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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
132 A B C D E F G H G F E D C B A
150 Atomistic simulation study on silicon carbide\\[0.2cm]
151 precipitation in silicon\\
158 \textsc{Frank Zirkelbach}
162 Defense of doctor's thesis
171 % no vertical centering
174 % skip for preparation
179 % motivation / properties / applications of silicon carbide
187 \begin{pspicture}(0,0)(13.5,5)
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194 \rput[lt](0,4.6){\color{gray}PROPERTIES}
196 \rput[lt](0.3,4){wide band gap}
197 \rput[lt](0.3,3.5){high electric breakdown field}
198 \rput[lt](0.3,3){good electron mobility}
199 \rput[lt](0.3,2.5){high electron saturation drift velocity}
200 \rput[lt](0.3,2){high thermal conductivity}
202 \rput[lt](0.3,1.5){hard and mechanically stable}
203 \rput[lt](0.3,1){chemically inert}
205 \rput[lt](0.3,0.5){radiation hardness}
207 \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
209 \rput[rt](12.5,3.85){high-temperature, high power}
210 \rput[rt](12.5,3.5){and high-frequency}
211 \rput[rt](12.5,3.15){electronic and optoelectronic devices}
213 \rput[rt](12.5,2.35){material suitable for extreme conditions}
214 \rput[rt](12.5,2){microelectromechanical systems}
215 \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
217 \rput[rt](12.5,0.85){first wall reactor material, detectors}
218 \rput[rt](12.5,0.5){and electronic devices for space}
222 \begin{picture}(0,0)(5,-162)
223 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
225 \begin{picture}(0,0)(-120,-162)
226 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
228 \begin{picture}(0,0)(-270,-162)
229 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
232 \begin{picture}(0,0)(10,65)
233 \includegraphics[height=2.8cm]{sic_switch.eps}
235 %\begin{picture}(0,0)(-243,65)
236 \begin{picture}(0,0)(-110,65)
237 \includegraphics[height=2.8cm]{ise_99.eps}
239 %\begin{picture}(0,0)(-135,65)
240 \begin{picture}(0,0)(-100,65)
241 \includegraphics[height=1.2cm]{infineon_schottky.eps}
243 \begin{picture}(0,0)(-233,65)
244 \includegraphics[height=2.8cm]{solar_car.eps}
255 Polytypes of SiC\\[0.6cm]
260 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
261 \begin{minipage}{1.9cm}
262 {\tiny cubic (twist)}
264 \begin{minipage}{2.9cm}
265 {\tiny hexagonal (no twist)}
268 \begin{picture}(0,0)(-150,0)
269 \includegraphics[width=7cm]{polytypes.eps}
276 \begin{tabular}{l c c c c c c}
278 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
280 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
281 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
282 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
283 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
284 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
285 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
286 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
290 \begin{pspicture}(0,0)(0,0)
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293 \begin{pspicture}(0,0)(0,0)
294 \psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
296 \begin{pspicture}(0,0)(0,0)
297 \psellipse[linecolor=red](10.45,0.42)(0.4,0.20)
308 Fabrication of silicon carbide
317 \emph{Silicon carbide --- Born from the stars, perfected on earth.}
323 SiC thin films by MBE \& CVD
325 \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
326 \item \underline{Commercially available} semiconductor power devices based on
327 \underline{\foreignlanguage{greek}{a}-SiC}
328 \item Production of favored \underline{3C-SiC} material
329 \underline{less advanced}
330 \item Quality and size not yet sufficient
332 \begin{picture}(0,0)(-310,-20)
333 \includegraphics[width=2.0cm]{cree.eps}
341 {\footnotesize\color{black}
342 Mismatch in \underline{thermal expansion coeefficient}
343 and \underline{lattice parameter} w.r.t. substrate
350 {\bf Alternative approach}\\
351 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
358 \begin{minipage}{3.15cm}
360 \includegraphics[width=3cm]{imp.eps}\\
366 \begin{minipage}{3.15cm}
368 \includegraphics[width=3cm]{annealing.eps}\\
370 Postannealing at $>$ \degc{1200}
375 \begin{minipage}{5.5cm}
378 No surface bending effects\\
379 High areal homogenity\\[0.1cm]
380 $\Downarrow$\\[0.1cm]
381 Synthesis of large area SiC films possible
392 IBS of epitaxial single crystalline 3C-SiC
401 \item \underline{Implantation step 1}\\[0.1cm]
402 Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
403 $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
404 {\color{blue}precipitates}
