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32 \graphicspath{{../img/}}
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42 \usepackage{semlayer} % Seminar overlays
43 \usepackage{slidesec} % Seminar sections and list of slides
45 \input{seminar.bug} % Official bugs corrections
46 \input{seminar.bg2} % Unofficial bugs corrections
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71 % specify width and height
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101 \begin{pspicture}(0,0)(0,0)
102 \rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=hb,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{
103 \begin{minipage}{14cm}
112 \newcommand{\si}{Si$_{\text{i}}${}}
113 \newcommand{\ci}{C$_{\text{i}}${}}
114 \newcommand{\cs}{C$_{\text{sub}}${}}
115 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
116 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
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118 \newcommand{\perc}[1]{\unit[#1]{\%}{}}
120 % no vertical centering
132 A B C D E F G H G F E D C B A
150 Atomistic simulation study on silicon carbide\\[0.2cm]
151 precipitation in silicon\\
158 \textsc{Frank Zirkelbach}
162 Defense of doctor's thesis
171 % no vertical centering
174 % skip for preparation
179 % motivation / properties / applications of silicon carbide
187 \begin{pspicture}(0,0)(13.5,5)
189 \psframe*[linecolor=hb](-0.2,0)(12.9,5)
191 \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.2,1)(6.5,1)(6.5,3)(5.2,3)
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194 \rput[lt](0,4.6){\color{gray}PROPERTIES}
196 \rput[lt](0.3,4){wide band gap}
197 \rput[lt](0.3,3.5){high electric breakdown field}
198 \rput[lt](0.3,3){good electron mobility}
199 \rput[lt](0.3,2.5){high electron saturation drift velocity}
200 \rput[lt](0.3,2){high thermal conductivity}
202 \rput[lt](0.3,1.5){hard and mechanically stable}
203 \rput[lt](0.3,1){chemically inert}
205 \rput[lt](0.3,0.5){radiation hardness}
207 \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
209 \rput[rt](12.5,3.85){high-temperature, high power}
210 \rput[rt](12.5,3.5){and high-frequency}
211 \rput[rt](12.5,3.15){electronic and optoelectronic devices}
213 \rput[rt](12.5,2.35){material suitable for extreme conditions}
214 \rput[rt](12.5,2){microelectromechanical systems}
215 \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
217 \rput[rt](12.5,0.85){first wall reactor material, detectors}
218 \rput[rt](12.5,0.5){and electronic devices for space}
222 \begin{picture}(0,0)(5,-162)
223 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
225 \begin{picture}(0,0)(-120,-162)
226 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
228 \begin{picture}(0,0)(-270,-162)
229 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
232 \begin{picture}(0,0)(10,65)
233 \includegraphics[height=2.8cm]{sic_switch.eps}
235 %\begin{picture}(0,0)(-243,65)
236 \begin{picture}(0,0)(-110,65)
237 \includegraphics[height=2.8cm]{ise_99.eps}
239 %\begin{picture}(0,0)(-135,65)
240 \begin{picture}(0,0)(-100,65)
241 \includegraphics[height=1.2cm]{infineon_schottky.eps}
243 \begin{picture}(0,0)(-233,65)
244 \includegraphics[height=2.8cm]{solar_car.eps}
255 IBS of epitaxial single crystalline 3C-SiC
264 \item \underline{Implantation step 1}\\[0.1cm]
265 Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
266 $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
267 {\color{blue}precipitates}
268 \item \underline{Implantation step 2}\\[0.1cm]
269 Low remaining amount of dose | \unit[180]{keV} | \degc{250}\\
271 Destruction/Amorphization of precipitates at layer interface
272 \item \underline{Annealing}\\[0.1cm]
273 \unit[10]{h} at \degc{1250}\\
274 $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
278 \begin{minipage}{6.9cm}
279 \includegraphics[width=7cm]{ibs_3c-sic.eps}\\[-0.4cm]
282 XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
286 \begin{minipage}{5cm}
288 \begin{pspicture}(0,0)(0,0)
290 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
291 \begin{minipage}{3.3cm}
294 3C-SiC precipitation\\
295 not yet fully understood
299 % \renewcommand\labelitemi{$\Rightarrow$}
300 % Details of the SiC precipitation
302 % \item significant technological progress\\
303 % in SiC thin film formation
304 % \item perspectives for processes relying\\
305 % upon prevention of SiC precipitation
309 \rput(-5.3,5.5){\pnode{h0}}
310 \rput(-1.95,5.5){\pnode{h1}}
311 \ncline[linecolor=blue]{-}{h0}{h1}
312 \ncline[linecolor=blue]{->}{h1}{box}
323 Supposed precipitation mechanism of SiC in Si
331 \begin{minipage}{3.6cm}
333 Si \& SiC lattice structure\\[0.1cm]
334 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
337 \begin{minipage}{1.7cm}
338 \underline{Silicon}\\
339 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
340 $a=\unit[5.429]{\\A}$\\
341 $\rho^*_{\text{Si}}=\unit[100]{\%}$
343 \begin{minipage}{1.7cm}
344 \underline{Silicon carbide}\\
345 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
346 $a=\unit[4.359]{\\A}$\\
347 $\rho^*_{\text{Si}}=\unit[97]{\%}$
353 \begin{minipage}{4.1cm}
355 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
359 \begin{minipage}{4.0cm}
361 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
367 \begin{minipage}{4.0cm}
369 C-Si dimers (dumbbells)\\[-0.1cm]
374 \begin{minipage}{4.1cm}
376 Agglomeration of C-Si dumbbells\\[-0.1cm]
377 $\Rightarrow$ dark contrasts
381 \begin{minipage}{4.0cm}
383 Precipitation of 3C-SiC in Si\\[-0.1cm]
384 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
385 \& release of Si self-interstitials
391 \begin{minipage}{4.0cm}
393 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
397 \begin{minipage}{4.1cm}
399 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
403 \begin{minipage}{4.0cm}
405 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
409 \begin{pspicture}(0,0)(0,0)
410 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
411 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
412 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
413 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
414 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
415 $4a_{\text{Si}}=5a_{\text{SiC}}$
417 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
418 \hkl(h k l) planes match
420 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
431 Supposed precipitation mechanism of SiC in Si
439 \begin{minipage}{3.6cm}
