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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
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46 \input{seminar.bg2} % Unofficial bugs corrections
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71 % specify width and height
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79 \newcommand{\pot}{\mathcal{V}}
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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}{}}
117 \newcommand{\dista}[1]{\unit[#1]{\AA}{}}
118 \newcommand{\perc}[1]{\unit[#1]{\%}{}}
120 % no vertical centering
131 A B C D E F G H G F E D C B A
146 Atomistic simulation study\\[0.2cm]
147 on silicon carbide precipitation\\[0.2cm]
153 \textsc{Frank Zirkelbach}
157 Defense of doctor's thesis
161 Augsburg, 10. Jan. 2012
166 % no vertical centering
171 % motivation / properties / applications of silicon carbide
179 \begin{pspicture}(0,0)(13.5,5)
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186 \rput[lt](0,4.6){\color{gray}PROPERTIES}
188 \rput[lt](0.3,4){wide band gap}
189 \rput[lt](0.3,3.5){high electric breakdown field}
190 \rput[lt](0.3,3){good electron mobility}
191 \rput[lt](0.3,2.5){high electron saturation drift velocity}
192 \rput[lt](0.3,2){high thermal conductivity}
194 \rput[lt](0.3,1.5){hard and mechanically stable}
195 \rput[lt](0.3,1){chemically inert}
197 \rput[lt](0.3,0.5){radiation hardness}
199 \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
201 \rput[rt](12.5,3.85){high-temperature, high power}
202 \rput[rt](12.5,3.5){and high-frequency}
203 \rput[rt](12.5,3.15){electronic and optoelectronic devices}
205 \rput[rt](12.5,2.35){material suitable for extreme conditions}
206 \rput[rt](12.5,2){microelectromechanical systems}
207 \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
209 \rput[rt](12.5,0.85){first wall reactor material, detectors}
210 \rput[rt](12.5,0.5){and electronic devices for space}
214 \begin{picture}(0,0)(5,-162)
215 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
217 \begin{picture}(0,0)(-120,-162)
218 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
220 \begin{picture}(0,0)(-270,-162)
221 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
224 \begin{picture}(0,0)(10,65)
225 \includegraphics[height=2.8cm]{sic_switch.eps}
227 %\begin{picture}(0,0)(-243,65)
228 \begin{picture}(0,0)(-110,65)
229 \includegraphics[height=2.8cm]{ise_99.eps}
231 %\begin{picture}(0,0)(-135,65)
232 \begin{picture}(0,0)(-100,65)
233 \includegraphics[height=1.2cm]{infineon_schottky.eps}
235 \begin{picture}(0,0)(-233,65)
236 \includegraphics[height=2.8cm]{solar_car.eps}
246 Polytypes of SiC\\[0.4cm]
249 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
250 \begin{minipage}{1.9cm}
251 {\tiny cubic (twist)}
253 \begin{minipage}{2.9cm}
254 {\tiny hexagonal (no twist)}
257 \begin{picture}(0,0)(-150,0)
258 \includegraphics[width=7cm]{polytypes.eps}
265 \begin{tabular}{l c c c c c c}
267 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
269 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
270 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
271 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
272 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
273 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
274 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
275 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
279 \begin{pspicture}(0,0)(0,0)
280 \psellipse[linecolor=green](5.7,2.10)(0.4,0.5)
282 \begin{pspicture}(0,0)(0,0)
283 \psellipse[linecolor=green](5.6,0.92)(0.4,0.2)
285 \begin{pspicture}(0,0)(0,0)
286 \psellipse[linecolor=red](10.45,0.45)(0.4,0.2)
297 Fabrication of silicon carbide
306 \emph{Silicon carbide --- Born from the stars, perfected on earth.}
312 SiC thin films by MBE \& CVD
314 \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
315 \item \underline{Commercially available} semiconductor power devices based on
316 \underline{\foreignlanguage{greek}{a}-SiC}
317 \item Production of favored \underline{3C-SiC} material
318 \underline{less advanced}
319 \item Quality and size not yet sufficient
321 \begin{picture}(0,0)(-310,-20)
322 \includegraphics[width=2.0cm]{cree.eps}
327 Alternative approach:
328 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
335 \begin{minipage}{3.15cm}
337 \includegraphics[width=3cm]{imp.eps}\\
343 \begin{minipage}{3.15cm}
345 \includegraphics[width=3cm]{annealing.eps}\\
347 Postannealing at $>$ \degc{1200}
352 \begin{minipage}{5.5cm}
353 \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
356 XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
373 \item Supposed precipitation mechanism of SiC in Si
374 \item Utilized simulation techniques
376 \item Molecular dynamics (MD) simulations
377 \item Density functional theory (DFT) calculations
379 \item C and Si self-interstitial point defects in silicon
380 \item Silicon carbide precipitation simulations
381 \item Summary / Conclusion / Outlook
