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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}{}}
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120 % no vertical centering
131 A B C D E F G H G F E D C B A
148 Atomistic simulation study on silicon carbide\\[0.2cm]
149 precipitation in silicon\\
156 \textsc{Frank Zirkelbach}
160 Defense of doctor's thesis
169 % no vertical centering
172 % skip for preparation
177 % motivation / properties / applications of silicon carbide
185 \begin{pspicture}(0,0)(13.5,5)
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192 \rput[lt](0,4.6){\color{gray}PROPERTIES}
194 \rput[lt](0.3,4){wide band gap}
195 \rput[lt](0.3,3.5){high electric breakdown field}
196 \rput[lt](0.3,3){good electron mobility}
197 \rput[lt](0.3,2.5){high electron saturation drift velocity}
198 \rput[lt](0.3,2){high thermal conductivity}
200 \rput[lt](0.3,1.5){hard and mechanically stable}
201 \rput[lt](0.3,1){chemically inert}
203 \rput[lt](0.3,0.5){radiation hardness}
205 \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
207 \rput[rt](12.5,3.85){high-temperature, high power}
208 \rput[rt](12.5,3.5){and high-frequency}
209 \rput[rt](12.5,3.15){electronic and optoelectronic devices}
211 \rput[rt](12.5,2.35){material suitable for extreme conditions}
212 \rput[rt](12.5,2){microelectromechanical systems}
213 \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
215 \rput[rt](12.5,0.85){first wall reactor material, detectors}
216 \rput[rt](12.5,0.5){and electronic devices for space}
220 \begin{picture}(0,0)(5,-162)
221 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
223 \begin{picture}(0,0)(-120,-162)
224 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
226 \begin{picture}(0,0)(-270,-162)
227 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
230 \begin{picture}(0,0)(10,65)
231 \includegraphics[height=2.8cm]{sic_switch.eps}
233 %\begin{picture}(0,0)(-243,65)
234 \begin{picture}(0,0)(-110,65)
235 \includegraphics[height=2.8cm]{ise_99.eps}
237 %\begin{picture}(0,0)(-135,65)
238 \begin{picture}(0,0)(-100,65)
239 \includegraphics[height=1.2cm]{infineon_schottky.eps}
241 \begin{picture}(0,0)(-233,65)
242 \includegraphics[height=2.8cm]{solar_car.eps}
252 Polytypes of SiC\\[0.6cm]
257 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
258 \begin{minipage}{1.9cm}
259 {\tiny cubic (twist)}
261 \begin{minipage}{2.9cm}
262 {\tiny hexagonal (no twist)}
265 \begin{picture}(0,0)(-150,0)
266 \includegraphics[width=7cm]{polytypes.eps}
273 \begin{tabular}{l c c c c c c}
275 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
277 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
278 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
279 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
280 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
281 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
282 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
283 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
287 \begin{pspicture}(0,0)(0,0)
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290 \begin{pspicture}(0,0)(0,0)
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293 \begin{pspicture}(0,0)(0,0)
294 \psellipse[linecolor=red](10.45,0.45)(0.4,0.23)
307 Fabrication of silicon carbide
316 \emph{Silicon carbide --- Born from the stars, perfected on earth.}
322 SiC thin films by MBE \& CVD
324 \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
325 \item \underline{Commercially available} semiconductor power devices based on
326 \underline{\foreignlanguage{greek}{a}-SiC}
327 \item Production of favored \underline{3C-SiC} material
328 \underline{less advanced}
329 \item Quality and size not yet sufficient
331 \begin{picture}(0,0)(-310,-20)
332 \includegraphics[width=2.0cm]{cree.eps}
340 {\footnotesize\color{black}
341 Mismatch in \underline{thermal expansion coeefficient}
342 and \underline{lattice parameter} w.r.t. substrate
349 {\bf Alternative approach}\\
350 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
357 \begin{minipage}{3.15cm}
359 \includegraphics[width=3cm]{imp.eps}\\
365 \begin{minipage}{3.15cm}
367 \includegraphics[width=3cm]{annealing.eps}\\
369 Postannealing at $>$ \degc{1200}
374 \begin{minipage}{5.5cm}
377 No surface bending effects\\
378 High areal homogenity\\[0.1cm]
379 $\Downarrow$\\[0.1cm]
380 Synthesis of large area SiC films possible
391 IBS of epitaxial single crystalline 3C-SiC
400 \item \underline{Implantation step 1}\\[0.1cm]
401 Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
402 $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
403 {\color{blue}precipitates}
404 \item \underline{Implantation step 2}\\[0.1cm]
405 Little remaining dose | \unit[180]{keV} | \degc{250}\\
407 Destruction/Amorphization of precipitates at layer interface
