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1 \pdfoutput=0
2 \documentclass[landscape,semhelv]{seminar}
3
4 \usepackage{verbatim}
5 \usepackage[german]{babel}
6 \usepackage[latin1]{inputenc}
7 \usepackage[T1]{fontenc}
8 \usepackage{amsmath}
9 \usepackage{latexsym}
10 \usepackage{ae}
11
12 \usepackage{calc}               % Simple computations with LaTeX variables
13 \usepackage{caption}            % Improved captions
14 \usepackage{fancybox}           % To have several backgrounds
15
16 \usepackage{fancyhdr}           % Headers and footers definitions
17 \usepackage{fancyvrb}           % Fancy verbatim environments
18 \usepackage{pstricks}           % PSTricks with the standard color package
19
20 \usepackage{pstricks}
21 \usepackage{pst-node}
22
23 %\usepackage{epic}
24 %\usepackage{eepic}
25
26 \usepackage{graphicx}
27 \graphicspath{{../img/}}
28
29 \usepackage[setpagesize=false]{hyperref}
30
31 \usepackage{semcolor}
32 \usepackage{semlayer}           % Seminar overlays
33 \usepackage{slidesec}           % Seminar sections and list of slides
34
35 \input{seminar.bug}             % Official bugs corrections
36 \input{seminar.bg2}             % Unofficial bugs corrections
37
38 \articlemag{1}
39
40 \special{landscape}
41
42 \begin{document}
43
44 \extraslideheight{10in}
45 \slideframe{none}
46
47 \pagestyle{empty}
48
49 % specify width and height
50 \slidewidth 27.7cm 
51 \slideheight 19.1cm 
52
53 % shift it into visual area properly
54 \def\slideleftmargin{3.3cm}
55 \def\slidetopmargin{0.6cm}
56
57 \newcommand{\ham}{\mathcal{H}}
58 \newcommand{\pot}{\mathcal{V}}
59 \newcommand{\foo}{\mathcal{U}}
60 \newcommand{\vir}{\mathcal{W}}
61
62 % itemize level ii
63 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
64
65 % topic
66
67 \begin{slide}
68 \begin{center}
69
70  \vspace{16pt}
71
72  {\LARGE\bf
73   Molecular dynamics simulation study\\
74   of the silicon carbide precipitation process
75  }
76
77  \vspace{24pt}
78
79  \textsc{\small \underline{F. Zirkelbach}$^1$, J. K. N. Lindner$^1$,
80          K. Nordlund$^2$, B. Stritzker$^1$}\\
81
82  \vspace{32pt}
83
84  \begin{minipage}{2.0cm}
85   \begin{center}
86   \includegraphics[height=1.6cm]{uni-logo.eps}
87   \end{center}
88  \end{minipage}
89  \begin{minipage}{8.0cm}
90   \begin{center}
91    {\footnotesize
92     $^1$ Experimentalphysik IV, Institut f"ur Physik,\\
93          Universit"at Augsburg, Universit"atsstr. 1,\\
94          D-86135 Augsburg, Germany
95    }
96   \end{center}
97  \end{minipage}
98  \begin{minipage}{2.3cm}
99   \begin{center}
100   \includegraphics[height=1.5cm]{Lehrstuhl-Logo.eps}
101   \end{center}
102  \end{minipage}
103
104  \vspace{16pt}
105
106  \begin{minipage}{4.0cm}
107   \begin{center}
108   \includegraphics[height=1.6cm]{logo_eng.eps}
109   \end{center}
110  \end{minipage}
111  \begin{minipage}{8.0cm}
112   \begin{center}
113   {\footnotesize
114    $^2$ Accelerator Laboratory, Department of Physical Sciences,\\
115    University of Helsinki, Pietari Kalmink. 2,\\
116    00014 Helsinki, Finland
117   }
118   \end{center}
119  \end{minipage}
120 \end{center}
121 \end{slide}
122
123 % contents
124
125 % no contents for such a short talk!
