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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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66 \extraslideheight{10in}
71 % specify width and height
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79 \newcommand{\pot}{\mathcal{V}}
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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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118 \newcommand{\perc}[1]{\unit[#1]{\%}{}}
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}
255 IBS of epitaxial single crystalline 3C-SiC
264 \item \underline{Implantation step 1}\\[0.1cm]
265 Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
266 $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
267 {\color{blue}precipitates}
268 \item \underline{Implantation step 2}\\[0.1cm]
269 Low remaining amount of dose | \unit[180]{keV} | \degc{250}\\
271 Destruction/Amorphization of precipitates at layer interface
272 \item \underline{Annealing}\\[0.1cm]
273 \unit[10]{h} at \degc{1250}\\
274 $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
278 \begin{minipage}{6.9cm}
279 \includegraphics[width=7cm]{ibs_3c-sic.eps}\\[-0.4cm]
282 XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
286 \begin{minipage}{5cm}
287 \begin{pspicture}(0,0)(0,0)
289 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
290 \begin{minipage}{5.3cm}
293 3C-SiC precipitation\\
294 not yet fully understood
298 % \renewcommand\labelitemi{$\Rightarrow$}
299 % Details of the SiC precipitation
301 % \item significant technological progress\\
302 % in SiC thin film formation
303 % \item perspectives for processes relying\\
304 % upon prevention of SiC precipitation
308 \rput(-6.8,5.5){\pnode{h0}}
309 \rput(-3.0,5.5){\pnode{h1}}
310 \ncline[linecolor=blue]{-}{h0}{h1}
311 \ncline[linecolor=blue]{->}{h1}{box}
321 Supposed precipitation mechanism of SiC in Si
329 \begin{minipage}{3.6cm}
331 Si \& SiC lattice structure\\[0.1cm]
332 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
335 \begin{minipage}{1.7cm}
336 \underline{Silicon}\\
337 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
338 $a=\unit[5.429]{\\A}$\\
339 $\rho^*_{\text{Si}}=\unit[100]{\%}$
341 \begin{minipage}{1.7cm}
342 \underline{Silicon carbide}\\
343 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
344 $a=\unit[4.359]{\\A}$\\
345 $\rho^*_{\text{Si}}=\unit[97]{\%}$
351 \begin{minipage}{4.1cm}
353 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
357 \begin{minipage}{4.0cm}
359 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
365 \begin{minipage}{4.0cm}
367 C-Si dimers (dumbbells)\\[-0.1cm]
372 \begin{minipage}{4.1cm}
374 Agglomeration of C-Si dumbbells\\[-0.1cm]
375 $\Rightarrow$ dark contrasts
379 \begin{minipage}{4.0cm}
381 Precipitation of 3C-SiC in Si\\[-0.1cm]
382 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
383 \& release of Si self-interstitials
389 \begin{minipage}{4.0cm}
391 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
395 \begin{minipage}{4.1cm}
397 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
401 \begin{minipage}{4.0cm}
403 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
407 \begin{pspicture}(0,0)(0,0)
408 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
409 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
410 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
411 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
412 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
413 $4a_{\text{Si}}=5a_{\text{SiC}}$
415 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
416 \hkl(h k l) planes match
418 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
429 Supposed precipitation mechanism of SiC in Si
437 \begin{minipage}{3.6cm}
439 Si \& SiC lattice structure\\[0.1cm]
440 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
443 \begin{minipage}{1.7cm}
444 \underline{Silicon}\\
445 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
446 $a=\unit[5.429]{\\A}$\\
447 $\rho^*_{\text{Si}}=\unit[100]{\%}$
449 \begin{minipage}{1.7cm}
450 \underline{Silicon carbide}\\
451 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
452 $a=\unit[4.359]{\\A}$\\
453 $\rho^*_{\text{Si}}=\unit[97]{\%}$
459 \begin{minipage}{4.1cm}
461 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
465 \begin{minipage}{4.0cm}
467 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
473 \begin{minipage}{4.0cm}
475 C-Si dimers (dumbbells)\\[-0.1cm]
476 on Si interstitial sites
480 \begin{minipage}{4.1cm}
482 Agglomeration of C-Si dumbbells\\[-0.1cm]
483 $\Rightarrow$ dark contrasts
487 \begin{minipage}{4.0cm}
489 Precipitation of 3C-SiC in Si\\[-0.1cm]
490 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
491 \& release of Si self-interstitials
497 \begin{minipage}{4.0cm}
499 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
503 \begin{minipage}{4.1cm}
505 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
509 \begin{minipage}{4.0cm}
511 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
515 \begin{pspicture}(0,0)(0,0)
516 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
517 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
518 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
519 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
520 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
521 $4a_{\text{Si}}=5a_{\text{SiC}}$
523 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
524 \hkl(h k l) planes match
526 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
529 % controversial view!