390 Formation of epitaxial single crystalline 3C-SiC
399 \item \underline{Implantation step 1}\\[0.1cm]
400 Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
401 $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
402 {\color{blue}precipitates}
403 \item \underline{Implantation step 2}\\[0.1cm]
404 Little remaining dose | \unit[180]{keV} | \degc{250}\\
406 Destruction/Amorphization of precipitates at layer interface
407 \item \underline{Annealing}\\[0.1cm]
408 \unit[10]{h} at \degc{1250}\\
409 $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
413 \begin{minipage}{7cm}
414 \includegraphics[width=7cm]{ibs_3c-sic.eps}
416 \begin{minipage}{5cm}
417 \begin{pspicture}(0,0)(0,0)
419 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
420 \begin{minipage}{5.3cm}
423 3C-SiC precipitation\\
424 not yet fully understood
428 \renewcommand\labelitemi{$\Rightarrow$}
429 Details of the SiC precipitation
431 \item significant technological progress\\
432 in SiC thin film formation
433 \item perspectives for processes relying\\
434 upon prevention of SiC precipitation
438 \rput(-6.8,5.4){\pnode{h0}}
439 \rput(-3.0,5.4){\pnode{h1}}
440 \ncline[linecolor=blue]{-}{h0}{h1}
441 \ncline[linecolor=blue]{->}{h1}{box}
451 Supposed precipitation mechanism of SiC in Si
459 \begin{minipage}{3.6cm}
461 Si \& SiC lattice structure\\[0.1cm]
462 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
465 \begin{minipage}{1.7cm}
466 \underline{Silicon}\\
467 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
468 $a=\unit[5.429]{\\A}$\\
469 $\rho^*_{\text{Si}}=\unit[100]{\%}$
471 \begin{minipage}{1.7cm}
472 \underline{Silicon carbide}\\
473 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
474 $a=\unit[4.359]{\\A}$\\
475 $\rho^*_{\text{Si}}=\unit[97]{\%}$
481 \begin{minipage}{4.1cm}
483 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
487 \begin{minipage}{4.0cm}
489 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
495 \begin{minipage}{4.0cm}
497 C-Si dimers (dumbbells)\\[-0.1cm]
498 on Si interstitial sites
502 \begin{minipage}{4.1cm}
504 Agglomeration of C-Si dumbbells\\[-0.1cm]
505 $\Rightarrow$ dark contrasts
509 \begin{minipage}{4.0cm}
511 Precipitation of 3C-SiC in Si\\[-0.1cm]
512 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
513 \& release of Si self-interstitials
519 \begin{minipage}{4.0cm}
521 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
525 \begin{minipage}{4.1cm}
527 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
531 \begin{minipage}{4.0cm}
533 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
537 \begin{pspicture}(0,0)(0,0)
538 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
539 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
540 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
541 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
542 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
543 $4a_{\text{Si}}=5a_{\text{SiC}}$
545 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
546 \hkl(h k l) planes match
548 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
559 Supposed precipitation mechanism of SiC in Si
567 \begin{minipage}{3.6cm}
569 Si \& SiC lattice structure\\[0.1cm]
570 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
573 \begin{minipage}{1.7cm}
574 \underline{Silicon}\\
575 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
576 $a=\unit[5.429]{\\A}$\\
577 $\rho^*_{\text{Si}}=\unit[100]{\%}$
579 \begin{minipage}{1.7cm}
580 \underline{Silicon carbide}\\
581 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
582 $a=\unit[4.359]{\\A}$\\
583 $\rho^*_{\text{Si}}=\unit[97]{\%}$
589 \begin{minipage}{4.1cm}
591 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
595 \begin{minipage}{4.0cm}
597 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
603 \begin{minipage}{4.0cm}
605 C-Si dimers (dumbbells)\\[-0.1cm]
606 on Si interstitial sites
610 \begin{minipage}{4.1cm}
612 Agglomeration of C-Si dumbbells\\[-0.1cm]
613 $\Rightarrow$ dark contrasts
617 \begin{minipage}{4.0cm}
619 Precipitation of 3C-SiC in Si\\[-0.1cm]
620 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
621 \& release of Si self-interstitials
627 \begin{minipage}{4.0cm}
629 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
633 \begin{minipage}{4.1cm}
635 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
639 \begin{minipage}{4.0cm}
641 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
645 \begin{pspicture}(0,0)(0,0)
646 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
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648 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
649 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
650 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
651 $4a_{\text{Si}}=5a_{\text{SiC}}$
653 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
654 \hkl(h k l) planes match
656 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
659 % controversial view!
