}[t]{3cm}
1483 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
1484 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
1485 \end{minipage}
1486 \begin{minipage}[t]{7cm}
1487 \vspace{0.2cm}
1488 \begin{center}
1489  Low activation energies\\
1490  High activation energies for reverse processes\\
1491  $\Downarrow$\\
1492  {\color{blue}C$_{\text{sub}}$ very stable}\\
1493 \vspace*{0.1cm}
1494  \hrule
1495 \vspace*{0.1cm}
1496  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
1497  $\Downarrow$\\
1498  {\color{blue}Formation of SiC by successive substitution by C}
1499
1500 \end{center}
1501 \end{minipage}
1502 \begin{minipage}[t]{3cm}
1503 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
1504 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
1505 \end{minipage}
1506
1507
1508 \framebox{
1509 \begin{minipage}{5.9cm}
1510 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
1511 \begin{center}
1512 \begin{picture}(0,0)(70,0)
1513 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
1514 \end{picture}
1515 \begin{picture}(0,0)(30,0)
1516 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
1517 \end{picture}
1518 \begin{picture}(0,0)(-10,0)
1519 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
1520 \end{picture}
1521 \begin{picture}(0,0)(-48,0)
1522 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
1523 \end{picture}
1524 \begin{picture}(0,0)(12.5,5)
1525 \includegraphics[width=1cm]{100_arrow.eps}
1526 \end{picture}
1527 \begin{picture}(0,0)(97,-10)
1528 \includegraphics[height=0.9cm]{001_arrow.eps}
1529 \end{picture}
1530 \end{center}
1531 \vspace{0.1cm}
1532 \end{minipage}
1533 }
1534 \begin{minipage}{0.3cm}
1535 \hfill
1536 \end{minipage}
1537 \framebox{
1538 \begin{minipage}{5.9cm}
1539 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
1540 \begin{center}
1541 \begin{picture}(0,0)(60,0)
1542 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
1543 \end{picture}
1544 \begin{picture}(0,0)(25,0)
1545 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
1546 \end{picture}
1547 \begin{picture}(0,0)(-20,0)
1548 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
1549 \end{picture}
1550 \begin{picture}(0,0)(-55,0)
1551 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
1552 \end{picture}
1553 \begin{picture}(0,0)(12.5,5)
1554 \includegraphics[width=1cm]{100_arrow.eps}
1555 \end{picture}
1556 \begin{picture}(0,0)(95,0)