405 \item \underline{Implantation step 2}\\[0.1cm]
406 Little remaining dose | \unit[180]{keV} | \degc{250}\\
408 Destruction/Amorphization of precipitates at layer interface
409 \item \underline{Annealing}\\[0.1cm]
410 \unit[10]{h} at \degc{1250}\\
411 $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
415 \begin{minipage}{6.9cm}
416 \includegraphics[width=7cm]{ibs_3c-sic.eps}\\[-0.4cm]
419 XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
423 \begin{minipage}{5cm}
424 \begin{pspicture}(0,0)(0,0)
426 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
427 \begin{minipage}{5.3cm}
430 3C-SiC precipitation\\
431 not yet fully understood
435 \renewcommand\labelitemi{$\Rightarrow$}
436 Details of the SiC precipitation
438 \item significant technological progress\\
439 in SiC thin film formation
440 \item perspectives for processes relying\\
441 upon prevention of SiC precipitation
445 \rput(-6.8,5.5){\pnode{h0}}
446 \rput(-3.0,5.5){\pnode{h1}}
447 \ncline[linecolor=blue]{-}{h0}{h1}
448 \ncline[linecolor=blue]{->}{h1}{box}
460 Supposed precipitation mechanism of SiC in Si
468 \begin{minipage}{3.6cm}
470 Si \& SiC lattice structure\\[0.1cm]
471 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
474 \begin{minipage}{1.7cm}
475 \underline{Silicon}\\
476 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
477 $a=\unit[5.429]{\\A}$\\
478 $\rho^*_{\text{Si}}=\unit[100]{\%}$
480 \begin{minipage}{1.7cm}
481 \underline{Silicon carbide}\\
482 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
483 $a=\unit[4.359]{\\A}$\\
484 $\rho^*_{\text{Si}}=\unit[97]{\%}$
490 \begin{minipage}{4.1cm}
492 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
496 \begin{minipage}{4.0cm}
498 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
504 \begin{minipage}{4.0cm}
506 C-Si dimers (dumbbells)\\[-0.1cm]
511 \begin{minipage}{4.1cm}
513 Agglomeration of C-Si dumbbells\\[-0.1cm]
514 $\Rightarrow$ dark contrasts
518 \begin{minipage}{4.0cm}
520 Precipitation of 3C-SiC in Si\\[-0.1cm]
521 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
522 \& release of Si self-interstitials
528 \begin{minipage}{4.0cm}
530 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
534 \begin{minipage}{4.1cm}
536 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
540 \begin{minipage}{4.0cm}
542 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
546 \begin{pspicture}(0,0)(0,0)
547 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
548 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
549 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
550 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
551 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
552 $4a_{\text{Si}}=5a_{\text{SiC}}$
554 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
555 \hkl(h k l) planes match
557 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
568 Supposed precipitation mechanism of SiC in Si
576 \begin{minipage}{3.6cm}
578 Si \& SiC lattice structure\\[0.1cm]
579 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
582 \begin{minipage}{1.7cm}
583 \underline{Silicon}\\
584 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
585 $a=\unit[5.429]{\\A}$\\
586 $\rho^*_{\text{Si}}=\unit[100]{\%}$
588 \begin{minipage}{1.7cm}
589 \underline{Silicon carbide}\\
590 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
591 $a=\unit[4.359]{\\A}$\\
592 $\rho^*_{\text{Si}}=\unit[97]{\%}$
598 \begin{minipage}{4.1cm}
600 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
604 \begin{minipage}{4.0cm}
606 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
612 \begin{minipage}{4.0cm}
614 C-Si dimers (dumbbells)\\[-0.1cm]
615 on Si interstitial sites
619 \begin{minipage}{4.1cm}
621 Agglomeration of C-Si dumbbells\\[-0.1cm]
622 $\Rightarrow$ dark contrasts
626 \begin{minipage}{4.0cm}
628 Precipitation of 3C-SiC in Si\\[-0.1cm]
629 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
630 \& release of Si self-interstitials
636 \begin{minipage}{4.0cm}
638 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
642 \begin{minipage}{4.1cm}
644 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
648 \begin{minipage}{4.0cm}
650 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
654 \begin{pspicture}(0,0)(0,0)
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658 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
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660 $4a_{\text{Si}}=5a_{\text{SiC}}$
662 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
663 \hkl(h k l) planes match
665 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
668 % controversial view!