660 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
661 \begin{minipage}{14cm}
666 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
667 \begin{minipage}{10cm}
671 {\color{gray}\bf Controversial findings}
674 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
676 \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
677 \item \si{} reacting with further C in cleared volume
679 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
681 \item Room temperature implantation $\rightarrow$ high C diffusion
682 \item Elevated temperature implantation $\rightarrow$ no C redistribution
684 $\Rightarrow$ mobile {\color{red}\ci} opposed to
685 stable {\color{blue}\cs{}} configurations
686 \item Strained silicon \& Si/SiC heterostructures
687 {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
689 \item {\color{blue}Coherent} SiC precipitates (tensile strain)
690 \item Incoherent SiC (strain relaxation)
695 {\Huge${\lightning}$} \hspace{0.3cm}
696 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
697 {\Huge${\lightning}$}
710 Utilized computational methods
717 {\bf Molecular dynamics (MD)}\\[0.1cm]
719 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
721 System of $N$ particles &
722 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
723 Phase space propagation &
724 Velocity Verlet | timestep: \unit[1]{fs} \\
725 Analytical interaction potential &
726 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
729 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
730 \pot_{ij} = {\color{red}f_C(r_{ij})}
731 \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
733 Observables: time/ensemble averages &
734 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
742 {\bf Density functional theory (DFT)}
746 \begin{minipage}[t]{6cm}
748 \item Hohenberg-Kohn theorem:\\
749 $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
750 \item Kohn-Sham approach:\\
751 Single-particle effective theory
755 \item Code: \textsc{vasp}
756 \item Plane wave basis set
758 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
761 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
763 \item Ultrasoft pseudopotential
764 \item Exchange \& correlation: GGA
765 \item Brillouin zone sampling: $\Gamma$-point
766 \item Supercell: $N=216\pm2$
769 \begin{minipage}{6cm}
770 \begin{pspicture}(0,0)(0,0)
771 \pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
772 \rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
774 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
777 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
779 n(r)=\sum_i^N|\Phi_i(r)|^2
782 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
784 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
788 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
789 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
790 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
801 Point defects \& defect migration
808 \begin{minipage}[b]{7.5cm}
809 {\bf Defect structure}\\
810 \begin{pspicture}(0,0)(7,4.4)
811 \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
814 \item Creation of c-Si simulation volume
815 \item Periodic boundary conditions
816 \item $T=0\text{ K}$, $p=0\text{ bar}$
819 \rput(3.5,1.3){\rnode{insert}{\psframebox{
822 Insertion of interstitial C/Si atoms
825 \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
828 Relaxation / structural energy minimization
831 \ncline[]{->}{init}{insert}
832 \ncline[]{->}{insert}{cool}
835 \begin{minipage}[b]{4.5cm}
837 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
839 \begin{minipage}{2.21cm}
841 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
842 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
843 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
846 \begin{minipage}{2.21cm}
848 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
849 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
850 {\color{black}$\bullet$} Vac. / Sub.
857 \begin{minipage}[b]{6cm}
858 {\bf Defect formation energy}\\
860 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
861 Particle reservoir: Si \& SiC\\[0.2cm]
862 {\bf Binding energy}\\
866 E_{\text{f}}^{\text{comb}}-
867 E_{\text{f}}^{1^{\text{st}}}-
868 E_{\text{f}}^{2^{\text{nd}}}
872 $E_{\text{b}}<0$: energetically favorable configuration\\
873 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
875 \begin{minipage}[b]{6cm}
876 {\bf Migration barrier}
879 \item Displace diffusing atom
880 \item Constrain relaxation of (diffusing) atoms
881 \item Record configurational energy
883 \begin{picture}(0,0)(-60,-33)
884 \includegraphics[width=4.5cm]{crt_mod.eps}
896 Si self-interstitial point defects in silicon\\[0.1cm]
900 \begin{tabular}{l c c c c c}
902 $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
904 \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
905 Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
907 \end{tabular}\\[0.4cm]
910 \begin{minipage}{3cm}
912 \underline{Vacancy}\\
913 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
916 \begin{minipage}{3cm}
918 \underline{\hkl<1 1 0> DB}\\
919 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
922 \begin{minipage}{3cm}
924 \underline{\hkl<1 0 0> DB}\\
925 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
928 \begin{minipage}{3cm}
930 \underline{Tetrahedral}\\
931 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
935 \underline{Hexagonal} \hspace{2pt}
