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102 \rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=hb,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{
103 \begin{minipage}{14cm}
112 \newcommand{\si}{Si$_{\text{i}}${}}
113 \newcommand{\ci}{C$_{\text{i}}${}}
114 \newcommand{\cs}{C$_{\text{sub}}${}}
115 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
116 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
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120 % no vertical centering
132 A B C D E F G H G F E D C B A
150 Atomistic simulation study on silicon carbide\\[0.2cm]
151 precipitation in silicon\\
158 \textsc{Frank Zirkelbach}
162 Defense of doctor's thesis
171 % no vertical centering
174 % skip for preparation
179 % motivation / properties / applications of silicon carbide
187 \begin{pspicture}(0,0)(13.5,5)
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194 \rput[lt](0,4.6){\color{gray}PROPERTIES}
196 \rput[lt](0.3,4){wide band gap}
197 \rput[lt](0.3,3.5){high electric breakdown field}
198 \rput[lt](0.3,3){good electron mobility}
199 \rput[lt](0.3,2.5){high electron saturation drift velocity}
200 \rput[lt](0.3,2){high thermal conductivity}
202 \rput[lt](0.3,1.5){hard and mechanically stable}
203 \rput[lt](0.3,1){chemically inert}
205 \rput[lt](0.3,0.5){radiation hardness}
207 \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
209 \rput[rt](12.5,3.85){high-temperature, high power}
210 \rput[rt](12.5,3.5){and high-frequency}
211 \rput[rt](12.5,3.15){electronic and optoelectronic devices}
213 \rput[rt](12.5,2.35){material suitable for extreme conditions}
214 \rput[rt](12.5,2){microelectromechanical systems}
215 \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
217 \rput[rt](12.5,0.85){first wall reactor material, detectors}
218 \rput[rt](12.5,0.5){and electronic devices for space}
222 \begin{picture}(0,0)(5,-162)
223 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
225 \begin{picture}(0,0)(-120,-162)
226 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
228 \begin{picture}(0,0)(-270,-162)
229 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
232 \begin{picture}(0,0)(10,65)
233 \includegraphics[height=2.8cm]{sic_switch.eps}
235 %\begin{picture}(0,0)(-243,65)
236 \begin{picture}(0,0)(-110,65)
237 \includegraphics[height=2.8cm]{ise_99.eps}
239 %\begin{picture}(0,0)(-135,65)
240 \begin{picture}(0,0)(-100,65)
241 \includegraphics[height=1.2cm]{infineon_schottky.eps}
243 \begin{picture}(0,0)(-233,65)
244 \includegraphics[height=2.8cm]{solar_car.eps}
255 Polytypes of SiC\\[0.6cm]
260 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
261 \begin{minipage}{1.9cm}
262 {\tiny cubic (twist)}
264 \begin{minipage}{2.9cm}
265 {\tiny hexagonal (no twist)}
268 \begin{picture}(0,0)(-150,0)
269 \includegraphics[width=7cm]{polytypes.eps}
276 \begin{tabular}{l c c c c c c}
278 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
280 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
281 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
282 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
283 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
284 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
285 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
286 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
290 \begin{pspicture}(0,0)(0,0)
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293 \begin{pspicture}(0,0)(0,0)
294 \psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
296 \begin{pspicture}(0,0)(0,0)
297 \psellipse[linecolor=red](10.45,0.42)(0.4,0.20)
308 Fabrication of silicon carbide
317 \emph{Silicon carbide --- Born from the stars, perfected on earth.}
323 SiC thin films by MBE \& CVD
325 \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
326 \item \underline{Commercially available} semiconductor power devices based on
327 \underline{\foreignlanguage{greek}{a}-SiC}
328 \item Production of favored \underline{3C-SiC} material
329 \underline{less advanced}
330 \item Quality and size not yet sufficient
332 \begin{picture}(0,0)(-310,-20)
333 \includegraphics[width=2.0cm]{cree.eps}
341 %{\footnotesize\color{black}
342 % Mismatch in \underline{thermal expansion coeefficient}
343 % and \underline{lattice parameter} w.r.t. substrate
350 {\bf Alternative approach}\\
351 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
358 \begin{minipage}{3.15cm}
360 \includegraphics[width=3cm]{imp.eps}\\
366 \begin{minipage}{3.15cm}
368 \includegraphics[width=3cm]{annealing.eps}\\
370 Postannealing at $>$ \degc{1200}
375 \begin{minipage}{5.5cm}
376 \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
379 XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
384 %\begin{minipage}{5.5cm}
387 %No surface bending effects\\
388 %High areal homogenity\\[0.1cm]
389 %$\Downarrow$\\[0.1cm]
390 %Synthesis of large area SiC films possible