530 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
531 \begin{minipage}{14cm}
536 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
537 \begin{minipage}{10cm}
541 {\color{gray}\bf Controversial findings}
544 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
546 \item {\color{blue}Substitutionally} incorporated C on regular Si lattice sites
547 \item \si{} reacting with further C in cleared volume
549 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
551 \item Room temperature implantation $\rightarrow$ high C diffusion
552 \item Elevated temperature implantation $\rightarrow$ no C redistribution
554 $\Rightarrow$ mobile {\color{red}\ci} opposed to
555 stable {\color{blue}\cs{}} configurations
556 \item Strained Si$_{1-y}$C$_y$/Si heterostructures
557 {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
559 \item Initial {\color{blue}coherent} SiC structures (tensile strain)
560 \item Incoherent SiC nanocrystals (strain relaxation)
565 {\Huge${\lightning}$} \hspace{0.3cm}
566 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
567 {\Huge${\lightning}$}
587 \item Introduction / Motivation
588 \item Assumed SiC precipitation mechanisms / Controversy
590 \item Utilized simulation techniques
592 \item Molecular dynamics (MD) simulations
593 \item Density functional theory (DFT) calculations
595 \item Simulation results
597 \item C and Si self-interstitial point defects in silicon
598 \item Silicon carbide precipitation simulations
600 \item Summary / Conclusion
609 Utilized computational methods
616 {\bf Molecular dynamics (MD)}\\[0.1cm]
618 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
620 System of $N$ particles &
621 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
622 Phase space propagation &
623 Velocity Verlet | timestep: \unit[1]{fs} \\
624 Analytical interaction potential &
625 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
628 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
629 \pot_{ij} = {\color{red}f_C(r_{ij})}
630 \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
632 Observables: time/ensemble averages &
633 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
641 {\bf Density functional theory (DFT)}
645 \begin{minipage}[t]{6cm}
647 \item Hohenberg-Kohn theorem:\\
648 $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
649 \item Kohn-Sham approach:\\
650 Single-particle effective theory
654 \item Code: \textsc{vasp}
655 \item Plane wave basis set | $E_{\text{cut}}=\unit[300]{eV}$
657 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
660 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
662 \item Ultrasoft pseudopotential
663 \item Exchange \& correlation: GGA
664 \item Brillouin zone sampling: $\Gamma$-point
665 \item Supercell: $N=216\pm2$
668 \begin{minipage}{6cm}
669 \begin{pspicture}(0,0)(0,0)
670 \pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
671 \rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
673 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
676 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
678 n(r)=\sum_i^N|\Phi_i(r)|^2
681 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
683 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
687 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
688 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
689 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
700 Point defects \& defect migration
707 \begin{minipage}[b]{7.5cm}
708 {\bf Defect structure}\\
709 \begin{pspicture}(0,0)(7,4.4)
710 \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
713 \item Creation of c-Si simulation volume
714 \item Periodic boundary conditions
715 \item $T=0\text{ K}$, $p=0\text{ bar}$
718 \rput(3.5,1.3){\rnode{insert}{\psframebox{
721 Insertion of interstitial C/Si atoms
724 \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
727 Relaxation / structural energy minimization
730 \ncline[]{->}{init}{insert}
731 \ncline[]{->}{insert}{cool}
734 \begin{minipage}[b]{4.5cm}
736 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
738 \begin{minipage}{2.21cm}
740 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
741 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
742 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
745 \begin{minipage}{2.21cm}
747 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
748 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
749 {\color{black}$\bullet$} Vac. / Sub.