936 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
938 \begin{minipage}{2.7cm}
939 $E_{\text{f}}^*=4.48\text{ eV}$\\
940 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
942 \begin{minipage}{0.4cm}
947 \begin{minipage}{2.7cm}
948 $E_{\text{f}}=3.96\text{ eV}$\\
949 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
952 \begin{minipage}{5.5cm}
954 {\tiny nearly T $\rightarrow$ T}\\
956 \includegraphics[width=6.0cm]{nhex_tet.ps}
967 C interstitial point defects in silicon\\
970 \begin{tabular}{l c c c c c c r}
972 $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
973 {\color{black} \cs{} \& \si}\\
975 \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
976 Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
978 \end{tabular}\\[0.1cm]
981 \begin{minipage}{2.8cm}
982 \underline{Hexagonal} \hspace{2pt}
983 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
984 $E_{\text{f}}^*=9.05\text{ eV}$\\
985 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
987 \begin{minipage}{0.4cm}
992 \begin{minipage}{2.8cm}
993 \underline{\hkl<1 0 0>}\\
994 $E_{\text{f}}=3.88\text{ eV}$\\
995 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
998 \begin{minipage}{1.4cm}
1001 \begin{minipage}{3.0cm}
1003 \underline{Tetrahedral}\\
1004 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
1009 \begin{minipage}{2.8cm}
1010 \underline{Bond-centered}\\
1011 $E_{\text{f}}^*=5.59\text{ eV}$\\
1012 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
1014 \begin{minipage}{0.4cm}
1019 \begin{minipage}{2.8cm}
1020 \underline{\hkl<1 1 0> dumbbell}\\
1021 $E_{\text{f}}=5.18\text{ eV}$\\
1022 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
1025 \begin{minipage}{1.4cm}
1028 \begin{minipage}{3.0cm}
1030 \underline{Substitutional}\\
1031 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
1041 C-Si dimer \& bond-centered interstitial configuration
1048 \begin{minipage}[t]{4.1cm}
1049 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
1050 \begin{minipage}{2.0cm}
1052 \underline{Erhart/Albe}
1053 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
1056 \begin{minipage}{2.0cm}
1058 \underline{\textsc{vasp}}
1059 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
1061 \end{minipage}\\[0.2cm]
1062 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
1063 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
1064 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
1065 $\Rightarrow$ $sp^2$ hybridization
1067 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
1068 {\tiny Charge density isosurface}
1071 \begin{minipage}{0.2cm}
1074 \begin{minipage}[t]{8.1cm}
1076 {\bf Bond-centered interstitial}\\[0.1cm]
1077 \begin{minipage}{4.4cm}
1080 \item Linear Si-C-Si bond
1081 \item Si: one C \& 3 Si neighbours
1082 \item Spin polarized calculations
1083 \item No saddle point!\\
1087 \begin{minipage}{2.7cm}
1088 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1090 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
1095 \begin{minipage}[t]{6.5cm}
1096 \begin{minipage}[t]{1.2cm}
1098 {\tiny sp$^3$}\\[0.8cm]
1099 \underline{${\color{black}\uparrow}$}
1100 \underline{${\color{black}\uparrow}$}
1101 \underline{${\color{black}\uparrow}$}
1102 \underline{${\color{red}\uparrow}$}\\
1105 \begin{minipage}[t]{1.4cm}
1107 {\color{red}M}{\color{blue}O}\\[0.8cm]
1108 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1109 $\sigma_{\text{ab}}$\\[0.5cm]
1110 \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1114 \begin{minipage}[t]{1.0cm}
1118 \underline{${\color{white}\uparrow\uparrow}$}
1119 \underline{${\color{white}\uparrow\uparrow}$}\\
1121 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1122 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1126 \begin{minipage}[t]{1.4cm}
1128 {\color{blue}M}{\color{green}O}\\[0.8cm]
1129 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1130 $\sigma_{\text{ab}}$\\[0.5cm]
1131 \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1135 \begin{minipage}[t]{1.2cm}
1138 {\tiny sp$^3$}\\[0.8cm]
1139 \underline{${\color{green}\uparrow}$}
1140 \underline{${\color{black}\uparrow}$}
1141 \underline{${\color{black}\uparrow}$}
1142 \underline{${\color{black}\uparrow}$}\\
1150 \begin{minipage}{3.0cm}
1152 \underline{Charge density}\\
1153 {\color{gray}$\bullet$} Spin up\\
1154 {\color{green}$\bullet$} Spin down\\
1155 {\color{blue}$\bullet$} Resulting spin up\\
1156 {\color{yellow}$\bullet$} Si atoms\\
1157 {\color{red}$\bullet$} C atom
1159 \begin{minipage}{3.6cm}
1160 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
1167 \begin{pspicture}(0,0)(0,0)
1168 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
1177 C interstitial migration --- ab initio
1184 \begin{minipage}{6.8cm}
1185 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
1186 \begin{minipage}{2.0cm}
1187 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1189 \begin{minipage}{0.2cm}
1192 \begin{minipage}{2.0cm}
1193 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
1195 \begin{minipage}{0.2cm}
1198 \begin{minipage}{2.0cm}
1199 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
1200 \end{minipage}\\[0.1cm]
1202 $\Rightarrow$ BC configuration constitutes local minimum\\
1203 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
1205 \begin{minipage}{5.4cm}
1206 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
1207 \end{minipage}\\[0.2cm]
1210 \begin{minipage}{6.8cm}
1211 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