401 IBS of epitaxial single crystalline 3C-SiC
410 \item \underline{Implantation step 1}\\[0.1cm]
411 Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
412 $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
413 {\color{blue}precipitates}
414 \item \underline{Implantation step 2}\\[0.1cm]
415 Little remaining dose | \unit[180]{keV} | \degc{250}\\
417 Destruction/Amorphization of precipitates at layer interface
418 \item \underline{Annealing}\\[0.1cm]
419 \unit[10]{h} at \degc{1250}\\
420 $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
424 \begin{minipage}{6.9cm}
425 \includegraphics[width=7cm]{ibs_3c-sic.eps}\\[-0.4cm]
428 XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
432 \begin{minipage}{5cm}
433 \begin{pspicture}(0,0)(0,0)
435 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
436 \begin{minipage}{5.3cm}
439 3C-SiC precipitation\\
440 not yet fully understood
444 \renewcommand\labelitemi{$\Rightarrow$}
445 Details of the SiC precipitation
447 \item significant technological progress\\
448 in SiC thin film formation
449 \item perspectives for processes relying\\
450 upon prevention of SiC precipitation
454 \rput(-6.8,5.5){\pnode{h0}}
455 \rput(-3.0,5.5){\pnode{h1}}
456 \ncline[linecolor=blue]{-}{h0}{h1}
457 \ncline[linecolor=blue]{->}{h1}{box}
467 Supposed precipitation mechanism of SiC in Si
475 \begin{minipage}{3.6cm}
477 Si \& SiC lattice structure\\[0.1cm]
478 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
481 \begin{minipage}{1.7cm}
482 \underline{Silicon}\\
483 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
484 $a=\unit[5.429]{\\A}$\\
485 $\rho^*_{\text{Si}}=\unit[100]{\%}$
487 \begin{minipage}{1.7cm}
488 \underline{Silicon carbide}\\
489 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
490 $a=\unit[4.359]{\\A}$\\
491 $\rho^*_{\text{Si}}=\unit[97]{\%}$
497 \begin{minipage}{4.1cm}
499 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
503 \begin{minipage}{4.0cm}
505 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
511 \begin{minipage}{4.0cm}
513 C-Si dimers (dumbbells)\\[-0.1cm]
518 \begin{minipage}{4.1cm}
520 Agglomeration of C-Si dumbbells\\[-0.1cm]
521 $\Rightarrow$ dark contrasts
525 \begin{minipage}{4.0cm}
527 Precipitation of 3C-SiC in Si\\[-0.1cm]
528 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
529 \& release of Si self-interstitials
535 \begin{minipage}{4.0cm}
537 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
541 \begin{minipage}{4.1cm}
543 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
547 \begin{minipage}{4.0cm}
549 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
553 \begin{pspicture}(0,0)(0,0)
554 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
555 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
556 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
557 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
558 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
559 $4a_{\text{Si}}=5a_{\text{SiC}}$
561 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
562 \hkl(h k l) planes match
564 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
575 Supposed precipitation mechanism of SiC in Si
583 \begin{minipage}{3.6cm}
585 Si \& SiC lattice structure\\[0.1cm]
586 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
589 \begin{minipage}{1.7cm}
590 \underline{Silicon}\\
591 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
592 $a=\unit[5.429]{\\A}$\\
593 $\rho^*_{\text{Si}}=\unit[100]{\%}$
595 \begin{minipage}{1.7cm}
596 \underline{Silicon carbide}\\
597 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
598 $a=\unit[4.359]{\\A}$\\
599 $\rho^*_{\text{Si}}=\unit[97]{\%}$
605 \begin{minipage}{4.1cm}
607 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
611 \begin{minipage}{4.0cm}
613 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
619 \begin{minipage}{4.0cm}
621 C-Si dimers (dumbbells)\\[-0.1cm]
622 on Si interstitial sites
626 \begin{minipage}{4.1cm}
628 Agglomeration of C-Si dumbbells\\[-0.1cm]
629 $\Rightarrow$ dark contrasts
633 \begin{minipage}{4.0cm}
635 Precipitation of 3C-SiC in Si\\[-0.1cm]
636 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
637 \& release of Si self-interstitials
643 \begin{minipage}{4.0cm}
645 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
649 \begin{minipage}{4.1cm}
651 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
655 \begin{minipage}{4.0cm}
657 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
661 \begin{pspicture}(0,0)(0,0)
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665 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
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667 $4a_{\text{Si}}=5a_{\text{SiC}}$
669 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
670 \hkl(h k l) planes match
672 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
675 % controversial view!