669 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
670 \begin{minipage}{14cm}
675 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
676 \begin{minipage}{10cm}
680 {\color{gray}\bf Controversial findings}
683 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
685 \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
686 \item \si{} reacting with further C in cleared volume
688 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
690 \item Room temperature implantation $\rightarrow$ high C diffusion
691 \item Elevated temperature implantation $\rightarrow$ no C redistribution
693 $\Rightarrow$ mobile {\color{red}\ci} opposed to
694 stable {\color{blue}\cs{}} configurations
695 \item Strained silicon \& Si/SiC heterostructures
696 {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
698 \item {\color{blue}Coherent} SiC precipitates (tensile strain)
699 \item Incoherent SiC (strain relaxation)
704 {\Huge${\lightning}$} \hspace{0.3cm}
705 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
706 {\Huge${\lightning}$}
724 \item Introduction / Motivation
725 \item Assumed SiC precipitation mechanisms / Controversy
727 \item Utilized simulation techniques
729 \item Molecular dynamics (MD) simulations
730 \item Density functional theory (DFT) calculations
732 \item Simulation results
734 \item C and Si self-interstitial point defects in silicon
735 \item Silicon carbide precipitation simulations
737 \item Summary / Conclusion
746 Utilized computational methods
753 {\bf Molecular dynamics (MD)}\\[0.1cm]
755 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
757 System of $N$ particles &
758 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
759 Phase space propagation &
760 Velocity Verlet | timestep: \unit[1]{fs} \\
761 Analytical interaction potential &
762 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
765 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
766 \pot_{ij} = {\color{red}f_C(r_{ij})}
767 \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
769 Observables: time/ensemble averages &
770 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
778 {\bf Density functional theory (DFT)}
782 \begin{minipage}[t]{6cm}
784 \item Hohenberg-Kohn theorem:\\
785 $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
786 \item Kohn-Sham approach:\\
787 Single-particle effective theory
791 \item Code: \textsc{vasp}
792 \item Plane wave basis set | $E_{\text{cut}}=\unit[300]{eV}$
794 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
797 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
799 \item Ultrasoft pseudopotential
800 \item Exchange \& correlation: GGA
801 \item Brillouin zone sampling: $\Gamma$-point
802 \item Supercell: $N=216\pm2$
805 \begin{minipage}{6cm}
806 \begin{pspicture}(0,0)(0,0)
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810 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
813 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
815 n(r)=\sum_i^N|\Phi_i(r)|^2
818 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
820 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
824 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
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826 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
837 Point defects \& defect migration
844 \begin{minipage}[b]{7.5cm}
845 {\bf Defect structure}\\
846 \begin{pspicture}(0,0)(7,4.4)
847 \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
850 \item Creation of c-Si simulation volume
851 \item Periodic boundary conditions
852 \item $T=0\text{ K}$, $p=0\text{ bar}$
855 \rput(3.5,1.3){\rnode{insert}{\psframebox{
858 Insertion of interstitial C/Si atoms
861 \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
864 Relaxation / structural energy minimization
867 \ncline[]{->}{init}{insert}
868 \ncline[]{->}{insert}{cool}
871 \begin{minipage}[b]{4.5cm}
873 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
875 \begin{minipage}{2.21cm}
877 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
878 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
879 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
882 \begin{minipage}{2.21cm}
884 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
885 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
886 {\color{black}$\bullet$} Vac. / Sub.
893 \begin{minipage}[b]{6cm}
894 {\bf Defect formation energy}\\
896 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
897 Particle reservoir: Si \& SiC\\[0.2cm]
898 {\bf Binding energy}\\
902 E_{\text{f}}^{\text{comb}}-
903 E_{\text{f}}^{1^{\text{st}}}-
904 E_{\text{f}}^{2^{\text{nd}}}
908 $E_{\text{b}}<0$: energetically favorable configuration\\
909 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
911 \begin{minipage}[b]{6cm}
912 {\bf Migration barrier}
915 \item Displace diffusing atom
916 \item Constrain relaxation of (diffusing) atoms
917 \item Record configurational energy
919 \begin{picture}(0,0)(-60,-33)
920 \includegraphics[width=4.5cm]{crt_mod.eps}
932 Si self-interstitial point defects in silicon\\[0.1cm]
936 \begin{tabular}{l c c c c c}
938 $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
940 \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