1212 \begin{minipage}{2.0cm}
1213 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1215 \begin{minipage}{0.2cm}
1218 \begin{minipage}{2.0cm}
1219 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
1221 \begin{minipage}{0.2cm}
1224 \begin{minipage}{2.0cm}
1225 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
1226 \end{minipage}\\[0.1cm]
1227 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
1228 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
1229 Note: Change in orientation
1231 \begin{minipage}{5.4cm}
1232 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
1233 \end{minipage}\\[0.1cm]
1236 Reorientation pathway composed of two consecutive processes of the above type
1245 C interstitial migration --- analytical potential
1252 \begin{minipage}[t]{6.0cm}
1253 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
1254 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
1256 \item Lowermost migration barrier
1257 \item $\Delta E \approx \unit[2.2]{eV}$
1258 \item 2.4 times higher than ab initio result
1259 \item Different pathway
1262 \begin{minipage}[t]{0.2cm}
1265 \begin{minipage}[t]{6.0cm}
1266 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
1269 \item Bond-centered configuration unstable\\
1270 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1271 \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
1272 $\rightarrow$ \ci{} \hkl<1 1 0> DB
1275 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
1277 \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
1278 \item 2.4 -- 3.4 times higher than ab initio result
1279 \item After all: Change of the DB orientation
1285 {\color{red}\bf Drastically overestimated diffusion barrier}
1288 \begin{pspicture}(0,0)(0,0)
1289 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
1305 \begin{minipage}{9cm}
1307 Summary of combinations}\\[0.1cm]
1309 \begin{tabular}{l c c c c c c}
1311 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1313 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1314 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1315 \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}\\
1316 \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}\\
1317 \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}\\
1318 \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}\\
1320 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1321 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1328 $E_{\text{b}}$ explainable by stress compensation / increase
1332 \begin{minipage}{3cm}
1333 \includegraphics[width=3.5cm]{comb_pos.eps}
1338 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1339 \begin{minipage}[t]{3.2cm}
1340 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1341 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1343 \begin{minipage}[t]{3.0cm}
1344 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1345 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1347 \begin{minipage}[t]{6.1cm}
1350 \item \ci{} agglomeration energetically favorable
1351 \item Most favorable: C clustering\\
1352 {\color{red}However \ldots}\\
1353 \ldots high migration barrier ($>4\,\text{eV}$)\\
1355 $4\times{\color{cyan}[-2.25]}$ versus
1356 $2\times{\color{orange}[-2.39]}$
1359 {\color{blue}\ci{} agglomeration / no C clustering}
1376 \begin{minipage}{9cm}
1378 Summary of combinations}\\[0.1cm]
1380 \begin{tabular}{l c c c c c c}
1382 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1384 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1385 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1386 \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}\\
1387 \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}\\
1388 \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}\\
1389 \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}\\
1391 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1392 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1399 $E_{\text{b}}$ explainable by stress compensation / increase
1403 \begin{minipage}{3cm}
1404 \includegraphics[width=3.5cm]{comb_pos.eps}
1409 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1410 \begin{minipage}[t]{3.2cm}
1411 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1412 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1414 \begin{minipage}[t]{3.0cm}
1415 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1416 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1418 \begin{minipage}[t]{6.1cm}
1421 \item \ci{} agglomeration energetically favorable
1422 \item Most favorable: C clustering\\
1423 {\color{red}However \ldots}\\
1424 \ldots high migration barrier ($>4\,\text{eV}$)\\
1426 $4\times{\color{cyan}[-2.25]}$ versus
1427 $2\times{\color{orange}[-2.39]}$
1430 {\color{blue}\ci{} agglomeration / no C clustering}
1435 \begin{pspicture}(0,0)(0,0)
1436 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1437 \begin{minipage}{14cm}
1442 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1443 \begin{minipage}{8cm}
1447 Interaction along \hkl[1 1 0]
1448 \includegraphics[width=7cm]{db_along_110_cc.ps}
1460 Defect combinations of C-Si dimers and vacancies
1466 \begin{minipage}[b]{2.6cm}
1468 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1469 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1472 \begin{minipage}[b]{7cm}
1475 \begin{minipage}[b]{2.6cm}