676 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
677 \begin{minipage}{14cm}
682 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
683 \begin{minipage}{10cm}
687 {\color{gray}\bf Controversial findings}
690 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
692 \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
693 \item \si{} reacting with further C in cleared volume
695 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
697 \item Room temperature implantation $\rightarrow$ high C diffusion
698 \item Elevated temperature implantation $\rightarrow$ no C redistribution
700 $\Rightarrow$ mobile {\color{red}\ci} opposed to
701 stable {\color{blue}\cs{}} configurations
702 \item Strained silicon \& Si/SiC heterostructures
703 {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
705 \item {\color{blue}Coherent} SiC precipitates (tensile strain)
706 \item Incoherent SiC (strain relaxation)
711 {\Huge${\lightning}$} \hspace{0.3cm}
712 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
713 {\Huge${\lightning}$}
733 \item Introduction / Motivation
734 \item Assumed SiC precipitation mechanisms / Controversy
736 \item Utilized simulation techniques
738 \item Molecular dynamics (MD) simulations
739 \item Density functional theory (DFT) calculations
741 \item Simulation results
743 \item C and Si self-interstitial point defects in silicon
744 \item Silicon carbide precipitation simulations
746 \item Summary / Conclusion
755 Utilized computational methods
762 {\bf Molecular dynamics (MD)}\\[0.1cm]
764 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
766 System of $N$ particles &
767 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
768 Phase space propagation &
769 Velocity Verlet | timestep: \unit[1]{fs} \\
770 Analytical interaction potential &
771 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
774 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
775 \pot_{ij} = {\color{red}f_C(r_{ij})}
776 \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
778 Observables: time/ensemble averages &
779 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
787 {\bf Density functional theory (DFT)}
791 \begin{minipage}[t]{6cm}
793 \item Hohenberg-Kohn theorem:\\
794 $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
795 \item Kohn-Sham approach:\\
796 Single-particle effective theory
800 \item Code: \textsc{vasp}
801 \item Plane wave basis set | $E_{\text{cut}}=\unit[300]{eV}$
803 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
806 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
808 \item Ultrasoft pseudopotential
809 \item Exchange \& correlation: GGA
810 \item Brillouin zone sampling: $\Gamma$-point
811 \item Supercell: $N=216\pm2$
814 \begin{minipage}{6cm}
815 \begin{pspicture}(0,0)(0,0)
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819 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
822 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
824 n(r)=\sum_i^N|\Phi_i(r)|^2
827 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
829 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
833 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
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835 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
846 Point defects \& defect migration
853 \begin{minipage}[b]{7.5cm}
854 {\bf Defect structure}\\
855 \begin{pspicture}(0,0)(7,4.4)
856 \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
859 \item Creation of c-Si simulation volume
860 \item Periodic boundary conditions
861 \item $T=0\text{ K}$, $p=0\text{ bar}$
864 \rput(3.5,1.3){\rnode{insert}{\psframebox{
867 Insertion of interstitial C/Si atoms
870 \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
873 Relaxation / structural energy minimization
876 \ncline[]{->}{init}{insert}
877 \ncline[]{->}{insert}{cool}
880 \begin{minipage}[b]{4.5cm}
882 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
884 \begin{minipage}{2.21cm}
886 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
887 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
888 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
891 \begin{minipage}{2.21cm}
893 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
894 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
895 {\color{black}$\bullet$} Vac. / Sub.
902 \begin{minipage}[b]{6cm}
903 {\bf Defect formation energy}\\
905 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
906 Particle reservoir: Si \& SiC\\[0.2cm]
907 {\bf Binding energy}\\
911 E_{\text{f}}^{\text{comb}}-
912 E_{\text{f}}^{1^{\text{st}}}-
913 E_{\text{f}}^{2^{\text{nd}}}
917 $E_{\text{b}}<0$: energetically favorable configuration\\
918 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
920 \begin{minipage}[b]{6cm}
921 {\bf Migration barrier}
924 \item Displace diffusing atom
925 \item Constrain relaxation of (diffusing) atoms
926 \item Record configurational energy
928 \begin{picture}(0,0)(-60,-33)
929 \includegraphics[width=4.5cm]{crt_mod.eps}
941 Si self-interstitial point defects in silicon\\[0.1cm]
945 \begin{tabular}{l c c c c c}
947 $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
949 \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
