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32 \graphicspath{{../img/}}
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42 \usepackage{semlayer} % Seminar overlays
43 \usepackage{slidesec} % Seminar sections and list of slides
45 \input{seminar.bug} % Official bugs corrections
46 \input{seminar.bg2} % Unofficial bugs corrections
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71 % specify width and height
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101 \begin{pspicture}(0,0)(0,0)
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)
189 \psframe*[linecolor=hb](-0.2,0)(12.9,5)
191 \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.2,1)(6.5,1)(6.5,3)(5.2,3)
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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}
256 Fabrication of silicon carbide
265 \emph{Silicon carbide --- Born from the stars, perfected on earth.}
271 SiC thin films by MBE \& CVD
273 \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
274 \item \underline{Commercially available} semiconductor power devices based on
275 \underline{\foreignlanguage{greek}{a}-SiC}
276 \item Production of favored \underline{3C-SiC} material
277 \underline{less advanced}
278 \item Quality and size not yet sufficient
280 \begin{picture}(0,0)(-310,-20)
281 \includegraphics[width=2.0cm]{cree.eps}
289 %{\footnotesize\color{black}
290 % Mismatch in \underline{thermal expansion coeefficient}
291 % and \underline{lattice parameter} w.r.t. substrate
298 {\bf Alternative approach}\\
299 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
306 \begin{minipage}{3.15cm}
308 \includegraphics[width=3cm]{imp.eps}\\
314 \begin{minipage}{3.15cm}
316 \includegraphics[width=3cm]{annealing.eps}\\
318 Postannealing at $>$ \degc{1200}
323 \begin{minipage}{5.5cm}
324 \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
327 XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
332 %\begin{minipage}{5.5cm}
335 %No surface bending effects\\
336 %High areal homogenity\\[0.1cm]
337 %$\Downarrow$\\[0.1cm]
338 %Synthesis of large area SiC films possible
350 IBS of epitaxial single crystalline 3C-SiC
359 \item \underline{Implantation step 1}\\[0.1cm]
360 Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
361 $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
362 {\color{blue}precipitates}
363 \item \underline{Implantation step 2}\\[0.1cm]
364 Low remaining amount of dose | \unit[180]{keV} | \degc{250}\\
366 Destruction/Amorphization of precipitates at layer interface
367 \item \underline{Annealing}\\[0.1cm]
368 \unit[10]{h} at \degc{1250}\\
369 $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
373 \begin{minipage}{6.9cm}
374 \includegraphics[width=7cm]{ibs_3c-sic.eps}\\[-0.4cm]
377 XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
381 \begin{minipage}{5cm}
382 \begin{pspicture}(0,0)(0,0)
384 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
385 \begin{minipage}{5.3cm}
388 3C-SiC precipitation\\
389 not yet fully understood
393 \renewcommand\labelitemi{$\Rightarrow$}
394 Details of the SiC precipitation
396 \item significant technological progress\\
397 in SiC thin film formation
398 \item perspectives for processes relying\\
399 upon prevention of SiC precipitation
403 \rput(-6.8,5.5){\pnode{h0}}
404 \rput(-3.0,5.5){\pnode{h1}}
405 \ncline[linecolor=blue]{-}{h0}{h1}
406 \ncline[linecolor=blue]{->}{h1}{box}
416 Supposed precipitation mechanism of SiC in Si
424 \begin{minipage}{3.6cm}
426 Si \& SiC lattice structure\\[0.1cm]
427 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
430 \begin{minipage}{1.7cm}
431 \underline{Silicon}\\
432 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
433 $a=\unit[5.429]{\\A}$\\
434 $\rho^*_{\text{Si}}=\unit[100]{\%}$
436 \begin{minipage}{1.7cm}
437 \underline{Silicon carbide}\\
438 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
439 $a=\unit[4.359]{\\A}$\\
440 $\rho^*_{\text{Si}}=\unit[97]{\%}$
446 \begin{minipage}{4.1cm}
448 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
452 \begin{minipage}{4.0cm}
454 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
460 \begin{minipage}{4.0cm}
462 C-Si dimers (dumbbells)\\[-0.1cm]
467 \begin{minipage}{4.1cm}
469 Agglomeration of C-Si dumbbells\\[-0.1cm]
470 $\Rightarrow$ dark contrasts
474 \begin{minipage}{4.0cm}
476 Precipitation of 3C-SiC in Si\\[-0.1cm]
477 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
478 \& release of Si self-interstitials
484 \begin{minipage}{4.0cm}
486 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
490 \begin{minipage}{4.1cm}
492 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
496 \begin{minipage}{4.0cm}
498 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
502 \begin{pspicture}(0,0)(0,0)
503 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
504 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
505 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
506 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
507 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
508 $4a_{\text{Si}}=5a_{\text{SiC}}$
510 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
511 \hkl(h k l) planes match
513 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
524 Supposed precipitation mechanism of SiC in Si
532 \begin{minipage}{3.6cm}
534 Si \& SiC lattice structure\\[0.1cm]
535 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
538 \begin{minipage}{1.7cm}
539 \underline{Silicon}\\
540 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
541 $a=\unit[5.429]{\\A}$\\
542 $\rho^*_{\text{Si}}=\unit[100]{\%}$
544 \begin{minipage}{1.7cm}
545 \underline{Silicon carbide}\\
546 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
547 $a=\unit[4.359]{\\A}$\\
548 $\rho^*_{\text{Si}}=\unit[97]{\%}$
