2 \documentclass[landscape,semhelv]{seminar}
5 \usepackage[german]{babel}
6 \usepackage[latin1]{inputenc}
7 \usepackage[T1]{fontenc}
12 \usepackage{calc} % Simple computations with LaTeX variables
13 \usepackage{caption} % Improved captions
14 \usepackage{fancybox} % To have several backgrounds
16 \usepackage{fancyhdr} % Headers and footers definitions
17 \usepackage{fancyvrb} % Fancy verbatim environments
18 \usepackage{pstricks} % PSTricks with the standard color package
27 \graphicspath{{../img/}}
29 \usepackage[setpagesize=false]{hyperref}
32 \usepackage{semlayer} % Seminar overlays
33 \usepackage{slidesec} % Seminar sections and list of slides
35 \input{seminar.bug} % Official bugs corrections
36 \input{seminar.bg2} % Unofficial bugs corrections
43 %\usepackage{cmbright}
44 %\renewcommand{\familydefault}{\sfdefault}
45 %\usepackage{mathptmx}
49 \extraslideheight{10in}
54 % specify width and height
58 % shift it into visual area properly
59 \def\slideleftmargin{3.3cm}
60 \def\slidetopmargin{0.6cm}
62 \newcommand{\ham}{\mathcal{H}}
63 \newcommand{\pot}{\mathcal{V}}
64 \newcommand{\foo}{\mathcal{U}}
65 \newcommand{\vir}{\mathcal{W}}
68 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
71 \newrgbcolor{si-yellow}{.6 .6 0}
72 \newrgbcolor{hb}{0.75 0.77 0.89}
73 \newrgbcolor{lbb}{0.75 0.8 0.88}
74 \newrgbcolor{lachs}{1.0 .93 .81}
84 Molekulardynamische Untersuchung\\
85 zum SiC-Ausscheidungsvorgang
90 \textsc{F. Zirkelbach}
113 \item SiC-Ausscheidungsvorgang
116 \item Details der MD-Simulation
117 \item Zwischengitter-Konfigurationen
118 \item Simulationen zum Ausscheidungsvorgang
119 \item SiC-Ausscheidungen in Si
121 \item Zusammenfassung und Ausblick
136 Eigenschaften von SiC:
139 \item gro"se Bandl"ucke (3C: 2.39 eV, 4H: 3.28 eV, 6H: 3.03 eV)
140 \item hohe mechanische Stabilit"at
141 \item gute Ladungstr"agermobilit"at
142 \item sp"ate S"attigung der Elektronen-Driftgeschwindigkeit
143 \item chemisch inerte Substanz
144 \item hohe thermische Leitf"ahigkeit und Stabilit"at
145 \item geringer Neutroneneinfangquerschnitt
146 \item strahlungsresistent
152 \item Hochfrequenz-, Hochtemperatur und Hochleistungsbauelemente
154 \item Kandidat f"ur Tr"ager und W"ande in Fusionsreaktoren
155 \item Luft- und Raumfahrtindistrie, Milit"ar
156 \item kohlenfaserverst"arkte SiC-Verbundkeramik
161 \begin{picture}(0,0)(-275,-150)
162 \includegraphics[width=4cm]{sic_inverter_ise.eps}
165 \begin{picture}(0,0)(-275,-20)
166 \includegraphics[width=4cm]{cc_sic_brake_dlr.eps}
179 However, in order to become economically viable, several critical materials and processing issues still need to be solved. The most serious issue is the immature state of the crystal growth technology, where increases in wafer size and quality are urgently needed.
