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86 Molekulardynamische Untersuchung\\
87 zum SiC-Ausscheidungsvorgang
92 \textsc{F. Zirkelbach}
115 \item SiC-Ausscheidungsvorgang
118 \item Details der MD-Simulation
119 \item Zwischengitter-Konfigurationen
120 \item Simulationen zum Ausscheidungsvorgang
121 \item SiC-Ausscheidungen in Si
123 \item Zusammenfassung und Ausblick
138 Eigenschaften von SiC:
141 \item gro"se Bandl"ucke (3C: 2.39 eV, 4H: 3.28 eV, 6H: 3.03 eV)
142 \item hohe mechanische Stabilit"at
143 \item gute Ladungstr"agermobilit"at
144 \item sp"ate S"attigung der Elektronen-Driftgeschwindigkeit
145 \item chemisch inerte Substanz
146 \item hohe thermische Leitf"ahigkeit und Stabilit"at
147 \item geringer Neutroneneinfangquerschnitt
148 \item strahlungsresistent
154 \item Hochfrequenz-, Hochtemperatur- und Hochleistungsbauelemente
155 \item Optoelektronik (blaue LEDs), Sensoren
156 \item Kandidat f"ur Tr"ager und W"ande in Fusionsreaktoren
157 \item Luft- und Raumfahrtindustrie, Milit"ar
158 \item kohlenfaserverst"arkte SiC-Verbundkeramik
163 \begin{picture}(0,0)(-280,-150)
164 %\includegraphics[width=4cm]{sic_inverter_ise.eps}
167 \begin{picture}(0,0)(-280,-20)
168 %\includegraphics[width=4cm]{cc_sic_brake_dlr.eps}
181 3C-SiC (\foreignlanguage{greek}{b}-SiC) /
182 6H-SiC (\foreignlanguage{greek}{a}-SiC)