554 \begin{minipage}{4.1cm}
556 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
560 \begin{minipage}{4.0cm}
562 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
568 \begin{minipage}{4.0cm}
570 C-Si dimers (dumbbells)\\[-0.1cm]
571 on Si interstitial sites
575 \begin{minipage}{4.1cm}
577 Agglomeration of C-Si dumbbells\\[-0.1cm]
578 $\Rightarrow$ dark contrasts
582 \begin{minipage}{4.0cm}
584 Precipitation of 3C-SiC in Si\\[-0.1cm]
585 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
586 \& release of Si self-interstitials
592 \begin{minipage}{4.0cm}
594 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
598 \begin{minipage}{4.1cm}
600 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
604 \begin{minipage}{4.0cm}
606 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
610 \begin{pspicture}(0,0)(0,0)
611 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
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613 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
614 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
615 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
616 $4a_{\text{Si}}=5a_{\text{SiC}}$
618 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
619 \hkl(h k l) planes match
621 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
624 % controversial view!
625 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
626 \begin{minipage}{14cm}
631 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
632 \begin{minipage}{10cm}
636 {\color{gray}\bf Controversial findings}
639 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
641 \item {\color{blue}Substitutionally} incorporated C on regular Si lattice sites
642 \item \si{} reacting with further C in cleared volume
644 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
646 \item Room temperature implantation $\rightarrow$ high C diffusion
647 \item Elevated temperature implantation $\rightarrow$ no C redistribution
649 $\Rightarrow$ mobile {\color{red}\ci} opposed to
650 stable {\color{blue}\cs{}} configurations
651 \item Strained silicon \& Si$_{1-y}$C$_y$ heterostructures
652 {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
654 \item Initial {\color{blue}coherent} SiC precipitates (tensile strain)
655 \item Incoherent SiC (strain relaxation)
660 {\Huge${\lightning}$} \hspace{0.3cm}
661 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
662 {\Huge${\lightning}$}
682 \item Introduction / Motivation
683 \item Assumed SiC precipitation mechanisms / Controversy
685 \item Utilized simulation techniques
687 \item Molecular dynamics (MD) simulations
688 \item Density functional theory (DFT) calculations
690 \item Simulation results
692 \item C and Si self-interstitial point defects in silicon
693 \item Silicon carbide precipitation simulations
695 \item Summary / Conclusion
704 Utilized computational methods
711 {\bf Molecular dynamics (MD)}\\[0.1cm]
713 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
715 System of $N$ particles &
716 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
717 Phase space propagation &
718 Velocity Verlet | timestep: \unit[1]{fs} \\
719 Analytical interaction potential &
720 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
723 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
724 \pot_{ij} = {\color{red}f_C(r_{ij})}
725 \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
727 Observables: time/ensemble averages &
728 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
736 {\bf Density functional theory (DFT)}
740 \begin{minipage}[t]{6cm}
742 \item Hohenberg-Kohn theorem:\\
743 $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
744 \item Kohn-Sham approach:\\
745 Single-particle effective theory
749 \item Code: \textsc{vasp}
750 \item Plane wave basis set | $E_{\text{cut}}=\unit[300]{eV}$
752 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
755 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
757 \item Ultrasoft pseudopotential
758 \item Exchange \& correlation: GGA
759 \item Brillouin zone sampling: $\Gamma$-point
760 \item Supercell: $N=216\pm2$
763 \begin{minipage}{6cm}
764 \begin{pspicture}(0,0)(0,0)
765 \pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
766 \rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
768 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
771 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
773 n(r)=\sum_i^N|\Phi_i(r)|^2
776 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
778 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
782 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
783 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
784 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
795 Point defects \& defect migration
802 \begin{minipage}[b]{7.5cm}
803 {\bf Defect structure}\\
804 \begin{pspicture}(0,0)(7,4.4)
805 \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
808 \item Creation of c-Si simulation volume
809 \item Periodic boundary conditions
810 \item $T=0\text{ K}$, $p=0\text{ bar}$
813 \rput(3.5,1.3){\rnode{insert}{\psframebox{
816 Insertion of interstitial C/Si atoms
819 \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
822 Relaxation / structural energy minimization
825 \ncline[]{->}{init}{insert}
826 \ncline[]{->}{insert}{cool}
829 \begin{minipage}[b]{4.5cm}
831 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
833 \begin{minipage}{2.21cm}
835 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
836 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
837 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
840 \begin{minipage}{2.21cm}
842 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
843 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
844 {\color{black}$\bullet$} Vac. / Sub.