950 Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
952 \end{tabular}\\[0.4cm]
955 \begin{minipage}{3cm}
957 \underline{Vacancy}\\
958 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
961 \begin{minipage}{3cm}
963 \underline{\hkl<1 1 0> DB}\\
964 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
967 \begin{minipage}{3cm}
969 \underline{\hkl<1 0 0> DB}\\
970 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
973 \begin{minipage}{3cm}
975 \underline{Tetrahedral}\\
976 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
980 \underline{Hexagonal} \hspace{2pt}
981 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
983 \begin{minipage}{2.7cm}
984 $E_{\text{f}}^*=4.48\text{ eV}$\\
985 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
987 \begin{minipage}{0.4cm}
992 \begin{minipage}{2.7cm}
993 $E_{\text{f}}=3.96\text{ eV}$\\
994 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
997 \begin{minipage}{5.5cm}
999 {\tiny nearly T $\rightarrow$ T}\\
1001 \includegraphics[width=6.0cm]{nhex_tet.ps}
1012 C interstitial point defects in silicon\\
1015 \begin{tabular}{l c c c c c c r}
1017 $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
1018 {\color{black} \cs{} \& \si}\\
1020 \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1021 Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1023 \end{tabular}\\[0.1cm]
1026 \begin{minipage}{2.8cm}
1027 \underline{Hexagonal} \hspace{2pt}
1028 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1029 $E_{\text{f}}^*=9.05\text{ eV}$\\
1030 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
1032 \begin{minipage}{0.4cm}
1037 \begin{minipage}{2.8cm}
1038 \underline{\hkl<1 0 0>}\\
1039 $E_{\text{f}}=3.88\text{ eV}$\\
1040 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
1043 \begin{minipage}{1.4cm}
1046 \begin{minipage}{3.0cm}
1048 \underline{Tetrahedral}\\
1049 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
1054 \begin{minipage}{2.8cm}
1055 \underline{Bond-centered}\\
1056 $E_{\text{f}}^*=5.59\text{ eV}$\\
1057 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
1059 \begin{minipage}{0.4cm}
1064 \begin{minipage}{2.8cm}
1065 \underline{\hkl<1 1 0> dumbbell}\\
1066 $E_{\text{f}}=5.18\text{ eV}$\\
1067 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
1070 \begin{minipage}{1.4cm}
1073 \begin{minipage}{3.0cm}
1075 \underline{Substitutional}\\
1076 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
1086 C-Si dimer \& bond-centered interstitial configuration
1093 \begin{minipage}[t]{4.1cm}
1094 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
1095 \begin{minipage}{2.0cm}
1097 \underline{Erhart/Albe}
1098 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
1101 \begin{minipage}{2.0cm}
1103 \underline{\textsc{vasp}}
1104 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
1106 \end{minipage}\\[0.2cm]
1107 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
1108 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
1109 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
1110 $\Rightarrow$ $sp^2$ hybridization
1112 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
1113 {\tiny Charge density isosurface}
1116 \begin{minipage}{0.2cm}
1119 \begin{minipage}[t]{8.1cm}
1121 {\bf Bond-centered interstitial}\\[0.1cm]
1122 \begin{minipage}{4.4cm}
1125 \item Linear Si-C-Si bond
1126 \item Si: one C \& 3 Si neighbours
1127 \item Spin polarized calculations
1128 \item No saddle point!\\
1132 \begin{minipage}{2.7cm}
1133 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1135 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
1140 \begin{minipage}[t]{6.5cm}
1141 \begin{minipage}[t]{1.2cm}
1143 {\tiny sp$^3$}\\[0.8cm]
1144 \underline{${\color{black}\uparrow}$}
1145 \underline{${\color{black}\uparrow}$}
1146 \underline{${\color{black}\uparrow}$}
1147 \underline{${\color{red}\uparrow}$}\\
1150 \begin{minipage}[t]{1.4cm}
1152 {\color{red}M}{\color{blue}O}\\[0.8cm]
1153 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1154 $\sigma_{\text{ab}}$\\[0.5cm]
1155 \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1159 \begin{minipage}[t]{1.0cm}
1163 \underline{${\color{white}\uparrow\uparrow}$}
1164 \underline{${\color{white}\uparrow\uparrow}$}\\
1166 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1167 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1171 \begin{minipage}[t]{1.4cm}
1173 {\color{blue}M}{\color{green}O}\\[0.8cm]
1174 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1175 $\sigma_{\text{ab}}$\\[0.5cm]
1176 \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1180 \begin{minipage}[t]{1.2cm}
1183 {\tiny sp$^3$}\\[0.8cm]
1184 \underline{${\color{green}\uparrow}$}
1185 \underline{${\color{black}\uparrow}$}
1186 \underline{${\color{black}\uparrow}$}
1187 \underline{${\color{black}\uparrow}$}\\
1195 \begin{minipage}{3.0cm}
1197 \underline{Charge density}\\
1198 {\color{gray}$\bullet$} Spin up\\
1199 {\color{green}$\bullet$} Spin down\\
1200 {\color{blue}$\bullet$} Resulting spin up\\
1201 {\color{yellow}$\bullet$} Si atoms\\
1202 {\color{red}$\bullet$} C atom
1204 \begin{minipage}{3.6cm}
1205 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
1212 \begin{pspicture}(0,0)(0,0)
