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96 Atomistic simulation study of the silicon carbide precipitation
102 \textsc{F. Zirkelbach}
110 Paderborn am 7. Juli 2010
115 % motivation / properties / applications of silicon carbide
120 \begin{pspicture}(0,0)(13.5,5)
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129 \rput[lt](0.2,4.6){\color{gray}PROPERTIES}
131 \rput[lt](0.5,4){wide band gap}
132 \rput[lt](0.5,3.5){high electric breakdown field}
133 \rput[lt](0.5,3){good electron mobility}
134 \rput[lt](0.5,2.5){high electron saturation drift velocity}
135 \rput[lt](0.5,2){high thermal conductivity}
137 \rput[lt](0.5,1.5){hard and mechanically stable}
138 \rput[lt](0.5,1){chemically inert}
140 \rput[lt](0.5,0.5){radiation hardness}
142 \rput[rt](13.3,4.6){\color{gray}APPLICATIONS}
144 \rput[rt](13,3.85){high-temperature, high power}
145 \rput[rt](13,3.5){and high-frequency}
146 \rput[rt](13,3.15){electronic and optoelectronic devices}
148 \rput[rt](13,2.35){material suitable for extreme conditions}
149 \rput[rt](13,2){microelectromechanical systems}
150 \rput[rt](13,1.65){abrasives, cutting tools, heating elements}
152 \rput[rt](13,0.85){first wall reactor material, detectors}
153 \rput[rt](13,0.5){and electronic devices for space}
157 \begin{picture}(0,0)(-3,68)
158 \includegraphics[width=2.6cm]{wide_band_gap.eps}
160 \begin{picture}(0,0)(-285,-162)
161 \includegraphics[width=3.38cm]{sic_led.eps}
163 \begin{picture}(0,0)(-195,-162)
164 \includegraphics[width=2.8cm]{6h-sic_3c-sic.eps}
166 \begin{picture}(0,0)(-313,65)
167 \includegraphics[width=2.2cm]{infineon_schottky.eps}
169 \begin{picture}(0,0)(-220,65)
170 \includegraphics[width=2.9cm]{sic_wechselrichter_ise.eps}
172 \begin{picture}(0,0)(0,-160)
173 \includegraphics[width=3.0cm]{sic_proton.eps}
175 \begin{picture}(0,0)(-60,65)
176 \includegraphics[width=3.4cm]{sic_switch.eps}
193 \begin{tabular}{l c c c c c c}
195 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
197 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
198 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
199 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
200 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
201 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
202 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
203 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
211 \begin{picture}(0,0)(-160,-155)
212 \includegraphics[width=7cm]{polytypes.eps}
214 \begin{picture}(0,0)(-10,-185)
215 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
217 \begin{picture}(0,0)(-10,-175)
218 {\tiny cubic (twist)}
220 \begin{picture}(0,0)(-60,-175)
221 {\tiny hexagonal (no twist)}
223 \begin{pspicture}(0,0)(0,0)
224 \psellipse[linecolor=green](5.7,3.03)(0.4,0.5)
226 \begin{pspicture}(0,0)(0,0)
227 \psellipse[linecolor=green](5.6,1.68)(0.4,0.2)
229 \begin{pspicture}(0,0)(0,0)
230 \psellipse[linecolor=red](10.7,1.13)(0.4,0.2)
238 Fabrication of silicon carbide
245 SiC - \emph{Born from the stars, perfected on earth.}
249 Conventional thin film SiC growth:
251 \item \underline{Sublimation growth using the modified Lely method}
253 \item SiC single-crystalline seed at $T=1800 \, ^{\circ} \text{C}$
254 \item Surrounded by polycrystalline SiC in a graphite crucible\\
255 at $T=2100-2400 \, ^{\circ} \text{C}$
256 \item Deposition of supersaturated vapor on cooler seed crystal
258 \item \underline{Homoepitaxial growth using CVD}
260 \item Step-controlled epitaxy on off-oriented 6H-SiC substrates
261 \item C$_3$H$_8$/SiH$_4$/H$_2$ at $1100-1500 \, ^{\circ} \text{C}$
262 \item Angle, temperature $\rightarrow$ 3C/6H/4H-SiC
264 \item \underline{Heteroepitaxial growth of 3C-SiC on Si using CVD/MBE}
266 \item Two steps: carbonization and growth
267 \item $T=650-1050 \, ^{\circ} \text{C}$
268 \item SiC/Si lattice mismatch $\approx$ 20 \%
269 \item Quality and size not yet sufficient
273 \begin{picture}(0,0)(-280,-65)
274 \includegraphics[width=3.8cm]{6h-sic_3c-sic.eps}
276 \begin{picture}(0,0)(-280,-55)
277 \begin{minipage}{5cm}
279 NASA: 6H-SiC and 3C-SiC LED\\[-7pt]
284 \begin{picture}(0,0)(-265,-150)
285 \includegraphics[width=2.4cm]{m_lely.eps}
287 \begin{picture}(0,0)(-333,-175)
288 \begin{minipage}{5cm}
294 5. Insulation\\[-7pt]
299 \begin{picture}(0,0)(-230,-35)
301 {\footnotesize\color{blue}\bf Hex: micropipes along c-axis}
304 \begin{picture}(0,0)(-230,-10)
306 \begin{minipage}{3cm}
307 {\footnotesize\color{blue}\bf 3C-SiC fabrication\\
318 Fabrication of silicon carbide
323 Alternative approach:
324 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
326 \item \underline{Implantation step 1}\\
327 180 keV C$^+$, $D=7.9\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=500\,^{\circ}\mathrm{C}$\\