851 \begin{minipage}[b]{6cm}
852 {\bf Defect formation energy}\\
854 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
855 Particle reservoir: Si \& SiC\\[0.2cm]
856 {\bf Binding energy}\\
860 E_{\text{f}}^{\text{comb}}-
861 E_{\text{f}}^{1^{\text{st}}}-
862 E_{\text{f}}^{2^{\text{nd}}}
866 $E_{\text{b}}<0$: energetically favorable configuration\\
867 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
869 \begin{minipage}[b]{6cm}
870 {\bf Migration barrier}
873 \item Displace diffusing atom
874 \item Constrain relaxation of (diffusing) atoms
875 \item Record configurational energy
877 \begin{picture}(0,0)(-60,-33)
878 \includegraphics[width=4.5cm]{crt_mod.eps}
890 Si self-interstitial point defects in silicon\\[0.1cm]
894 \begin{tabular}{l c c c c c}
896 $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
898 \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
899 Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
901 \end{tabular}\\[0.4cm]
904 \begin{minipage}{3cm}
906 \underline{Vacancy}\\
907 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
910 \begin{minipage}{3cm}
912 \underline{\hkl<1 1 0> DB}\\
913 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
916 \begin{minipage}{3cm}
918 \underline{\hkl<1 0 0> DB}\\
919 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
922 \begin{minipage}{3cm}
924 \underline{Tetrahedral}\\
925 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
929 \underline{Hexagonal} \hspace{2pt}
930 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
932 \begin{minipage}{2.7cm}
933 $E_{\text{f}}^*=4.48\text{ eV}$\\
934 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
936 \begin{minipage}{0.4cm}
941 \begin{minipage}{2.7cm}
942 $E_{\text{f}}=3.96\text{ eV}$\\
943 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
946 \begin{minipage}{5.5cm}
948 {\tiny nearly T $\rightarrow$ T}\\
950 \includegraphics[width=6.0cm]{nhex_tet.ps}
961 C interstitial point defects in silicon\\
964 \begin{tabular}{l c c c c c c r}
966 $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
967 {\color{black} \cs{} \& \si}\\
969 \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
970 Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
972 \end{tabular}\\[0.1cm]
975 \begin{minipage}{2.8cm}
976 \underline{Hexagonal} \hspace{2pt}
977 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
978 $E_{\text{f}}^*=9.05\text{ eV}$\\
979 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
981 \begin{minipage}{0.4cm}
986 \begin{minipage}{2.8cm}
987 \underline{\hkl<1 0 0>}\\
988 $E_{\text{f}}=3.88\text{ eV}$\\
989 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
992 \begin{minipage}{1.4cm}
995 \begin{minipage}{3.0cm}
997 \underline{Tetrahedral}\\
998 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
1003 \begin{minipage}{2.8cm}
1004 \underline{Bond-centered}\\
1005 $E_{\text{f}}^*=5.59\text{ eV}$\\
1006 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
1008 \begin{minipage}{0.4cm}
1013 \begin{minipage}{2.8cm}
1014 \underline{\hkl<1 1 0> dumbbell}\\
1015 $E_{\text{f}}=5.18\text{ eV}$\\
1016 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
1019 \begin{minipage}{1.4cm}
1022 \begin{minipage}{3.0cm}
1024 \underline{Substitutional}\\
1025 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
1035 C-Si dimer \& bond-centered interstitial configuration
1042 \begin{minipage}[t]{4.1cm}
1043 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
1044 \begin{minipage}{2.0cm}
1046 \underline{Erhart/Albe}
1047 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
1050 \begin{minipage}{2.0cm}
1052 \underline{\textsc{vasp}}
1053 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
1055 \end{minipage}\\[0.2cm]
1056 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
1057 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
1058 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
1059 $\Rightarrow$ $sp^2$ hybridization
1061 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
1062 {\tiny Charge density isosurface}
1065 \begin{minipage}{0.2cm}
1068 \begin{minipage}[t]{8.1cm}
1070 {\bf Bond-centered interstitial}\\[0.1cm]
1071 \begin{minipage}{4.4cm}
1074 \item Linear Si-C-Si bond
1075 \item Si: one C \& 3 Si neighbours
1076 \item Spin polarized calculations
1077 \item No saddle point!\\
1081 \begin{minipage}{2.7cm}