183 Modifikation der Bandl"ucke und Spannungen in Heterostrukturen
185 Kein SiC-Ausscheidungsvorgang erw"unscht!
188 [1] J. H. Edgar, J. Mater. Res. 7 (1992) 235.}\\
190 [2] J. W. Strane, S. R. Lee, H. J. Stein, S. T. Picraux,
191 J. K. Watanabe, J. W. Mayer, J. Appl. Phys. 79 (1996) 637.}
201 Crystalline silicon and cubic silicon carbide
206 {\bf Lattice types and unit cells:}
208 \item Crystalline silicon (c-Si) has diamond structure\\
209 $\Rightarrow {\color{si-yellow}\bullet}$ and
210 ${\color{gray}\bullet}$ are Si atoms
211 \item Cubic silicon carbide (3C-SiC) has zincblende structure\\
212 $\Rightarrow {\color{si-yellow}\bullet}$ are Si atoms,
213 ${\color{gray}\bullet}$ are C atoms
216 \begin{minipage}{8cm}
217 {\bf Lattice constants:}
219 4a_{\text{c-Si}}\approx5a_{\text{3C-SiC}}
221 {\bf Silicon density:}
223 \frac{n_{\text{3C-SiC}}}{n_{\text{c-Si}}}=97,66\,\%
226 \begin{minipage}{5cm}
227 \includegraphics[width=5cm]{sic_unit_cell.eps}
236 Supposed Si to 3C-SiC conversion
242 Supposed conversion mechanism of heavily carbon doped Si into SiC:
246 \begin{minipage}{3.8cm}
247 \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
250 \begin{minipage}{3.8cm}
251 \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
254 \begin{minipage}{3.8cm}
255 \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
260 \begin{minipage}{3.8cm}
261 Formation of C-Si dumbbells on regular c-Si lattice sites
264 \begin{minipage}{3.8cm}
265 Agglomeration into large clusters (embryos)\\
268 \begin{minipage}{3.8cm}
269 Precipitation of 3C-SiC + Creation of interstitials\\
274 \begin{minipage}{7cm}
275 Experimentally observed [3]:
277 \item Minimal diameter of precipitation: 4 - 5 nm
278 \item Equal orientation of Si and SiC (hkl)-planes
281 \begin{minipage}{6cm}
284 {\tiny [3] J. K. N. Lindner, Appl. Phys. A 77 (2003) 27.}
299 \item Microscopic description of N particle system
300 \item Analytical interaction potential
301 \item Hamilton's equations of motion as propagation rule\\
302 in 6N-dimensional phase space
303 \item Observables obtained by time or ensemble averages
305 {\bf Application details:}
307 \item Integrator: Velocity Verlet, timestep: $1\text{ fs}$
308 \item Ensemble: isothermal-isobaric NPT [4]
310 \item Berendsen thermostat:
311 $\tau_{\text{T}}=100\text{ fs}$
312 \item Brendsen barostat:\\
313 $\tau_{\text{P}}=100\text{ fs}$,
314 $\beta^{-1}=100\text{ GPa}$
316 \item Potential: Tersoff-like bond order potential [5]
318 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
319 \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
323 [4] L. Verlet, Phys. Rev. 159 (1967) 98.}\\
325 [5] P. Erhart and K. Albe, Phys. Rev. B 71 (2005) 35211.}
327 \begin{picture}(0,0)(-240,-70)
328 \includegraphics[width=5cm]{tersoff_angle.eps}
341 Interstitial configurations:
345 \begin{pspicture}(0,0)(7,8)
346 \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
349 \item Initial configuration: $9\times9\times9$ unit cells Si
350 \item Periodic boundary conditions
351 \item $T=0\text{ K}$, $p=0\text{ bar}$
354 \rput(3.5,3.5){\rnode{insert}{\psframebox{
356 Insertion of C / Si atom:
358 \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
359 (${\color{red}\triangleleft}$)
360 \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
361 (${\color{green}\triangleright}$)
362 \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
363 $\rightarrow$ {\color{magenta}110 dumbbell}
364 (${\color{magenta}\Box}$,$\circ$)
365 \item random positions (critical distance check)
368 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
370 Relaxation time: $2\, ps$
372 \ncline[]{->}{init}{insert}
373 \ncline[]{->}{insert}{cool}
376 \begin{picture}(0,0)(-210,-45)
377 \includegraphics[width=6cm]{unit_cell_s.eps}
386 } - Si self-interstitial runs
390 \begin{minipage}[t]{4.3cm}
391 \underline{Tetrahedral}\\
393 \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
395 \begin{minipage}[t]{4.3cm}
396 \underline{110 dumbbell}\\
398 \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
400 \begin{minipage}[t]{4.3cm}
401 \underline{Hexagonal} \hspace{4pt}
402 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
403 $E_f^{\star}\approx4.48$ eV (unstable!)\\
404 \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
407 \underline{Random insertion}
409 \begin{minipage}{4.3cm}
411 \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
413 \begin{minipage}{4.3cm}
415 \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
417 \begin{minipage}{4.3cm}
419 \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
428 } - Carbon interstitial runs
432 \begin{minipage}[t]{4.3cm}
433 \underline{Tetrahedral}\\
435 \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
437 \begin{minipage}[t]{4.3cm}
438 \underline{110 dumbbell}\\
440 \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
442 \begin{minipage}[t]{4.3cm}
443 \underline{Hexagonal} \hspace{4pt}
444 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
445 $E_f^{\star}\approx5.6$ eV (unstable!)\\
446 \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
449 \underline{Random insertion}
453 \begin{minipage}[t]{3.3cm}
455 \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
456 \begin{picture}(0,0)(-15,-3)