1477 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1478 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1480 \end{minipage}\\[0.2cm]
1482 \begin{minipage}{6.5cm}
1483 \includegraphics[width=6.0cm]{059-539.ps}
1485 \begin{minipage}{5.7cm}
1486 \includegraphics[width=6.0cm]{314-539.ps}
1489 \begin{pspicture}(0,0)(0,0)
1490 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1492 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1493 \begin{minipage}{6.5cm}
1495 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1496 Low migration barrier towards C$_{\text{sub}}$\\
1498 High barrier for reverse process\\[0.3cm]
1500 High probability of stable C$_{\text{sub}}$ configuration
1513 Combinations of substitutional C and Si self-interstitials
1520 \begin{minipage}{6.2cm}
1522 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1524 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1525 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1526 \item Interaction drops quickly to zero\\
1527 $\rightarrow$ low capture radius
1531 \begin{minipage}{0.2cm}
1534 \begin{minipage}{6.0cm}
1536 {\bf Transition from the ground state}
1538 \item Low transition barrier
1539 \item Barrier smaller than \ci{} migration barrier
1540 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1541 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1544 \end{minipage}\\[0.3cm]
1546 \begin{minipage}{6.0cm}
1547 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1549 \begin{minipage}{0.4cm}
1552 \begin{minipage}{6.0cm}
1554 \includegraphics[width=6.0cm]{162-097.ps}
1558 \begin{pspicture}(0,0)(0,0)
1559 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1560 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1561 \begin{minipage}{8cm}
1565 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1566 IBS --- process far from equilibrium\\
1579 Combinations of substitutional C and Si self-interstitials
1586 \begin{minipage}{6.2cm}
1588 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1590 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1591 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1592 \item Interaction drops quickly to zero\\
1593 $\rightarrow$ low capture radius
1597 \begin{minipage}{0.2cm}
1600 \begin{minipage}{6.0cm}
1602 {\bf Transition from the ground state}
1604 \item Low transition barrier
1605 \item Barrier smaller than \ci{} migration barrier
1606 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1607 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1610 \end{minipage}\\[0.3cm]
1612 \begin{minipage}{6.0cm}
1613 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1615 \begin{minipage}{0.4cm}
1618 \begin{minipage}{6.0cm}
1620 \includegraphics[width=6.0cm]{162-097.ps}
1624 \begin{pspicture}(0,0)(0,0)
1625 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1626 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1627 \begin{minipage}{8cm}
1631 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1632 IBS --- process far from equilibrium\\
1640 \begin{pspicture}(0,0)(0,0)
1641 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1642 \begin{minipage}{14cm}
1647 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1648 \begin{minipage}{11cm}
1652 Ab initio MD at \degc{900}\\[0.4cm]
1653 \begin{minipage}{5.4cm}
1655 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1658 \begin{minipage}{5.4cm}
1660 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1662 \end{minipage}\\[0.5cm]
1664 Contribution of entropy to structural formation\\[0.1cm]
1677 Silicon carbide precipitation simulations
1687 \begin{pspicture}(0,0)(12,6.5)
1689 \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1692 \item Create c-Si volume
1693 \item Periodc boundary conditions
1694 \item Set requested $T$ and $p=0\text{ bar}$
1695 \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1698 \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1700 Insertion of C atoms at constant T
1702 \item total simulation volume {\pnode{in1}}
1703 \item volume of minimal SiC precipitate size {\pnode{in2}}
1704 \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1708 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1710 Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1712 \ncline[]{->}{init}{insert}
1713 \ncline[]{->}{insert}{cool}
1714 \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
1715 \rput(7.6,6){\footnotesize $V_1$}
1716 \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
1717 \rput(8.9,4.85){\tiny $V_2$}
1718 \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
1719 \rput(9.25,4.45){\footnotesize $V_3$}
1720 \rput(7.9,3.2){\pnode{ins1}}
1721 \rput(8.92,2.8){\pnode{ins2}}
1722 \rput(10.8,2.4){\pnode{ins3}}
1723 \ncline[]{->}{in1}{ins1}
1724 \ncline[]{->}{in2}{ins2}
1725 \ncline[]{->}{in3}{ins3}
1735 \begin{minipage}{5.7cm}
1737 \item Amount of C atoms: 6000\\
1738 ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
1739 \item Simulation volume: $31^3$ Si unit cells\\
1743 \begin{minipage}{0.3cm}
1747 \begin{minipage}{6.0cm}
1748 Restricted to classical potential caclulations\\
1749 $\rightarrow$ Low C diffusion / overestimated barrier\\
1750 $\rightarrow$ Consider $V_2$ and $V_3$
1752 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
1763 Silicon carbide precipitation simulations at \degc{450} as in IBS
1768 \begin{minipage}{6.3cm}
1769 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1770 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1773 \begin{minipage}{6.1cm}
