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79 Molecular dynamics simulation study\\
80 of the silicon carbide precipitation process
85 \textsc{\small \underline{F. Zirkelbach}$^1$, J. K. N. Lindner$^1$,
86 K. Nordlund$^2$, B. Stritzker$^1$}\\
90 \begin{minipage}{2.0cm}
92 \includegraphics[height=1.6cm]{uni-logo.eps}
95 \begin{minipage}{8.0cm}
98 $^1$ Experimentalphysik IV, Institut f"ur Physik,\\
99 Universit"at Augsburg, Universit"atsstr. 1,\\
100 D-86135 Augsburg, Germany
104 \begin{minipage}{2.3cm}
106 \includegraphics[height=1.5cm]{Lehrstuhl-Logo.eps}
112 \begin{minipage}{4.0cm}
114 \includegraphics[height=1.6cm]{logo_eng.eps}
117 \begin{minipage}{8.0cm}
120 $^2$ Accelerator Laboratory, Department of Physical Sciences,\\
121 University of Helsinki, Pietari Kalmink. 2,\\
122 00014 Helsinki, Finland
131 % no contents for such a short talk!
143 Reasons for understanding the SiC precipitation process:
148 \item 3C-SiC is a promising wide band gap material for high-temperature,
149 high-power, high-frequency semiconductor devices [1]
150 \item 3C-SiC epitaxial thin film formation on Si requires detailed
151 knowledge of SiC nucleation
152 \item Fabrication of high carbon doped, strained pseudomorphic
153 $\text{Si}_{1-y}\text{C}_y$ layers requires suppression of
154 3C-SiC nucleation [2]
160 [1] J. H. Edgar, J. Mater. Res. 7 (1992) 235.}\\
162 [2] J. W. Strane, S. R. Lee, H. J. Stein, S. T. Picraux,
163 J. K. Watanabe, J. W. Mayer, J. Appl. Phys. 79 (1996) 637.}
170 Crystalline silicon and cubic silicon carbide
175 {\bf Lattice types and unit cells:}
177 \item Crystalline silicon (c-Si) has diamond structure\\
178 $\Rightarrow {\color{si-yellow}\bullet}$ and
179 ${\color{gray}\bullet}$ are Si atoms
180 \item Cubic silicon carbide (3C-SiC) has zincblende structure\\
181 $\Rightarrow {\color{si-yellow}\bullet}$ are Si atoms,
182 ${\color{gray}\bullet}$ are C atoms
185 \begin{minipage}{8cm}
186 {\bf Lattice constants:}
188 4a_{\text{c-Si}}\approx5a_{\text{3C-SiC}}
190 {\bf Silicon density:}
192 \frac{n_{\text{3C-SiC}}}{n_{\text{c-Si}}}=97,66\,\%
195 \begin{minipage}{5cm}
196 \includegraphics[width=5cm]{sic_unit_cell.eps}
205 Motivation / Introduction
211 Supposed conversion mechanism of heavily carbon doped Si into SiC:
215 \begin{minipage}{3.8cm}
216 \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
219 \begin{minipage}{3.8cm}
220 \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
223 \begin{minipage}{3.8cm}
224 \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
229 \begin{minipage}{3.8cm}
230 Formation of C-Si dumbbells on regular c-Si lattice sites
233 \begin{minipage}{3.8cm}
234 Agglomeration into large clusters (embryos)\\
237 \begin{minipage}{3.8cm}
238 Precipitation of 3C-SiC + Creation of interstitials\\
243 \begin{minipage}{7cm}
244 Experimentally observed [3]:
246 \item Minimal diameter of precipitation: 4 - 5 nm
247 \item Equal orientation of Si and SiC (hkl)-planes
250 \begin{minipage}{6cm}
253 {\tiny [3] J. K. N. Lindner, Appl. Phys. A 77 (2003) 27.}
268 \item Microscopic description of N particle system
269 \item Analytical interaction potential
270 \item Hamilton's equations of motion as propagation rule\\
271 in 6N-dimensional phase space
272 \item Observables obtained by time or ensemble averages
274 {\bf Application details:}
276 \item Integrator: Velocity Verlet, timestep: $1\text{ fs}$
277 \item Ensemble: isothermal-isobaric NPT [4]
279 \item Berendsen thermostat:
280 $\tau_{\text{T}}=100\text{ fs}$
281 \item Brendsen barostat:\\
282 $\tau_{\text{P}}=100\text{ fs}$,
283 $\beta^{-1}=100\text{ GPa}$
285 \item Potential: Tersoff-like bond order potential [5]
287 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
288 \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
292 [4] L. Verlet, Phys. Rev. 159 (1967) 98.}\\
294 [5] P. Erhart and K. Albe, Phys. Rev. B 71 (2005) 35211.}
296 \begin{picture}(0,0)(-240,-70)
297 \includegraphics[width=5cm]{tersoff_angle.eps}
310 Interstitial configurations:
314 \begin{pspicture}(0,0)(7,8)
315 \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
318 \item Initial configuration: $9\times9\times9$ unit cells Si
319 \item Periodic boundary conditions
320 \item $T=0\text{ K}$, $p=0\text{ bar}$
323 \rput(3.5,3.5){\rnode{insert}{\psframebox{
325 Insertion of C / Si atom:
