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59 Molecular dynamics simulation study\\
60 of the silicon carbide precipitation process
65 \textsc{\small \underline{F. Zirkelbach}$^1$, J. K. N. Lindner$^1$,
66 K. Nordlund$^2$, B. Stritzker$^1$}\\
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78 $^1$ Experimentalphysik IV, Institut f"ur Physik,\\
79 Universit"at Augsburg, Universit"atsstr. 1,\\
80 D-86135 Augsburg, Germany
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100 $^2$ Accelerator Laboratory, Department of Physical Sciences,\\
101 University of Helsinki, Pietari Kalmink. 2,\\
102 00014 Helsinki, Finland
115 Molecular dynamics simulation study\\
116 of the silicon carbide precipitation process
129 \item Motivation / Introduction
130 \item Molecular dynamics simulation details
132 \item Integrator, potential, ensemble control
133 \item Simulation sequence
135 \item Results gained by simulation
137 \item Interstitials in silicon
138 \item $SiC$-precipitation experiments
140 \item Conclusion / Outlook
149 Motivation / Introduction
155 Supposed mechanism of the conversion of heavily carbon doped Si into SiC:
159 \begin{minipage}{3.8cm}
160 \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
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174 Formation of C-Si dumbbells on regular c-Si lattice sites
177 \begin{minipage}{3.8cm}
178 Agglomeration into large clusters (embryos)\\
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182 Precipitation of 3C-SiC + Creation of interstitials\\
186 \[5a_{SiC}=4a_{Si} \quad \Rightarrow \quad
187 \frac{n_{SiC}}{n_{Si}}=\frac{\frac{4}{a_{SiC}^3}}{\frac{8}{a_{Si}^3}}=
188 \frac{5^3}{2\cdot4^3}=97,66\%
192 Experimentally observed minimal diameter of precipitation: 4 - 5 nm
204 \item Microscopic description of N particle system
205 \item Analytical interaction potential
206 \item Hamilton's equations of motion as propagation rule\\
207 in 6N-dimemnsional phase space
208 \item Observables obtained by time average
215 \item Integrator: velocity verlet, timestep: $1\, fs$
216 \item Ensemble control: NVT, Berendsen thermostat, $\tau=100.0$
217 \item Potential: Tersoff-like bond order potential\\
219 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
220 \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
223 {\scriptsize P. Erhart und K. Albe. Phys. Rev. B 71 (2005) 035211}
235 Interstitial experiments:
237 \item Initial configuration: $9\times9\times9$ unit cells Si
238 \item Periodic boundary conditions
240 \item Insertion of Si / C atom at
242 \item $(0,0,0)$ $\rightarrow$ tetrahedral
243 \item $(-1/8,-1/8,1/8)$ $\rightarrow$ hexagonal
244 \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$
245 $\rightarrow$ 110 dumbbell
246 \item random positions (critical distance check)
248 \item Relaxation time: $2\, ps$
261 SiC precipitation experiments:
263 \item Initial configuration: $31\times31\times31$ unit cells Si
264 \item Periodic boundary conditions
265 \item $T=450\, ^{\circ}C$
266 \item Steady state time: $600\, fs$
267 \item C insertion steps:
269 \item If $T=450\pm 1\, ^{\circ}C$:\\
270 Insertion of 10 atoms at random positions within $V_{ins}$
271 \item Otherwise: Annealing for another $100\, fs$
273 \item Annealing: ($T_a: 450\rightarrow 20 \, ^{\circ}C$)
275 \item If $T=T_a$: Decrease $T_a$ by $1\, ^{\circ}C$
276 \item Otherwise: Annealing for another $50\, fs$
282 \item $V_{ins}$: total simulation volume $V$
283 \item $V_{ins}$: $12\times12\times12$ SiC unit cells
284 ($\sim$ volume of minimal SiC precipitation)
285 \item $V_{ins}$: $9\times9\times9$ SiC unit cells
286 ($\sim$ volume of necessary amount of Si)