941 Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
943 \end{tabular}\\[0.4cm]
946 \begin{minipage}{3cm}
948 \underline{Vacancy}\\
949 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
952 \begin{minipage}{3cm}
954 \underline{\hkl<1 1 0> DB}\\
955 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
958 \begin{minipage}{3cm}
960 \underline{\hkl<1 0 0> DB}\\
961 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
964 \begin{minipage}{3cm}
966 \underline{Tetrahedral}\\
967 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
971 \underline{Hexagonal} \hspace{2pt}
972 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
974 \begin{minipage}{2.7cm}
975 $E_{\text{f}}^*=4.48\text{ eV}$\\
976 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
978 \begin{minipage}{0.4cm}
983 \begin{minipage}{2.7cm}
984 $E_{\text{f}}=3.96\text{ eV}$\\
985 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
988 \begin{minipage}{5.5cm}
990 {\tiny nearly T $\rightarrow$ T}\\
992 \includegraphics[width=6.0cm]{nhex_tet.ps}
1003 C interstitial point defects in silicon\\
1006 \begin{tabular}{l c c c c c c r}
1008 $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
1009 {\color{black} \cs{} \& \si}\\
1011 \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1012 Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1014 \end{tabular}\\[0.1cm]
1017 \begin{minipage}{2.8cm}
1018 \underline{Hexagonal} \hspace{2pt}
1019 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1020 $E_{\text{f}}^*=9.05\text{ eV}$\\
1021 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
1023 \begin{minipage}{0.4cm}
1028 \begin{minipage}{2.8cm}
1029 \underline{\hkl<1 0 0>}\\
1030 $E_{\text{f}}=3.88\text{ eV}$\\
1031 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
1034 \begin{minipage}{1.4cm}
1037 \begin{minipage}{3.0cm}
1039 \underline{Tetrahedral}\\
1040 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
1045 \begin{minipage}{2.8cm}
1046 \underline{Bond-centered}\\
1047 $E_{\text{f}}^*=5.59\text{ eV}$\\
1048 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
1050 \begin{minipage}{0.4cm}
1055 \begin{minipage}{2.8cm}
1056 \underline{\hkl<1 1 0> dumbbell}\\
1057 $E_{\text{f}}=5.18\text{ eV}$\\
1058 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
1061 \begin{minipage}{1.4cm}
1064 \begin{minipage}{3.0cm}
1066 \underline{Substitutional}\\
1067 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
1077 C-Si dimer \& bond-centered interstitial configuration
1084 \begin{minipage}[t]{4.1cm}
1085 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
1086 \begin{minipage}{2.0cm}
1088 \underline{Erhart/Albe}
1089 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
1092 \begin{minipage}{2.0cm}
1094 \underline{\textsc{vasp}}
1095 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
1097 \end{minipage}\\[0.2cm]
1098 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
1099 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
1100 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
1101 $\Rightarrow$ $sp^2$ hybridization
1103 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
1104 {\tiny Charge density isosurface}
1107 \begin{minipage}{0.2cm}
1110 \begin{minipage}[t]{8.1cm}
1112 {\bf Bond-centered interstitial}\\[0.1cm]
1113 \begin{minipage}{4.4cm}
1116 \item Linear Si-C-Si bond
1117 \item Si: one C \& 3 Si neighbours
1118 \item Spin polarized calculations
1119 \item No saddle point!\\
1123 \begin{minipage}{2.7cm}
1124 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1126 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
1131 \begin{minipage}[t]{6.5cm}
1132 \begin{minipage}[t]{1.2cm}
1134 {\tiny sp$^3$}\\[0.8cm]
1135 \underline{${\color{black}\uparrow}$}
1136 \underline{${\color{black}\uparrow}$}
1137 \underline{${\color{black}\uparrow}$}
1138 \underline{${\color{red}\uparrow}$}\\
1141 \begin{minipage}[t]{1.4cm}
1143 {\color{red}M}{\color{blue}O}\\[0.8cm]
1144 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1145 $\sigma_{\text{ab}}$\\[0.5cm]
1146 \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1150 \begin{minipage}[t]{1.0cm}
1154 \underline{${\color{white}\uparrow\uparrow}$}
1155 \underline{${\color{white}\uparrow\uparrow}$}\\
1157 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1158 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1162 \begin{minipage}[t]{1.4cm}
1164 {\color{blue}M}{\color{green}O}\\[0.8cm]
1165 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1166 $\sigma_{\text{ab}}$\\[0.5cm]
1167 \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1171 \begin{minipage}[t]{1.2cm}
1174 {\tiny sp$^3$}\\[0.8cm]
1175 \underline{${\color{green}\uparrow}$}
1176 \underline{${\color{black}\uparrow}$}
1177 \underline{${\color{black}\uparrow}$}
1178 \underline{${\color{black}\uparrow}$}\\
1186 \begin{minipage}{3.0cm}
1188 \underline{Charge density}\\
1189 {\color{gray}$\bullet$} Spin up\\
1190 {\color{green}$\bullet$} Spin down\\
1191 {\color{blue}$\bullet$} Resulting spin up\\
1192 {\color{yellow}$\bullet$} Si atoms\\
1193 {\color{red}$\bullet$} C atom
1195 \begin{minipage}{3.6cm}
1196 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
1203 \begin{pspicture}(0,0)(0,0)