756 \begin{minipage}[t]{6cm}
757 {\bf Defect formation energy}\\
759 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.5cm]
760 %Particle reservoir: Si \& SiC\\[0.2cm]
761 {\bf Binding energy}\\
765 E_{\text{f}}^{\text{comb}}-
766 E_{\text{f}}^{1^{\text{st}}}-
767 E_{\text{f}}^{2^{\text{nd}}}
771 $E_{\text{b}}<0$: energetically favorable configuration\\
772 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
774 \begin{minipage}[t]{6cm}
776 {\bf Migration barrier}
779 \item Displace diffusing atom
780 \item Constrain relaxation of (diffusing) atoms
781 \item Record configurational energy
783 \begin{picture}(0,0)(-60,-33)
784 \includegraphics[width=4.5cm]{crt_mod.eps}
796 C interstitial point defects in silicon\\
799 \begin{tabular}{l c c c c c c r}
801 $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
802 {\color{black} \cs{} \& \si}\\
804 \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
805 Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
807 \end{tabular}\\[0.1cm]
810 \begin{minipage}{2.8cm}
811 \underline{Hexagonal} \hspace{2pt}
812 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
813 $E_{\text{f}}^*=9.05\text{ eV}$\\
814 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
816 \begin{minipage}{0.4cm}
821 \begin{minipage}{2.8cm}
822 \underline{\hkl<1 0 0>}\\
823 $E_{\text{f}}=3.88\text{ eV}$\\
824 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
827 \begin{minipage}{1.4cm}
830 \begin{minipage}{3.0cm}
832 \underline{Tetrahedral}\\
833 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
838 \begin{minipage}{2.8cm}
839 \underline{Bond-centered}\\
840 $E_{\text{f}}^*=5.59\text{ eV}$\\
841 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
843 \begin{minipage}{0.4cm}
848 \begin{minipage}{2.8cm}
849 \underline{\hkl<1 1 0> dumbbell}\\
850 $E_{\text{f}}=5.18\text{ eV}$\\
851 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
854 \begin{minipage}{1.4cm}
857 \begin{minipage}{3.0cm}
859 \underline{Substitutional}\\
860 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
870 C interstitial migration --- ab initio
877 \begin{minipage}{6.8cm}
878 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
879 \begin{minipage}{2.0cm}
880 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
882 \begin{minipage}{0.2cm}
885 \begin{minipage}{2.0cm}
886 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
888 \begin{minipage}{0.2cm}
891 \begin{minipage}{2.0cm}
892 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
893 \end{minipage}\\[0.1cm]
895 $\Rightarrow$ Sufficient to consider \hkl[00-1] to BC transition\\
896 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
898 \begin{minipage}{5.4cm}
899 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
900 %\end{minipage}\\[0.2cm]
901 \end{minipage}\\[0.4cm]
904 \begin{minipage}{6.8cm}
905 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
906 \begin{minipage}{2.0cm}
907 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
909 \begin{minipage}{0.2cm}
912 \begin{minipage}{2.0cm}
913 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
915 \begin{minipage}{0.2cm}
918 \begin{minipage}{2.0cm}
919 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
920 \end{minipage}\\[0.1cm]
921 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
922 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
923 Note: Change in orientation
925 \begin{minipage}{5.4cm}
926 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
927 \end{minipage}\\[0.1cm]
930 %Reorientation pathway composed of two consecutive processes of the above type
939 C interstitial migration --- analytical potential
946 \begin{minipage}[t]{6.0cm}
947 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
948 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
950 \item Lowermost migration barrier
951 \item $\Delta E \approx \unit[2.2]{eV}$
952 \item 2.4 times higher than ab initio result
953 \item Different pathway
956 \begin{minipage}[t]{0.2cm}
959 \begin{minipage}[t]{6.0cm}
960 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
963 \item Bond-centered configuration unstable\\
964 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
965 \item Minimum of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
966 $\rightarrow$ \ci{} \hkl<1 1 0> DB
969 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
971 \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
972 \item 2.4 -- 3.4 times higher than ab initio result
973 \item After all: Change of the DB orientation
979 {\color{red}\bf Drastically overestimated diffusion barrier}
982 \begin{pspicture}(0,0)(0,0)
983 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
992 Defect combinations --- ab inito
999 \begin{minipage}{9cm}
1001 Summary of combinations}\\[0.1cm]
1003 \begin{tabular}{l c c c c c c}