460 \begin{minipage}[t]{3.3cm}
462 \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
464 \begin{minipage}[t]{3.3cm}
466 \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
468 \begin{minipage}[t]{3.0cm}
470 \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
479 } - <100> dumbbell configuration
485 \begin{minipage}{4cm}
488 \item Very often observed
489 \item Most energetically\\
490 favorable configuration
496 [6] G. D. Watkins and K. L. Brower,\\
497 Phys. Rev. Lett. 36 (1976) 1329.
500 \begin{minipage}{8cm}
501 \includegraphics[width=9cm]{100-c-si-db_s.eps}
516 SiC precipitation simulations:
520 \begin{pspicture}(0,0)(12,8)
522 \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
525 \item Initial configuration: $31\times31\times31$ unit cells Si
526 \item Periodic boundary conditions
527 \item $T=450\, ^{\circ}\text{C}$, $p=0\text{ bar}$
528 \item Equilibration of $E_{kin}$ and $E_{pot}$
531 \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
533 Insertion of 6000 carbon atoms at constant\\
536 \item Total simulation volume {\pnode{in1}}
537 \item Volume of minimal SiC precipitation {\pnode{in2}}
538 \item Volume of necessary amount of Si {\pnode{in3}}
541 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
543 Cooling down to $20\, ^{\circ}C$
545 \ncline[]{->}{init}{insert}
546 \ncline[]{->}{insert}{cool}
547 \psframe[fillstyle=solid,fillcolor=white](7.5,1.8)(13.5,7.8)
548 \psframe[fillstyle=solid,fillcolor=lightgray](9,3.3)(12,6.3)
549 \psframe[fillstyle=solid,fillcolor=gray](9.25,3.55)(11.75,6.05)
550 \rput(7.9,4.8){\pnode{ins1}}
551 \rput(9.22,4.4){\pnode{ins2}}
552 \rput(10.5,4.8){\pnode{ins3}}
553 \ncline[]{->}{in1}{ins1}
554 \ncline[]{->}{in2}{ins2}
555 \ncline[]{->}{in3}{ins3}
564 } - SiC precipitation runs
567 \includegraphics[width=6.3cm]{pc_si-c_c-c.eps}
568 \includegraphics[width=6.3cm]{pc_si-si.eps}
570 \begin{minipage}[t]{6.3cm}
573 \item C-C peak at 0.15 nm similar to next neighbour distance of graphite
575 $\Rightarrow$ Formation of strong C-C bonds
576 (almost only for high C concentrations)
577 \item Si-C peak at 0.19 nm similar to next neighbour distance in 3C-SiC
578 \item C-C peak at 0.31 nm equals C-C distance in 3C-SiC\\
579 (due to concatenated, differently oriented
580 <100> dumbbell interstitials)
581 \item Si-Si shows non-zero g(r) values around 0.31 nm like in 3C-SiC\\
582 and a decrease at regular distances\\
584 interval of enhanced g(r) corresponds to C-C peak width)
587 \begin{minipage}[t]{6.3cm}
590 \item Low C concentration (i.e. $V_1$):
591 The <100> dumbbell configuration
593 \item is identified to stretch the Si-Si next neighbour distance
595 \item is identified to contribute to the Si-C peak at 0.19 nm
596 \item explains further C-Si peaks (dashed vertical lines)
598 $\Rightarrow$ C atoms are first elements arranged at distances
599 expected for 3C-SiC\\
600 $\Rightarrow$ C atoms pull the Si atoms into the right
601 configuration at a later stage
602 \item High C concentration (i.e. $V_2$ and $V_3$):
604 \item High amount of damage introduced into the system
605 \item Short range order observed but almost no long range order
607 $\Rightarrow$ Start of amorphous SiC-like phase formation\\
608 $\Rightarrow$ Higher temperatures required for proper SiC formation
617 Very first results of the SiC precipitation runs
620 \begin{minipage}[t]{6.9cm}
621 \includegraphics[width=6.3cm]{../plot/sic_pc.ps}
622 \includegraphics[width=6.3cm]{../plot/foo_end.ps}
625 \begin{minipage}[c]{5.5cm}
626 \includegraphics[width=6.0cm]{sic_si-c-n.eps}
640 \item Importance of understanding the SiC precipitation mechanism
641 \item Interstitial configurations in silicon using the Albe potential
642 \item Indication of SiC precipitation
648 \item Displacement and stress calculations
649 \item Refinement of simulation sequence to create 3C-SiC
650 \item Analyzing self-designed Si/SiC interface