1204 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
1213 C interstitial migration --- ab initio
1220 \begin{minipage}{6.8cm}
1221 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
1222 \begin{minipage}{2.0cm}
1223 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1225 \begin{minipage}{0.2cm}
1228 \begin{minipage}{2.0cm}
1229 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
1231 \begin{minipage}{0.2cm}
1234 \begin{minipage}{2.0cm}
1235 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
1236 \end{minipage}\\[0.1cm]
1238 $\Rightarrow$ BC configuration constitutes local minimum\\
1239 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
1241 \begin{minipage}{5.4cm}
1242 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
1243 \end{minipage}\\[0.2cm]
1246 \begin{minipage}{6.8cm}
1247 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
1248 \begin{minipage}{2.0cm}
1249 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1251 \begin{minipage}{0.2cm}
1254 \begin{minipage}{2.0cm}
1255 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
1257 \begin{minipage}{0.2cm}
1260 \begin{minipage}{2.0cm}
1261 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
1262 \end{minipage}\\[0.1cm]
1263 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
1264 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
1265 Note: Change in orientation
1267 \begin{minipage}{5.4cm}
1268 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
1269 \end{minipage}\\[0.1cm]
1272 Reorientation pathway composed of two consecutive processes of the above type
1281 C interstitial migration --- analytical potential
1288 \begin{minipage}[t]{6.0cm}
1289 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
1290 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
1292 \item Lowermost migration barrier
1293 \item $\Delta E \approx \unit[2.2]{eV}$
1294 \item 2.4 times higher than ab initio result
1295 \item Different pathway
1298 \begin{minipage}[t]{0.2cm}
1301 \begin{minipage}[t]{6.0cm}
1302 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
1305 \item Bond-centered configuration unstable\\
1306 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1307 \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
1308 $\rightarrow$ \ci{} \hkl<1 1 0> DB
1311 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
1313 \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
1314 \item 2.4 -- 3.4 times higher than ab initio result
1315 \item After all: Change of the DB orientation
1321 {\color{red}\bf Drastically overestimated diffusion barrier}
1324 \begin{pspicture}(0,0)(0,0)
1325 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
1341 \begin{minipage}{9cm}
1343 Summary of combinations}\\[0.1cm]
1345 \begin{tabular}{l c c c c c c}
1347 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1349 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1350 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1351 \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}\\
1352 \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}\\
1353 \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}\\
1354 \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}\\
1356 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1357 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1364 $E_{\text{b}}$ explainable by stress compensation / increase
1368 \begin{minipage}{3cm}
1369 \includegraphics[width=3.5cm]{comb_pos.eps}
1374 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1375 \begin{minipage}[t]{3.2cm}
1376 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1377 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1379 \begin{minipage}[t]{3.0cm}
1380 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1381 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1383 \begin{minipage}[t]{6.1cm}
1386 \item \ci{} agglomeration energetically favorable
1387 \item Most favorable: C clustering\\
1388 {\color{red}However \ldots}\\
1389 \ldots high migration barrier ($>4\,\text{eV}$)\\
1391 $4\times{\color{cyan}[-2.25]}$ versus
1392 $2\times{\color{orange}[-2.39]}$
1395 {\color{blue}\ci{} agglomeration / no C clustering}
1412 \begin{minipage}{9cm}
1414 Summary of combinations}\\[0.1cm]
1416 \begin{tabular}{l c c c c c c}
1418 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1420 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1421 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1422 \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}\\
1423 \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}\\
1424 \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}\\
1425 \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}\\
1427 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1428 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1435 $E_{\text{b}}$ explainable by stress compensation / increase
1439 \begin{minipage}{3cm}
1440 \includegraphics[width=3.5cm]{comb_pos.eps}
1445 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1446 \begin{minipage}[t]{3.2cm}
1447 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1448 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1450 \begin{minipage}[t]{3.0cm}