1005 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1007 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1008 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1009 \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}\\
1010 \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}\\
1011 \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}\\
1012 \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}\\
1014 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1015 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1022 $E_{\text{b}}$ explainable by stress compensation / increase
1026 \begin{minipage}{3cm}
1027 \includegraphics[width=3.5cm]{comb_pos.eps}
1032 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1033 \begin{minipage}[t]{3.2cm}
1034 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1035 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1037 \begin{minipage}[t]{3.0cm}
1038 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1039 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1041 \begin{minipage}[t]{6.1cm}
1044 \item \ci{} agglomeration energetically favorable
1045 \item Most favorable: C clustering\\
1046 {\color{red}However \ldots}\\
1047 \ldots high migration barrier ($>4\,\text{eV}$)\\
1049 $4\times{\color{cyan}[-2.25]}$ versus
1050 $2\times{\color{orange}[-2.39]}$
1053 {\color{blue}\ci{} agglomeration / no C clustering}
1070 \begin{minipage}{9cm}
1072 Summary of combinations}\\[0.1cm]
1074 \begin{tabular}{l c c c c c c}
1076 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1078 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1079 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1080 \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}\\
1081 \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}\\
1082 \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}\\
1083 \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}\\
1085 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1086 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1093 $E_{\text{b}}$ explainable by stress compensation / increase
1097 \begin{minipage}{3cm}
1098 \includegraphics[width=3.5cm]{comb_pos.eps}
1103 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1104 \begin{minipage}[t]{3.2cm}
1105 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1106 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1108 \begin{minipage}[t]{3.0cm}
1109 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1110 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1112 \begin{minipage}[t]{6.1cm}
1115 \item \ci{} agglomeration energetically favorable
1116 \item Most favorable: C clustering\\
1117 {\color{red}However \ldots}\\
1118 \ldots high migration barrier ($>4\,\text{eV}$)\\
1120 $4\times{\color{cyan}[-2.25]}$ versus
1121 $2\times{\color{orange}[-2.39]}$
1124 {\color{blue}\ci{} agglomeration / no C clustering}
1129 \begin{pspicture}(0,0)(0,0)
1130 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1131 \begin{minipage}{14cm}
1136 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1137 \begin{minipage}{8cm}
1141 Interaction along \hkl[1 1 0]
1142 \includegraphics[width=7cm]{db_along_110_cc.ps}
1154 Defect combinations of C-Si dimers and vacancies
1160 \begin{minipage}[b]{2.6cm}
1162 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1163 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1166 \begin{minipage}[b]{7cm}
1169 \begin{minipage}[b]{2.6cm}
1171 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1172 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1174 \end{minipage}\\[0.2cm]
1176 \begin{minipage}{6.5cm}
1177 \includegraphics[width=6.0cm]{059-539.ps}
1179 \begin{minipage}{5.7cm}
1180 \includegraphics[width=6.0cm]{314-539.ps}
1183 \begin{pspicture}(0,0)(0,0)
1184 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1186 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1187 \begin{minipage}{6.5cm}
1189 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1190 Low migration barrier towards C$_{\text{sub}}$\\
1192 High barrier for reverse process\\[0.3cm]
1194 High probability of stable C$_{\text{sub}}$ configuration
1207 Combinations of substitutional C and Si self-interstitials
1214 \begin{minipage}{6.2cm}
1216 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1218 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1219 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1220 \item Interaction drops quickly to zero\\
1221 $\rightarrow$ low capture radius
1225 \begin{minipage}{0.2cm}
1228 \begin{minipage}{6.0cm}
1230 {\bf Transition from the ground state}
1232 \item Low transition barrier
1233 \item Barrier smaller than \ci{} migration barrier
1234 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1235 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1238 \end{minipage}\\[0.3cm]