184 \item h"ohere Ladungstr"agerbeweglichkeit in \foreignlanguage{greek}{b}-SiC
185 \item Micropipes (Offene Kerne von Schraubenversetzungen) in c-Richtung
186 bei \foreignlanguage{greek}{a}-SiC
187 \item Herstellung gro"sfl"achiger einkristalliner 3C-SiC Filme
195 Genaues Verst"andnis des 3C-SiC-Ausscheidungsvorganges\\
198 signifikanter technologischen Fortschritt in 3C-SiC D"unnschichtherstellung
203 Vermeidung von SiC-Ausscheidungen in
204 $\text{Si}_{\text{1-y}}\text{C}_{\text{y}}$ Legierungen
207 \item Ma"sschneidern der elektronischen Eigenschaften von Si
208 \item gestreckte Heterostrukturen
216 Motivation bzw. SiC-Ausscheidungsvorgang
221 Noch was zur Herstellung rein ...
228 SiC-Ausscheidungsvorgang
233 {\bf Kristallstruktur und Einheitszelle:}
235 \item kristallines Silizium (c-Si): Diamantstruktur\\
236 ${\color{si-yellow}\bullet}$, ${\color{gray}\bullet}$
237 $\leftarrow$ Si-Atome
238 \item kubisches SiC (3C-SiC): Zinkblende-Struktur\\
239 ${\color{si-yellow}\bullet} \leftarrow$ Si-Atome\\
240 ${\color{gray}\bullet} \leftarrow$ C-Atome
243 \begin{minipage}{8cm}
244 {\bf Gitterkonstanten:}
246 4a_{\text{c-Si}}\approx5a_{\text{3C-SiC}}
248 {\bf Siliziumdichten:}
250 \frac{n_{\text{3C-SiC}}}{n_{\text{c-Si}}}=97,66\,\%
253 \begin{minipage}{5cm}
254 \includegraphics[width=5cm]{sic_unit_cell.eps}
262 SiC-Ausscheidungsvorgang
267 Hier die aus experimentellen Untersuchungen heraus vermuteten
268 Ausscheidungsvorgaenge rein.
275 SiC-Ausscheidungsvorgang
282 Vermuteter 3C-SiC-Ausscheidungsvorgang in c-Si:
286 \begin{minipage}{3.8cm}
287 \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
290 \begin{minipage}{3.8cm}
291 \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
294 \begin{minipage}{3.8cm}
295 \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
300 \begin{minipage}{3.8cm}
301 Bildung von C-Si Dumbbells auf regul"aren c-Si Gitterpl"atzen
304 \begin{minipage}{3.8cm}
305 Anh"aufung hin zu gro"sen Clustern (Embryos)\\
308 \begin{minipage}{3.8cm}
309 Ausscheidung von 3C-SiC + Erzeugung von Si-Zwischengitteratomen
314 Aus experimentellen Untersuchungen:
316 \item kritischer Durchmesser einer Ausscheidung: 4 - 5 nm
317 \item gleiche Orientierung der c-Si and 3C-SiC (hkl)-Ebenen
325 Details der MD-Simulation
333 \item Mikroskopische Beschreibung eines N-Teilchensystems
334 \item Analytisches Wechselwirkungspotential
335 \item Numerische Integration der Newtonschen Bewegungsgleichung\\
336 als Propagationsvorschrift im 6N-dimensionalen Phasenraum
337 \item Observablen sind die Zeit- und/oder Ensemblemittelwerte
339 {\bf Details der Simulation:}
341 \item Integration: Velocity Verlet, Zeitschritt: $1\text{ fs}$
342 \item Ensemble: NpT, isothermal-isobares Ensemble
344 \item Berendsen Thermostat:
345 $\tau_{\text{T}}=100\text{ fs}$
346 \item Berendsen Barostat:\\
347 $\tau_{\text{P}}=100\text{ fs}$,
348 $\beta^{-1}=100\text{ GPa}$
350 \item Potential: Tersoff-"ahnliches 'bond order' Potential
353 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
354 \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
358 \begin{picture}(0,0)(-230,-30)
359 \includegraphics[width=5cm]{tersoff_angle.eps}
367 Zwischengitter-Konfigurationen
372 Simulationssequenz:\\
376 \begin{pspicture}(0,0)(7,8)
377 \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
380 \item initiale Konfiguration:\\
381 $9\times9\times9$ Einheitszellen c-Si
382 \item periodische Randbedingungen
383 \item $T=0\text{ K}$, $p=0\text{ bar}$
386 \rput(3.5,3.5){\rnode{insert}{\psframebox{
388 Einf"ugen der C/Si Atome:
390 \item $(0,0,0)$ $\rightarrow$ {\color{red}tetraedrisch}
391 (${\color{red}\triangleleft}$)
392 \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
393 (${\color{green}\triangleright}$)
394 \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
395 $\rightarrow$ {\color{magenta}110 Dumbbell}
396 (${\color{magenta}\Box}$,$\circ$)
397 \item zuf"allige Position (Minimalabstand)
400 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
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408 \begin{picture}(0,0)(-210,-45)
409 \includegraphics[width=6cm]{unit_cell_s.eps}
417 Zwischengitter-Konfigurationen
422 \begin{minipage}[t]{4.3cm}
423 \underline{Tetraedrisch}\\
425 \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
427 \begin{minipage}[t]{4.3cm}
428 \underline{110 Dumbbell}\\
430 \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
432 \begin{minipage}[t]{4.3cm}
433 \underline{Hexagonal} \hspace{4pt}
434 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
435 $E_f^{\star}\approx4.48$ eV (nicht stabil!)\\
436 \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
439 \underline{zuf"allige Positionen}
441 \begin{minipage}{4.3cm}
443 \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
445 \begin{minipage}{4.3cm}
447 \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
449 \begin{minipage}{4.3cm}
451 \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
459 Zwischengitter-Konfigurationen
464 \begin{minipage}[t]{4.3cm}
465 \underline{Tetraedrisch}\\
467 \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
469 \begin{minipage}[t]{4.3cm}
470 \underline{110 Dumbbell}\\
472 \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
474 \begin{minipage}[t]{4.3cm}
475 \underline{Hexagonal} \hspace{4pt}
476 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
477 $E_f^{\star}\approx5.6$ eV (nicht stabil!)\\
478 \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
481 \underline{zuf"allige Positionen}
485 \begin{minipage}[t]{3.3cm}
487 \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
488 \begin{picture}(0,0)(-15,-3)