126
127 % start of contents
128
129 \begin{slide}
130
131  {\large\bf
132   Motivation / Introduction
133  }
134
135  \vspace{16pt}
136
137  Reasons for understanding the SiC precipitation process:
138
139  \begin{itemize}
140   \item 3C-SiC wide band gap semiconductor formation
141   \item Strained Si (no precipitation wanted!)
142  \end{itemize}
143
144  \vspace{16pt}
145
146  Si / 3C-SiC facts:
147
148  \begin{minipage}{8cm}
149  \begin{itemize}
150   \item Unit cell:
151         \begin{itemize}
152          \item {\color{orange}fcc} $+$
153          \item {\color{gray}fcc shifted $1/4$ of volume diagonal}
154         \end{itemize}
155   \item Lattice constants:
156         \[
157         4a_{Si}\approx5a_{SiC}
158         \]
159   \item Silicon density: 
160         \[
161         \frac{n_{SiC}}{n_{Si}}=97,66\,\%
162         \]
163  \end{itemize}
164  \end{minipage}
165  \hspace{8pt}
166  \begin{minipage}{4cm}
167  \includegraphics[width=4cm]{sic_unit_cell.eps}
168  \end{minipage}
169
170 \end{slide}
171
172  \small
173 \begin{slide}
174
175  {\large\bf
176   Motivation / Introduction
177  }
178
179  \small
180  \vspace{6pt}
181
182  Supposed conversion mechanism of heavily carbon doped Si into SiC:
183
184  \vspace{8pt}
185
186  \begin{minipage}{3.8cm}
187  \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
188  \end{minipage}
189  \hspace{0.6cm}
190  \begin{minipage}{3.8cm}
191  \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
192  \end{minipage}
193  \hspace{0.6cm}
194  \begin{minipage}{3.8cm}
195  \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
196  \end{minipage}
197
198  \vspace{8pt}
199
200  \begin{minipage}{3.8cm}
201  Formation of C-Si dumbbells on regular c-Si lattice sites
202  \end{minipage}
203  \hspace{0.6cm}
204  \begin{minipage}{3.8cm}
205  Agglomeration into large clusters (embryos)\\
206  \end{minipage}
207  \hspace{0.6cm}
208  \begin{minipage}{3.8cm}
209  Precipitation of 3C-SiC + Creation of interstitials\\
210  \end{minipage}
211
212  \vspace{12pt}
213
214  Experimentally observed:
215  \begin{itemize}
216   \item Minimal diameter of precipitation: 4 - 5 nm
217   \item Equal orientation of Si and SiC (hkl)-planes
218  \end{itemize}
219
220 \end{slide}
221
222 \begin{slide}
223
224  {\large\bf
225   Simulation details
226  }
227
228  \vspace{12pt}
229
230  MD basics:
231  \begin{itemize}
232   \item Microscopic description of N particle system
233   \item Analytical interaction potential
234   \item Hamilton's equations of motion as propagation rule\\
235         in 6N-dimensional phase space
236   \item Observables obtained by time average
237  \end{itemize}
238
239  \vspace{12pt}
240
241  Application details:
242  \begin{itemize}
243   \item Integrator: Velocity Verlet, timestep: $1\, fs$
244   \item Ensemble: NVT, Berendsen thermostat, $\tau=100.0$
245   \item Potential: Tersoff-like bond order potential\\
246         \[
247         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
248         \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
249         \]
250         \begin{center}
251         {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211}
252         \end{center}
253  \end{itemize}
254
255  \begin{picture}(0,0)(-240,-70)
256   \includegraphics[width=5cm]{tersoff_angle.eps} 
257  \end{picture}
258
259 \end{slide}
260
261 \begin{slide}
262
263  {\large\bf
264   Simulation details
265  }
266
267  \vspace{8pt}
268
269  Interstitial simulations:
270
271  \vspace{8pt}