1082 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1084 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
1089 \begin{minipage}[t]{6.5cm}
1090 \begin{minipage}[t]{1.2cm}
1092 {\tiny sp$^3$}\\[0.8cm]
1093 \underline{${\color{black}\uparrow}$}
1094 \underline{${\color{black}\uparrow}$}
1095 \underline{${\color{black}\uparrow}$}
1096 \underline{${\color{red}\uparrow}$}\\
1099 \begin{minipage}[t]{1.4cm}
1101 {\color{red}M}{\color{blue}O}\\[0.8cm]
1102 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1103 $\sigma_{\text{ab}}$\\[0.5cm]
1104 \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1108 \begin{minipage}[t]{1.0cm}
1112 \underline{${\color{white}\uparrow\uparrow}$}
1113 \underline{${\color{white}\uparrow\uparrow}$}\\
1115 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1116 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1120 \begin{minipage}[t]{1.4cm}
1122 {\color{blue}M}{\color{green}O}\\[0.8cm]
1123 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1124 $\sigma_{\text{ab}}$\\[0.5cm]
1125 \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1129 \begin{minipage}[t]{1.2cm}
1132 {\tiny sp$^3$}\\[0.8cm]
1133 \underline{${\color{green}\uparrow}$}
1134 \underline{${\color{black}\uparrow}$}
1135 \underline{${\color{black}\uparrow}$}
1136 \underline{${\color{black}\uparrow}$}\\
1144 \begin{minipage}{3.0cm}
1146 \underline{Charge density}\\
1147 {\color{gray}$\bullet$} Spin up\\
1148 {\color{green}$\bullet$} Spin down\\
1149 {\color{blue}$\bullet$} Resulting spin up\\
1150 {\color{yellow}$\bullet$} Si atoms\\
1151 {\color{red}$\bullet$} C atom
1153 \begin{minipage}{3.6cm}
1154 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
1161 \begin{pspicture}(0,0)(0,0)
1162 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
1171 C interstitial migration --- ab initio
1178 \begin{minipage}{6.8cm}
1179 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
1180 \begin{minipage}{2.0cm}
1181 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1183 \begin{minipage}{0.2cm}
1186 \begin{minipage}{2.0cm}
1187 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
1189 \begin{minipage}{0.2cm}
1192 \begin{minipage}{2.0cm}
1193 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
1194 \end{minipage}\\[0.1cm]
1196 $\Rightarrow$ BC configuration constitutes local minimum\\
1197 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
1199 \begin{minipage}{5.4cm}
1200 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
1201 %\end{minipage}\\[0.2cm]
1202 \end{minipage}\\[0.3cm]
1205 \begin{minipage}{6.8cm}
1206 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
1207 \begin{minipage}{2.0cm}
1208 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1210 \begin{minipage}{0.2cm}
1213 \begin{minipage}{2.0cm}
1214 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
1216 \begin{minipage}{0.2cm}
1219 \begin{minipage}{2.0cm}
1220 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
1221 \end{minipage}\\[0.1cm]
1222 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
1223 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
1224 Note: Change in orientation
1226 \begin{minipage}{5.4cm}
1227 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
1228 \end{minipage}\\[0.1cm]
1231 %Reorientation pathway composed of two consecutive processes of the above type
1240 C interstitial migration --- analytical potential
1247 \begin{minipage}[t]{6.0cm}
1248 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
1249 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
1251 \item Lowermost migration barrier
1252 \item $\Delta E \approx \unit[2.2]{eV}$
1253 \item 2.4 times higher than ab initio result
1254 \item Different pathway
1257 \begin{minipage}[t]{0.2cm}
1260 \begin{minipage}[t]{6.0cm}
1261 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
1264 \item Bond-centered configuration unstable\\
1265 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1266 \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
1267 $\rightarrow$ \ci{} \hkl<1 1 0> DB
1270 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
1272 \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
1273 \item 2.4 -- 3.4 times higher than ab initio result
1274 \item After all: Change of the DB orientation
1280 {\color{red}\bf Drastically overestimated diffusion barrier}
1283 \begin{pspicture}(0,0)(0,0)