1240 \begin{minipage}{6.0cm}
1241 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1243 \begin{minipage}{0.4cm}
1246 \begin{minipage}{6.0cm}
1248 \includegraphics[width=6.0cm]{162-097.ps}
1252 \begin{pspicture}(0,0)(0,0)
1253 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1254 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1255 \begin{minipage}{8cm}
1259 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1260 IBS --- process far from equilibrium\\
1273 Combinations of substitutional C and Si self-interstitials
1280 \begin{minipage}{6.2cm}
1282 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1284 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1285 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1286 \item Interaction drops quickly to zero\\
1287 $\rightarrow$ low capture radius
1291 \begin{minipage}{0.2cm}
1294 \begin{minipage}{6.0cm}
1296 {\bf Transition from the ground state}
1298 \item Low transition barrier
1299 \item Barrier smaller than \ci{} migration barrier
1300 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1301 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1304 \end{minipage}\\[0.3cm]
1306 \begin{minipage}{6.0cm}
1307 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1309 \begin{minipage}{0.4cm}
1312 \begin{minipage}{6.0cm}
1314 \includegraphics[width=6.0cm]{162-097.ps}
1318 \begin{pspicture}(0,0)(0,0)
1319 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1320 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1321 \begin{minipage}{8cm}
1325 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1326 IBS --- process far from equilibrium\\
1334 \begin{pspicture}(0,0)(0,0)
1335 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1336 \begin{minipage}{14cm}
1341 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1342 \begin{minipage}{11cm}
1346 Ab initio MD at \degc{900}\\[0.4cm]
1347 \begin{minipage}{5.4cm}
1349 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1352 \begin{minipage}{5.4cm}
1354 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1356 \end{minipage}\\[0.5cm]
1358 Contribution of entropy to structural formation\\[0.1cm]
1371 Silicon carbide precipitation simulations
1381 \begin{pspicture}(0,0)(12,6.5)
1383 \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1386 \item Create c-Si volume
1387 \item Periodc boundary conditions
1388 \item Set requested $T$ and $p=0\text{ bar}$
1389 \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1392 \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1394 Insertion of C atoms at constant T
1396 \item total simulation volume {\pnode{in1}}
1397 \item volume of minimal SiC precipitate size {\pnode{in2}}
1398 \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1402 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1404 Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1406 \ncline[]{->}{init}{insert}
1407 \ncline[]{->}{insert}{cool}
1408 \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
1409 \rput(7.6,6){\footnotesize $V_1$}
1410 \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
1411 \rput(8.9,4.85){\tiny $V_2$}
1412 \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
1413 \rput(9.25,4.45){\footnotesize $V_3$}
1414 \rput(7.9,3.2){\pnode{ins1}}
1415 \rput(8.92,2.8){\pnode{ins2}}
1416 \rput(10.8,2.4){\pnode{ins3}}
1417 \ncline[]{->}{in1}{ins1}
1418 \ncline[]{->}{in2}{ins2}
1419 \ncline[]{->}{in3}{ins3}
1429 \begin{minipage}{5.7cm}
1431 \item Amount of C atoms: 6000\\
1432 ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
1433 \item Simulation volume: $31^3$ Si unit cells\\
1437 \begin{minipage}{0.3cm}
1441 \begin{minipage}{6.0cm}
1442 Restricted to classical potential caclulations\\
1443 $\rightarrow$ Low C diffusion / overestimated barrier\\
1444 $\rightarrow$ Consider $V_2$ and $V_3$
1446 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
1457 Silicon carbide precipitation simulations at \degc{450} as in IBS
1462 \begin{minipage}{6.3cm}
1463 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1464 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1467 \begin{minipage}{6.1cm}
1469 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1470 \ci{} \hkl<1 0 0> dumbbell dominated structure
1472 \item Si-C bumbs around \unit[0.19]{nm}
1473 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1474 concatenated differently oriented \ci{} DBs
1475 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1477 \begin{pspicture}(0,0)(6.0,1.0)
1478 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1479 \begin{minipage}{6cm}
1481 Formation of \ci{} dumbbells\\
1482 C atoms separated as expected in 3C-SiC
1485 \end{pspicture}\\[0.1cm]
1486 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1488 \item High amount of strongly bound C-C bonds
1489 \item Increased defect \& damage density\\
