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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}
263 SiC-Ausscheidungsvorgang
269 Vermuteter SiC-Ausscheidungsvorgang in Si:
273 \begin{minipage}{3.8cm}
274 \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
277 \begin{minipage}{3.8cm}
278 \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
281 \begin{minipage}{3.8cm}
282 \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
287 \begin{minipage}{3.8cm}
288 Bildung von C-Si Dumbbells auf regul"aren c-Si Gitterpl"atzen
291 \begin{minipage}{3.8cm}
292 Anh"aufung hin zu gro"sen Clustern (Embryos)\\
295 \begin{minipage}{3.8cm}
296 Ausscheidung von 3C-SiC + Erzeugung von Si-Zwischengitteratomen\\
301 \begin{minipage}{7cm}
302 Experimentally observed [3]:
304 \item Minimal diameter of precipitation: 4 - 5 nm
305 \item Equal orientation of Si and SiC (hkl)-planes
308 \begin{minipage}{6cm}
311 {\tiny [3] J. K. N. Lindner, Appl. Phys. A 77 (2003) 27.}
328 \item Microscopic description of N particle system
329 \item Analytical interaction potential
330 \item Hamilton's equations of motion as propagation rule\\
331 in 6N-dimensional phase space
332 \item Observables obtained by time or ensemble averages
334 {\bf Application details:}
336 \item Integrator: Velocity Verlet, timestep: $1\text{ fs}$
337 \item Ensemble: isothermal-isobaric NPT [4]
339 \item Berendsen thermostat:
340 $\tau_{\text{T}}=100\text{ fs}$
341 \item Brendsen barostat:\\
342 $\tau_{\text{P}}=100\text{ fs}$,
343 $\beta^{-1}=100\text{ GPa}$
345 \item Potential: Tersoff-like bond order potential [5]
347 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
348 \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
352 [4] L. Verlet, Phys. Rev. 159 (1967) 98.}\\
354 [5] P. Erhart and K. Albe, Phys. Rev. B 71 (2005) 35211.}
356 \begin{picture}(0,0)(-240,-70)
357 \includegraphics[width=5cm]{tersoff_angle.eps}
370 Interstitial configurations:
374 \begin{pspicture}(0,0)(7,8)
375 \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
378 \item Initial configuration: $9\times9\times9$ unit cells Si
379 \item Periodic boundary conditions
380 \item $T=0\text{ K}$, $p=0\text{ bar}$
383 \rput(3.5,3.5){\rnode{insert}{\psframebox{
385 Insertion of C / Si atom:
387 \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
388 (${\color{red}\triangleleft}$)
389 \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
390 (${\color{green}\triangleright}$)
391 \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
392 $\rightarrow$ {\color{magenta}110 dumbbell}
393 (${\color{magenta}\Box}$,$\circ$)
394 \item random positions (critical distance check)
397 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
399 Relaxation time: $2\, ps$
401 \ncline[]{->}{init}{insert}
402 \ncline[]{->}{insert}{cool}
405 \begin{picture}(0,0)(-210,-45)
406 \includegraphics[width=6cm]{unit_cell_s.eps}
415 } - Si self-interstitial runs
419 \begin{minipage}[t]{4.3cm}
420 \underline{Tetrahedral}\\
422 \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
424 \begin{minipage}[t]{4.3cm}
425 \underline{110 dumbbell}\\
427 \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
429 \begin{minipage}[t]{4.3cm}
430 \underline{Hexagonal} \hspace{4pt}
431 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
432 $E_f^{\star}\approx4.48$ eV (unstable!)\\
433 \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
436 \underline{Random insertion}
438 \begin{minipage}{4.3cm}
440 \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
442 \begin{minipage}{4.3cm}
444 \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
446 \begin{minipage}{4.3cm}
448 \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
457 } - Carbon interstitial runs
461 \begin{minipage}[t]{4.3cm}
462 \underline{Tetrahedral}\\
464 \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
466 \begin{minipage}[t]{4.3cm}
467 \underline{110 dumbbell}\\
469 \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
471 \begin{minipage}[t]{4.3cm}
472 \underline{Hexagonal} \hspace{4pt}
473 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
474 $E_f^{\star}\approx5.6$ eV (unstable!)\\
475 \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
478 \underline{Random insertion}
482 \begin{minipage}[t]{3.3cm}
484 \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
485 \begin{picture}(0,0)(-15,-3)