1284 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
1300 \begin{minipage}{9cm}
1302 Summary of combinations}\\[0.1cm]
1304 \begin{tabular}{l c c c c c c}
1306 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1308 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1309 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1310 \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}\\
1311 \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}\\
1312 \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}\\
1313 \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}\\
1315 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1316 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1323 $E_{\text{b}}$ explainable by stress compensation / increase
1327 \begin{minipage}{3cm}
1328 \includegraphics[width=3.5cm]{comb_pos.eps}
1333 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1334 \begin{minipage}[t]{3.2cm}
1335 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1336 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1338 \begin{minipage}[t]{3.0cm}
1339 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1340 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1342 \begin{minipage}[t]{6.1cm}
1345 \item \ci{} agglomeration energetically favorable
1346 \item Most favorable: C clustering\\
1347 {\color{red}However \ldots}\\
1348 \ldots high migration barrier ($>4\,\text{eV}$)\\
1350 $4\times{\color{cyan}[-2.25]}$ versus
1351 $2\times{\color{orange}[-2.39]}$
1354 {\color{blue}\ci{} agglomeration / no C clustering}
1371 \begin{minipage}{9cm}
1373 Summary of combinations}\\[0.1cm]
1375 \begin{tabular}{l c c c c c c}
1377 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1379 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1380 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1381 \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}\\
1382 \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}\\
1383 \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}\\
1384 \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}\\
1386 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1387 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1394 $E_{\text{b}}$ explainable by stress compensation / increase
1398 \begin{minipage}{3cm}
1399 \includegraphics[width=3.5cm]{comb_pos.eps}
1404 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1405 \begin{minipage}[t]{3.2cm}
1406 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1407 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1409 \begin{minipage}[t]{3.0cm}
1410 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1411 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1413 \begin{minipage}[t]{6.1cm}
1416 \item \ci{} agglomeration energetically favorable
1417 \item Most favorable: C clustering\\
1418 {\color{red}However \ldots}\\
1419 \ldots high migration barrier ($>4\,\text{eV}$)\\
1421 $4\times{\color{cyan}[-2.25]}$ versus
1422 $2\times{\color{orange}[-2.39]}$
1425 {\color{blue}\ci{} agglomeration / no C clustering}
1430 \begin{pspicture}(0,0)(0,0)
1431 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1432 \begin{minipage}{14cm}
1437 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1438 \begin{minipage}{8cm}
1442 Interaction along \hkl[1 1 0]
1443 \includegraphics[width=7cm]{db_along_110_cc.ps}
1455 Defect combinations of C-Si dimers and vacancies
1461 \begin{minipage}[b]{2.6cm}
1463 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1464 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1467 \begin{minipage}[b]{7cm}
1470 \begin{minipage}[b]{2.6cm}
1472 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1473 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1475 \end{minipage}\\[0.2cm]
1477 \begin{minipage}{6.5cm}
1478 \includegraphics[width=6.0cm]{059-539.ps}
1480 \begin{minipage}{5.7cm}
1481 \includegraphics[width=6.0cm]{314-539.ps}
1484 \begin{pspicture}(0,0)(0,0)
1485 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1487 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1488 \begin{minipage}{6.5cm}
1490 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1491 Low migration barrier towards C$_{\text{sub}}$\\
1493 High barrier for reverse process\\[0.3cm]
1495 High probability of stable C$_{\text{sub}}$ configuration
