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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
173 {\bf Lattice types and unit cells:}
175 \item Crystalline silicon (c-Si) has diamond structure\\
176 $\Rightarrow {\color{si-yellow}\bullet}$ and
177 ${\color{gray}\bullet}$ are Si atoms
178 \item Cubic silicon carbide (3C-SiC) has zincblende structure\\
179 $\Rightarrow {\color{si-yellow}\bullet}$ are Si atoms,
180 ${\color{gray}\bullet}$ are C atoms
182 \begin{minipage}{8cm}
183 {\bf Lattice constants:}
185 4a_{\text{c-Si}}\approx5a_{\text{3C-SiC}}
187 {\bf Silicon density:}
189 \frac{n_{\text{3C-SiC}}}{n_{\text{c-Si}}}=97,66\,\%
192 \begin{minipage}{5cm}
193 \includegraphics[width=5cm]{sic_unit_cell.eps}
202 Motivation / Introduction
208 Supposed conversion mechanism of heavily carbon doped Si into SiC:
212 \begin{minipage}{3.8cm}
213 \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
216 \begin{minipage}{3.8cm}
217 \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
220 \begin{minipage}{3.8cm}
221 \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
226 \begin{minipage}{3.8cm}
227 Formation of C-Si dumbbells on regular c-Si lattice sites
230 \begin{minipage}{3.8cm}
231 Agglomeration into large clusters (embryos)\\
234 \begin{minipage}{3.8cm}
235 Precipitation of 3C-SiC + Creation of interstitials\\
240 Experimentally observed:
242 \item Minimal diameter of precipitation: 4 - 5 nm
243 \item Equal orientation of Si and SiC (hkl)-planes
258 \item Microscopic description of N particle system
259 \item Analytical interaction potential
260 \item Hamilton's equations of motion as propagation rule\\
261 in 6N-dimensional phase space
262 \item Observables obtained by time average
269 \item Integrator: Velocity Verlet, timestep: $1\, fs$
270 \item Ensemble: NVT, Berendsen thermostat, $\tau=100.0$
271 \item Potential: Tersoff-like bond order potential\\
273 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
274 \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
277 {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211}
281 \begin{picture}(0,0)(-240,-70)
282 \includegraphics[width=5cm]{tersoff_angle.eps}
295 Interstitial simulations:
299 \begin{pspicture}(0,0)(7,8)
300 \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
303 \item Initial configuration: $9\times9\times9$ unit cells Si
304 \item Periodic boundary conditions
308 \rput(3.5,3.5){\rnode{insert}{\psframebox{
310 Insertion of C / Si atom:
312 \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
313 \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
314 \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
315 $\rightarrow$ {\color{magenta}110 dumbbell}
316 \item random positions (critical distance check)
319 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
321 Relaxation time: $2\, ps$
323 \ncline[]{->}{init}{insert}
324 \ncline[]{->}{insert}{cool}
327 \begin{picture}(0,0)(-210,-45)
328 \includegraphics[width=6cm]{unit_cell.eps}
337 } - Si self-interstitial runs
341 \begin{minipage}[t]{4.3cm}
342 \underline{Tetrahedral}\\
344 \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
346 \begin{minipage}[t]{4.3cm}
347 \underline{110 dumbbell}\\
349 \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
351 \begin{minipage}[t]{4.3cm}
352 \underline{Hexagonal} \hspace{4pt}
353 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
354 $E_f^{\star}\approx4.48\, eV$ (unstable!)\\
355 \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
358 \underline{Random insertion}
360 \begin{minipage}{4.3cm}
362 \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
364 \begin{minipage}{4.3cm}
366 \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
368 \begin{minipage}{4.3cm}
370 \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
379 } - Carbon interstitial runs
383 \begin{minipage}[t]{4.3cm}
384 \underline{Tetrahedral}\\
386 \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
388 \begin{minipage}[t]{4.3cm}
389 \underline{110 dumbbell}\\
391 \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
393 \begin{minipage}[t]{4.3cm}
394 \underline{Hexagonal} \hspace{4pt}
395 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
396 $E_f^{\star}\approx5.6\, eV$ (unstable!)\\
397 \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
400 \underline{Random insertion}
404 \begin{minipage}[t]{3.3cm}
406 \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
407 \begin{picture}(0,0)(-15,-3)
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413 \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
415 \begin{minipage}[t]{3.3cm}
417 \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
419 \begin{minipage}[t]{3.0cm}
421 \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
436 SiC precipitation simulations:
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445 \item Initial configuration: $31\times31\times31$ unit cells Si
446 \item Periodic boundary conditions
447 \item $T=450\, ^{\circ}C$
448 \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
451 \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
453 Insertion of $6000$ carbon atoms at constant\\
456 \item Total simulation volume {\pnode{in1}}
457 \item Volume of minimal SiC precipitation {\pnode{in2}}
458 \item Volume of necessary amount of Si {\pnode{in3}}
461 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
463 Cooling down to $20\, ^{\circ}C$
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483 Very first results of the SiC precipitation runs
488 \begin{minipage}[b]{6.9cm}
489 \includegraphics[width=6.3cm]{../plot/sic_prec_energy.ps}
490 \includegraphics[width=6.3cm]{../plot/sic_prec_temp.ps}
492 \begin{minipage}[b]{5.5cm}
494 \item {\color{red} Total simulation volume}
495 \item {\color{green} Volume of minimal SiC precipitation}
496 \item {\color{blue} Volume of necessary amount of Si}
499 \includegraphics[width=6.3cm]{../plot/foo150.ps}
507 Very first results of the SiC precipitation runs
510 \begin{minipage}[t]{6.9cm}
511 \includegraphics[width=6.3cm]{../plot/sic_pc.ps}
512 \includegraphics[width=6.3cm]{../plot/foo_end.ps}
515 \begin{minipage}[c]{5.5cm}
516 \includegraphics[width=6.0cm]{sic_si-c-n.eps}
530 \item Importance of understanding the SiC precipitation mechanism
531 \item Interstitial configurations in silicon using the Albe potential
532 \item Indication of SiC precipitation
538 \item Displacement and stress calculations
539 \item Refinement of simulation sequence to create 3C-SiC
540 \item Analyzing self-designed Si/SiC interface