1557 \includegraphics[height=0.9cm]{001_arrow.eps}
1558 \end{picture}
1559 \end{center}
1560 \vspace{0.1cm}
1561 \end{minipage}
1562 }
1563
1564 \end{slide}
1565
1566 \begin{slide}
1567
1568  {\large\bf
1569   Conclusion of defect / migration / combined defect simulations
1570  }
1571
1572  \small
1573
1574 \vspace*{0.1cm}
1575
1576 Defect structures
1577 \begin{itemize}
1578  \item Accurately described by quantum-mechanical simulations
1579  \item Less accurate description by classical potential simulations
1580 \end{itemize}
1581 \vspace*{0.2cm}
1582 \begin{itemize}
1583  \item \hkl<1 0 0> C-Si dumbbell interstitial ground state configuration
1584  \item Consistent with reorientation and diffusion experiments
1585  \item C migration pathway in Si identified
1586 \end{itemize} 
1587
1588 Concerning the precipitation mechanism
1589 \begin{itemize}
1590  \item Agglomeration of C-Si dumbbells energetically favorable
1591  \item C-Si indeed favored compared to
1592        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
1593  \item Possible low interaction capture radius of
1594        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
1595  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
1596        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
1597 \end{itemize} 
1598 \begin{center}
1599 {\color{blue}Some results point to a different precipitation mechanism!}
1600 \end{center}
1601 In progress ...
1602 \begin{itemize}
1603  \item \hkl<1 0 0> C-Si $\rightarrow$
1604        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
1605  \item \hkl<1 0 0> C-Si combinations: C-C $\rightarrow$ C-...-C
1606 \end{itemize} 
1607
1608
1609 \end{slide}
1610
1611 \begin{slide}
1612
1613  {\large\bf
1614   Silicon carbide precipitation simulations
1615  }
1616
1617  \small
1618
1619 {\scriptsize
1620  \begin{pspicture}(0,0)(12,6.5)
1621   % nodes
1622   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1623    \parbox{7cm}{
1624    \begin{itemize}
1625     \item Create c-Si volume
1626     \item Periodc boundary conditions
1627     \item Set requested $T$ and $p=0\text{ bar}$
1628     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1629    \end{itemize}
1630   }}}}
1631   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1632    \parbox{7cm}{
1633    Insertion of C atoms at constant T
1634    \begin{itemize}
1635     \item total simulation volume {\pnode{in1}}
1636     \item volume of minimal SiC precipitate {\pnode{in2}}
1637     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1638           precipitate
1639    \end{itemize} 
1640   }}}}
1641   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1642    \parbox{7.0cm}{
1643    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1644   }}}}
1645   \ncline[]{->}{init}{insert}
1646   \ncline[]{->}{insert}{cool}
1647   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
1648   \rput(7.8,6){\footnotesize $V_1$}
1649   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
1650   \rput(9.2,4.85){\tiny $V_2$}
1651   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
1652   \rput(9.55,4.45){\footnotesize $V_3$}
1653   \rput(7.9,3.2){\pnode{ins1}}
1654   \rput(9.22,2.8){\pnode{ins2}}
1655   \rput(11.0,2.4){\pnode{ins3}}
1656   \ncline[]{->}{in1}{ins1}
1657   \ncline[]{->}{in2}{ins2}
1658   \ncline[]{->}{in3}{ins3}
1659  \end{pspicture}
1660 }
1661
1662 \begin{itemize}
1663  \item Restricted to classical potential simulations
1664  \item $V_2$ and $V_3$ considered due to low diffusion
1665  \item Amount of C atoms: 6000
1666        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
1667  \item Simulation volume: $31\times 31\times 31$ unit cells
1668        (238328 Si atoms)
1669 \end{itemize}
1670
1671 \end{slide}
1672
1673 \begin{slide}
1674
1675  {\large\bf\boldmath
1676   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
1677  }
1678
1679  \small
1680
1681 \begin{minipage}{6.5cm}
1682 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
1683 \end{minipage} 
1684 \begin{minipage}{6.5cm}
1685 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
1686 \end{minipage} 
1687
1688 \begin{minipage}{6.5cm}
1689 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
1690 \end{minipage} 
1691 \begin{minipage}{6.5cm}
1692 \scriptsize
1693 \underline{Low C concentration ($V_1$)}\\
1694 \hkl<1 0 0> C-Si dumbbell dominated structure
1695 \begin{itemize}
1696  \item Si-C bumbs around 0.19 nm
1697  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
1698        concatenated dumbbells of various orientation
1699  \item Si-Si NN distance stretched to 0.3 nm
1700 \end{itemize}
1701 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
1702 \underline{High C concentration ($V_2$, $V_3$)}\\
1703 High amount of strongly bound C-C bonds\\
1704 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
1705 Only short range order observable\\
1706 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
1707 \end{minipage} 
1708
1709 \end{slide}
1710
1711 \begin{slide}
1712
1713  {\large\bf
1714   Limitations of molecular dynamics and short range potentials
1715  }
1716
1717 \footnotesize
1718
1719 \vspace{0.2cm}
1720
1721 \underline{Time scale problem of MD}\\[0.2cm]
1722 Minimize integration error\\