328 $\Rightarrow$ box-like distribution of equally sized
329 and epitactically oriented SiC precipitates
331 \item \underline{Implantation step 2}\\
332 180 keV C$^+$, $D=0.6\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=250\,^{\circ}\mathrm{C}$\\
333 $\Rightarrow$ destruction of SiC nanocrystals
334 in growing amorphous interface layers
335 \item \underline{Annealing}\\
336 $T=1250\,^{\circ}\mathrm{C}$, $t=10\,\text{h}$\\
337 $\Rightarrow$ homogeneous, stoichiometric SiC layer
338 with sharp interfaces
341 \begin{minipage}{6.3cm}
342 \includegraphics[width=6cm]{ibs_3c-sic.eps}\\[-0.2cm]
344 XTEM micrograph of single crystalline 3C-SiC in Si\hkl(1 0 0)
348 \begin{minipage}{6.3cm}
351 Precipitation mechanism not yet fully understood!
353 \renewcommand\labelitemi{$\Rightarrow$}
355 \underline{Understanding the SiC precipitation}
357 \item significant technological progress in SiC thin film formation
358 \item perspectives for processes relying upon prevention of SiC precipitation
375 \item Supposed precipitation mechanism of SiC in Si
376 \item Utilized simulation techniques
378 \item Molecular dynamics (MD) simulations
379 \item Density functional theory (DFT) calculations
381 \item C and Si self-interstitial point defects in silicon
382 \item Silicon carbide precipitation simulations
383 \item Summary / Conclusion / Outlook
391 Supposed precipitation mechanism of SiC in Si
398 \begin{minipage}{3.8cm}
399 Si \& SiC lattice structure\\[0.2cm]
400 \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
404 \begin{minipage}{3.8cm}
406 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
410 \begin{minipage}{3.8cm}
412 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
416 \begin{minipage}{4cm}
418 C-Si dimers (dumbbells)\\[-0.1cm]
419 on Si interstitial sites
423 \begin{minipage}{4.2cm}
425 Agglomeration of C-Si dumbbells\\[-0.1cm]
426 $\Rightarrow$ dark contrasts
430 \begin{minipage}{4cm}
432 Precipitation of 3C-SiC in Si\\[-0.1cm]
433 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
434 \& release of Si self-interstitials
438 \begin{minipage}{3.8cm}
440 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
444 \begin{minipage}{3.8cm}
446 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
450 \begin{minipage}{3.8cm}
452 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
456 \begin{pspicture}(0,0)(0,0)
457 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
458 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
459 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
460 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
461 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
462 $4a_{\text{Si}}=5a_{\text{SiC}}$
464 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
465 \hkl(h k l) planes match
467 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
477 Molecular dynamics (MD) simulations
486 \item Microscopic description of N particle system
487 \item Analytical interaction potential
488 \item Numerical integration using Newtons equation of motion\\
489 as a propagation rule in 6N-dimensional phase space
490 \item Observables obtained by time and/or ensemble averages
492 {\bf Details of the simulation:}
494 \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
495 \item Ensemble: NpT (isothermal-isobaric)
497 \item Berendsen thermostat:
498 $\tau_{\text{T}}=100\text{ fs}$
499 \item Berendsen barostat:\\
500 $\tau_{\text{P}}=100\text{ fs}$,
501 $\beta^{-1}=100\text{ GPa}$
503 \item Erhart/Albe potential: Tersoff-like bond order potential
506 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
507 \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
511 \begin{picture}(0,0)(-230,-30)
512 \includegraphics[width=5cm]{tersoff_angle.eps}
520 Density functional theory (DFT) calculations
525 Basic ingredients necessary for DFT
528 \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
530 \item ... uniquely determines the ground state potential
532 \item ... minimizes the systems total energy
534 \item \underline{Born-Oppenheimer}
535 - $N$ moving electrons in an external potential of static nuclei
537 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
538 +\sum_i^N V_{\text{ext}}(r_i)
539 +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
541 \item \underline{Effective potential}
542 - averaged electrostatic potential \& exchange and correlation
544 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
547 \item \underline{Kohn-Sham system}
548 - Schr\"odinger equation of N non-interacting particles
550 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
555 n(r)=\sum_i^N|\Phi_i(r)|^2
557 \item \underline{Self-consistent solution}\\