489 \begin{minipage}[t]{3.3cm}
491 \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
493 \begin{minipage}[t]{3.3cm}
495 \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
497 \begin{minipage}[t]{3.0cm}
499 \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
508 } - <100> dumbbell configuration
514 \begin{minipage}{4cm}
517 \item Very often observed
518 \item Most energetically\\
519 favorable configuration
525 [6] G. D. Watkins and K. L. Brower,\\
526 Phys. Rev. Lett. 36 (1976) 1329.
529 \begin{minipage}{8cm}
530 \includegraphics[width=9cm]{100-c-si-db_s.eps}
545 SiC precipitation simulations:
549 \begin{pspicture}(0,0)(12,8)
551 \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
554 \item Initial configuration: $31\times31\times31$ unit cells Si
555 \item Periodic boundary conditions
556 \item $T=450\, ^{\circ}\text{C}$, $p=0\text{ bar}$
557 \item Equilibration of $E_{kin}$ and $E_{pot}$
560 \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
562 Insertion of 6000 carbon atoms at constant\\
565 \item Total simulation volume {\pnode{in1}}
566 \item Volume of minimal SiC precipitation {\pnode{in2}}
567 \item Volume of necessary amount of Si {\pnode{in3}}
570 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
572 Cooling down to $20\, ^{\circ}C$
574 \ncline[]{->}{init}{insert}
575 \ncline[]{->}{insert}{cool}
576 \psframe[fillstyle=solid,fillcolor=white](7.5,1.8)(13.5,7.8)
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578 \psframe[fillstyle=solid,fillcolor=gray](9.25,3.55)(11.75,6.05)
579 \rput(7.9,4.8){\pnode{ins1}}
580 \rput(9.22,4.4){\pnode{ins2}}
581 \rput(10.5,4.8){\pnode{ins3}}
582 \ncline[]{->}{in1}{ins1}
583 \ncline[]{->}{in2}{ins2}
584 \ncline[]{->}{in3}{ins3}
593 } - SiC precipitation runs
596 \includegraphics[width=6.3cm]{pc_si-c_c-c.eps}
597 \includegraphics[width=6.3cm]{pc_si-si.eps}
599 \begin{minipage}[t]{6.3cm}
602 \item C-C peak at 0.15 nm similar to next neighbour distance of graphite
604 $\Rightarrow$ Formation of strong C-C bonds
605 (almost only for high C concentrations)
606 \item Si-C peak at 0.19 nm similar to next neighbour distance in 3C-SiC
607 \item C-C peak at 0.31 nm equals C-C distance in 3C-SiC\\
608 (due to concatenated, differently oriented
609 <100> dumbbell interstitials)
610 \item Si-Si shows non-zero g(r) values around 0.31 nm like in 3C-SiC\\
611 and a decrease at regular distances\\
613 interval of enhanced g(r) corresponds to C-C peak width)
616 \begin{minipage}[t]{6.3cm}
619 \item Low C concentration (i.e. $V_1$):
620 The <100> dumbbell configuration
622 \item is identified to stretch the Si-Si next neighbour distance
624 \item is identified to contribute to the Si-C peak at 0.19 nm
625 \item explains further C-Si peaks (dashed vertical lines)
627 $\Rightarrow$ C atoms are first elements arranged at distances
628 expected for 3C-SiC\\
629 $\Rightarrow$ C atoms pull the Si atoms into the right
630 configuration at a later stage
631 \item High C concentration (i.e. $V_2$ and $V_3$):
633 \item High amount of damage introduced into the system
634 \item Short range order observed but almost no long range order
636 $\Rightarrow$ Start of amorphous SiC-like phase formation\\
637 $\Rightarrow$ Higher temperatures required for proper SiC formation
646 Very first results of the SiC precipitation runs
649 \begin{minipage}[t]{6.9cm}
650 \includegraphics[width=6.3cm]{../plot/sic_pc.ps}
651 \includegraphics[width=6.3cm]{../plot/foo_end.ps}
654 \begin{minipage}[c]{5.5cm}
655 \includegraphics[width=6.0cm]{sic_si-c-n.eps}
669 \item Importance of understanding the SiC precipitation mechanism
670 \item Interstitial configurations in silicon using the Albe potential
671 \item Indication of SiC precipitation
677 \item Displacement and stress calculations
678 \item Refinement of simulation sequence to create 3C-SiC
679 \item Analyzing self-designed Si/SiC interface