272
273  \begin{pspicture}(0,0)(7,8)
274   \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
275    \parbox{7cm}{
276    \begin{itemize}
277     \item Initial configuration: $9\times9\times9$ unit cells Si
278     \item Periodic boundary conditions
279     \item $T=0 \, K$
280    \end{itemize}
281   }}}}
282 \rput(3.5,3.5){\rnode{insert}{\psframebox{
283  \parbox{7cm}{
284   Insertion of C / Si atom:
285   \begin{itemize}
286    \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
287    \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
288    \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
289          $\rightarrow$ {\color{magenta}110 dumbbell}
290    \item random positions (critical distance check)
291   \end{itemize}
292   }}}}
293   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
294    \parbox{3.5cm}{
295    Relaxation time: $2\, ps$
296   }}}}
297   \ncline[]{->}{init}{insert}
298   \ncline[]{->}{insert}{cool}
299  \end{pspicture}
300
301  \begin{picture}(0,0)(-210,-45)
302   \includegraphics[width=6cm]{unit_cell.eps}
303  \end{picture}
304
305 \end{slide}
306
307 \begin{slide}
308
309  {\large\bf
310   Results
311  } - Si self-interstitial runs
312
313  \small
314
315  \begin{minipage}[t]{4.3cm}
316  \underline{Tetrahedral}\\
317  $E_f=3.41\, eV$\\
318  \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
319  \end{minipage}
320  \begin{minipage}[t]{4.3cm}
321  \underline{110 dumbbell}\\
322  $E_f=4.39\, eV$\\
323  \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
324  \end{minipage}
325  \begin{minipage}[t]{4.3cm}
326  \underline{Hexagonal} \hspace{4pt}
327  \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
328  $E_f^{\star}\approx4.48\, eV$ (unstable!)\\
329  \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
330  \end{minipage}
331
332  \underline{Random insertion}
333
334  \begin{minipage}{4.3cm}
335  $E_f=3.97\, eV$\\
336  \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
337  \end{minipage}
338  \begin{minipage}{4.3cm}
339  $E_f=3.75\, eV$\\
340  \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
341  \end{minipage}
342  \begin{minipage}{4.3cm}
343  $E_f=3.56\, eV$\\
344  \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
345  \end{minipage}
346
347 \end{slide}
348
349 \begin{slide}
350
351  {\large\bf
352   Results
353  } - Carbon interstitial runs
354
355  \small
356
357  \begin{minipage}[t]{4.3cm}
358  \underline{Tetrahedral}\\
359  $E_f=2.67\, eV$\\
360  \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
361  \end{minipage}
362  \begin{minipage}[t]{4.3cm}
363  \underline{110 dumbbell}\\
364  $E_f=1.76\, eV$\\
365  \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
366  \end{minipage}
367  \begin{minipage}[t]{4.3cm}
368  \underline{Hexagonal} \hspace{4pt}
369  \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
370  $E_f^{\star}\approx5.6\, eV$ (unstable!)\\
371  \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
372  \end{minipage}
373
374  \underline{Random insertion}
375
376  \footnotesize
377
378 \begin{minipage}[t]{3.3cm}
379    $E_f=0.47\, eV$\\
380    \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
381    \begin{picture}(0,0)(-15,-3)
382     001 dumbbell
383    \end{picture}
384 \end{minipage}
385 \begin{minipage}[t]{3.3cm}
386    $E_f=1.62\, eV$\\
387    \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
388 \end{minipage}
389 \begin{minipage}[t]{3.3cm}
390    $E_f=2.39\, eV$\\
391    \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