558 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
559 which in turn depends on $n(r)$
560 \item \underline{Variational principle}
561 - minimize total energy with respect to $n(r)$
569 Density functional theory (DFT) calculations
576 Details of applied DFT calculations in this work
579 \item \underline{Exchange correlation functional}
580 - approximations for the inhomogeneous electron gas
582 \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
583 \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
585 \item \underline{Plane wave basis set}
586 - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
589 \text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
590 \qquad ({\color{blue}300\text{ eV}})
592 \item \underline{Brillouin zone sampling} -
593 {\color{blue}$\Gamma$-point only} calculations
594 \item \underline{Pseudo potential}
595 - consider only the valence electrons
596 \item \underline{Code} - VASP 4.6
601 MD and structural optimization
604 \item MD integration: Gear predictor corrector algorithm
605 \item Pressure control: Parrinello-Rahman pressure control
606 \item Structural optimization: Conjugate gradient method
609 \begin{pspicture}(0,0)(0,0)
610 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
618 C and Si self-interstitial point defects in silicon
625 \begin{minipage}{8cm}
627 \begin{pspicture}(0,0)(7,5)
628 \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
631 \item Creation of c-Si simulation volume
632 \item Periodic boundary conditions
633 \item $T=0\text{ K}$, $p=0\text{ bar}$
636 \rput(3.5,2.1){\rnode{insert}{\psframebox{
639 Insertion of interstitial C/Si atoms
642 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
645 Relaxation / structural energy minimization
648 \ncline[]{->}{init}{insert}
649 \ncline[]{->}{insert}{cool}
652 \begin{minipage}{5cm}
653 \includegraphics[width=5cm]{unit_cell_e.eps}\\
656 \begin{minipage}{9cm}
657 \begin{tabular}{l c c}
659 & size [unit cells] & \# atoms\\
661 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
662 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
666 \begin{minipage}{4cm}
667 {\color{red}$\bullet$} Tetrahedral\\
668 {\color{green}$\bullet$} Hexagonal\\
669 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
670 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
671 {\color{cyan}$\bullet$} Bond-centered\\
672 {\color{black}$\bullet$} Vacancy / Substitutional
681 \begin{minipage}{9.5cm}
684 Si self-interstitial point defects in silicon\\
687 \begin{tabular}{l c c c c c}
689 $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
691 VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
692 Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
694 \end{tabular}\\[0.2cm]
696 \begin{minipage}{4.7cm}
697 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
699 \begin{minipage}{4.7cm}
701 {\tiny nearly T $\rightarrow$ T}\\
703 \includegraphics[width=4.7cm]{nhex_tet.ps}
706 \underline{Hexagonal} \hspace{2pt}
707 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
709 \begin{minipage}{2.7cm}
710 $E_{\text{f}}^*=4.48\text{ eV}$\\
711 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
713 \begin{minipage}{0.4cm}
718 \begin{minipage}{2.7cm}
719 $E_{\text{f}}=3.96\text{ eV}$\\
720 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
723 \begin{minipage}{2.9cm}
725 \underline{Vacancy}\\
726 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
731 \begin{minipage}{3.5cm}
734 \underline{\hkl<1 1 0> dumbbell}\\
735 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
736 \underline{Tetrahedral}\\
737 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
738 \underline{\hkl<1 0 0> dumbbell}\\
739 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
751 C interstitial point defects in silicon\\[-0.1cm]
754 \begin{tabular}{l c c c c c c}
756 $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B \\
758 VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 \\
759 Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & 0.75 & 5.59$^*$ \\
761 \end{tabular}\\[0.1cm]
764 \begin{minipage}{2.7cm}
765 \underline{Hexagonal} \hspace{2pt}
766 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
767 $E_{\text{f}}^*=9.05\text{ eV}$\\
768 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
770 \begin{minipage}{0.4cm}
775 \begin{minipage}{2.7cm}
776 \underline{\hkl<1 0 0>}\\
777 $E_{\text{f}}=3.88\text{ eV}$\\
778 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
781 \begin{minipage}{2cm}
784 \begin{minipage}{3cm}
786 \underline{Tetrahedral}\\
787 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
792 \begin{minipage}{2.7cm}
793 \underline{Bond-centered}\\
794 $E_{\text{f}}^*=5.59\text{ eV}$\\