1213 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
1222 C interstitial migration --- ab initio
1229 \begin{minipage}{6.8cm}
1230 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
1231 \begin{minipage}{2.0cm}
1232 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1234 \begin{minipage}{0.2cm}
1237 \begin{minipage}{2.0cm}
1238 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
1240 \begin{minipage}{0.2cm}
1243 \begin{minipage}{2.0cm}
1244 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
1245 \end{minipage}\\[0.1cm]
1247 $\Rightarrow$ BC configuration constitutes local minimum\\
1248 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
1250 \begin{minipage}{5.4cm}
1251 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
1252 \end{minipage}\\[0.2cm]
1255 \begin{minipage}{6.8cm}
1256 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
1257 \begin{minipage}{2.0cm}
1258 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1260 \begin{minipage}{0.2cm}
1263 \begin{minipage}{2.0cm}
1264 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
1266 \begin{minipage}{0.2cm}
1269 \begin{minipage}{2.0cm}
1270 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
1271 \end{minipage}\\[0.1cm]
1272 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
1273 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
1274 Note: Change in orientation
1276 \begin{minipage}{5.4cm}
1277 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
1278 \end{minipage}\\[0.1cm]
1281 Reorientation pathway composed of two consecutive processes of the above type
1290 C interstitial migration --- analytical potential
1297 \begin{minipage}[t]{6.0cm}
1298 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
1299 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
1301 \item Lowermost migration barrier
1302 \item $\Delta E \approx \unit[2.2]{eV}$
1303 \item 2.4 times higher than ab initio result
1304 \item Different pathway
1307 \begin{minipage}[t]{0.2cm}
1310 \begin{minipage}[t]{6.0cm}
1311 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
1314 \item Bond-centered configuration unstable\\
1315 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1316 \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
1317 $\rightarrow$ \ci{} \hkl<1 1 0> DB
1320 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
1322 \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
1323 \item 2.4 -- 3.4 times higher than ab initio result
1324 \item After all: Change of the DB orientation
1330 {\color{red}\bf Drastically overestimated diffusion barrier}
1333 \begin{pspicture}(0,0)(0,0)
1334 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
1350 \begin{minipage}{9cm}
1352 Summary of combinations}\\[0.1cm]
1354 \begin{tabular}{l c c c c c c}
1356 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1358 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1359 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1360 \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}\\
1361 \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}\\
1362 \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}\\
1363 \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}\\
1365 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1366 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1373 $E_{\text{b}}$ explainable by stress compensation / increase
1377 \begin{minipage}{3cm}
1378 \includegraphics[width=3.5cm]{comb_pos.eps}
1383 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1384 \begin{minipage}[t]{3.2cm}
1385 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1386 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1388 \begin{minipage}[t]{3.0cm}
1389 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1390 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1392 \begin{minipage}[t]{6.1cm}
1395 \item \ci{} agglomeration energetically favorable
1396 \item Most favorable: C clustering\\
1397 {\color{red}However \ldots}\\
1398 \ldots high migration barrier ($>4\,\text{eV}$)\\
1400 $4\times{\color{cyan}[-2.25]}$ versus
1401 $2\times{\color{orange}[-2.39]}$
1404 {\color{blue}\ci{} agglomeration / no C clustering}
1421 \begin{minipage}{9cm}
1423 Summary of combinations}\\[0.1cm]
1425 \begin{tabular}{l c c c c c c}
1427 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1429 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1430 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1431 \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}\\
1432 \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}\\
1433 \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}\\
1434 \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}\\
1436 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1437 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1444 $E_{\text{b}}$ explainable by stress compensation / increase
1448 \begin{minipage}{3cm}
1449 \includegraphics[width=3.5cm]{comb_pos.eps}
1454 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1455 \begin{minipage}[t]{3.2cm}
1456 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1457 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1459 \begin{minipage}[t]{3.0cm}