1451 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1452 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1454 \begin{minipage}[t]{6.1cm}
1457 \item \ci{} agglomeration energetically favorable
1458 \item Most favorable: C clustering\\
1459 {\color{red}However \ldots}\\
1460 \ldots high migration barrier ($>4\,\text{eV}$)\\
1462 $4\times{\color{cyan}[-2.25]}$ versus
1463 $2\times{\color{orange}[-2.39]}$
1466 {\color{blue}\ci{} agglomeration / no C clustering}
1471 \begin{pspicture}(0,0)(0,0)
1472 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1473 \begin{minipage}{14cm}
1478 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1479 \begin{minipage}{8cm}
1483 Interaction along \hkl[1 1 0]
1484 \includegraphics[width=7cm]{db_along_110_cc.ps}
1496 Defect combinations of C-Si dimers and vacancies
1502 \begin{minipage}[b]{2.6cm}
1504 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1505 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1508 \begin{minipage}[b]{7cm}
1511 \begin{minipage}[b]{2.6cm}
1513 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1514 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1516 \end{minipage}\\[0.2cm]
1518 \begin{minipage}{6.5cm}
1519 \includegraphics[width=6.0cm]{059-539.ps}
1521 \begin{minipage}{5.7cm}
1522 \includegraphics[width=6.0cm]{314-539.ps}
1525 \begin{pspicture}(0,0)(0,0)
1526 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1528 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1529 \begin{minipage}{6.5cm}
1531 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1532 Low migration barrier towards C$_{\text{sub}}$\\
1534 High barrier for reverse process\\[0.3cm]
1536 High probability of stable C$_{\text{sub}}$ configuration
1549 Combinations of substitutional C and Si self-interstitials
1556 \begin{minipage}{6.2cm}
1558 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1560 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1561 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1562 \item Interaction drops quickly to zero\\
1563 $\rightarrow$ low capture radius
1567 \begin{minipage}{0.2cm}
1570 \begin{minipage}{6.0cm}
1572 {\bf Transition from the ground state}
1574 \item Low transition barrier
1575 \item Barrier smaller than \ci{} migration barrier
1576 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1577 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1580 \end{minipage}\\[0.3cm]
1582 \begin{minipage}{6.0cm}
1583 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1585 \begin{minipage}{0.4cm}
1588 \begin{minipage}{6.0cm}
1590 \includegraphics[width=6.0cm]{162-097.ps}
1594 \begin{pspicture}(0,0)(0,0)
1595 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1596 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1597 \begin{minipage}{8cm}
1601 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1602 IBS --- process far from equilibrium\\
1615 Combinations of substitutional C and Si self-interstitials
1622 \begin{minipage}{6.2cm}
1624 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1626 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1627 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1628 \item Interaction drops quickly to zero\\
1629 $\rightarrow$ low capture radius
1633 \begin{minipage}{0.2cm}
1636 \begin{minipage}{6.0cm}
1638 {\bf Transition from the ground state}
1640 \item Low transition barrier
1641 \item Barrier smaller than \ci{} migration barrier
1642 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1643 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1646 \end{minipage}\\[0.3cm]
1648 \begin{minipage}{6.0cm}
1649 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1651 \begin{minipage}{0.4cm}
1654 \begin{minipage}{6.0cm}
1656 \includegraphics[width=6.0cm]{162-097.ps}
1660 \begin{pspicture}(0,0)(0,0)
1661 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1662 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1663 \begin{minipage}{8cm}
1667 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1668 IBS --- process far from equilibrium\\
1676 \begin{pspicture}(0,0)(0,0)
1677 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1678 \begin{minipage}{14cm}
1683 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1684 \begin{minipage}{11cm}
1688 Ab initio MD at \degc{900}\\[0.4cm]
1689 \begin{minipage}{5.4cm}
1691 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1694 \begin{minipage}{5.4cm}
1696 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1698 \end{minipage}\\[0.5cm]
1700 Contribution of entropy to structural formation\\[0.1cm]
1713 Silicon carbide precipitation simulations
1723 \begin{pspicture}(0,0)(12,6.5)
1725 \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1728 \item Create c-Si volume
1729 \item Periodc boundary conditions
1730 \item Set requested $T$ and $p=0\text{ bar}$
1731 \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1734 \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1736 Insertion of C atoms at constant T
1738 \item total simulation volume {\pnode{in1}}
1739 \item volume of minimal SiC precipitate size {\pnode{in2}}
1740 \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1744 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1746 Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1748 \ncline[]{->}{init}{insert}