392 \end{minipage}
393 \begin{minipage}[t]{3.0cm}
394    $E_f=3.41\, eV$\\
395    \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
396 \end{minipage}
397
398 \end{slide}
399
400 \begin{slide}
401
402  {\large\bf
403   Simulation details
404  }
405
406  \small
407
408  \vspace{8pt}
409
410  SiC precipitation simulations:
411
412  \vspace{8pt}
413
414  \begin{pspicture}(0,0)(12,8)
415   % nodes
416   \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
417    \parbox{7cm}{
418    \begin{itemize}
419     \item Initial configuration: $31\times31\times31$ unit cells Si
420     \item Periodic boundary conditions
421     \item $T=450\, ^{\circ}C$
422     \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
423    \end{itemize}
424   }}}}
425   \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
426    \parbox{7cm}{
427    Insertion of $6000$ carbon atoms at constant\\
428    temperature into:
429    \begin{itemize}
430     \item Total simulation volume {\pnode{in1}}
431     \item Volume of minimal SiC precipitation {\pnode{in2}}
432     \item Volume of necessary amount of Si {\pnode{in3}}
433    \end{itemize} 
434   }}}}
435   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
436    \parbox{3.5cm}{
437    Cooling down to $20\, ^{\circ}C$
438   }}}}
439   \ncline[]{->}{init}{insert}
440   \ncline[]{->}{insert}{cool}
441   \psframe[fillstyle=solid,fillcolor=white](7.5,1.8)(13.5,7.8)
442   \psframe[fillstyle=solid,fillcolor=lightgray](9,3.3)(12,6.3)
443   \psframe[fillstyle=solid,fillcolor=gray](9.25,3.55)(11.75,6.05)
444   \rput(7.9,4.8){\pnode{ins1}}
445   \rput(9.22,4.4){\pnode{ins2}}
446   \rput(10.5,4.8){\pnode{ins3}}
447   \ncline[]{->}{in1}{ins1}
448   \ncline[]{->}{in2}{ins2}
449   \ncline[]{->}{in3}{ins3}
450  \end{pspicture}
451
452 \end{slide}
453
454 \begin{slide}
455
456  {\large\bf
457   Very first results of the SiC precipitation runs
458  }
459
460  \footnotesize
461
462  \begin{minipage}[b]{6.9cm}
463   \includegraphics[width=6.3cm]{../plot/sic_prec_energy.ps}
464   \includegraphics[width=6.3cm]{../plot/sic_prec_temp.ps}
465  \end{minipage}
466  \begin{minipage}[b]{5.5cm}
467   \begin{itemize}
468    \item {\color{red} Total simulation volume}
469    \item {\color{green} Volume of minimal SiC precipitation}
470    \item {\color{blue} Volume of necessary amount of Si}
471   \end{itemize}
472   \vspace{40pt}
473   \includegraphics[width=6.3cm]{../plot/foo150.ps}
474  \end{minipage}
475
476 \end{slide}
477
478 \begin{slide}
479
480  {\large\bf
481   Very first results of the SiC precipitation runs
482  }
483
484  \begin{minipage}[t]{6.9cm}
485   \includegraphics[width=6.3cm]{../plot/sic_pc.ps}
486   \includegraphics[width=6.3cm]{../plot/foo_end.ps}
487   \hspace{12pt}
488  \end{minipage}
489  \begin{minipage}[c]{5.5cm}
490   \includegraphics[width=6.0cm]{sic_si-c-n.eps}
491  \end{minipage}
492
493 \end{slide}
494
495 \begin{slide}
496
497  {\large\bf
498   Summary / Outlook
499  }
500
501 \vspace{24pt}
502
503 \begin{itemize}
504  \item Importance of understanding the SiC precipitation mechanism
505  \item Interstitial configurations in silicon using the Albe potential
506  \item Indication of SiC precipitation
507 \end{itemize}
508
509 \vspace{24pt}
510
511 \begin{itemize}
512  \item Displacement and stress calculations
513  \item Refinement of simulation sequence to create 3C-SiC
514  \item Analyzing self-designed Si/SiC interface
515 \end{itemize}
516
517 \end{slide}
518
519 \end{document}
520