408 \item \underline{Annealing}\\[0.1cm]
409 \unit[10]{h} at \degc{1250}\\
410 $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
414 \begin{minipage}{6.9cm}
415 \includegraphics[width=7cm]{ibs_3c-sic.eps}\\[-0.4cm]
418 XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
422 \begin{minipage}{5cm}
423 \begin{pspicture}(0,0)(0,0)
425 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
426 \begin{minipage}{5.3cm}
429 3C-SiC precipitation\\
430 not yet fully understood
434 \renewcommand\labelitemi{$\Rightarrow$}
435 Details of the SiC precipitation
437 \item significant technological progress\\
438 in SiC thin film formation
439 \item perspectives for processes relying\\
440 upon prevention of SiC precipitation
444 \rput(-6.8,5.5){\pnode{h0}}
445 \rput(-3.0,5.5){\pnode{h1}}
446 \ncline[linecolor=blue]{-}{h0}{h1}
447 \ncline[linecolor=blue]{->}{h1}{box}
467 \item Supposed precipitation mechanism of SiC in Si
468 \item Utilized simulation techniques
470 \item Molecular dynamics (MD) simulations
471 \item Density functional theory (DFT) calculations
473 \item C and Si self-interstitial point defects in silicon
474 \item Silicon carbide precipitation simulations
475 \item Summary / Conclusion
484 Supposed precipitation mechanism of SiC in Si
492 \begin{minipage}{3.6cm}
494 Si \& SiC lattice structure\\[0.1cm]
495 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
498 \begin{minipage}{1.7cm}
499 \underline{Silicon}\\
500 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
501 $a=\unit[5.429]{\\A}$\\
502 $\rho^*_{\text{Si}}=\unit[100]{\%}$
504 \begin{minipage}{1.7cm}
505 \underline{Silicon carbide}\\
506 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
507 $a=\unit[4.359]{\\A}$\\
508 $\rho^*_{\text{Si}}=\unit[97]{\%}$
514 \begin{minipage}{4.1cm}
516 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
520 \begin{minipage}{4.0cm}
522 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
528 \begin{minipage}{4.0cm}
530 C-Si dimers (dumbbells)\\[-0.1cm]
531 on Si interstitial sites
535 \begin{minipage}{4.1cm}
537 Agglomeration of C-Si dumbbells\\[-0.1cm]
538 $\Rightarrow$ dark contrasts
542 \begin{minipage}{4.0cm}
544 Precipitation of 3C-SiC in Si\\[-0.1cm]
545 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
546 \& release of Si self-interstitials
552 \begin{minipage}{4.0cm}
554 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
558 \begin{minipage}{4.1cm}
560 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
564 \begin{minipage}{4.0cm}
566 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
570 \begin{pspicture}(0,0)(0,0)
571 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
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573 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
574 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
575 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
576 $4a_{\text{Si}}=5a_{\text{SiC}}$
578 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
579 \hkl(h k l) planes match
581 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
592 Supposed precipitation mechanism of SiC in Si
600 \begin{minipage}{3.6cm}
602 Si \& SiC lattice structure\\[0.1cm]
603 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
606 \begin{minipage}{1.7cm}
607 \underline{Silicon}\\
608 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
609 $a=\unit[5.429]{\\A}$\\
610 $\rho^*_{\text{Si}}=\unit[100]{\%}$
612 \begin{minipage}{1.7cm}
613 \underline{Silicon carbide}\\
614 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
615 $a=\unit[4.359]{\\A}$\\
616 $\rho^*_{\text{Si}}=\unit[97]{\%}$
622 \begin{minipage}{4.1cm}
624 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
628 \begin{minipage}{4.0cm}
630 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
636 \begin{minipage}{4.0cm}
638 C-Si dimers (dumbbells)\\[-0.1cm]
639 on Si interstitial sites
643 \begin{minipage}{4.1cm}
645 Agglomeration of C-Si dumbbells\\[-0.1cm]
646 $\Rightarrow$ dark contrasts
650 \begin{minipage}{4.0cm}
652 Precipitation of 3C-SiC in Si\\[-0.1cm]
653 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
654 \& release of Si self-interstitials
660 \begin{minipage}{4.0cm}
662 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
666 \begin{minipage}{4.1cm}
668 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
672 \begin{minipage}{4.0cm}
674 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
678 \begin{pspicture}(0,0)(0,0)
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682 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
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684 $4a_{\text{Si}}=5a_{\text{SiC}}$
686 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
687 \hkl(h k l) planes match
689 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
692 % controversial view!