795 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
797 \begin{minipage}{0.4cm}
802 \begin{minipage}{2.7cm}
803 \underline{\hkl<1 1 0> dumbbell}\\
804 $E_{\text{f}}=5.18\text{ eV}$\\
805 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
808 \begin{minipage}{2cm}
811 \begin{minipage}{3cm}
813 \underline{Substitutional}\\
814 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
825 C \hkl<1 0 0> dumbbell interstitial configuration\\
829 \begin{tabular}{l c c c c c c c c}
831 Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
833 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
834 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
836 \end{tabular}\\[0.2cm]
837 \begin{tabular}{l c c c c }
839 Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
841 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
842 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
844 \end{tabular}\\[0.2cm]
845 \begin{tabular}{l c c c}
847 Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
849 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
850 VASP & 0.109 & -0.065 & 0.174 \\
852 \end{tabular}\\[0.6cm]
855 \begin{minipage}{3.0cm}
857 \underline{Erhart/Albe}
858 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
861 \begin{minipage}{3.0cm}
864 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
868 \begin{picture}(0,0)(-185,10)
869 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
871 \begin{picture}(0,0)(-280,-150)
872 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
875 \begin{pspicture}(0,0)(0,0)
876 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
877 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
878 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
879 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
888 \begin{minipage}{8.5cm}
891 Bond-centered interstitial configuration\\[-0.1cm]
894 \begin{minipage}{3.0cm}
895 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
897 \begin{minipage}{5.2cm}
899 \item Linear Si-C-Si bond
900 \item Si: one C \& 3 Si neighbours
901 \item Spin polarized calculations
902 \item No saddle point!\\
909 \begin{minipage}[t]{6.5cm}
910 \begin{minipage}[t]{1.2cm}
912 {\tiny sp$^3$}\\[0.8cm]
913 \underline{${\color{black}\uparrow}$}
914 \underline{${\color{black}\uparrow}$}
915 \underline{${\color{black}\uparrow}$}
916 \underline{${\color{red}\uparrow}$}\\
919 \begin{minipage}[t]{1.4cm}
921 {\color{red}M}{\color{blue}O}\\[0.8cm]
922 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
923 $\sigma_{\text{ab}}$\\[0.5cm]
924 \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
928 \begin{minipage}[t]{1.0cm}
932 \underline{${\color{white}\uparrow\uparrow}$}
933 \underline{${\color{white}\uparrow\uparrow}$}\\
935 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
936 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
940 \begin{minipage}[t]{1.4cm}
942 {\color{blue}M}{\color{green}O}\\[0.8cm]
943 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
944 $\sigma_{\text{ab}}$\\[0.5cm]
945 \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
949 \begin{minipage}[t]{1.2cm}
952 {\tiny sp$^3$}\\[0.8cm]
953 \underline{${\color{green}\uparrow}$}
954 \underline{${\color{black}\uparrow}$}
955 \underline{${\color{black}\uparrow}$}
956 \underline{${\color{black}\uparrow}$}\\
964 \begin{minipage}{4.5cm}
965 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
967 \begin{minipage}{3.5cm}
968 {\color{gray}$\bullet$} Spin up\\
969 {\color{green}$\bullet$} Spin down\\
970 {\color{blue}$\bullet$} Resulting spin up\\
971 {\color{yellow}$\bullet$} Si atoms\\
972 {\color{red}$\bullet$} C atom
977 \begin{minipage}{4.2cm}
979 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
980 {\color{green}$\Box$} {\tiny unoccupied}\\
981 {\color{red}$\bullet$} {\tiny occupied}
990 Migration of the C \hkl<1 0 0> dumbbell interstitial
995 {\small Investigated pathways}
997 \begin{minipage}{8.5cm}
998 \begin{minipage}{8.3cm}
999 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1000 \begin{minipage}{2.4cm}
1001 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1003 \begin{minipage}{0.4cm}
1006 \begin{minipage}{2.4cm}
1007 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1009 \begin{minipage}{0.4cm}
1012 \begin{minipage}{2.4cm}
1013 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1016 \begin{minipage}{8.3cm}
1017 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1018 \begin{minipage}{2.4cm}
1019 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1021 \begin{minipage}{0.4cm}
1024 \begin{minipage}{2.4cm}
1025 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1027 \begin{minipage}{0.4cm}
1030 \begin{minipage}{2.4cm}
1031 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1034 \begin{minipage}{8.3cm}