1749 \ncline[]{->}{insert}{cool}
1750 \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
1751 \rput(7.6,6){\footnotesize $V_1$}
1752 \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
1753 \rput(8.9,4.85){\tiny $V_2$}
1754 \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
1755 \rput(9.25,4.45){\footnotesize $V_3$}
1756 \rput(7.9,3.2){\pnode{ins1}}
1757 \rput(8.92,2.8){\pnode{ins2}}
1758 \rput(10.8,2.4){\pnode{ins3}}
1759 \ncline[]{->}{in1}{ins1}
1760 \ncline[]{->}{in2}{ins2}
1761 \ncline[]{->}{in3}{ins3}
1771 \begin{minipage}{5.7cm}
1773 \item Amount of C atoms: 6000\\
1774 ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
1775 \item Simulation volume: $31^3$ Si unit cells\\
1779 \begin{minipage}{0.3cm}
1783 \begin{minipage}{6.0cm}
1784 Restricted to classical potential caclulations\\
1785 $\rightarrow$ Low C diffusion / overestimated barrier\\
1786 $\rightarrow$ Consider $V_2$ and $V_3$
1788 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
1799 Silicon carbide precipitation simulations at \degc{450} as in IBS
1804 \begin{minipage}{6.3cm}
1805 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1806 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1809 \begin{minipage}{6.1cm}
1811 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1812 \hkl<1 0 0> C-Si dumbbell dominated structure
1814 \item Si-C bumbs around \unit[0.19]{nm}
1815 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1816 concatenated differently oriented \ci{} DBs
1817 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1819 \begin{pspicture}(0,0)(6.0,1.0)
1820 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1821 \begin{minipage}{6cm}
1823 Formation of \ci{} dumbbells\\
1824 C atoms in proper 3C-SiC distance first
1827 \end{pspicture}\\[0.1cm]
1828 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1830 \item High amount of strongly bound C-C bonds
1831 \item Increased defect \& damage density\\
1832 $\rightarrow$ Arrangements hard to categorize and trace
1833 \item Only short range order observable
1835 \begin{pspicture}(0,0)(6.0,0.8)
1836 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1837 \begin{minipage}{6cm}
1839 Amorphous SiC-like phase
1842 \end{pspicture}\\[0.3cm]
1843 \begin{pspicture}(0,0)(6.0,2.0)
1844 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
1845 \begin{minipage}{6cm}
1859 Silicon carbide precipitation simulations at \degc{450} as in IBS
1864 \begin{minipage}{6.3cm}
1865 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1866 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1869 \begin{minipage}{6.1cm}
1871 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1872 \hkl<1 0 0> C-Si dumbbell dominated structure
1874 \item Si-C bumbs around \unit[0.19]{nm}
1875 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1876 concatenated differently oriented \ci{} DBs
1877 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1879 \begin{pspicture}(0,0)(6.0,1.0)
1880 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1881 \begin{minipage}{6cm}
1883 Formation of \ci{} dumbbells\\
1884 C atoms in proper 3C-SiC distance first
1887 \end{pspicture}\\[0.1cm]
1888 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1890 \item High amount of strongly bound C-C bonds
1891 \item Increased defect \& damage density\\
1892 $\rightarrow$ Arrangements hard to categorize and trace
1893 \item Only short range order observable
1895 \begin{pspicture}(0,0)(6.0,0.8)
1896 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1897 \begin{minipage}{6cm}
1899 Amorphous SiC-like phase
1902 \end{pspicture}\\[0.3cm]
1903 \begin{pspicture}(0,0)(6.0,2.0)
1904 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
1905 \begin{minipage}{6cm}
1908 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
1909 \begin{minipage}{0.8cm}
1910 {\bf\boldmath $V_1$:}
1912 \begin{minipage}{5.1cm}
1913 Formation of \ci{} indeed occurs\\
1914 Agllomeration not observed
1915 \end{minipage}\\[0.3cm]
1916 \begin{minipage}{0.8cm}
1917 {\bf\boldmath $V_{2,3}$:}
1919 \begin{minipage}{5.1cm}
1920 Amorphous SiC-like structure\\
1921 (not expected at \degc{450})\\[0.05cm]
1922 No rearrangement/transition into 3C-SiC
1923 \end{minipage}\\[0.1cm]
1935 Limitations of MD and short range potentials
1942 {\bf Time scale problem of MD}\\[0.2cm]
1943 Precise integration \& thermodynamic sampling\\
1944 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
1945 $\omega$: vibrational mode\\
1946 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
1947 Several local minima separated by large energy barriers\\
1948 $\Rightarrow$ Transition event corresponds to a multiple
1949 of vibrational periods\\
1950 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
1951 infrequent transition events\\[0.2cm]
1952 {\color{blue}Accelerated methods:}
1953 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1957 {\bf Limitations related to the short range potential}\\[0.2cm]
1958 Cut-off function limits interaction to next neighbours\\
1959 $\Rightarrow$ Overestimated unphysical high forces of next neighbours
1964 {\bf Approach to the (twofold) problem}\\[0.2cm]