693 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
694 \begin{minipage}{14cm}
699 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
700 \begin{minipage}{10cm}
704 {\color{gray}\bf Controversial findings}
707 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
709 \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
710 \item \si{} reacting with further C in cleared volume
712 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
714 \item Room temperature implantation $\rightarrow$ high C diffusion
715 \item Elevated temperature implantation $\rightarrow$ no C redistribution
717 $\Rightarrow$ mobile {\color{red}\ci} opposed to
718 stable {\color{blue}\cs{}} configurations
719 \item Strained silicon \& Si/SiC heterostructures
720 {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
722 \item {\color{blue}Coherent} SiC precipitates (tensile strain)
723 \item Incoherent SiC (strain relaxation)
728 {\Huge${\lightning}$} \hspace{0.3cm}
729 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
730 {\Huge${\lightning}$}
743 Utilized computational methods
750 {\bf Molecular dynamics (MD)}\\[0.1cm]
752 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
754 System of $N$ particles &
755 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
756 Phase space propagation &
757 Velocity Verlet | timestep: \unit[1]{fs} \\
758 Analytical interaction potential &
759 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
762 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
763 \pot_{ij} = {\color{red}f_C(r_{ij})}
764 \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
766 Observables: time/ensemble averages &
767 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
775 {\bf Density functional theory (DFT)}
779 \begin{minipage}[t]{6cm}
781 \item Hohenberg-Kohn theorem:\\
782 $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
783 \item Kohn-Sham approach:\\
784 Single-particle effective theory
788 \item Code: \textsc{vasp}
789 \item Plane wave basis set
791 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
794 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
796 \item Ultrasoft pseudopotential
797 \item Exchange \& correlation: GGA
798 \item Brillouin zone sampling: $\Gamma$-point
799 \item Supercell: $N=216\pm2$
802 \begin{minipage}{6cm}
803 \begin{pspicture}(0,0)(0,0)
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807 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
810 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
812 n(r)=\sum_i^N|\Phi_i(r)|^2
815 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
817 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
821 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
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823 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
834 Point defects \& defect migration
841 \begin{minipage}[b]{7.5cm}
842 {\bf Defect structure}\\
843 \begin{pspicture}(0,0)(7,4.4)
844 \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
847 \item Creation of c-Si simulation volume
848 \item Periodic boundary conditions
849 \item $T=0\text{ K}$, $p=0\text{ bar}$
852 \rput(3.5,1.3){\rnode{insert}{\psframebox{
855 Insertion of interstitial C/Si atoms
858 \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
861 Relaxation / structural energy minimization
864 \ncline[]{->}{init}{insert}
865 \ncline[]{->}{insert}{cool}
868 \begin{minipage}[b]{4.5cm}
870 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
872 \begin{minipage}{2.21cm}
874 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
875 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
876 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
879 \begin{minipage}{2.21cm}
881 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
882 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
883 {\color{black}$\bullet$} Vac. / Sub.
890 \begin{minipage}[b]{6cm}
891 {\bf Defect formation energy}\\
893 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
894 Particle reservoir: Si \& SiC\\[0.2cm]
895 {\bf Binding energy}\\
899 E_{\text{f}}^{\text{comb}}-
900 E_{\text{f}}^{1^{\text{st}}}-
901 E_{\text{f}}^{2^{\text{nd}}}
905 $E_{\text{b}}<0$: energetically favorable configuration\\
906 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
908 \begin{minipage}[b]{6cm}
909 {\bf Migration barrier}
912 \item Displace diffusing atom
913 \item Constrain relaxation of (diffusing) atoms
914 \item Record configurational energy
916 \begin{picture}(0,0)(-60,-33)
917 \includegraphics[width=4.5cm]{crt_mod.eps}
929 Si self-interstitial point defects in silicon\\[0.1cm]
933 \begin{tabular}{l c c c c c}
935 $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
937 \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
938 Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
940 \end{tabular}\\[0.4cm]
943 \begin{minipage}{3cm}
945 \underline{Vacancy}\\
946 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
949 \begin{minipage}{3cm}
951 \underline{\hkl<1 1 0> DB}\\
952 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
955 \begin{minipage}{3cm}
957 \underline{\hkl<1 0 0> DB}\\
958 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
961 \begin{minipage}{3cm}
963 \underline{Tetrahedral}\\
964 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
968 \underline{Hexagonal} \hspace{2pt}
969 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