1490 $\rightarrow$ Arrangements hard to categorize and trace
1491 \item Only short range order observable
1493 \begin{pspicture}(0,0)(6.0,0.8)
1494 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1495 \begin{minipage}{6cm}
1497 Amorphous SiC-like phase
1500 \end{pspicture}\\[0.3cm]
1501 \begin{pspicture}(0,0)(6.0,2.0)
1502 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
1503 \begin{minipage}{6cm}
1517 Silicon carbide precipitation simulations at \degc{450} as in IBS
1522 \begin{minipage}{6.3cm}
1523 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1524 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1527 \begin{minipage}{6.1cm}
1529 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1530 \ci{} \hkl<1 0 0> dumbbell dominated structure
1532 \item Si-C bumbs around \unit[0.19]{nm}
1533 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1534 concatenated differently oriented \ci{} DBs
1535 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1537 \begin{pspicture}(0,0)(6.0,1.0)
1538 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1539 \begin{minipage}{6cm}
1541 Formation of \ci{} dumbbells\\
1542 C atoms separated as expected in 3C-SiC
1545 \end{pspicture}\\[0.1cm]
1546 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1548 \item High amount of strongly bound C-C bonds
1549 \item Increased defect \& damage density\\
1550 $\rightarrow$ Arrangements hard to categorize and trace
1551 \item Only short range order observable
1553 \begin{pspicture}(0,0)(6.0,0.8)
1554 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1555 \begin{minipage}{6cm}
1557 Amorphous SiC-like phase
1560 \end{pspicture}\\[0.3cm]
1561 \begin{pspicture}(0,0)(6.0,2.0)
1562 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
1563 \begin{minipage}{6cm}
1566 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
1567 \begin{minipage}{0.8cm}
1568 {\bf\boldmath $V_1$:}
1570 \begin{minipage}{5.1cm}
1571 Formation of \ci{} indeed occurs\\
1572 Agllomeration not observed
1573 \end{minipage}\\[0.3cm]
1574 \begin{minipage}{0.8cm}
1575 {\bf\boldmath $V_{2,3}$:}
1577 \begin{minipage}{5.1cm}
1578 Amorphous SiC-like structure\\
1579 (not expected at \degc{450})\\[0.05cm]
1580 No rearrangement/transition into 3C-SiC
1581 \end{minipage}\\[0.1cm]
1593 Limitations of MD and short range potentials
1600 {\bf Time scale problem of MD}\\[0.2cm]
1601 Minimize integration error \& precise thermodynamic sampling\\
1602 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
1603 $\omega$: vibrational mode\\
1604 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
1605 Several local minima separated by large energy barriers\\
1606 $\Rightarrow$ Transition event corresponds to a multiple
1607 of vibrational periods\\
1608 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
1609 infrequent transition events\\[0.2cm]
1610 {\color{blue}Accelerated methods:}
1611 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1615 {\bf Limitations related to the short range potential}\\[0.2cm]
1616 Cut-off function limits interaction to next neighbours\\
1617 $\Rightarrow$ Overestimated diffusion barrier (factor: 2.4--3.4)
1621 {\bf Approach to the (twofold) problem}\\[0.2cm]
1622 Increased temperature simulations without TAD corrections\\
1623 Accelerated methods or higher time scales exclusively not sufficient!
1625 \begin{pspicture}(0,0)(0,0)
1626 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
1627 \begin{minipage}{7.5cm}
1630 Potential enhanced slow phase space propagation
1633 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1634 \begin{minipage}{2.7cm}
1638 thermodynamic sampling
1641 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
1642 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
1643 \begin{minipage}{3.6cm}
1646 \underline{IBS}\\[0.1cm]
1647 3C-SiC also observed for higher T\\[0.1cm]
1648 Higher T inside sample\\[0.1cm]
1649 Structural evolution vs.\\
1650 equilibrium properties
1653 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
1662 Increased temperature simulations --- $V_1$
1667 \begin{minipage}{6.2cm}
1668 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1671 \begin{minipage}{6.2cm}
1672 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
1675 \begin{minipage}{6.2cm}
1676 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
1679 \begin{minipage}{6.3cm}
1681 \underline{Si-C bonds:}
1683 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1684 \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$
1687 \underline{Si-Si bonds:}
1688 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1689 ($\rightarrow$ 0.325 nm)\\[0.1cm]
1690 \underline{C-C bonds:}
1692 \item C-C next neighbour pairs reduced (mandatory)
1693 \item Peak at 0.3 nm slightly shifted\\[0.05cm]
1694 $\searrow$ \ci{} combinations (dashed arrows)\\
