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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: $4a_{Si}\approx5a_{SiC}$
156 \item Silicon density:
158 \frac{n_{SiC}}{n_{Si}}=
159 \frac{4/a_{SiC}^3}{8/a_{Si}^3}=
160 \frac{5^3}{2\cdot4^3}={\color{cyan}97,66}\,\%
165 \begin{minipage}{4cm}
166 \includegraphics[width=4cm]{sic_unit_cell.eps}
175 Motivation / Introduction
181 Supposed conversion mechanism of heavily carbon doped Si into SiC:
185 \begin{minipage}{3.8cm}
186 \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
189 \begin{minipage}{3.8cm}
190 \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
193 \begin{minipage}{3.8cm}
194 \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
199 \begin{minipage}{3.8cm}
200 Formation of C-Si dumbbells on regular c-Si lattice sites
203 \begin{minipage}{3.8cm}
204 Agglomeration into large clusters (embryos)\\
207 \begin{minipage}{3.8cm}
208 Precipitation of 3C-SiC + Creation of interstitials\\
213 Experimentally observed:
215 \item Minimal diameter of precipitation: 4 - 5 nm
216 \item (hkl)-planes identical for Si and SiC
231 \item Microscopic description of N particle system
232 \item Analytical interaction potential
233 \item Hamilton's equations of motion as propagation rule\\
234 in 6N-dimensional phase space
235 \item Observables obtained by time average
242 \item Integrator: Velocity Verlet, timestep: $1\, fs$
243 \item Ensemble: NVT, Berendsen thermostat, $\tau=100.0$
244 \item Potential: Tersoff-like bond order potential\\
246 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
247 \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
250 {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211}
254 \begin{picture}(0,0)(-240,-70)
255 \includegraphics[width=5cm]{tersoff_angle.eps}
268 Interstitial experiments:
272 \begin{pspicture}(0,0)(7,8)
273 \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
276 \item Initial configuration: $9\times9\times9$ unit cells Si
277 \item Periodic boundary conditions
281 \rput(3.5,3.5){\rnode{insert}{\psframebox{
283 Insertion of C / Si atom:
285 \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
286 \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
287 \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
288 $\rightarrow$ {\color{magenta}110 dumbbell}
289 \item random positions (critical distance check)
292 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
294 Relaxation time: $2\, ps$
296 \ncline[]{->}{init}{insert}
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300 \begin{picture}(0,0)(-210,-45)
301 \includegraphics[width=6cm]{unit_cell.eps}
310 } - Si self-interstitial experiments
314 \begin{minipage}[t]{4.3cm}
315 \underline{Tetrahedral}\\
317 \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
319 \begin{minipage}[t]{4.3cm}
320 \underline{110 dumbbell}\\
322 \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
324 \begin{minipage}[t]{4.3cm}
325 \underline{Hexagonal} \hspace{4pt}
326 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
327 $E_f^{\star}\approx4.48\, eV$ (unstable!)\\
328 \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
331 \underline{Random insertion}
333 \begin{minipage}{4.3cm}
335 \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
337 \begin{minipage}{4.3cm}
339 \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
341 \begin{minipage}{4.3cm}
343 \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
352 } - Carbon interstitial experiments
356 \begin{minipage}[t]{4.3cm}
357 \underline{Tetrahedral}\\
359 \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
361 \begin{minipage}[t]{4.3cm}
362 \underline{110 dumbbell}\\
364 \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
366 \begin{minipage}[t]{4.3cm}
367 \underline{Hexagonal} \hspace{4pt}
368 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
369 $E_f^{\star}\approx5.6\, eV$ (unstable!)\\
370 \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
373 \underline{Random insertion}
377 \begin{minipage}[t]{3.3cm}
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388 \begin{minipage}[t]{3.3cm}
389 $E_f=2.39\, eV$ \hspace{2pt}
390 \href{../video/c_in_si_int_rand_239.avi}{$\rhd$}\\
391 \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
393 \begin{minipage}[t]{3.0cm}
394 $E_f=3.41\, eV$ \hspace{2pt}
395 \href{../video/c_in_si_int_rand_341.avi}{$\rhd$}\\
396 \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
411 SiC precipitation experiments:
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420 \item Initial configuration: $31\times31\times31$ unit cells Si
421 \item Periodic boundary conditions
422 \item $T=450\, ^{\circ}C$
423 \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
426 \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
428 Insertion of $6000$ carbon atoms at constant\\
431 \item Total simulation volume {\pnode{in1}}
432 \item Volume of minimal SiC precipitation {\pnode{in2}}
433 \item Volume of necessary amount of Si {\pnode{in3}}
436 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
438 Cooling down to $20\, ^{\circ}C$
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461 SiC-precipitation experiments:
463 \begin{minipage}[t]{6.3cm}
464 \includegraphics[width=6.0cm]{../plot/sic_prec_energy.ps}
465 \includegraphics[width=6.0cm]{../plot/sic_prec_temp.ps}
467 \begin{minipage}[t]{6cm}
468 \includegraphics[width=6.0cm]{../plot/sic_pc.ps}
469 \includegraphics[width=6.0cm]{../plot/sic_prec_pc.ps}
483 \item Importance of understanding C in Si
484 \item Interstitial configurations in silicon using the Albe potential
485 \item Indication of SiC precipitation
491 \item Displacement and stress calculations
492 \item Diffusion dependence of temperature and carbon concentration
493 \item Analyzing results of the precipitation simulation runs
494 \item Analyzing self-designed Si/SiC interface