1035 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1036 \begin{minipage}{2.4cm}
1037 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1039 \begin{minipage}{0.4cm}
1042 \begin{minipage}{2.4cm}
1043 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1045 \begin{minipage}{0.4cm}
1048 \begin{minipage}{2.4cm}
1049 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1054 \begin{minipage}{4.2cm}
1055 {\small Constrained relaxation\\
1056 technique (CRT) method}\\
1057 \includegraphics[width=4cm]{crt_orig.eps}
1059 \item Constrain diffusing atom
1060 \item Static constraints
1063 {\small Modifications}\\
1064 \includegraphics[width=4cm]{crt_mod.eps}
1066 \item Constrain all atoms
1067 \item Update individual\\
1078 Migration of the C \hkl<1 0 0> dumbbell interstitial
1084 \begin{minipage}{5.9cm}
1086 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
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1112 \begin{minipage}{5.9cm}
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1129 \begin{picture}(0,0)(90,0)
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1140 \begin{minipage}{5.9cm}
1142 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
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1152 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1154 \begin{picture}(0,0)(12.5,10)
1155 \includegraphics[width=1cm]{100_arrow.eps}
1157 \begin{picture}(0,0)(90,0)
1158 \includegraphics[height=0.9cm]{001_arrow.eps}
1164 \begin{minipage}{0.3cm}
1167 \begin{minipage}{6.5cm}
1170 \item Energetically most favorable path
1173 \item Activation energy: $\approx$ 0.9 eV
1174 \item Experimental values: 0.73 ... 0.87 eV
1176 $\Rightarrow$ {\color{blue}Diffusion} path identified!
1177 \item Reorientation (path 3)
1179 \item More likely composed of two consecutive steps of type 2
1180 \item Experimental values: 0.77 ... 0.88 eV
1182 $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1191 Migration of the C \hkl<1 0 0> dumbbell interstitial
1196 \begin{minipage}{6.5cm}
1199 \begin{minipage}{5.9cm}
1201 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
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1238 \includegraphics[width=1cm]{100_arrow.eps}
1240 \begin{picture}(0,0)(90,-15)
1241 \includegraphics[height=0.9cm]{010_arrow.eps}
1247 \begin{minipage}{5.9cm}
1250 \item Lowest activation energy: $\approx$ 2.2 eV
1251 \item 2.4 times higher than VASP
1252 \item Different pathway
1253 \item Transition minima ($\rightarrow$ \hkl<1 1 0> dumbbell)
1258 \begin{minipage}{6.5cm}
1261 \begin{minipage}{5.9cm}
1263 \includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1266 \begin{pspicture}(0,0)(0,0)
1267 \psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1269 \begin{picture}(0,0)(60,-5)
1270 \includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
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1273 \includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
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1279 \includegraphics[width=1cm]{100_arrow.eps}
1281 \begin{picture}(0,0)(90,0)
1282 \includegraphics[height=0.9cm]{001_arrow.eps}
1290 \begin{minipage}{5.9cm}
1291 \includegraphics[width=5.9cm]{00-1_ip0-10.ps}
1302 Combinations with a C-Si \hkl<1 0 0>-type interstitial
1312 E_{\text{f}}^{\text{defect combination}}-
1313 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1314 E_{\text{f}}^{\text{2nd defect}}
1320 \begin{tabular}{l c c c c c c}
1322 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1324 \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1325 \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1326 \hkl<0 -1 0> & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
1327 \hkl<0 1 0> & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
1328 \hkl<-1 0 0> & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
1329 \hkl<1 0 0> & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
1331 C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1332 Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1341 \begin{minipage}[t]{3.8cm}
1342 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1343 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1345 \begin{minipage}[t]{3.5cm}
1346 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1347 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1349 \begin{minipage}[t]{5.5cm}
1351 \item Restricted to VASP simulations
1352 \item $E_{\text{b}}=0$ for isolated non-interacting defects
1353 \item $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1354 \item Stress compensation / increase
1355 \item Most favorable: C clustering
1356 \item Unfavored: antiparallel orientations
1357 \item Indication of energetically favored\\