1965 Increased temperature simulations without TAD corrections\\
1966 Accelerated methods or higher time scales exclusively not sufficient!
1968 \begin{pspicture}(0,0)(0,0)
1969 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
1970 \begin{minipage}{7.5cm}
1973 Potential enhanced slow phase space propagation
1976 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1977 \begin{minipage}{2.7cm}
1981 thermodynamic sampling
1984 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
1985 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
1986 \begin{minipage}{3.6cm}
1989 \underline{IBS}\\[0.1cm]
1990 3C-SiC also observed for higher T\\[0.1cm]
1991 Higher T inside sample\\[0.1cm]
1992 Structural evolution vs.\\
1993 equilibrium properties
1996 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
2005 Increased temperature simulations --- $V_1$
2010 \begin{minipage}{6.2cm}
2011 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2014 \begin{minipage}{6.2cm}
2015 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2018 \begin{minipage}{6.2cm}
2019 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2022 \begin{minipage}{6.3cm}
2024 \underline{Si-C bonds:}
2026 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2027 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2029 \underline{Si-Si bonds:}
2030 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2031 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2032 \underline{C-C bonds:}
2034 \item C-C next neighbour pairs reduced (mandatory)
2035 \item Peak at 0.3 nm slightly shifted
2037 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2038 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2040 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2042 \item Range [|-$\downarrow$]:
2043 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2044 with nearby Si$_{\text{I}}$}
2055 Increased temperature simulations --- $V_1$
2060 \begin{minipage}{6.2cm}
2061 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2064 \begin{minipage}{6.2cm}
2065 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2068 \begin{minipage}{6.2cm}
2069 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2072 \begin{minipage}{6.3cm}
2074 \underline{Si-C bonds:}
2076 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2077 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2079 \underline{Si-Si bonds:}
2080 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2081 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2082 \underline{C-C bonds:}
2084 \item C-C next neighbour pairs reduced (mandatory)
2085 \item Peak at 0.3 nm slightly shifted
2087 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2088 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2090 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2092 \item Range [|-$\downarrow$]:
2093 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2094 with nearby Si$_{\text{I}}$}
2100 \begin{pspicture}(0,0)(0,0)
2101 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
2102 \begin{minipage}{14cm}
2107 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
2108 \begin{minipage}{9cm}
2112 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
2113 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
2116 \item Stretched coherent SiC structures\\
2117 $\Rightarrow$ Precipitation process involves {\color{blue}\cs}
2120 \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
2121 \item Building block for surrounding Si host \& further SiC
2122 \item Strain compensation \ldots\\
2123 \ldots Si/SiC interface\\
2124 \ldots within stretched coherent SiC structure
2126 \item Explains annealing behavior of high/low T C implantations
2128 \item Low T: highly mobile {\color{red}\ci}
2129 \item High T: stable configurations of {\color{blue}\cs}
2134 \psframebox[linecolor=blue,linewidth=0.05cm]{
2135 \begin{minipage}{7cm}
2137 Precipitation mechanism involving \cs\\
2138 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2148 % skip high c conc results
2154 Increased temperature simulations at high C concentration
2159 \begin{minipage}{6.0cm}
2160 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2162 \begin{minipage}{6.0cm}
2163 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2171 \begin{minipage}[t]{6.0cm}
2172 0.186 nm: Si-C pairs $\uparrow$\\
2173 (as expected in 3C-SiC)\\[0.2cm]
2174 0.282 nm: Si-C-C\\[0.2cm]
2175 $\approx$0.35 nm: C-Si-Si
2178 \begin{minipage}{0.2cm}
2182 \begin{minipage}[t]{6.0cm}
2183 0.15 nm: C-C pairs $\uparrow$\\
2184 (as expected in graphite/diamond)\\[0.2cm]
2185 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2186 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2191 \item Decreasing cut-off artifact
2192 \item {\color{red}Amorphous} SiC-like phase remains
2193 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2194 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2203 High C \& small $V$ \& short $t$
2206 Slow restructuring due to strong C-C bonds
2209 High C \& low T implants
2227 Summary / Conclusions
2233 \begin{minipage}{12.3cm}
2238 \item Point defects excellently / fairly well described
2240 \item C$_{\text{sub}}$ drastically underestimated by EA
2241 \item EA predicts correct ground state:
2242 C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2243 \item Identified migration path explaining
2244 diffusion and reorientation experiments by DFT
2245 \item EA fails to describe \ci{} migration:
2246 Wrong path \& overestimated barrier
2248 \item Combinations of defects
2250 \item Agglomeration of point defects energetically favorable
2251 by compensation of stress
2252 \item Formation of C-C unlikely
2253 \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2254 \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2255 Low barrier (\unit[0.77]{eV}) \& low capture radius
2262 \begin{minipage}[t]{12.3cm}
2263 \underline{Pecipitation simulations}
2265 \item High C concentration $\rightarrow$ amorphous SiC like phase
2266 \item Problem of potential enhanced slow phase space propagation
2267 \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2268 \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2269 \item High T necessary to simulate IBS conditions (far from equilibrium)
2270 \item Precipitation by successive agglomeration of \cs (epitaxy)
2271 \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2272 (stretched SiC, interface)
2279 \framebox{Precipitation by successive agglomeration of \cs{}}
2297 \underline{Augsburg}
2299 \item Prof. B. Stritzker (accomodation at EP \RM{4})
2300 \item Ralf Utermann (EDV)
2303 \underline{Berlin/Brandenburg}
2305 \item PD Volker Eyert (Ref)
2308 \underline{Helsinki}
2310 \item Prof. K. Nordlund (MD)
2315 \item Bayerische Forschungsstiftung (financial support)
2318 \underline{Paderborn}
2320 \item Prof. J. Lindner (SiC)
2321 \item Prof. G. Schmidt (DFT + financial support)
2322 \item Dr. E. Rauls (DFT + SiC)
2327 \bf Thank you for your attention!