1723 $\Rightarrow$ discretization considerably smaller than
1724               reciprocal of fastest vibrational mode\\[0.1cm]
1725 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
1726 $\Rightarrow$ suitable choice of time step:
1727               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
1728 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
1729 Several local minima in energy surface separated by large energy barriers\\
1730 $\Rightarrow$ transition event corresponds to a multiple
1731               of vibrational periods\\
1732 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
1733               infrequent transition events\\[0.1cm]
1734 {\color{blue}Accelerated methods:}
1735 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1736
1737 \vspace{0.3cm}
1738
1739 \underline{Limitations related to the short range potential}\\[0.2cm]
1740 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
1741 and 2$^{\text{nd}}$ next neighbours\\
1742 $\Rightarrow$ overestimated unphysical high forces of next neighbours
1743
1744 \vspace{0.3cm}
1745
1746 \framebox{
1747 \color{red}
1748 Potential enhanced problem of slow phase space propagation
1749 }
1750
1751 \vspace{0.3cm}
1752
1753 \underline{Approach to the (twofold) problem}\\[0.2cm]
1754 Increased temperature simulations without TAD corrections\\
1755 (accelerated methods or higher time scales exclusively not sufficient)
1756
1757 \begin{picture}(0,0)(-260,-30)
1758 \framebox{
1759 \begin{minipage}{4.2cm}
1760 \tiny
1761 \begin{center}
1762 \vspace{0.03cm}
1763 \underline{IBS}
1764 \end{center}
1765 \begin{itemize}
1766 \item 3C-SiC also observed for higher T
1767 \item higher T inside sample
1768 \item structural evolution vs.\\
1769       equilibrium properties
1770 \end{itemize}
1771 \end{minipage}
1772 }
1773 \end{picture}
1774
1775 \begin{picture}(0,0)(-305,-155)
1776 \framebox{
1777 \begin{minipage}{2.5cm}
1778 \tiny
1779 \begin{center}
1780 retain proper\\
1781 thermodynmic sampling
1782 \end{center}
1783 \end{minipage}
1784 }
1785 \end{picture}
1786
1787 \end{slide}
1788
1789 \begin{slide}
1790
1791  {\large\bf
1792   Increased temperature simulations at low C concentration
1793  }
1794
1795 \small
1796
1797 \begin{minipage}{6.5cm}
1798 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
1799 \end{minipage}
1800 \begin{minipage}{6.5cm}
1801 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
1802 \end{minipage}
1803
1804 \begin{minipage}{6.5cm}
1805 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
1806 \end{minipage}
1807 \begin{minipage}{6.5cm}
1808 \scriptsize
1809  \underline{Si-C bonds:}
1810  \begin{itemize}
1811   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1812   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
1813  \end{itemize}
1814  \underline{Si-Si bonds:}
1815  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1816  ($\rightarrow$ 0.325 nm)\\[0.1cm]
1817  \underline{C-C bonds:}
1818  \begin{itemize}
1819   \item C-C next neighbour pairs reduced (mandatory)
1820   \item Peak at 0.3 nm slightly shifted
1821         \begin{itemize}
1822          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
1823                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
1824                combinations (|)\\
1825                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
1826                ($\downarrow$)
1827          \item Range [|-$\downarrow$]:
1828                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
1829                with nearby Si$_{\text{I}}$}
1830         \end{itemize}
1831  \end{itemize}
1832 \end{minipage}
1833
1834 \begin{picture}(0,0)(-330,-74)
1835 \color{blue}
1836 \framebox{
1837 \begin{minipage}{1.6cm}
1838 \tiny
1839 \begin{center}
1840 stretched SiC\\[-0.1cm]
1841 in c-Si
1842 \end{center}
1843 \end{minipage}
1844 }
1845 \end{picture}
1846
1847 \end{slide}
1848
1849 \begin{slide}
1850
1851  {\large\bf
1852   Increased temperature simulations at high C concentration
1853  }
1854
1855 \footnotesize
1856
1857 \begin{minipage}{6.5cm}
1858 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
1859 \end{minipage}
1860 \begin{minipage}{6.5cm}
1861 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
1862 \end{minipage}
1863
1864 \begin{center}
1865 Decreasing cut-off artifact\\
1866 High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
1867 $\Rightarrow$ hard to categorize
1868 \end{center}
1869
1870 \vspace{0.1cm}
1871
1872 \framebox{
1873 \begin{minipage}[t]{6.0cm}
1874 0.186 nm: Si-C pairs $\uparrow$\\
1875 (as expected in 3C-SiC)\\[0.2cm]
1876 0.282 nm: Si-C-C\\[0.2cm]
1877 $\approx$0.35 nm: C-Si-Si
1878 \end{minipage}
1879 }
1880 \begin{minipage}{0.2cm}
1881 \hfill
1882 \end{minipage}
1883 \framebox{
1884 \begin{minipage}[t]{6.0cm}
1885 0.15 nm: C-C pairs $\uparrow$\\
1886 (as expected in graphite/diamond)\\[0.2cm]
1887 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
1888 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
1889 \end{minipage}
1890 }
1891
1892 \vspace{0.1cm}
1893
1894 \begin{center}
1895 {\color{red}Amorphous} SiC-like phase remains\\
1896 Slightly sharper peaks
1897 $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics}
1898 due to temperature\\[0.1cm]