971 \begin{minipage}{2.7cm}
972 $E_{\text{f}}^*=4.48\text{ eV}$\\
973 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
975 \begin{minipage}{0.4cm}
980 \begin{minipage}{2.7cm}
981 $E_{\text{f}}=3.96\text{ eV}$\\
982 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
985 \begin{minipage}{5.5cm}
987 {\tiny nearly T $\rightarrow$ T}\\
989 \includegraphics[width=6.0cm]{nhex_tet.ps}
1000 C interstitial point defects in silicon\\
1003 \begin{tabular}{l c c c c c c r}
1005 $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
1006 {\color{black} \cs{} \& \si}\\
1008 \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1009 Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1011 \end{tabular}\\[0.1cm]
1014 \begin{minipage}{2.8cm}
1015 \underline{Hexagonal} \hspace{2pt}
1016 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1017 $E_{\text{f}}^*=9.05\text{ eV}$\\
1018 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
1020 \begin{minipage}{0.4cm}
1025 \begin{minipage}{2.8cm}
1026 \underline{\hkl<1 0 0>}\\
1027 $E_{\text{f}}=3.88\text{ eV}$\\
1028 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
1031 \begin{minipage}{1.4cm}
1034 \begin{minipage}{3.0cm}
1036 \underline{Tetrahedral}\\
1037 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
1042 \begin{minipage}{2.8cm}
1043 \underline{Bond-centered}\\
1044 $E_{\text{f}}^*=5.59\text{ eV}$\\
1045 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
1047 \begin{minipage}{0.4cm}
1052 \begin{minipage}{2.8cm}
1053 \underline{\hkl<1 1 0> dumbbell}\\
1054 $E_{\text{f}}=5.18\text{ eV}$\\
1055 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
1058 \begin{minipage}{1.4cm}
1061 \begin{minipage}{3.0cm}
1063 \underline{Substitutional}\\
1064 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
1074 C-Si dimer \& bond-centered interstitial configuration
1081 \begin{minipage}[t]{4.1cm}
1082 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
1083 \begin{minipage}{2.0cm}
1085 \underline{Erhart/Albe}
1086 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
1089 \begin{minipage}{2.0cm}
1091 \underline{\textsc{vasp}}
1092 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
1094 \end{minipage}\\[0.2cm]
1095 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
1096 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
1097 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
1098 $\Rightarrow$ $sp^2$ hybridization
1100 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
1101 {\tiny Charge density isosurface}
1104 \begin{minipage}{0.2cm}
1107 \begin{minipage}[t]{8.1cm}
1109 {\bf Bond-centered interstitial}\\[0.1cm]
1110 \begin{minipage}{4.4cm}
1113 \item Linear Si-C-Si bond
1114 \item Si: one C \& 3 Si neighbours
1115 \item Spin polarized calculations
1116 \item No saddle point!\\
1120 \begin{minipage}{2.7cm}
1121 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1123 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
1128 \begin{minipage}[t]{6.5cm}
1129 \begin{minipage}[t]{1.2cm}
1131 {\tiny sp$^3$}\\[0.8cm]
1132 \underline{${\color{black}\uparrow}$}
1133 \underline{${\color{black}\uparrow}$}
1134 \underline{${\color{black}\uparrow}$}
1135 \underline{${\color{red}\uparrow}$}\\
1138 \begin{minipage}[t]{1.4cm}
1140 {\color{red}M}{\color{blue}O}\\[0.8cm]
1141 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1142 $\sigma_{\text{ab}}$\\[0.5cm]
1143 \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1147 \begin{minipage}[t]{1.0cm}
1151 \underline{${\color{white}\uparrow\uparrow}$}
1152 \underline{${\color{white}\uparrow\uparrow}$}\\
1154 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1155 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1159 \begin{minipage}[t]{1.4cm}
1161 {\color{blue}M}{\color{green}O}\\[0.8cm]
1162 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1163 $\sigma_{\text{ab}}$\\[0.5cm]
1164 \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1168 \begin{minipage}[t]{1.2cm}
1171 {\tiny sp$^3$}\\[0.8cm]
1172 \underline{${\color{green}\uparrow}$}
1173 \underline{${\color{black}\uparrow}$}
1174 \underline{${\color{black}\uparrow}$}
1175 \underline{${\color{black}\uparrow}$}\\
1183 \begin{minipage}{3.0cm}
1185 \underline{Charge density}\\
1186 {\color{gray}$\bullet$} Spin up\\
1187 {\color{green}$\bullet$} Spin down\\
1188 {\color{blue}$\bullet$} Resulting spin up\\
1189 {\color{yellow}$\bullet$} Si atoms\\
1190 {\color{red}$\bullet$} C atom
1192 \begin{minipage}{3.6cm}
1193 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
1200 \begin{pspicture}(0,0)(0,0)
1201 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
1210 C interstitial migration --- ab initio
1217 \begin{minipage}{6.8cm}
1218 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
1219 \begin{minipage}{2.0cm}
1220 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1222 \begin{minipage}{0.2cm}
1225 \begin{minipage}{2.0cm}
1226 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
1228 \begin{minipage}{0.2cm}
1231 \begin{minipage}{2.0cm}
1232 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
1233 \end{minipage}\\[0.1cm]
1235 $\Rightarrow$ BC configuration constitutes local minimum\\
1236 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
1238 \begin{minipage}{5.4cm}
1239 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
1240 \end{minipage}\\[0.2cm]
1243 \begin{minipage}{6.8cm}
1244 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
1245 \begin{minipage}{2.0cm}
