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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)(-278,-150)
164 %\includegraphics[width=4cm]{sic_inverter_ise.eps}
167 \begin{picture}(0,0)(-278,-20)
168 %\includegraphics[width=4cm]{cc_sic_brake_dlr.eps}
179 3C-SiC (\foreignlanguage{greek}{b}-SiC) /
180 6H-SiC (\foreignlanguage{greek}{a}-SiC)
182 \item h"ohere Ladungstr"agerbeweglichkeit in \foreignlanguage{greek}{b}-SiC
183 \item Micropipes (Offene Kerne von Schraubenversetzungen) in c-Richtung
184 bei \foreignlanguage{greek}{a}-SiC
185 \item Herstellung gro"sfl"achiger einkristalliner 3C-SiC Filme
191 Einsicht in den Mechanismus des 3C-SiC-Ausscheidungsvorganges\\
194 signifikanter technologischen Fortschritt in 3C-SiC D"unnschichtherstellung
199 Vermeidung von SiC-Ausscheidungen
202 \item Ma"sschneidern der Bandl"ucke
203 \item gestreckte Heterostrukturen
211 Crystalline silicon and cubic silicon carbide
216 {\bf Lattice types and unit cells:}
218 \item Crystalline silicon (c-Si) has diamond structure\\
219 $\Rightarrow {\color{si-yellow}\bullet}$ and
220 ${\color{gray}\bullet}$ are Si atoms
221 \item Cubic silicon carbide (3C-SiC) has zincblende structure\\
222 $\Rightarrow {\color{si-yellow}\bullet}$ are Si atoms,
223 ${\color{gray}\bullet}$ are C atoms
226 \begin{minipage}{8cm}
227 {\bf Lattice constants:}
229 4a_{\text{c-Si}}\approx5a_{\text{3C-SiC}}
231 {\bf Silicon density:}
233 \frac{n_{\text{3C-SiC}}}{n_{\text{c-Si}}}=97,66\,\%
236 \begin{minipage}{5cm}
237 \includegraphics[width=5cm]{sic_unit_cell.eps}
248 Supposed Si to 3C-SiC conversion
254 Supposed conversion mechanism of heavily carbon doped Si into SiC:
258 \begin{minipage}{3.8cm}
259 \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
262 \begin{minipage}{3.8cm}
263 \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
266 \begin{minipage}{3.8cm}
267 \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
272 \begin{minipage}{3.8cm}
273 Formation of C-Si dumbbells on regular c-Si lattice sites
276 \begin{minipage}{3.8cm}
277 Agglomeration into large clusters (embryos)\\
280 \begin{minipage}{3.8cm}
281 Precipitation of 3C-SiC + Creation of interstitials\\
286 \begin{minipage}{7cm}
287 Experimentally observed [3]:
289 \item Minimal diameter of precipitation: 4 - 5 nm
290 \item Equal orientation of Si and SiC (hkl)-planes
293 \begin{minipage}{6cm}
296 {\tiny [3] J. K. N. Lindner, Appl. Phys. A 77 (2003) 27.}
311 \item Microscopic description of N particle system
312 \item Analytical interaction potential
313 \item Hamilton's equations of motion as propagation rule\\
314 in 6N-dimensional phase space
315 \item Observables obtained by time or ensemble averages
317 {\bf Application details:}
319 \item Integrator: Velocity Verlet, timestep: $1\text{ fs}$
320 \item Ensemble: isothermal-isobaric NPT [4]
322 \item Berendsen thermostat:
323 $\tau_{\text{T}}=100\text{ fs}$
324 \item Brendsen barostat:\\
325 $\tau_{\text{P}}=100\text{ fs}$,
326 $\beta^{-1}=100\text{ GPa}$
328 \item Potential: Tersoff-like bond order potential [5]
330 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
331 \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
335 [4] L. Verlet, Phys. Rev. 159 (1967) 98.}\\
337 [5] P. Erhart and K. Albe, Phys. Rev. B 71 (2005) 35211.}
339 \begin{picture}(0,0)(-240,-70)
340 \includegraphics[width=5cm]{tersoff_angle.eps}
353 Interstitial configurations:
357 \begin{pspicture}(0,0)(7,8)
358 \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
361 \item Initial configuration: $9\times9\times9$ unit cells Si
362 \item Periodic boundary conditions
363 \item $T=0\text{ K}$, $p=0\text{ bar}$
366 \rput(3.5,3.5){\rnode{insert}{\psframebox{
368 Insertion of C / Si atom:
370 \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
371 (${\color{red}\triangleleft}$)
372 \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
373 (${\color{green}\triangleright}$)
374 \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
375 $\rightarrow$ {\color{magenta}110 dumbbell}
376 (${\color{magenta}\Box}$,$\circ$)
377 \item random positions (critical distance check)
380 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
382 Relaxation time: $2\, ps$
384 \ncline[]{->}{init}{insert}
385 \ncline[]{->}{insert}{cool}
388 \begin{picture}(0,0)(-210,-45)
389 \includegraphics[width=6cm]{unit_cell_s.eps}
398 } - Si self-interstitial runs
402 \begin{minipage}[t]{4.3cm}
403 \underline{Tetrahedral}\\
405 \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
407 \begin{minipage}[t]{4.3cm}
408 \underline{110 dumbbell}\\
410 \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
412 \begin{minipage}[t]{4.3cm}
413 \underline{Hexagonal} \hspace{4pt}
414 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
415 $E_f^{\star}\approx4.48$ eV (unstable!)\\
416 \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
419 \underline{Random insertion}
421 \begin{minipage}{4.3cm}
423 \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
425 \begin{minipage}{4.3cm}
427 \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
429 \begin{minipage}{4.3cm}
431 \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
440 } - Carbon interstitial runs
444 \begin{minipage}[t]{4.3cm}
445 \underline{Tetrahedral}\\
447 \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
449 \begin{minipage}[t]{4.3cm}
450 \underline{110 dumbbell}\\
452 \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
454 \begin{minipage}[t]{4.3cm}
455 \underline{Hexagonal} \hspace{4pt}
456 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
457 $E_f^{\star}\approx5.6$ eV (unstable!)\\
458 \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
461 \underline{Random insertion}
465 \begin{minipage}[t]{3.3cm}
467 \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
468 \begin{picture}(0,0)(-15,-3)