1899 \framebox{
1900 \bf
1901 Continue with higher temperatures and longer time scales
1902 }
1903 \end{center}
1904
1905 \end{slide}
1906
1907 \begin{slide}
1908
1909  {\large\bf
1910   Long time scale simulations at maximum temperature
1911  }
1912
1913 \small
1914
1915 \vspace{0.1cm}
1916  
1917 \underline{Differences}
1918 \begin{itemize}
1919  \item Temperature set to $0.95 \cdot T_{\text{m}}$
1920  \item Cubic insertion volume $\Rightarrow$ spherical insertion volume
1921  \item Amount of C atoms: 6000 $\rightarrow$ 5500
1922        $\Leftrightarrow r_{\text{prec}}=0.3\text{ nm}$
1923  \item Simulation volume: 21 unit cells of c-Si in each direction
1924 \end{itemize}
1925
1926 \footnotesize
1927
1928 \vspace{0.3cm}
1929
1930 \begin{minipage}[t]{4.5cm}
1931 \begin{center}
1932 \underline{Low C concentration, Si-C}
1933 \includegraphics[width=4.5cm]{c_in_si_95_v1_si-c.ps}\\
1934 Sharper peaks!
1935 \end{center}
1936 \end{minipage}
1937 \begin{minipage}[t]{4.5cm}
1938 \begin{center}
1939 \underline{Low C concentration, C-C}
1940 \includegraphics[width=4.5cm]{c_in_si_95_v1_c-c.ps}\\
1941 Sharper peaks!\\
1942 No C agglomeration!
1943 \end{center}
1944 \end{minipage}
1945 \begin{minipage}[t]{4cm}
1946 \begin{center}
1947 \underline{High C concentration}
1948 \includegraphics[width=4.5cm]{c_in_si_95_v2.ps}\\
1949 No significant changes\\
1950 C-Si-Si $\uparrow$\\
1951 C-Si-C $\downarrow$
1952 \end{center}
1953 \end{minipage}
1954
1955 \begin{center}
1956 \framebox{
1957 Long time scales and high temperatures most probably not sufficient enough!
1958 }
1959 \end{center}
1960
1961 \end{slide}
1962
1963 \begin{slide}
1964
1965  {\large\bf
1966   Summary / Conclusion / Outlook
1967  }
1968
1969  \scriptsize
1970
1971 \vspace{0.1cm}
1972
1973 \framebox{
1974 \begin{minipage}{12.9cm}
1975  \underline{Defects}
1976  \begin{itemize}
1977   \item Summary \& conclusion
1978         \begin{itemize}
1979          \item Point defects excellently / fairly well described
1980                by QM / classical potential simulations
1981          \item Identified migration path explaining
1982                diffusion and reorientation experiments
1983          \item Agglomeration of point defects energetically favorable
1984          \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
1985         \end{itemize}
1986   \item In progress
1987         \begin{itemize}
1988          \item Migrations separating C-C bond in \hkl<1 0 0> C-Si dumbbell
1989                interstitial combination
1990          \item Migration: \hkl<1 0 0> C-Si $\rightarrow$
1991                           C$_{\text{sub}}$ \& Si \hkl<1 1 0> interstitial
1992         \end{itemize}
1993   \item Todo
1994         \begin{itemize}
1995          \item Discussions concerning interpretation of QM results (Paderborn)
1996          \item Compare migration barrier of
1997                \hkl<1 1 0> Si and C-Si \hkl<1 0 0> dumbbell
1998          \item Combination: Vacancy \& \hkl<1 1 0> Si self-interstitial \&
1999                             C-Si \hkl<1 0 0> dumbbell (IBS)
2000         \end{itemize}
2001  \end{itemize}
2002 \end{minipage}
2003 }
2004
2005 \vspace{0.2cm}
2006
2007 \framebox{
2008 \begin{minipage}[t]{12.9cm}
2009  \underline{Pecipitation simulations}
2010  \begin{itemize}
2011   \item Summary \& conclusion
2012         \begin{itemize}
2013          \item Low T
2014                $\rightarrow$ C-Si \hkl<1 0 0> dumbbell
2015                dominated structure
2016          \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2017          \item High C concentration
2018                $\rightarrow$ amorphous SiC like phase
2019         \end{itemize}
2020   \item Todo
2021         \begin{itemize}
2022          \item Accelerated method: self-guided MD
2023          \item Activation relaxation technique
2024          \item Constrainted transition path
2025         \end{itemize}
2026  \end{itemize}
2027 \end{minipage}
2028 }
2029
2030  \small
2031
2032 \end{slide}
2033
2034 \begin{slide}
2035
2036  {\large\bf
2037   Acknowledgements
2038  }
2039
2040  \vspace{0.1cm}
2041
2042  \small
2043
2044  Thanks to \ldots
2045
2046  \underline{Augsburg}
2047  \begin{itemize}
2048   \item Prof. B. Stritzker (accepting a simulator at EP \RM{4})
2049   \item Ralf Utermann (EDV)
2050  \end{itemize}
2051  
2052  \underline{Helsinki}
2053  \begin{itemize}
2054   \item Prof. K. Nordlund (MD)
2055  \end{itemize}
2056  
2057  \underline{Munich}
2058  \begin{itemize}
2059   \item Bayerische Forschungsstiftung (financial support)
2060  \end{itemize}
2061  
2062  \underline{Paderborn}
2063  \begin{itemize}
2064   \item Prof. J. Lindner (SiC)
2065   \item Prof. G. Schmidt (DFT + financial support)
2066   \item Dr. E. Rauls (DFT + SiC)
2067   \item Dr. S. Sanna (VASP)
2068  \end{itemize}
2069
2070 \vspace{0.2cm}
2071
2072 \begin{center}
2073 \framebox{
2074 \bf Thank you for your attention!
2075 }
2076 \end{center}
2077
2078 \end{slide}
2079
2080 \end{document}