1246 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1248 \begin{minipage}{0.2cm}
1251 \begin{minipage}{2.0cm}
1252 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
1254 \begin{minipage}{0.2cm}
1257 \begin{minipage}{2.0cm}
1258 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
1259 \end{minipage}\\[0.1cm]
1260 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
1261 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
1262 Note: Change in orientation
1264 \begin{minipage}{5.4cm}
1265 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
1266 \end{minipage}\\[0.1cm]
1269 Reorientation pathway composed of two consecutive processes of the above type
1278 C interstitial migration --- analytical potential
1285 \begin{minipage}[t]{6.0cm}
1286 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
1287 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
1289 \item Lowermost migration barrier
1290 \item $\Delta E \approx \unit[2.2]{eV}$
1291 \item 2.4 times higher than ab initio result
1292 \item Different pathway
1295 \begin{minipage}[t]{0.2cm}
1298 \begin{minipage}[t]{6.0cm}
1299 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
1302 \item Bond-centered configuration unstable\\
1303 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1304 \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
1305 $\rightarrow$ \ci{} \hkl<1 1 0> DB
1308 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
1310 \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
1311 \item 2.4 -- 3.4 times higher than ab initio result
1312 \item After all: Change of the DB orientation
1318 {\color{red}\bf Drastically overestimated diffusion barrier}
1321 \begin{pspicture}(0,0)(0,0)
1322 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
1338 \begin{minipage}{9cm}
1340 Summary of combinations}\\[0.1cm]
1342 \begin{tabular}{l c c c c c c}
1344 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1346 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1347 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1348 \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}\\
1349 \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}\\
1350 \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}\\
1351 \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}\\
1353 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1354 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1361 $E_{\text{b}}$ explainable by stress compensation / increase
1365 \begin{minipage}{3cm}
1366 \includegraphics[width=3.5cm]{comb_pos.eps}
1371 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1372 \begin{minipage}[t]{3.2cm}
1373 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1374 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1376 \begin{minipage}[t]{3.0cm}
1377 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1378 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1380 \begin{minipage}[t]{6.1cm}
1383 \item \ci{} agglomeration energetically favorable
1384 \item Most favorable: C clustering\\
1385 {\color{red}However \ldots}\\
1386 \ldots high migration barrier ($>4\,\text{eV}$)\\
1388 $4\times{\color{cyan}[-2.25]}$ versus
1389 $2\times{\color{orange}[-2.39]}$
1392 {\color{blue}\ci{} agglomeration / no C clustering}
1409 \begin{minipage}{9cm}
1411 Summary of combinations}\\[0.1cm]
1413 \begin{tabular}{l c c c c c c}
1415 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1417 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1418 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1419 \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}\\
1420 \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}\\
1421 \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}\\
1422 \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}\\
1424 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1425 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1432 $E_{\text{b}}$ explainable by stress compensation / increase
1436 \begin{minipage}{3cm}
1437 \includegraphics[width=3.5cm]{comb_pos.eps}
1442 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1443 \begin{minipage}[t]{3.2cm}
1444 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1445 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1447 \begin{minipage}[t]{3.0cm}
1448 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1449 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1451 \begin{minipage}[t]{6.1cm}
1454 \item \ci{} agglomeration energetically favorable
1455 \item Most favorable: C clustering\\
1456 {\color{red}However \ldots}\\
1457 \ldots high migration barrier ($>4\,\text{eV}$)\\
1459 $4\times{\color{cyan}[-2.25]}$ versus
1460 $2\times{\color{orange}[-2.39]}$
1463 {\color{blue}\ci{} agglomeration / no C clustering}
1468 \begin{pspicture}(0,0)(0,0)
1469 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1470 \begin{minipage}{14cm}
1475 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1476 \begin{minipage}{8cm}
1480 Interaction along \hkl[1 1 0]
1481 \includegraphics[width=7cm]{db_along_110_cc.ps}
1493 Defect combinations of C-Si dimers and vacancies
1499 \begin{minipage}[b]{2.6cm}
1501 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1502 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1505 \begin{minipage}[b]{7cm}
1508 \begin{minipage}[b]{2.6cm}
1510 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1511 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1513 \end{minipage}\\[0.2cm]