1362 \begin{picture}(0,0)(-295,-130)
1363 \includegraphics[width=3.5cm]{comb_pos.eps}
1371 Combinations of C-Si \hkl<1 0 0>-type interstitials
1378 Energetically most favorable combinations along \hkl<1 1 0>
1383 \begin{tabular}{l c c c c c c}
1385 & 1 & 2 & 3 & 4 & 5 & 6\\
1387 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1388 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1389 Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\
1396 \begin{minipage}{7.0cm}
1397 \includegraphics[width=7cm]{db_along_110_cc.ps}
1399 \begin{minipage}{6.0cm}
1402 Interaction proportional to reciprocal cube of C-C distance
1404 Saturation in the immediate vicinity
1415 Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1421 \begin{minipage}{3.2cm}
1422 \includegraphics[width=3cm]{sub_110_combo.eps}
1424 \begin{minipage}{7.8cm}
1425 \begin{tabular}{l c c c c c c}
1427 C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
1428 \hkl<1 0 1> & \hkl<-1 0 1> \\
1430 1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
1431 2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
1432 3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
1433 4 & \RM{4} & B & D & E & E & D \\
1434 5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
1441 \begin{tabular}{l c c c c c c c c c c}
1443 Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
1445 $E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
1446 $E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
1447 $r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
1452 \begin{minipage}{6.0cm}
1453 \includegraphics[width=5.8cm]{c_sub_si110.ps}
1455 \begin{minipage}{7cm}
1458 \item IBS: C may displace Si\\
1459 $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
1461 \hkl<1 1 0>-type $\rightarrow$ favored combination
1462 \renewcommand\labelitemi{$\Rightarrow$}
1463 \item Less favorable than C-Si \hkl<1 0 0> dumbbell\\
1464 ($E_{\text{f}}=3.88\text{ eV}$)
1465 \item Interaction drops quickly to zero\\
1466 (low interaction capture radius)
1475 Migration in C-Si \hkl<1 0 0> and vacancy combinations
1482 \begin{minipage}[t]{3cm}
1483 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
1484 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
1486 \begin{minipage}[t]{7cm}
1489 Low activation energies\\
1490 High activation energies for reverse processes\\
1492 {\color{blue}C$_{\text{sub}}$ very stable}\\
1496 Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
1498 {\color{blue}Formation of SiC by successive substitution by C}
1502 \begin{minipage}[t]{3cm}
1503 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
1504 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
1509 \begin{minipage}{5.9cm}
1510 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
1512 \begin{picture}(0,0)(70,0)
1513 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
1515 \begin{picture}(0,0)(30,0)
1516 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
1518 \begin{picture}(0,0)(-10,0)
1519 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
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1522 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
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1527 \begin{picture}(0,0)(97,-10)
1528 \includegraphics[height=0.9cm]{001_arrow.eps}
1534 \begin{minipage}{0.3cm}
1538 \begin{minipage}{5.9cm}
1539 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
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1544 \begin{picture}(0,0)(25,0)
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1547 \begin{picture}(0,0)(-20,0)
1548 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
1550 \begin{picture}(0,0)(-55,0)
1551 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
1553 \begin{picture}(0,0)(12.5,5)
1554 \includegraphics[width=1cm]{100_arrow.eps}
1556 \begin{picture}(0,0)(95,0)
1557 \includegraphics[height=0.9cm]{001_arrow.eps}
1569 Conclusion of defect / migration / combined defect simulations
1578 \item Accurately described by quantum-mechanical simulations
1579 \item Less accurate description by classical potential simulations
1583 \item \hkl<1 0 0> C-Si dumbbell interstitial ground state configuration
1584 \item Consistent with reorientation and diffusion experiments
1585 \item C migration pathway in Si identified
1588 Concerning the precipitation mechanism
1590 \item Agglomeration of C-Si dumbbells energetically favorable
1591 \item C-Si indeed favored compared to
1592 C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
1593 \item Possible low interaction capture radius of
1594 C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
1595 \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