1695 $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
1696 $\nearrow$ \ci{} pure \cs{} combinations ($\Downarrow$)\\[0.05cm]
1697 Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
1707 Increased temperature simulations --- $V_1$
1712 \begin{minipage}{6.2cm}
1713 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1716 \begin{minipage}{6.2cm}
1717 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
1720 \begin{minipage}{6.2cm}
1721 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
1724 \begin{minipage}{6.3cm}
1726 \underline{Si-C bonds:}
1728 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1729 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
1731 \underline{Si-Si bonds:}
1732 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1733 ($\rightarrow$ 0.325 nm)\\[0.1cm]
1734 \underline{C-C bonds:}
1736 \item C-C next neighbour pairs reduced (mandatory)
1737 \item Peak at 0.3 nm slightly shifted
1738 \item Peak at 0.3 nm slightly shifted\\[0.05cm]
1739 $\searrow$ \ci{} combinations (dashed arrows)\\
1740 $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
1741 $\nearrow$ \ci{} pure \cs{} combinations ($\Downarrow$)\\[0.05cm]
1742 Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
1747 \begin{pspicture}(0,0)(0,0)
1748 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1749 \begin{minipage}{14cm}
1754 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1755 \begin{minipage}{9cm}
1759 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
1760 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
1763 \item Stretched coherent SiC structures directly observed
1765 \psframebox[linecolor=blue,linewidth=0.05cm]{
1766 \begin{minipage}{7cm}
1768 \cs{} extensively involved in the precipitation mechanism\\
1772 \item Emission of \si{} serves several needs:
1774 \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
1775 \item Building block for surrounding Si host \& further SiC
1776 \item Strain compensation \ldots\\
1777 \ldots Si/SiC interface\\
1778 \ldots within stretched coherent SiC structure
1780 \item Explains annealing behavior of high/low T C implantations
1782 \item Low T: highly mobile {\color{red}\ci}
1783 \item High T: stable configurations of {\color{blue}\cs}
1788 \psframebox[linecolor=blue,linewidth=0.05cm]{
1789 \begin{minipage}{7cm}
1791 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
1801 % skip high c conc results
1807 Increased temperature simulations at high C concentration
1812 \begin{minipage}{6.0cm}
1813 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
1815 \begin{minipage}{6.0cm}
1816 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
1824 \begin{minipage}[t]{6.0cm}
1825 0.186 nm: Si-C pairs $\uparrow$\\
1826 (as expected in 3C-SiC)\\[0.2cm]
1827 0.282 nm: Si-C-C\\[0.2cm]
1828 $\approx$0.35 nm: C-Si-Si
1831 \begin{minipage}{0.2cm}
1835 \begin{minipage}[t]{6.0cm}
1836 0.15 nm: C-C pairs $\uparrow$\\
1837 (as expected in graphite/diamond)\\[0.2cm]
1838 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
1839 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
1844 \item Decreasing cut-off artifact
1845 \item {\color{red}Amorphous} SiC-like phase remains
1846 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
1847 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
1856 High C \& small $V$ \& short $t$
1859 Slow restructuring due to strong C-C bonds
1862 High C \& low T implants
1877 Summary and Conclusions
1885 \begin{minipage}{12.3cm}
1890 \item Point defects excellently / fairly well described
1892 \item Identified \ci{} migration path
1893 \item EA drastically overestimates the diffusion barrier
1895 \item Combinations of defects (DFT)
1897 \item Agglomeration of point defects energetically favorable
1898 \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
1899 \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
1900 Low barrier (\unit[0.77]{eV}) \& low capture radius
1907 \begin{minipage}[t]{12.3cm}
1908 \underline{Pecipitation simulations}
1910 \item Problem of potential enhanced slow phase space propagation
1911 \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
1912 \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
1913 \item High T necessary to simulate IBS conditions (far from equilibrium)
1914 \item \cs{} involved in the precipitation process at elevated temperatures
1915 \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
1916 (stretched SiC, interface)
1923 \framebox{IBS: 3C-SiC precipitation occurs by successive agglomeration of \cs{}}
1942 \underline{Augsburg}
1944 \item Prof. B. Stritzker
1949 \underline{Helsinki}
1951 \item Prof. K. Nordlund
1956 \item Bayerische Forschungsstiftung
1959 \underline{Paderborn}
1961 \item Prof. J. Lindner
1962 \item Prof. G. Schmidt
1970 \normalsize\bf Thank you for your attention!