1515 \begin{minipage}{6.5cm}
1516 \includegraphics[width=6.0cm]{059-539.ps}
1518 \begin{minipage}{5.7cm}
1519 \includegraphics[width=6.0cm]{314-539.ps}
1522 \begin{pspicture}(0,0)(0,0)
1523 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1525 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1526 \begin{minipage}{6.5cm}
1528 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1529 Low migration barrier towards C$_{\text{sub}}$\\
1531 High barrier for reverse process\\[0.3cm]
1533 High probability of stable C$_{\text{sub}}$ configuration
1546 Combinations of substitutional C and Si self-interstitials
1553 \begin{minipage}{6.2cm}
1555 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1557 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1558 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1559 \item Interaction drops quickly to zero\\
1560 $\rightarrow$ low capture radius
1564 \begin{minipage}{0.2cm}
1567 \begin{minipage}{6.0cm}
1569 {\bf Transition from the ground state}
1571 \item Low transition barrier
1572 \item Barrier smaller than \ci{} migration barrier
1573 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1574 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1577 \end{minipage}\\[0.3cm]
1579 \begin{minipage}{6.0cm}
1580 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1582 \begin{minipage}{0.4cm}
1585 \begin{minipage}{6.0cm}
1587 \includegraphics[width=6.0cm]{162-097.ps}
1591 \begin{pspicture}(0,0)(0,0)
1592 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1593 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1594 \begin{minipage}{8cm}
1598 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1599 IBS --- process far from equilibrium\\
1612 Combinations of substitutional C and Si self-interstitials
1619 \begin{minipage}{6.2cm}
1621 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1623 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1624 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1625 \item Interaction drops quickly to zero\\
1626 $\rightarrow$ low capture radius
1630 \begin{minipage}{0.2cm}
1633 \begin{minipage}{6.0cm}
1635 {\bf Transition from the ground state}
1637 \item Low transition barrier
1638 \item Barrier smaller than \ci{} migration barrier
1639 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1640 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1643 \end{minipage}\\[0.3cm]
1645 \begin{minipage}{6.0cm}
1646 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1648 \begin{minipage}{0.4cm}
1651 \begin{minipage}{6.0cm}
1653 \includegraphics[width=6.0cm]{162-097.ps}
1657 \begin{pspicture}(0,0)(0,0)
1658 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1659 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1660 \begin{minipage}{8cm}
1664 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1665 IBS --- process far from equilibrium\\
1673 \begin{pspicture}(0,0)(0,0)
1674 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1675 \begin{minipage}{14cm}
1680 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1681 \begin{minipage}{11cm}
1685 Ab initio MD at \degc{900}\\[0.4cm]
1686 \begin{minipage}{5.4cm}
1688 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1691 \begin{minipage}{5.4cm}
1693 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1695 \end{minipage}\\[0.5cm]
1697 Contribution of entropy to structural formation\\[0.1cm]
1710 Silicon carbide precipitation simulations
1720 \begin{pspicture}(0,0)(12,6.5)
1722 \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1725 \item Create c-Si volume
1726 \item Periodc boundary conditions
1727 \item Set requested $T$ and $p=0\text{ bar}$
1728 \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1731 \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1733 Insertion of C atoms at constant T
1735 \item total simulation volume {\pnode{in1}}
1736 \item volume of minimal SiC precipitate size {\pnode{in2}}
1737 \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1741 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1743 Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1745 \ncline[]{->}{init}{insert}
1746 \ncline[]{->}{insert}{cool}
1747 \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
1748 \rput(7.6,6){\footnotesize $V_1$}
1749 \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
1750 \rput(8.9,4.85){\tiny $V_2$}
1751 \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
1752 \rput(9.25,4.45){\footnotesize $V_3$}
1753 \rput(7.9,3.2){\pnode{ins1}}
1754 \rput(8.92,2.8){\pnode{ins2}}
1755 \rput(10.8,2.4){\pnode{ins3}}
1756 \ncline[]{->}{in1}{ins1}
1757 \ncline[]{->}{in2}{ins2}
1758 \ncline[]{->}{in3}{ins3}
1768 \begin{minipage}{5.7cm}
1770 \item Amount of C atoms: 6000\\
1771 ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
1772 \item Simulation volume: $31^3$ Si unit cells\\
1776 \begin{minipage}{0.3cm}
1780 \begin{minipage}{6.0cm}
1781 Restricted to classical potential caclulations\\
1782 $\rightarrow$ Low C diffusion / overestimated barrier\\
1783 $\rightarrow$ Consider $V_2$ and $V_3$
1785 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
1796 Silicon carbide precipitation simulations at \degc{450} as in IBS
1801 \begin{minipage}{6.3cm}
1802 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1803 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1806 \begin{minipage}{6.1cm}