1508 Combinations of substitutional C and Si self-interstitials
1515 \begin{minipage}{6.2cm}
1517 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1519 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1520 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1521 \item Interaction drops quickly to zero\\
1522 $\rightarrow$ low capture radius
1526 \begin{minipage}{0.2cm}
1529 \begin{minipage}{6.0cm}
1531 {\bf Transition from the ground state}
1533 \item Low transition barrier
1534 \item Barrier smaller than \ci{} migration barrier
1535 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1536 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1539 \end{minipage}\\[0.3cm]
1541 \begin{minipage}{6.0cm}
1542 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1544 \begin{minipage}{0.4cm}
1547 \begin{minipage}{6.0cm}
1549 \includegraphics[width=6.0cm]{162-097.ps}
1553 \begin{pspicture}(0,0)(0,0)
1554 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1555 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1556 \begin{minipage}{8cm}
1560 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1561 IBS --- process far from equilibrium\\
1574 Combinations of substitutional C and Si self-interstitials
1581 \begin{minipage}{6.2cm}
1583 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1585 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1586 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1587 \item Interaction drops quickly to zero\\
1588 $\rightarrow$ low capture radius
1592 \begin{minipage}{0.2cm}
1595 \begin{minipage}{6.0cm}
1597 {\bf Transition from the ground state}
1599 \item Low transition barrier
1600 \item Barrier smaller than \ci{} migration barrier
1601 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1602 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1605 \end{minipage}\\[0.3cm]
1607 \begin{minipage}{6.0cm}
1608 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1610 \begin{minipage}{0.4cm}
1613 \begin{minipage}{6.0cm}
1615 \includegraphics[width=6.0cm]{162-097.ps}
1619 \begin{pspicture}(0,0)(0,0)
1620 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1621 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1622 \begin{minipage}{8cm}
1626 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1627 IBS --- process far from equilibrium\\
1635 \begin{pspicture}(0,0)(0,0)
1636 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1637 \begin{minipage}{14cm}
1642 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1643 \begin{minipage}{11cm}
1647 Ab initio MD at \degc{900}\\[0.4cm]
1648 \begin{minipage}{5.4cm}
1650 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1653 \begin{minipage}{5.4cm}
1655 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1657 \end{minipage}\\[0.5cm]
1659 Contribution of entropy to structural formation\\[0.1cm]
1672 Silicon carbide precipitation simulations
1682 \begin{pspicture}(0,0)(12,6.5)
1684 \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1687 \item Create c-Si volume
1688 \item Periodc boundary conditions
1689 \item Set requested $T$ and $p=0\text{ bar}$
1690 \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1693 \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1695 Insertion of C atoms at constant T
1697 \item total simulation volume {\pnode{in1}}
1698 \item volume of minimal SiC precipitate size {\pnode{in2}}
1699 \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1703 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1705 Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1707 \ncline[]{->}{init}{insert}
1708 \ncline[]{->}{insert}{cool}
1709 \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
1710 \rput(7.6,6){\footnotesize $V_1$}
1711 \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
1712 \rput(8.9,4.85){\tiny $V_2$}
1713 \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
1714 \rput(9.25,4.45){\footnotesize $V_3$}
1715 \rput(7.9,3.2){\pnode{ins1}}
1716 \rput(8.92,2.8){\pnode{ins2}}
1717 \rput(10.8,2.4){\pnode{ins3}}
1718 \ncline[]{->}{in1}{ins1}
1719 \ncline[]{->}{in2}{ins2}
1720 \ncline[]{->}{in3}{ins3}
1730 \begin{minipage}{5.7cm}
1732 \item Amount of C atoms: 6000\\
1733 ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
1734 \item Simulation volume: $31^3$ Si unit cells\\
1738 \begin{minipage}{0.3cm}
1742 \begin{minipage}{6.0cm}