1596 C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
1599 {\color{blue}Some results point to a different precipitation mechanism!}
1603 \item \hkl<1 0 0> C-Si $\rightarrow$
1604 C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
1605 \item \hkl<1 0 0> C-Si combinations: C-C $\rightarrow$ C-...-C
1614 Silicon carbide precipitation simulations
1620 \begin{pspicture}(0,0)(12,6.5)
1622 \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1625 \item Create c-Si volume
1626 \item Periodc boundary conditions
1627 \item Set requested $T$ and $p=0\text{ bar}$
1628 \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1631 \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1633 Insertion of C atoms at constant T
1635 \item total simulation volume {\pnode{in1}}
1636 \item volume of minimal SiC precipitate {\pnode{in2}}
1637 \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1641 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1643 Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1645 \ncline[]{->}{init}{insert}
1646 \ncline[]{->}{insert}{cool}
1647 \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
1648 \rput(7.8,6){\footnotesize $V_1$}
1649 \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
1650 \rput(9.2,4.85){\tiny $V_2$}
1651 \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
1652 \rput(9.55,4.45){\footnotesize $V_3$}
1653 \rput(7.9,3.2){\pnode{ins1}}
1654 \rput(9.22,2.8){\pnode{ins2}}
1655 \rput(11.0,2.4){\pnode{ins3}}
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1657 \ncline[]{->}{in2}{ins2}
1658 \ncline[]{->}{in3}{ins3}
1663 \item Restricted to classical potential simulations
1664 \item $V_2$ and $V_3$ considered due to low diffusion
1665 \item Amount of C atoms: 6000
1666 ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
1667 \item Simulation volume: $31\times 31\times 31$ unit cells
1676 Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
1681 \begin{minipage}{6.5cm}
1682 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
1684 \begin{minipage}{6.5cm}
1685 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
1688 \begin{minipage}{6.5cm}
1689 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
1691 \begin{minipage}{6.5cm}
1693 \underline{Low C concentration ($V_1$)}\\
1694 \hkl<1 0 0> C-Si dumbbell dominated structure
1696 \item Si-C bumbs around 0.19 nm
1697 \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
1698 concatenated dumbbells of various orientation
1699 \item Si-Si NN distance stretched to 0.3 nm
1701 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
1702 \underline{High C concentration ($V_2$, $V_3$)}\\
1703 High amount of strongly bound C-C bonds\\
1704 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
1705 Only short range order observable\\
1706 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
1714 Limitations of molecular dynamics and short range potentials
1721 \underline{Time scale problem of MD}\\[0.2cm]
1722 Minimize integration error\\
1723 $\Rightarrow$ discretization considerably smaller than
1724 reciprocal of fastest vibrational mode\\[0.1cm]
1725 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
1726 $\Rightarrow$ suitable choice of time step:
1727 $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
1728 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
1729 Several local minima in energy surface separated by large energy barriers\\
1730 $\Rightarrow$ transition event corresponds to a multiple
1731 of vibrational periods\\
1732 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
1733 infrequent transition events\\[0.1cm]
1734 {\color{blue}Accelerated methods:}
1735 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1739 \underline{Limitations related to the short range potential}\\[0.2cm]
1740 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
1741 and 2$^{\text{nd}}$ next neighbours\\
1742 $\Rightarrow$ overestimated unphysical high forces of next neighbours
1748 Potential enhanced problem of slow phase space propagation
1753 \underline{Approach to the (twofold) problem}\\[0.2cm]
1754 Increased temperature simulations without TAD corrections\\
1755 (accelerated methods or higher time scales exclusively not sufficient)
1757 \begin{picture}(0,0)(-260,-30)
1759 \begin{minipage}{4.2cm}
1766 \item 3C-SiC also observed for higher T
1767 \item higher T inside sample
1768 \item structural evolution vs.\\
1769 equilibrium properties
1775 \begin{picture}(0,0)(-305,-155)
1777 \begin{minipage}{2.5cm}
1781 thermodynmic sampling
1792 Increased temperature simulations at low C concentration
1797 \begin{minipage}{6.5cm}
1798 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
1800 \begin{minipage}{6.5cm}