1775 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1776 \hkl<1 0 0> C-Si dumbbell dominated structure
1778 \item Si-C bumbs around \unit[0.19]{nm}
1779 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1780 concatenated differently oriented \ci{} DBs
1781 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1783 \begin{pspicture}(0,0)(6.0,1.0)
1784 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1785 \begin{minipage}{6cm}
1787 Formation of \ci{} dumbbells\\
1788 C atoms in proper 3C-SiC distance first
1791 \end{pspicture}\\[0.1cm]
1792 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1794 \item High amount of strongly bound C-C bonds
1795 \item Increased defect \& damage density\\
1796 $\rightarrow$ Arrangements hard to categorize and trace
1797 \item Only short range order observable
1799 \begin{pspicture}(0,0)(6.0,0.8)
1800 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1801 \begin{minipage}{6cm}
1803 Amorphous SiC-like phase
1806 \end{pspicture}\\[0.3cm]
1807 \begin{pspicture}(0,0)(6.0,2.0)
1808 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
1809 \begin{minipage}{6cm}
1823 Silicon carbide precipitation simulations at \degc{450} as in IBS
1828 \begin{minipage}{6.3cm}
1829 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1830 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1833 \begin{minipage}{6.1cm}
1835 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1836 \hkl<1 0 0> C-Si dumbbell dominated structure
1838 \item Si-C bumbs around \unit[0.19]{nm}
1839 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1840 concatenated differently oriented \ci{} DBs
1841 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1843 \begin{pspicture}(0,0)(6.0,1.0)
1844 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1845 \begin{minipage}{6cm}
1847 Formation of \ci{} dumbbells\\
1848 C atoms in proper 3C-SiC distance first
1851 \end{pspicture}\\[0.1cm]
1852 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1854 \item High amount of strongly bound C-C bonds
1855 \item Increased defect \& damage density\\
1856 $\rightarrow$ Arrangements hard to categorize and trace
1857 \item Only short range order observable
1859 \begin{pspicture}(0,0)(6.0,0.8)
1860 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1861 \begin{minipage}{6cm}
1863 Amorphous SiC-like phase
1866 \end{pspicture}\\[0.3cm]
1867 \begin{pspicture}(0,0)(6.0,2.0)
1868 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
1869 \begin{minipage}{6cm}
1872 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
1873 \begin{minipage}{0.8cm}
1874 {\bf\boldmath $V_1$:}
1876 \begin{minipage}{5.1cm}
1877 Formation of \ci{} indeed occurs\\
1878 Agllomeration not observed
1879 \end{minipage}\\[0.3cm]
1880 \begin{minipage}{0.8cm}
1881 {\bf\boldmath $V_{2,3}$:}
1883 \begin{minipage}{5.1cm}
1884 Amorphous SiC-like structure\\
1885 (not expected at \degc{450})\\[0.05cm]
1886 No rearrangement/transition into 3C-SiC
1887 \end{minipage}\\[0.1cm]
1899 Limitations of MD and short range potentials
1906 {\bf Time scale problem of MD}\\[0.2cm]
1907 Precise integration \& thermodynamic sampling\\
1908 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
1909 $\omega$: vibrational mode\\
1910 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
1911 Several local minima separated by large energy barriers\\
1912 $\Rightarrow$ Transition event corresponds to a multiple
1913 of vibrational periods\\
1914 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
1915 infrequent transition events\\[0.2cm]
1916 {\color{blue}Accelerated methods:}
1917 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1921 {\bf Limitations related to the short range potential}\\[0.2cm]
1922 Cut-off function limits interaction to next neighbours\\
1923 $\Rightarrow$ Overestimated unphysical high forces of next neighbours
1928 {\bf Approach to the (twofold) problem}\\[0.2cm]
1929 Increased temperature simulations without TAD corrections\\
1930 Accelerated methods or higher time scales exclusively not sufficient!
1932 \begin{pspicture}(0,0)(0,0)
1933 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
1934 \begin{minipage}{7.5cm}
1937 Potential enhanced slow phase space propagation
1940 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1941 \begin{minipage}{2.7cm}
1945 thermodynamic sampling
1948 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
1949 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
1950 \begin{minipage}{3.6cm}
1953 \underline{IBS}\\[0.1cm]
1954 3C-SiC also observed for higher T\\[0.1cm]
1955 Higher T inside sample\\[0.1cm]
1956 Structural evolution vs.\\
1957 equilibrium properties
1960 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
1969 Increased temperature simulations --- $V_1$
1974 \begin{minipage}{6.2cm}
1975 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1978 \begin{minipage}{6.2cm}
1979 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
1982 \begin{minipage}{6.2cm}
1983 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
1986 \begin{minipage}{6.3cm}
1988 \underline{Si-C bonds:}
1990 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1991 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
1993 \underline{Si-Si bonds:}
1994 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1995 ($\rightarrow$ 0.325 nm)\\[0.1cm]
1996 \underline{C-C bonds:}
1998 \item C-C next neighbour pairs reduced (mandatory)