1743 Restricted to classical potential caclulations\\
1744 $\rightarrow$ Low C diffusion / overestimated barrier\\
1745 $\rightarrow$ Consider $V_2$ and $V_3$
1747 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
1758 Silicon carbide precipitation simulations at \degc{450} as in IBS
1763 \begin{minipage}{6.3cm}
1764 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1765 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1768 \begin{minipage}{6.1cm}
1770 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1771 \hkl<1 0 0> C-Si dumbbell dominated structure
1773 \item Si-C bumbs around \unit[0.19]{nm}
1774 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1775 concatenated differently oriented \ci{} DBs
1776 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1778 \begin{pspicture}(0,0)(6.0,1.0)
1779 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1780 \begin{minipage}{6cm}
1782 Formation of \ci{} dumbbells\\
1783 C atoms in proper 3C-SiC distance first
1786 \end{pspicture}\\[0.1cm]
1787 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1789 \item High amount of strongly bound C-C bonds
1790 \item Increased defect \& damage density\\
1791 $\rightarrow$ Arrangements hard to categorize and trace
1792 \item Only short range order observable
1794 \begin{pspicture}(0,0)(6.0,0.8)
1795 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1796 \begin{minipage}{6cm}
1798 Amorphous SiC-like phase
1801 \end{pspicture}\\[0.3cm]
1802 \begin{pspicture}(0,0)(6.0,2.0)
1803 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
1804 \begin{minipage}{6cm}
1818 Silicon carbide precipitation simulations at \degc{450} as in IBS
1823 \begin{minipage}{6.3cm}
1824 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1825 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1828 \begin{minipage}{6.1cm}
1830 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1831 \hkl<1 0 0> C-Si dumbbell dominated structure
1833 \item Si-C bumbs around \unit[0.19]{nm}
1834 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1835 concatenated differently oriented \ci{} DBs
1836 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1838 \begin{pspicture}(0,0)(6.0,1.0)
1839 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1840 \begin{minipage}{6cm}
1842 Formation of \ci{} dumbbells\\
1843 C atoms in proper 3C-SiC distance first
1846 \end{pspicture}\\[0.1cm]
1847 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1849 \item High amount of strongly bound C-C bonds
1850 \item Increased defect \& damage density\\
1851 $\rightarrow$ Arrangements hard to categorize and trace
1852 \item Only short range order observable
1854 \begin{pspicture}(0,0)(6.0,0.8)
1855 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1856 \begin{minipage}{6cm}
1858 Amorphous SiC-like phase
1861 \end{pspicture}\\[0.3cm]
1862 \begin{pspicture}(0,0)(6.0,2.0)
1863 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
1864 \begin{minipage}{6cm}
1867 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
1868 \begin{minipage}{0.8cm}
1869 {\bf\boldmath $V_1$:}
1871 \begin{minipage}{5.1cm}
1872 Formation of \ci{} indeed occurs\\
1873 Agllomeration not observed
1874 \end{minipage}\\[0.3cm]
1875 \begin{minipage}{0.8cm}
1876 {\bf\boldmath $V_{2,3}$:}
1878 \begin{minipage}{5.1cm}
1879 Amorphous SiC-like structure\\
1880 (not expected at \degc{450})\\[0.05cm]
1881 No rearrangement/transition into 3C-SiC
1882 \end{minipage}\\[0.1cm]
1894 Limitations of MD and short range potentials
1901 {\bf Time scale problem of MD}\\[0.2cm]
1902 Precise integration \& thermodynamic sampling\\
1903 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
1904 $\omega$: vibrational mode\\
1905 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
1906 Several local minima separated by large energy barriers\\
1907 $\Rightarrow$ Transition event corresponds to a multiple
1908 of vibrational periods\\
1909 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
1910 infrequent transition events\\[0.2cm]
1911 {\color{blue}Accelerated methods:}
1912 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1916 {\bf Limitations related to the short range potential}\\[0.2cm]
1917 Cut-off function limits interaction to next neighbours\\
1918 $\Rightarrow$ Overestimated unphysical high forces of next neighbours
1923 {\bf Approach to the (twofold) problem}\\[0.2cm]
