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73 Molecular dynamics simulation study\\
74 of the silicon carbide precipitation process
79 \textsc{\small \underline{F. Zirkelbach}$^1$, J. K. N. Lindner$^1$,
80 K. Nordlund$^2$, B. Stritzker$^1$}\\
84 \begin{minipage}{2.0cm}
86 \includegraphics[height=1.6cm]{uni-logo.eps}
89 \begin{minipage}{8.0cm}
92 $^1$ Experimentalphysik IV, Institut f"ur Physik,\\
93 Universit"at Augsburg, Universit"atsstr. 1,\\
94 D-86135 Augsburg, Germany
98 \begin{minipage}{2.3cm}
100 \includegraphics[height=1.5cm]{Lehrstuhl-Logo.eps}
106 \begin{minipage}{4.0cm}
108 \includegraphics[height=1.6cm]{logo_eng.eps}
111 \begin{minipage}{8.0cm}
114 $^2$ Accelerator Laboratory, Department of Physical Sciences,\\
115 University of Helsinki, Pietari Kalmink. 2,\\
116 00014 Helsinki, Finland
125 % no contents for such a short talk!
132 Motivation / Introduction
137 Reasons for understanding the SiC precipitation process:
140 \item 3C-SiC wide band gap semiconductor formation
141 \item Strained Si (no precipitation wanted!)
148 \begin{minipage}{8cm}
152 \item {\color{orange}fcc} $+$
153 \item {\color{gray}fcc shifted $1/4$ of volume diagonal}
155 \item Lattice constants:
157 4a_{Si}\approx5a_{SiC}
159 \item Silicon density:
161 \frac{n_{SiC}}{n_{Si}}=97,66\,\%
166 \begin{minipage}{4cm}
167 \includegraphics[width=4cm]{sic_unit_cell.eps}
176 Motivation / Introduction
182 Supposed conversion mechanism of heavily carbon doped Si into SiC:
186 \begin{minipage}{3.8cm}
187 \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
190 \begin{minipage}{3.8cm}
191 \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
194 \begin{minipage}{3.8cm}
195 \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
200 \begin{minipage}{3.8cm}
201 Formation of C-Si dumbbells on regular c-Si lattice sites
204 \begin{minipage}{3.8cm}
205 Agglomeration into large clusters (embryos)\\
208 \begin{minipage}{3.8cm}
209 Precipitation of 3C-SiC + Creation of interstitials\\
214 Experimentally observed:
216 \item Minimal diameter of precipitation: 4 - 5 nm
217 \item Equal orientation of Si and SiC (hkl)-planes
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
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\\
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]
251 {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211}
255 \begin{picture}(0,0)(-240,-70)
256 \includegraphics[width=5cm]{tersoff_angle.eps}
269 Interstitial simulations:
273 \begin{pspicture}(0,0)(7,8)
274 \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
277 \item Initial configuration: $9\times9\times9$ unit cells Si
278 \item Periodic boundary conditions
282 \rput(3.5,3.5){\rnode{insert}{\psframebox{
284 Insertion of C / Si atom:
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)
293 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
295 Relaxation time: $2\, ps$
297 \ncline[]{->}{init}{insert}
298 \ncline[]{->}{insert}{cool}
301 \begin{picture}(0,0)(-210,-45)
302 \includegraphics[width=6cm]{unit_cell.eps}
311 } - Si self-interstitial runs
315 \begin{minipage}[t]{4.3cm}
316 \underline{Tetrahedral}\\
318 \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
320 \begin{minipage}[t]{4.3cm}
321 \underline{110 dumbbell}\\
323 \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
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}
332 \underline{Random insertion}
334 \begin{minipage}{4.3cm}
336 \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
338 \begin{minipage}{4.3cm}
340 \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
342 \begin{minipage}{4.3cm}
344 \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
353 } - Carbon interstitial runs
357 \begin{minipage}[t]{4.3cm}
358 \underline{Tetrahedral}\\
360 \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
362 \begin{minipage}[t]{4.3cm}
363 \underline{110 dumbbell}\\
365 \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
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}
374 \underline{Random insertion}
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380 \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
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391 \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
393 \begin{minipage}[t]{3.0cm}
395 \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
410 SiC precipitation simulations:
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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 $600\, fs$
425 \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
427 Insertion of $6000$ carbon atoms at constant\\
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}}
435 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
437 Cooling down to $20\, ^{\circ}C$
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457 Very first results of the SiC precipitation runs
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}
466 \begin{minipage}[b]{5.5cm}
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}
473 \includegraphics[width=6.3cm]{../plot/foo150.ps}
481 Very first results of the SiC precipitation runs
484 \begin{minipage}[t]{6.9cm}
485 \includegraphics[width=6.3cm]{../plot/sic_pc.ps}
486 \includegraphics[width=6.3cm]{../plot/foo_end.ps}
489 \begin{minipage}[c]{5.5cm}
490 \includegraphics[width=6.0cm]{sic_si-c-n.eps}
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
512 \item Displacement and stress calculations
513 \item Refinement of simulation sequence to create 3C-SiC
514 \item Analyzing self-designed Si/SiC interface