492 \begin{minipage}[t]{3.3cm}
494 \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
496 \begin{minipage}[t]{3.3cm}
498 \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
500 \begin{minipage}[t]{3.0cm}
502 \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
510 Zwischengitter-Konfigurationen
519 \begin{minipage}{4cm}
522 \item Very often observed
523 \item Most energetically\\
524 favorable configuration
530 [6] G. D. Watkins and K. L. Brower,\\
531 Phys. Rev. Lett. 36 (1976) 1329.
534 \begin{minipage}{8cm}
535 \includegraphics[width=9cm]{100-c-si-db_s.eps}
543 Simulationen zum Ausscheidungsvorgang
550 Simulationssequenz:\\
554 \begin{pspicture}(0,0)(12,8)
556 \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
559 \item initiale Konfiguration:\\
560 $31\times31\times31$ c-Si Einheitszellen
561 \item periodsche Randbedingungen
562 \item $T=450\, ^{\circ}\text{C}$, $p=0\text{ bar}$
563 \item "Aquilibrierung von $E_{\text{kin}}$ and $E_{\text{pot}}$
566 \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
568 Einf"ugen von 6000 C-Atomen bei konstanter Temperatur\\
570 \item gesamte Simulationsvolumen {\pnode{in1}}
571 \item Volumen einer minimal SiC-Ausscheidung {\pnode{in2}}
572 \item Bereich der ben"otigten Si-Atome {\pnode{in3}}
575 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
577 Abk"uhlen auf $20\, ^{\circ}\textrm{C}$
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585 \rput(9.22,4.4){\pnode{ins2}}
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587 \ncline[]{->}{in1}{ins1}
588 \ncline[]{->}{in2}{ins2}
589 \ncline[]{->}{in3}{ins3}
600 } - SiC precipitation runs
603 \includegraphics[width=6.3cm]{pc_si-c_c-c.eps}
604 \includegraphics[width=6.3cm]{pc_si-si.eps}
606 \begin{minipage}[t]{6.3cm}
609 \item C-C peak at 0.15 nm similar to next neighbour distance of graphite
611 $\Rightarrow$ Formation of strong C-C bonds
612 (almost only for high C concentrations)
613 \item Si-C peak at 0.19 nm similar to next neighbour distance in 3C-SiC
614 \item C-C peak at 0.31 nm equals C-C distance in 3C-SiC\\
615 (due to concatenated, differently oriented
616 <100> dumbbell interstitials)
617 \item Si-Si shows non-zero g(r) values around 0.31 nm like in 3C-SiC\\
618 and a decrease at regular distances\\
620 interval of enhanced g(r) corresponds to C-C peak width)
623 \begin{minipage}[t]{6.3cm}
626 \item Low C concentration (i.e. $V_1$):
627 The <100> dumbbell configuration
629 \item is identified to stretch the Si-Si next neighbour distance
631 \item is identified to contribute to the Si-C peak at 0.19 nm
632 \item explains further C-Si peaks (dashed vertical lines)
634 $\Rightarrow$ C atoms are first elements arranged at distances
635 expected for 3C-SiC\\
636 $\Rightarrow$ C atoms pull the Si atoms into the right
637 configuration at a later stage
638 \item High C concentration (i.e. $V_2$ and $V_3$):
640 \item High amount of damage introduced into the system
641 \item Short range order observed but almost no long range order
643 $\Rightarrow$ Start of amorphous SiC-like phase formation\\
644 $\Rightarrow$ Higher temperatures required for proper SiC formation
653 Very first results of the SiC precipitation runs
656 \begin{minipage}[t]{6.9cm}
657 \includegraphics[width=6.3cm]{../plot/sic_pc.ps}
658 \includegraphics[width=6.3cm]{../plot/foo_end.ps}
661 \begin{minipage}[c]{5.5cm}
662 \includegraphics[width=6.0cm]{sic_si-c-n.eps}
676 \item Importance of understanding the SiC precipitation mechanism
677 \item Interstitial configurations in silicon using the Albe potential
678 \item Indication of SiC precipitation
684 \item Displacement and stress calculations
685 \item Refinement of simulation sequence to create 3C-SiC
686 \item Analyzing self-designed Si/SiC interface