1460 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1461 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1463 \begin{minipage}[t]{6.1cm}
1466 \item \ci{} agglomeration energetically favorable
1467 \item Most favorable: C clustering\\
1468 {\color{red}However \ldots}\\
1469 \ldots high migration barrier ($>4\,\text{eV}$)\\
1471 $4\times{\color{cyan}[-2.25]}$ versus
1472 $2\times{\color{orange}[-2.39]}$
1475 {\color{blue}\ci{} agglomeration / no C clustering}
1480 \begin{pspicture}(0,0)(0,0)
1481 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1482 \begin{minipage}{14cm}
1487 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1488 \begin{minipage}{8cm}
1492 Interaction along \hkl[1 1 0]
1493 \includegraphics[width=7cm]{db_along_110_cc.ps}
1505 Defect combinations of C-Si dimers and vacancies
1511 \begin{minipage}[b]{2.6cm}
1513 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1514 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1517 \begin{minipage}[b]{7cm}
1520 \begin{minipage}[b]{2.6cm}
1522 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1523 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1525 \end{minipage}\\[0.2cm]
1527 \begin{minipage}{6.5cm}
1528 \includegraphics[width=6.0cm]{059-539.ps}
1530 \begin{minipage}{5.7cm}
1531 \includegraphics[width=6.0cm]{314-539.ps}
1534 \begin{pspicture}(0,0)(0,0)
1535 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1537 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1538 \begin{minipage}{6.5cm}
1540 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1541 Low migration barrier towards C$_{\text{sub}}$\\
1543 High barrier for reverse process\\[0.3cm]
1545 High probability of stable C$_{\text{sub}}$ configuration
1558 Combinations of substitutional C and Si self-interstitials
1565 \begin{minipage}{6.2cm}
1567 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1569 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1570 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1571 \item Interaction drops quickly to zero\\
1572 $\rightarrow$ low capture radius
1576 \begin{minipage}{0.2cm}
1579 \begin{minipage}{6.0cm}
1581 {\bf Transition from the ground state}
1583 \item Low transition barrier
1584 \item Barrier smaller than \ci{} migration barrier
1585 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1586 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1589 \end{minipage}\\[0.3cm]
1591 \begin{minipage}{6.0cm}
1592 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1594 \begin{minipage}{0.4cm}
1597 \begin{minipage}{6.0cm}
1599 \includegraphics[width=6.0cm]{162-097.ps}
1603 \begin{pspicture}(0,0)(0,0)
1604 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1605 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1606 \begin{minipage}{8cm}
1610 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1611 IBS --- process far from equilibrium\\
1624 Combinations of substitutional C and Si self-interstitials
1631 \begin{minipage}{6.2cm}
1633 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1635 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1636 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1637 \item Interaction drops quickly to zero\\
1638 $\rightarrow$ low capture radius
1642 \begin{minipage}{0.2cm}
1645 \begin{minipage}{6.0cm}
1647 {\bf Transition from the ground state}
1649 \item Low transition barrier
1650 \item Barrier smaller than \ci{} migration barrier
1651 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1652 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1655 \end{minipage}\\[0.3cm]
1657 \begin{minipage}{6.0cm}
1658 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1660 \begin{minipage}{0.4cm}
1663 \begin{minipage}{6.0cm}
1665 \includegraphics[width=6.0cm]{162-097.ps}
1669 \begin{pspicture}(0,0)(0,0)
1670 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1671 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1672 \begin{minipage}{8cm}
1676 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1677 IBS --- process far from equilibrium\\
1685 \begin{pspicture}(0,0)(0,0)
1686 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1687 \begin{minipage}{14cm}
1692 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1693 \begin{minipage}{11cm}
1697 Ab initio MD at \degc{900}\\[0.4cm]
1698 \begin{minipage}{5.4cm}
1700 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1703 \begin{minipage}{5.4cm}
1705 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1707 \end{minipage}\\[0.5cm]
1709 Contribution of entropy to structural formation\\[0.1cm]
1722 Silicon carbide precipitation simulations
1732 \begin{pspicture}(0,0)(12,6.5)
1734 \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1737 \item Create c-Si volume
1738 \item Periodc boundary conditions
1739 \item Set requested $T$ and $p=0\text{ bar}$
1740 \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1743 \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1745 Insertion of C atoms at constant T
1747 \item total simulation volume {\pnode{in1}}
1748 \item volume of minimal SiC precipitate size {\pnode{in2}}
1749 \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1753 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1755 Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1757 \ncline[]{->}{init}{insert}