1808 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1809 \hkl<1 0 0> C-Si dumbbell dominated structure
1811 \item Si-C bumbs around \unit[0.19]{nm}
1812 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1813 concatenated differently oriented \ci{} DBs
1814 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1816 \begin{pspicture}(0,0)(6.0,1.0)
1817 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1818 \begin{minipage}{6cm}
1820 Formation of \ci{} dumbbells\\
1821 C atoms in proper 3C-SiC distance first
1824 \end{pspicture}\\[0.1cm]
1825 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1827 \item High amount of strongly bound C-C bonds
1828 \item Increased defect \& damage density\\
1829 $\rightarrow$ Arrangements hard to categorize and trace
1830 \item Only short range order observable
1832 \begin{pspicture}(0,0)(6.0,0.8)
1833 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1834 \begin{minipage}{6cm}
1836 Amorphous SiC-like phase
1839 \end{pspicture}\\[0.3cm]
1840 \begin{pspicture}(0,0)(6.0,2.0)
1841 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
1842 \begin{minipage}{6cm}
1856 Silicon carbide precipitation simulations at \degc{450} as in IBS
1861 \begin{minipage}{6.3cm}
1862 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1863 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1866 \begin{minipage}{6.1cm}
1868 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1869 \hkl<1 0 0> C-Si dumbbell dominated structure
1871 \item Si-C bumbs around \unit[0.19]{nm}
1872 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1873 concatenated differently oriented \ci{} DBs
1874 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1876 \begin{pspicture}(0,0)(6.0,1.0)
1877 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1878 \begin{minipage}{6cm}
1880 Formation of \ci{} dumbbells\\
1881 C atoms in proper 3C-SiC distance first
1884 \end{pspicture}\\[0.1cm]
1885 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1887 \item High amount of strongly bound C-C bonds
1888 \item Increased defect \& damage density\\
1889 $\rightarrow$ Arrangements hard to categorize and trace
1890 \item Only short range order observable
1892 \begin{pspicture}(0,0)(6.0,0.8)
1893 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1894 \begin{minipage}{6cm}
1896 Amorphous SiC-like phase
1899 \end{pspicture}\\[0.3cm]
1900 \begin{pspicture}(0,0)(6.0,2.0)
1901 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
1902 \begin{minipage}{6cm}
1905 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
1906 \begin{minipage}{0.8cm}
1907 {\bf\boldmath $V_1$:}
1909 \begin{minipage}{5.1cm}
1910 Formation of \ci{} indeed occurs\\
1911 Agllomeration not observed
1912 \end{minipage}\\[0.3cm]
1913 \begin{minipage}{0.8cm}
1914 {\bf\boldmath $V_{2,3}$:}
1916 \begin{minipage}{5.1cm}
1917 Amorphous SiC-like structure\\
1918 (not expected at \degc{450})\\[0.05cm]
1919 No rearrangement/transition into 3C-SiC
1920 \end{minipage}\\[0.1cm]
1932 Limitations of MD and short range potentials
1939 {\bf Time scale problem of MD}\\[0.2cm]
1940 Precise integration \& thermodynamic sampling\\
1941 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
1942 $\omega$: vibrational mode\\
1943 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
1944 Several local minima separated by large energy barriers\\
1945 $\Rightarrow$ Transition event corresponds to a multiple
1946 of vibrational periods\\
1947 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
1948 infrequent transition events\\[0.2cm]
1949 {\color{blue}Accelerated methods:}
1950 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1954 {\bf Limitations related to the short range potential}\\[0.2cm]
1955 Cut-off function limits interaction to next neighbours\\
1956 $\Rightarrow$ Overestimated unphysical high forces of next neighbours
1961 {\bf Approach to the (twofold) problem}\\[0.2cm]
1962 Increased temperature simulations without TAD corrections\\
1963 Accelerated methods or higher time scales exclusively not sufficient!
1965 \begin{pspicture}(0,0)(0,0)
1966 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
1967 \begin{minipage}{7.5cm}
1970 Potential enhanced slow phase space propagation
1973 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1974 \begin{minipage}{2.7cm}
1978 thermodynamic sampling
1981 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
1982 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
1983 \begin{minipage}{3.6cm}
1986 \underline{IBS}\\[0.1cm]
1987 3C-SiC also observed for higher T\\[0.1cm]
1988 Higher T inside sample\\[0.1cm]
1989 Structural evolution vs.\\
1990 equilibrium properties
1993 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
2002 Increased temperature simulations --- $V_1$
2007 \begin{minipage}{6.2cm}
2008 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2011 \begin{minipage}{6.2cm}
2012 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2015 \begin{minipage}{6.2cm}
2016 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2019 \begin{minipage}{6.3cm}
2021 \underline{Si-C bonds:}
2023 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2024 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2026 \underline{Si-Si bonds:}
2027 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2028 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2029 \underline{C-C bonds:}
2031 \item C-C next neighbour pairs reduced (mandatory)