1973 Referees: PD V. Eyert \& Prof. Haider
1981 Polytypes of SiC\\[0.6cm]
1986 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
1987 \begin{minipage}{1.9cm}
1988 {\tiny cubic (twist)}
1990 \begin{minipage}{2.9cm}
1991 {\tiny hexagonal (no twist)}
1994 \begin{picture}(0,0)(-150,0)
1995 \includegraphics[width=7cm]{polytypes.eps}
2002 \begin{tabular}{l c c c c c c}
2004 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
2006 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
2007 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
2008 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
2009 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
2010 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
2011 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
2012 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
2016 \begin{pspicture}(0,0)(0,0)
2017 \psellipse[linecolor=green](5.7,2.05)(0.4,0.50)
2019 \begin{pspicture}(0,0)(0,0)
2020 \psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
2022 \begin{pspicture}(0,0)(0,0)
2023 \psellipse[linecolor=red](10.45,0.42)(0.4,0.20)
2034 Si self-interstitial point defects in silicon\\[0.1cm]
2038 \begin{tabular}{l c c c c c}
2040 $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
2042 \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
2043 Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
2045 \end{tabular}\\[0.4cm]
2048 \begin{minipage}{3cm}
2050 \underline{Vacancy}\\
2051 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
2054 \begin{minipage}{3cm}
2056 \underline{\hkl<1 1 0> DB}\\
2057 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
2060 \begin{minipage}{3cm}
2062 \underline{\hkl<1 0 0> DB}\\
2063 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
2066 \begin{minipage}{3cm}
2068 \underline{Tetrahedral}\\
2069 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
2073 \underline{Hexagonal} \hspace{2pt}
2074 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
2076 \begin{minipage}{2.7cm}
2077 $E_{\text{f}}^*=4.48\text{ eV}$\\
2078 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
2080 \begin{minipage}{0.4cm}
2085 \begin{minipage}{2.7cm}
2086 $E_{\text{f}}=3.96\text{ eV}$\\
2087 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
2090 \begin{minipage}{5.5cm}
2092 {\tiny nearly T $\rightarrow$ T}\\
2094 \includegraphics[width=6.0cm]{nhex_tet.ps}
2103 C-Si dimer \& bond-centered interstitial configuration
2110 \begin{minipage}[t]{4.1cm}
2111 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
2112 \begin{minipage}{2.0cm}
2114 \underline{Erhart/Albe}
2115 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
2118 \begin{minipage}{2.0cm}
2120 \underline{\textsc{vasp}}
2121 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
2123 \end{minipage}\\[0.2cm]
2124 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
2125 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
2126 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
2127 $\Rightarrow$ $sp^2$ hybridization
2129 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
2130 {\tiny Charge density isosurface}
2133 \begin{minipage}{0.2cm}
2136 \begin{minipage}[t]{8.1cm}
2138 {\bf Bond-centered interstitial}\\[0.1cm]
2139 \begin{minipage}{4.4cm}
2142 \item Linear Si-C-Si bond
2143 \item Si: one C \& 3 Si neighbours
2144 \item Spin polarized calculations
2145 \item No saddle point!\\
2149 \begin{minipage}{2.7cm}
2150 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
2152 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
2157 \begin{minipage}[t]{6.5cm}
2158 \begin{minipage}[t]{1.2cm}
2160 {\tiny sp$^3$}\\[0.8cm]
2161 \underline{${\color{black}\uparrow}$}
2162 \underline{${\color{black}\uparrow}$}
2163 \underline{${\color{black}\uparrow}$}
2164 \underline{${\color{red}\uparrow}$}\\
2167 \begin{minipage}[t]{1.4cm}
2169 {\color{red}M}{\color{blue}O}\\[0.8cm]
2170 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
2171 $\sigma_{\text{ab}}$\\[0.5cm]
2172 \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
2176 \begin{minipage}[t]{1.0cm}
2180 \underline{${\color{white}\uparrow\uparrow}$}
2181 \underline{${\color{white}\uparrow\uparrow}$}\\
2183 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
2184 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
2188 \begin{minipage}[t]{1.4cm}
2190 {\color{blue}M}{\color{green}O}\\[0.8cm]
2191 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
2192 $\sigma_{\text{ab}}$\\[0.5cm]
2193 \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
2197 \begin{minipage}[t]{1.2cm}
2200 {\tiny sp$^3$}\\[0.8cm]
2201 \underline{${\color{green}\uparrow}$}
2202 \underline{${\color{black}\uparrow}$}
2203 \underline{${\color{black}\uparrow}$}
2204 \underline{${\color{black}\uparrow}$}\\
2212 \begin{minipage}{3.0cm}
2214 \underline{Charge density}\\
2215 {\color{gray}$\bullet$} Spin up\\
2216 {\color{green}$\bullet$} Spin down\\
2217 {\color{blue}$\bullet$} Resulting spin up\\
2218 {\color{yellow}$\bullet$} Si atoms\\
2219 {\color{red}$\bullet$} C atom
2221 \begin{minipage}{3.6cm}
2222 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
2229 \begin{pspicture}(0,0)(0,0)
2230 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)