1758 \ncline[]{->}{insert}{cool}
1759 \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
1760 \rput(7.6,6){\footnotesize $V_1$}
1761 \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
1762 \rput(8.9,4.85){\tiny $V_2$}
1763 \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
1764 \rput(9.25,4.45){\footnotesize $V_3$}
1765 \rput(7.9,3.2){\pnode{ins1}}
1766 \rput(8.92,2.8){\pnode{ins2}}
1767 \rput(10.8,2.4){\pnode{ins3}}
1768 \ncline[]{->}{in1}{ins1}
1769 \ncline[]{->}{in2}{ins2}
1770 \ncline[]{->}{in3}{ins3}
1780 \begin{minipage}{5.7cm}
1782 \item Amount of C atoms: 6000\\
1783 ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
1784 \item Simulation volume: $31^3$ Si unit cells\\
1788 \begin{minipage}{0.3cm}
1792 \begin{minipage}{6.0cm}
1793 Restricted to classical potential caclulations\\
1794 $\rightarrow$ Low C diffusion / overestimated barrier\\
1795 $\rightarrow$ Consider $V_2$ and $V_3$
1797 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
1808 Silicon carbide precipitation simulations at \degc{450} as in IBS
1813 \begin{minipage}{6.3cm}
1814 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1815 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1818 \begin{minipage}{6.1cm}
1820 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1821 \hkl<1 0 0> C-Si dumbbell dominated structure
1823 \item Si-C bumbs around \unit[0.19]{nm}
1824 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1825 concatenated differently oriented \ci{} DBs
1826 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1828 \begin{pspicture}(0,0)(6.0,1.0)
1829 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1830 \begin{minipage}{6cm}
1832 Formation of \ci{} dumbbells\\
1833 C atoms in proper 3C-SiC distance first
1836 \end{pspicture}\\[0.1cm]
1837 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1839 \item High amount of strongly bound C-C bonds
1840 \item Increased defect \& damage density\\
1841 $\rightarrow$ Arrangements hard to categorize and trace
1842 \item Only short range order observable
1844 \begin{pspicture}(0,0)(6.0,0.8)
1845 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1846 \begin{minipage}{6cm}
1848 Amorphous SiC-like phase
1851 \end{pspicture}\\[0.3cm]
1852 \begin{pspicture}(0,0)(6.0,2.0)
1853 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
1854 \begin{minipage}{6cm}
1868 Silicon carbide precipitation simulations at \degc{450} as in IBS
1873 \begin{minipage}{6.3cm}
1874 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1875 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1878 \begin{minipage}{6.1cm}
1880 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1881 \hkl<1 0 0> C-Si dumbbell dominated structure
1883 \item Si-C bumbs around \unit[0.19]{nm}
1884 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1885 concatenated differently oriented \ci{} DBs
1886 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1888 \begin{pspicture}(0,0)(6.0,1.0)
1889 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1890 \begin{minipage}{6cm}
1892 Formation of \ci{} dumbbells\\
1893 C atoms in proper 3C-SiC distance first
1896 \end{pspicture}\\[0.1cm]
1897 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1899 \item High amount of strongly bound C-C bonds
1900 \item Increased defect \& damage density\\
1901 $\rightarrow$ Arrangements hard to categorize and trace
1902 \item Only short range order observable
1904 \begin{pspicture}(0,0)(6.0,0.8)
1905 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1906 \begin{minipage}{6cm}
1908 Amorphous SiC-like phase
1911 \end{pspicture}\\[0.3cm]
1912 \begin{pspicture}(0,0)(6.0,2.0)
1913 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
1914 \begin{minipage}{6cm}
1917 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
1918 \begin{minipage}{0.8cm}
1919 {\bf\boldmath $V_1$:}
1921 \begin{minipage}{5.1cm}
1922 Formation of \ci{} indeed occurs\\
1923 Agllomeration not observed
1924 \end{minipage}\\[0.3cm]
1925 \begin{minipage}{0.8cm}
1926 {\bf\boldmath $V_{2,3}$:}
1928 \begin{minipage}{5.1cm}
1929 Amorphous SiC-like structure\\
1930 (not expected at \degc{450})\\[0.05cm]
1931 No rearrangement/transition into 3C-SiC
1932 \end{minipage}\\[0.1cm]
1944 Limitations of MD and short range potentials
1951 {\bf Time scale problem of MD}\\[0.2cm]
1952 Precise integration \& thermodynamic sampling\\
1953 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
1954 $\omega$: vibrational mode\\
1955 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
1956 Several local minima separated by large energy barriers\\
1957 $\Rightarrow$ Transition event corresponds to a multiple
1958 of vibrational periods\\
1959 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
1960 infrequent transition events\\[0.2cm]
1961 {\color{blue}Accelerated methods:}
1962 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1966 {\bf Limitations related to the short range potential}\\[0.2cm]
1967 Cut-off function limits interaction to next neighbours\\
1968 $\Rightarrow$ Overestimated unphysical high forces of next neighbours
1973 {\bf Approach to the (twofold) problem}\\[0.2cm]