1801 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
1804 \begin{minipage}{6.5cm}
1805 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
1807 \begin{minipage}{6.5cm}
1809 \underline{Si-C bonds:}
1811 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1812 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
1814 \underline{Si-Si bonds:}
1815 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1816 ($\rightarrow$ 0.325 nm)\\[0.1cm]
1817 \underline{C-C bonds:}
1819 \item C-C next neighbour pairs reduced (mandatory)
1820 \item Peak at 0.3 nm slightly shifted
1822 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
1823 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
1825 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
1827 \item Range [|-$\downarrow$]:
1828 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
1829 with nearby Si$_{\text{I}}$}
1834 \begin{picture}(0,0)(-330,-74)
1837 \begin{minipage}{1.6cm}
1840 stretched SiC\\[-0.1cm]
1852 Increased temperature simulations at high C concentration
1857 \begin{minipage}{6.5cm}
1858 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
1860 \begin{minipage}{6.5cm}
1861 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
1865 Decreasing cut-off artifact\\
1866 High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
1867 $\Rightarrow$ hard to categorize
1873 \begin{minipage}[t]{6.0cm}
1874 0.186 nm: Si-C pairs $\uparrow$\\
1875 (as expected in 3C-SiC)\\[0.2cm]
1876 0.282 nm: Si-C-C\\[0.2cm]
1877 $\approx$0.35 nm: C-Si-Si
1880 \begin{minipage}{0.2cm}
1884 \begin{minipage}[t]{6.0cm}
1885 0.15 nm: C-C pairs $\uparrow$\\
1886 (as expected in graphite/diamond)\\[0.2cm]
1887 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
1888 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
1895 {\color{red}Amorphous} SiC-like phase remains\\
1896 Slightly sharper peaks
1897 $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics}
1898 due to temperature\\[0.1cm]
1901 Continue with higher temperatures and longer time scales
1910 Long time scale simulations at maximum temperature
1917 \underline{Differences}
1919 \item Temperature set to $0.95 \cdot T_{\text{m}}$
1920 \item Cubic insertion volume $\Rightarrow$ spherical insertion volume
1921 \item Amount of C atoms: 6000 $\rightarrow$ 5500
1922 $\Leftrightarrow r_{\text{prec}}=0.3\text{ nm}$
1923 \item Simulation volume: 21 unit cells of c-Si in each direction
1930 \begin{minipage}[t]{4.5cm}
1932 \underline{Low C concentration, Si-C}
1933 \includegraphics[width=4.5cm]{c_in_si_95_v1_si-c.ps}\\
1937 \begin{minipage}[t]{4.5cm}
1939 \underline{Low C concentration, C-C}
1940 \includegraphics[width=4.5cm]{c_in_si_95_v1_c-c.ps}\\
1945 \begin{minipage}[t]{4cm}
1947 \underline{High C concentration}
1948 \includegraphics[width=4.5cm]{c_in_si_95_v2.ps}\\
1949 No significant changes\\
1950 C-Si-Si $\uparrow$\\
1957 Long time scales and high temperatures most probably not sufficient enough!
1966 Summary / Conclusion / Outlook
1974 \begin{minipage}{12.9cm}
1977 \item Summary \& conclusion
1979 \item Point defects excellently / fairly well described
1980 by QM / classical potential simulations
1981 \item Identified migration path explaining
1982 diffusion and reorientation experiments
1983 \item Agglomeration of point defects energetically favorable
1984 \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
1988 \item Migrations separating C-C bond in \hkl<1 0 0> C-Si dumbbell
1989 interstitial combination
1990 \item Migration: \hkl<1 0 0> C-Si $\rightarrow$
1991 C$_{\text{sub}}$ \& Si \hkl<1 1 0> interstitial
1995 \item Discussions concerning interpretation of QM results (Paderborn)
1996 \item Compare migration barrier of
1997 \hkl<1 1 0> Si and C-Si \hkl<1 0 0> dumbbell
1998 \item Combination: Vacancy \& \hkl<1 1 0> Si self-interstitial \&
1999 C-Si \hkl<1 0 0> dumbbell (IBS)
2008 \begin{minipage}[t]{12.9cm}
2009 \underline{Pecipitation simulations}
2011 \item Summary \& conclusion
2014 $\rightarrow$ C-Si \hkl<1 0 0> dumbbell
2016 \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2017 \item High C concentration
2018 $\rightarrow$ amorphous SiC like phase
2022 \item Accelerated method: self-guided MD
2023 \item Activation relaxation technique
2024 \item Constrainted transition path
2046 \underline{Augsburg}
2048 \item Prof. B. Stritzker (accepting a simulator at EP \RM{4})
2049 \item Ralf Utermann (EDV)
2052 \underline{Helsinki}
2054 \item Prof. K. Nordlund (MD)
2059 \item Bayerische Forschungsstiftung (financial support)
2062 \underline{Paderborn}
2064 \item Prof. J. Lindner (SiC)
2065 \item Prof. G. Schmidt (DFT + financial support)
2066 \item Dr. E. Rauls (DFT + SiC)
2067 \item Dr. S. Sanna (VASP)
2074 \bf Thank you for your attention!