1924 Increased temperature simulations without TAD corrections\\
1925 Accelerated methods or higher time scales exclusively not sufficient!
1927 \begin{pspicture}(0,0)(0,0)
1928 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
1929 \begin{minipage}{7.5cm}
1932 Potential enhanced slow phase space propagation
1935 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1936 \begin{minipage}{2.7cm}
1940 thermodynamic sampling
1943 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
1944 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
1945 \begin{minipage}{3.6cm}
1948 \underline{IBS}\\[0.1cm]
1949 3C-SiC also observed for higher T\\[0.1cm]
1950 Higher T inside sample\\[0.1cm]
1951 Structural evolution vs.\\
1952 equilibrium properties
1955 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
1964 Increased temperature simulations --- $V_1$
1969 \begin{minipage}{6.2cm}
1970 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1973 \begin{minipage}{6.2cm}
1974 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
1977 \begin{minipage}{6.2cm}
1978 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
1981 \begin{minipage}{6.3cm}
1983 \underline{Si-C bonds:}
1985 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1986 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
1988 \underline{Si-Si bonds:}
1989 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1990 ($\rightarrow$ 0.325 nm)\\[0.1cm]
1991 \underline{C-C bonds:}
1993 \item C-C next neighbour pairs reduced (mandatory)
1994 \item Peak at 0.3 nm slightly shifted
1996 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
1997 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
1999 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2001 \item Range [|-$\downarrow$]:
2002 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2003 with nearby Si$_{\text{I}}$}
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$_{\text{I}}$}
2059 \begin{pspicture}(0,0)(0,0)
2060 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
2061 \begin{minipage}{14cm}
2066 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
2067 \begin{minipage}{9cm}
2071 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
2072 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
2075 \item Stretched coherent SiC structures\\
2076 $\Rightarrow$ Precipitation process involves {\color{blue}\cs}
2079 \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
2080 \item Building block for surrounding Si host \& further SiC
2081 \item Strain compensation \ldots\\
2082 \ldots Si/SiC interface\\
2083 \ldots within stretched coherent SiC structure
2085 \item Explains annealing behavior of high/low T C implantations
2087 \item Low T: highly mobile {\color{red}\ci}
2088 \item High T: stable configurations of {\color{blue}\cs}
2093 \psframebox[linecolor=blue,linewidth=0.05cm]{
2094 \begin{minipage}{7cm}
2096 Precipitation mechanism involving \cs\\
2097 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2107 % skip high c conc results
2113 Increased temperature simulations at high C concentration
2118 \begin{minipage}{6.0cm}
2119 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2121 \begin{minipage}{6.0cm}
2122 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2130 \begin{minipage}[t]{6.0cm}
2131 0.186 nm: Si-C pairs $\uparrow$\\
2132 (as expected in 3C-SiC)\\[0.2cm]
2133 0.282 nm: Si-C-C\\[0.2cm]
2134 $\approx$0.35 nm: C-Si-Si
2137 \begin{minipage}{0.2cm}
2141 \begin{minipage}[t]{6.0cm}
2142 0.15 nm: C-C pairs $\uparrow$\\
2143 (as expected in graphite/diamond)\\[0.2cm]
2144 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2145 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2150 \item Decreasing cut-off artifact
2151 \item {\color{red}Amorphous} SiC-like phase remains
2152 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2153 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2162 High C \& small $V$ \& short $t$
2165 Slow restructuring due to strong C-C bonds
2168 High C \& low T implants
2186 Summary and Conclusions
2194 \begin{minipage}{12.3cm}
2199 \item Point defects excellently / fairly well described
2201 \item Identified \ci{} migration path
2202 \item EA drastically overestimates the diffusion barrier
2204 \item Combinations of defects
2206 \item Agglomeration of point defects energetically favorable
2207 \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2208 \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2209 Low barrier (\unit[0.77]{eV}) \& low capture radius
2216 \begin{minipage}[t]{12.3cm}
2217 \underline{Pecipitation simulations}
2219 \item Problem of potential enhanced slow phase space propagation
2220 \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2221 \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2222 \item High T necessary to simulate IBS conditions (far from equilibrium)
2223 \item Increased participation of \cs{} in the precipitation process
2224 \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2225 (stretched SiC, interface)
2232 \framebox{Precipitation by successive agglomeration of \cs{}}
2251 \underline{Augsburg}
2253 \item Prof. B. Stritzker
2257 \underline{Helsinki}
2259 \item Prof. K. Nordlund
2264 \item Bayerische Forschungsstiftung
2267 \underline{Paderborn}
2269 \item Prof. J. Lindner
2270 \item Prof. G. Schmidt
2278 \normalsize\bf Thank you for your attention!
2288 Polytypes of SiC\\[0.6cm]
2293 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
2294 \begin{minipage}{1.9cm}
2295 {\tiny cubic (twist)}
2297 \begin{minipage}{2.9cm}
2298 {\tiny hexagonal (no twist)}
2301 \begin{picture}(0,0)(-150,0)
2302 \includegraphics[width=7cm]{polytypes.eps}
2309 \begin{tabular}{l c c c c c c}
2311 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
2313 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
2314 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
2315 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
2316 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
2317 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
2318 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
2319 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
2323 \begin{pspicture}(0,0)(0,0)
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2326 \begin{pspicture}(0,0)(0,0)
2327 \psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
2329 \begin{pspicture}(0,0)(0,0)
2330 \psellipse[linecolor=red](10.45,0.42)(0.4,0.20)