1974 Increased temperature simulations without TAD corrections\\
1975 Accelerated methods or higher time scales exclusively not sufficient!
1977 \begin{pspicture}(0,0)(0,0)
1978 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
1979 \begin{minipage}{7.5cm}
1982 Potential enhanced slow phase space propagation
1985 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1986 \begin{minipage}{2.7cm}
1990 thermodynamic sampling
1993 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
1994 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
1995 \begin{minipage}{3.6cm}
1998 \underline{IBS}\\[0.1cm]
1999 3C-SiC also observed for higher T\\[0.1cm]
2000 Higher T inside sample\\[0.1cm]
2001 Structural evolution vs.\\
2002 equilibrium properties
2005 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
2014 Increased temperature simulations --- $V_1$
2019 \begin{minipage}{6.2cm}
2020 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2023 \begin{minipage}{6.2cm}
2024 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2027 \begin{minipage}{6.2cm}
2028 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2031 \begin{minipage}{6.3cm}
2033 \underline{Si-C bonds:}
2035 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2036 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2038 \underline{Si-Si bonds:}
2039 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2040 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2041 \underline{C-C bonds:}
2043 \item C-C next neighbour pairs reduced (mandatory)
2044 \item Peak at 0.3 nm slightly shifted
2046 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2047 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2049 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2051 \item Range [|-$\downarrow$]:
2052 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2053 with nearby Si$_{\text{I}}$}
2064 Increased temperature simulations --- $V_1$
2069 \begin{minipage}{6.2cm}
2070 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2073 \begin{minipage}{6.2cm}
2074 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2077 \begin{minipage}{6.2cm}
2078 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2081 \begin{minipage}{6.3cm}
2083 \underline{Si-C bonds:}
2085 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2086 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2088 \underline{Si-Si bonds:}
2089 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2090 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2091 \underline{C-C bonds:}
2093 \item C-C next neighbour pairs reduced (mandatory)
2094 \item Peak at 0.3 nm slightly shifted
2096 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2097 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2099 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2101 \item Range [|-$\downarrow$]:
2102 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2103 with nearby Si$_{\text{I}}$}
2109 \begin{pspicture}(0,0)(0,0)
2110 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
2111 \begin{minipage}{14cm}
2116 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
2117 \begin{minipage}{9cm}
2121 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
2122 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
2125 \item Stretched coherent SiC structures\\
2126 $\Rightarrow$ Precipitation process involves {\color{blue}\cs}
2129 \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
2130 \item Building block for surrounding Si host \& further SiC
2131 \item Strain compensation \ldots\\
2132 \ldots Si/SiC interface\\
2133 \ldots within stretched coherent SiC structure
2135 \item Explains annealing behavior of high/low T C implantations
2137 \item Low T: highly mobile {\color{red}\ci}
2138 \item High T: stable configurations of {\color{blue}\cs}
2143 \psframebox[linecolor=blue,linewidth=0.05cm]{
2144 \begin{minipage}{7cm}
2146 Precipitation mechanism involving \cs\\
2147 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2157 % skip high c conc results
2163 Increased temperature simulations at high C concentration
2168 \begin{minipage}{6.0cm}
2169 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2171 \begin{minipage}{6.0cm}
2172 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2180 \begin{minipage}[t]{6.0cm}
2181 0.186 nm: Si-C pairs $\uparrow$\\
2182 (as expected in 3C-SiC)\\[0.2cm]
2183 0.282 nm: Si-C-C\\[0.2cm]
2184 $\approx$0.35 nm: C-Si-Si
2187 \begin{minipage}{0.2cm}
2191 \begin{minipage}[t]{6.0cm}
2192 0.15 nm: C-C pairs $\uparrow$\\
2193 (as expected in graphite/diamond)\\[0.2cm]
2194 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2195 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2200 \item Decreasing cut-off artifact
2201 \item {\color{red}Amorphous} SiC-like phase remains
2202 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2203 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2212 High C \& small $V$ \& short $t$
2215 Slow restructuring due to strong C-C bonds
2218 High C \& low T implants
2236 Summary and Conclusions
2244 \begin{minipage}{12.3cm}
2249 \item Point defects excellently / fairly well described
2251 \item Identified \ci{} migration path
2252 \item EA drastically overestimates the diffusion barrier
2254 \item Combinations of defects
2256 \item Agglomeration of point defects energetically favorable
2257 \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2258 \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2259 Low barrier (\unit[0.77]{eV}) \& low capture radius
2266 \begin{minipage}[t]{12.3cm}
2267 \underline{Pecipitation simulations}
2269 \item Problem of potential enhanced slow phase space propagation
2270 \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2271 \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2272 \item High T necessary to simulate IBS conditions (far from equilibrium)
2273 \item Increased participation of \cs{} in the precipitation process
2274 \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2275 (stretched SiC, interface)
2282 \framebox{Precipitation by successive agglomeration of \cs{}}
2301 \underline{Augsburg}
2303 \item Prof. B. Stritzker
2304 \item Prof. F. Haider
2308 \underline{Berlin/Brandenburg}
2313 \underline{Helsinki}
2315 \item Prof. K. Nordlund
2320 \item Bayerische Forschungsstiftung
2323 \underline{Paderborn}
2325 \item Prof. J. Lindner
2326 \item Prof. G. Schmidt
2334 \bf Thank you for your attention!