2032 \item Peak at 0.3 nm slightly shifted
2034 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2035 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2037 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2039 \item Range [|-$\downarrow$]:
2040 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2041 with nearby Si$_{\text{I}}$}
2052 Increased temperature simulations --- $V_1$
2057 \begin{minipage}{6.2cm}
2058 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2061 \begin{minipage}{6.2cm}
2062 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2065 \begin{minipage}{6.2cm}
2066 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2069 \begin{minipage}{6.3cm}
2071 \underline{Si-C bonds:}
2073 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2074 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2076 \underline{Si-Si bonds:}
2077 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2078 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2079 \underline{C-C bonds:}
2081 \item C-C next neighbour pairs reduced (mandatory)
2082 \item Peak at 0.3 nm slightly shifted
2084 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2085 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2087 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2089 \item Range [|-$\downarrow$]:
2090 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2091 with nearby Si$_{\text{I}}$}
2097 \begin{pspicture}(0,0)(0,0)
2098 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
2099 \begin{minipage}{14cm}
2104 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
2105 \begin{minipage}{9cm}
2109 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
2110 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
2113 \item Stretched coherent SiC structures\\
2114 $\Rightarrow$ Precipitation process involves {\color{blue}\cs}
2115 \item Explains annealing behavior of high/low T C implantations
2117 \item Low T: highly mobile {\color{red}\ci}
2118 \item High T: stable configurations of {\color{blue}\cs}
2122 \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
2123 \item Building block for surrounding Si host \& further SiC
2124 \item Strain compensation \ldots\\
2125 \ldots Si/SiC interface\\
2126 \ldots within stretched coherent SiC structure
2131 \psframebox[linecolor=blue,linewidth=0.05cm]{
2132 \begin{minipage}{7cm}
2134 Precipitation mechanism involving \cs\\
2135 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2145 % skip high T / C conc ... only here!
2151 Increased temperature simulations at high C concentration
2156 \begin{minipage}{6.5cm}
2157 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2159 \begin{minipage}{6.5cm}
2160 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2168 \begin{minipage}[t]{6.0cm}
2169 0.186 nm: Si-C pairs $\uparrow$\\
2170 (as expected in 3C-SiC)\\[0.2cm]
2171 0.282 nm: Si-C-C\\[0.2cm]
2172 $\approx$0.35 nm: C-Si-Si
2175 \begin{minipage}{0.2cm}
2179 \begin{minipage}[t]{6.0cm}
2180 0.15 nm: C-C pairs $\uparrow$\\
2181 (as expected in graphite/diamond)\\[0.2cm]
2182 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2183 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2188 \item Decreasing cut-off artifact
2189 \item {\color{red}Amorphous} SiC-like phase remains
2190 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2191 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2200 High C \& small $V$ \& short $t$
2203 Slow restructuring due to strong C-C bonds
2206 High C \& low T implants
2214 % skipped high T / C conc
2225 \begin{pspicture}(0,0)(12,1.0)
2226 \psframebox[fillstyle=gradient,gradbegin=hred,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
2227 \begin{minipage}{11cm}
2228 {\color{black}Diploma thesis}\\
2229 \underline{Monte Carlo} simulation modeling the selforganization process\\
2230 leading to periodic arrays of nanometric amorphous SiC precipitates
2233 \end{pspicture}\\[0.4cm]
2234 \begin{pspicture}(0,0)(12,2)
2235 \psframebox[fillstyle=gradient,gradbegin=hblue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
2236 \begin{minipage}{11cm}
2237 {\color{black}Doctoral studies}\\
2238 Classical potential \underline{molecular dynamics} simulations \ldots\\
2239 \underline{Density functional theory} calculations \ldots\\[0.2cm]
2240 \ldots on defect formation and SiC precipitation in Si
2243 \end{pspicture}\\[0.5cm]
2244 \begin{pspicture}(0,0)(12,3)
2245 \psframebox[fillstyle=solid,fillcolor=white,linestyle=solid]{
2246 \begin{minipage}{11cm}
2248 {\color{black}\bf How to proceed \ldots}\\[0.1cm]
2249 MC $\rightarrow$ empirical potential MD $\rightarrow$ Ground-state DFT \ldots
2251 \renewcommand\labelitemi{$\ldots$}
2252 \item beyond LDA/GGA methods \& ground-state DFT
2254 Investigation of structure \& structural evolution \ldots
2256 \renewcommand\labelitemi{$\ldots$}
2257 \item electronic/optical properties
2258 \item electronic correlations
2259 \item non-equilibrium systems
2263 \end{pspicture}\\[0.5cm]
2279 \underline{Augsburg}
2281 \item Prof. B. Stritzker (accomodation at EP \RM{4})
2282 \item Ralf Utermann (EDV)
2285 \underline{Helsinki}
2287 \item Prof. K. Nordlund (MD)
2292 \item Bayerische Forschungsstiftung (financial support)
2295 \underline{Paderborn}
2297 \item Prof. J. Lindner (SiC)
2298 \item Prof. G. Schmidt (DFT + financial support)
2299 \item Dr. E. Rauls (DFT + SiC)
2302 \underline{Stuttgart}
2305 \bf Thank you for your attention / invitation!