1999 \item Peak at 0.3 nm slightly shifted
2001 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2002 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2004 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2006 \item Range [|-$\downarrow$]:
2007 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2008 with nearby Si$_{\text{I}}$}
2019 Increased temperature simulations --- $V_1$
2024 \begin{minipage}{6.2cm}
2025 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2028 \begin{minipage}{6.2cm}
2029 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2032 \begin{minipage}{6.2cm}
2033 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2036 \begin{minipage}{6.3cm}
2038 \underline{Si-C bonds:}
2040 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2041 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2043 \underline{Si-Si bonds:}
2044 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2045 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2046 \underline{C-C bonds:}
2048 \item C-C next neighbour pairs reduced (mandatory)
2049 \item Peak at 0.3 nm slightly shifted
2051 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2052 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2054 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2056 \item Range [|-$\downarrow$]:
2057 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2058 with nearby Si$_{\text{I}}$}
2064 \begin{pspicture}(0,0)(0,0)
2065 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
2066 \begin{minipage}{14cm}
2071 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
2072 \begin{minipage}{9cm}
2076 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
2077 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
2080 \item Stretched coherent SiC structures\\
2081 $\Rightarrow$ Precipitation process involves {\color{blue}\cs}
2082 \item Explains annealing behavior of high/low T C implantations
2084 \item Low T: highly mobile {\color{red}\ci}
2085 \item High T: stable configurations of {\color{blue}\cs}
2089 \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
2090 \item Building block for surrounding Si host \& further SiC
2091 \item Strain compensation \ldots\\
2092 \ldots Si/SiC interface\\
2093 \ldots within stretched coherent SiC structure
2098 \psframebox[linecolor=blue,linewidth=0.05cm]{
2099 \begin{minipage}{7cm}
2101 Precipitation mechanism involving \cs\\
2102 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2112 % skip high T / C conc ... only here!
2118 Increased temperature simulations at high C concentration
2123 \begin{minipage}{6.5cm}
2124 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2126 \begin{minipage}{6.5cm}
2127 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2135 \begin{minipage}[t]{6.0cm}
2136 0.186 nm: Si-C pairs $\uparrow$\\
2137 (as expected in 3C-SiC)\\[0.2cm]
2138 0.282 nm: Si-C-C\\[0.2cm]
2139 $\approx$0.35 nm: C-Si-Si
2142 \begin{minipage}{0.2cm}
2146 \begin{minipage}[t]{6.0cm}
2147 0.15 nm: C-C pairs $\uparrow$\\
2148 (as expected in graphite/diamond)\\[0.2cm]
2149 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2150 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2155 \item Decreasing cut-off artifact
2156 \item {\color{red}Amorphous} SiC-like phase remains
2157 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2158 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2167 High C \& small $V$ \& short $t$
2170 Slow restructuring due to strong C-C bonds
2173 High C \& low T implants
2181 % skipped high T / C conc
2192 \begin{pspicture}(0,0)(12,1.0)
2193 \psframebox[fillstyle=gradient,gradbegin=hred,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
2194 \begin{minipage}{11cm}
2195 {\color{black}Diploma thesis}\\
2196 \underline{Monte Carlo} simulation modeling the selforganization process\\
2197 leading to periodic arrays of nanometric amorphous SiC precipitates
2200 \end{pspicture}\\[0.4cm]
2201 \begin{pspicture}(0,0)(12,2)
2202 \psframebox[fillstyle=gradient,gradbegin=hblue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
2203 \begin{minipage}{11cm}
2204 {\color{black}Doctoral studies}\\
2205 Classical potential \underline{molecular dynamics} simulations \ldots\\
2206 \underline{Density functional theory} calculations \ldots\\[0.2cm]
2207 \ldots on defect formation and SiC precipitation in Si
2210 \end{pspicture}\\[0.5cm]
2211 \begin{pspicture}(0,0)(12,3)
2212 \psframebox[fillstyle=solid,fillcolor=white,linestyle=solid]{
2213 \begin{minipage}{11cm}
2215 {\color{black}\bf How to proceed \ldots}\\[0.1cm]
2216 MC $\rightarrow$ empirical potential MD $\rightarrow$ Ground-state DFT \ldots
2218 \renewcommand\labelitemi{$\ldots$}
2219 \item beyond LDA/GGA methods \& ground-state DFT
2221 Investigation of structure \& structural evolution \ldots
2223 \renewcommand\labelitemi{$\ldots$}
2224 \item electronic/optical properties
2225 \item electronic correlations
2226 \item non-equilibrium systems
2230 \end{pspicture}\\[0.5cm]
2246 \underline{Augsburg}
2248 \item Prof. B. Stritzker (accomodation at EP \RM{4})
2249 \item Ralf Utermann (EDV)
2252 \underline{Helsinki}
2254 \item Prof. K. Nordlund (MD)
2259 \item Bayerische Forschungsstiftung (financial support)
2262 \underline{Paderborn}
2264 \item Prof. J. Lindner (SiC)
2265 \item Prof. G. Schmidt (DFT + financial support)
2266 \item Dr. E. Rauls (DFT + SiC)
2269 \underline{Stuttgart}
2272 \bf Thank you for your attention / invitation!