327 \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
328 (${\color{red}\triangleleft}$)
329 \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
330 (${\color{green}\triangleright}$)
331 \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
332 $\rightarrow$ {\color{magenta}110 dumbbell}
333 (${\color{magenta}\Box}$,$\circ$)
334 \item random positions (critical distance check)
337 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
339 Relaxation time: $2\, ps$
341 \ncline[]{->}{init}{insert}
342 \ncline[]{->}{insert}{cool}
345 \begin{picture}(0,0)(-210,-45)
346 \includegraphics[width=6cm]{unit_cell_s.eps}
355 } - Si self-interstitial runs
359 \begin{minipage}[t]{4.3cm}
360 \underline{Tetrahedral}\\
362 \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
364 \begin{minipage}[t]{4.3cm}
365 \underline{110 dumbbell}\\
367 \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
369 \begin{minipage}[t]{4.3cm}
370 \underline{Hexagonal} \hspace{4pt}
371 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
372 $E_f^{\star}\approx4.48\, eV$ (unstable!)\\
373 \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
376 \underline{Random insertion}
378 \begin{minipage}{4.3cm}
380 \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
382 \begin{minipage}{4.3cm}
384 \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
386 \begin{minipage}{4.3cm}
388 \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
397 } - Carbon interstitial runs
401 \begin{minipage}[t]{4.3cm}
402 \underline{Tetrahedral}\\
404 \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
406 \begin{minipage}[t]{4.3cm}
407 \underline{110 dumbbell}\\
409 \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
411 \begin{minipage}[t]{4.3cm}
412 \underline{Hexagonal} \hspace{4pt}
413 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
414 $E_f^{\star}\approx5.6\, eV$ (unstable!)\\
415 \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
418 \underline{Random insertion}
422 \begin{minipage}[t]{3.3cm}
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425 \begin{picture}(0,0)(-15,-3)
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431 \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
433 \begin{minipage}[t]{3.3cm}
435 \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
437 \begin{minipage}[t]{3.0cm}
439 \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
454 SiC precipitation simulations:
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463 \item Initial configuration: $31\times31\times31$ unit cells Si
464 \item Periodic boundary conditions
465 \item $T=450\, ^{\circ}\text{C}$, $p=0\text{ bar}$
466 \item Equilibration of $E_{kin}$ and $E_{pot}$
469 \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
471 Insertion of 6000 carbon atoms at constant\\
474 \item Total simulation volume {\pnode{in1}}
475 \item Volume of minimal SiC precipitation {\pnode{in2}}
476 \item Volume of necessary amount of Si {\pnode{in3}}
479 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
481 Cooling down to $20\, ^{\circ}C$
483 \ncline[]{->}{init}{insert}
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488 \rput(7.9,4.8){\pnode{ins1}}
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491 \ncline[]{->}{in1}{ins1}
492 \ncline[]{->}{in2}{ins2}
493 \ncline[]{->}{in3}{ins3}
502 } - SiC precipitation runs
506 \begin{minipage}[b]{6.9cm}
507 \includegraphics[width=6.3cm]{../plot/sic_prec_energy.ps}
508 \includegraphics[width=6.3cm]{../plot/sic_prec_temp.ps}
510 \begin{minipage}[b]{5.5cm}
512 \item {\color{red} Total simulation volume}
513 \item {\color{green} Volume of minimal SiC precipitation}
514 \item {\color{blue} Volume of necessary amount of Si}
517 \includegraphics[width=6.3cm]{../plot/foo150.ps}
525 Very first results of the SiC precipitation runs
528 \begin{minipage}[t]{6.9cm}
529 \includegraphics[width=6.3cm]{../plot/sic_pc.ps}
530 \includegraphics[width=6.3cm]{../plot/foo_end.ps}
533 \begin{minipage}[c]{5.5cm}
534 \includegraphics[width=6.0cm]{sic_si-c-n.eps}
548 \item Importance of understanding the SiC precipitation mechanism
549 \item Interstitial configurations in silicon using the Albe potential
550 \item Indication of SiC precipitation
556 \item Displacement and stress calculations
557 \item Refinement of simulation sequence to create 3C-SiC
558 \item Analyzing self-designed Si/SiC interface