472 \begin{minipage}[t]{3.3cm}
474 \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
476 \begin{minipage}[t]{3.3cm}
478 \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
480 \begin{minipage}[t]{3.0cm}
482 \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
491 } - <100> dumbbell configuration
497 \begin{minipage}{4cm}
500 \item Very often observed
501 \item Most energetically\\
502 favorable configuration
508 [6] G. D. Watkins and K. L. Brower,\\
509 Phys. Rev. Lett. 36 (1976) 1329.
512 \begin{minipage}{8cm}
513 \includegraphics[width=9cm]{100-c-si-db_s.eps}
528 SiC precipitation simulations:
532 \begin{pspicture}(0,0)(12,8)
534 \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
537 \item Initial configuration: $31\times31\times31$ unit cells Si
538 \item Periodic boundary conditions
539 \item $T=450\, ^{\circ}\text{C}$, $p=0\text{ bar}$
540 \item Equilibration of $E_{kin}$ and $E_{pot}$
543 \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
545 Insertion of 6000 carbon atoms at constant\\
548 \item Total simulation volume {\pnode{in1}}
549 \item Volume of minimal SiC precipitation {\pnode{in2}}
550 \item Volume of necessary amount of Si {\pnode{in3}}
553 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
555 Cooling down to $20\, ^{\circ}C$
557 \ncline[]{->}{init}{insert}
558 \ncline[]{->}{insert}{cool}
559 \psframe[fillstyle=solid,fillcolor=white](7.5,1.8)(13.5,7.8)
560 \psframe[fillstyle=solid,fillcolor=lightgray](9,3.3)(12,6.3)
561 \psframe[fillstyle=solid,fillcolor=gray](9.25,3.55)(11.75,6.05)
562 \rput(7.9,4.8){\pnode{ins1}}
563 \rput(9.22,4.4){\pnode{ins2}}
564 \rput(10.5,4.8){\pnode{ins3}}
565 \ncline[]{->}{in1}{ins1}
566 \ncline[]{->}{in2}{ins2}
567 \ncline[]{->}{in3}{ins3}
576 } - SiC precipitation runs
579 \includegraphics[width=6.3cm]{pc_si-c_c-c.eps}
580 \includegraphics[width=6.3cm]{pc_si-si.eps}
582 \begin{minipage}[t]{6.3cm}
585 \item C-C peak at 0.15 nm similar to next neighbour distance of graphite
587 $\Rightarrow$ Formation of strong C-C bonds
588 (almost only for high C concentrations)
589 \item Si-C peak at 0.19 nm similar to next neighbour distance in 3C-SiC
590 \item C-C peak at 0.31 nm equals C-C distance in 3C-SiC\\
591 (due to concatenated, differently oriented
592 <100> dumbbell interstitials)
593 \item Si-Si shows non-zero g(r) values around 0.31 nm like in 3C-SiC\\
594 and a decrease at regular distances\\
596 interval of enhanced g(r) corresponds to C-C peak width)
599 \begin{minipage}[t]{6.3cm}
602 \item Low C concentration (i.e. $V_1$):
603 The <100> dumbbell configuration
605 \item is identified to stretch the Si-Si next neighbour distance
607 \item is identified to contribute to the Si-C peak at 0.19 nm
608 \item explains further C-Si peaks (dashed vertical lines)
610 $\Rightarrow$ C atoms are first elements arranged at distances
611 expected for 3C-SiC\\
612 $\Rightarrow$ C atoms pull the Si atoms into the right
613 configuration at a later stage
614 \item High C concentration (i.e. $V_2$ and $V_3$):
616 \item High amount of damage introduced into the system
617 \item Short range order observed but almost no long range order
619 $\Rightarrow$ Start of amorphous SiC-like phase formation\\
620 $\Rightarrow$ Higher temperatures required for proper SiC formation
629 Very first results of the SiC precipitation runs
632 \begin{minipage}[t]{6.9cm}
633 \includegraphics[width=6.3cm]{../plot/sic_pc.ps}
634 \includegraphics[width=6.3cm]{../plot/foo_end.ps}
637 \begin{minipage}[c]{5.5cm}
638 \includegraphics[width=6.0cm]{sic_si-c-n.eps}
652 \item Importance of understanding the SiC precipitation mechanism
653 \item Interstitial configurations in silicon using the Albe potential
654 \item Indication of SiC precipitation
660 \item Displacement and stress calculations
661 \item Refinement of simulation sequence to create 3C-SiC
662 \item Analyzing self-designed Si/SiC interface