441 Si \& SiC lattice structure\\[0.1cm]
442 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
445 \begin{minipage}{1.7cm}
446 \underline{Silicon}\\
447 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
448 $a=\unit[5.429]{\\A}$\\
449 $\rho^*_{\text{Si}}=\unit[100]{\%}$
451 \begin{minipage}{1.7cm}
452 \underline{Silicon carbide}\\
453 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
454 $a=\unit[4.359]{\\A}$\\
455 $\rho^*_{\text{Si}}=\unit[97]{\%}$
461 \begin{minipage}{4.1cm}
463 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
467 \begin{minipage}{4.0cm}
469 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
475 \begin{minipage}{4.0cm}
477 C-Si dimers (dumbbells)\\[-0.1cm]
478 on Si interstitial sites
482 \begin{minipage}{4.1cm}
484 Agglomeration of C-Si dumbbells\\[-0.1cm]
485 $\Rightarrow$ dark contrasts
489 \begin{minipage}{4.0cm}
491 Precipitation of 3C-SiC in Si\\[-0.1cm]
492 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
493 \& release of Si self-interstitials
499 \begin{minipage}{4.0cm}
501 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
505 \begin{minipage}{4.1cm}
507 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
511 \begin{minipage}{4.0cm}
513 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
517 \begin{pspicture}(0,0)(0,0)
518 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
519 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
520 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
521 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
522 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
523 $4a_{\text{Si}}=5a_{\text{SiC}}$
525 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
526 \hkl(h k l) planes match
528 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
531 % controversial view!
532 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
533 \begin{minipage}{14cm}
538 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
539 \begin{minipage}{10cm}
543 {\color{gray}\bf Controversial findings}
546 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
548 \item {\color{blue}Substitutionally} incorporated C on regular Si lattice sites
549 \item \si{} reacting with further C in cleared volume
551 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
553 \item Room temperature implantation $\rightarrow$ high C diffusion
554 \item Elevated temperature implantation $\rightarrow$ no C redistribution
556 $\Rightarrow$ mobile {\color{red}\ci} opposed to
557 stable {\color{blue}\cs{}} configurations
558 \item Strained Si$_{1-y}$C$_y$/Si heterostructures
559 {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
561 \item Initial {\color{blue}coherent} SiC structures (tensile strain)
562 \item Incoherent SiC nanocrystals (strain relaxation)
567 {\Huge${\lightning}$} \hspace{0.3cm}
568 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
569 {\Huge${\lightning}$}
589 \item Introduction / Motivation
590 \item Assumed SiC precipitation mechanisms / Controversy
592 \item Utilized simulation techniques
594 \item Molecular dynamics (MD) simulations
595 \item Density functional theory (DFT) calculations
597 \item Simulation results
599 \item C and Si self-interstitial point defects in silicon
600 \item Silicon carbide precipitation simulations
602 \item Summary / Conclusion
611 Utilized computational methods
618 {\bf Molecular dynamics (MD)}\\[0.1cm]
620 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
622 System of $N$ particles &
623 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
624 Phase space propagation &
625 Velocity Verlet | timestep: \unit[1]{fs} \\
626 Analytical interaction potential &
627 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
630 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
631 \pot_{ij} = {\color{red}f_C(r_{ij})}
632 \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
634 Observables: time/ensemble averages &
635 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
643 {\bf Density functional theory (DFT)}
647 \begin{minipage}[t]{6cm}
649 \item Hohenberg-Kohn theorem:\\
650 $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
651 \item Kohn-Sham approach:\\
652 Single-particle effective theory
656 \item Code: \textsc{vasp}
657 \item Plane wave basis set | $E_{\text{cut}}=\unit[300]{eV}$
659 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
662 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
664 \item Ultrasoft pseudopotential
665 \item Exchange \& correlation: GGA
666 \item Brillouin zone sampling: $\Gamma$-point
667 \item Supercell: $N=216\pm2$
670 \begin{minipage}{6cm}
671 \begin{pspicture}(0,0)(0,0)
672 \pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
673 \rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
675 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
678 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
680 n(r)=\sum_i^N|\Phi_i(r)|^2
683 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
685 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
689 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
690 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
691 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
702 Point defects \& defect migration
709 \begin{minipage}[b]{7.5cm}
710 {\bf Defect structure}\\
711 \begin{pspicture}(0,0)(7,4.4)
712 \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
715 \item Creation of c-Si simulation volume
716 \item Periodic boundary conditions
717 \item $T=0\text{ K}$, $p=0\text{ bar}$
720 \rput(3.5,1.3){\rnode{insert}{\psframebox{
723 Insertion of interstitial C/Si atoms
726 \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
729 Relaxation / structural energy minimization
732 \ncline[]{->}{init}{insert}
733 \ncline[]{->}{insert}{cool}
736 \begin{minipage}[b]{4.5cm}
738 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
740 \begin{minipage}{2.21cm}
742 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
743 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
744 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
747 \begin{minipage}{2.21cm}
749 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
750 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
751 {\color{black}$\bullet$} Vac. / Sub.
758 \begin{minipage}[t]{6cm}
759 {\bf Defect formation energy}\\
761 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.5cm]
762 %Particle reservoir: Si \& SiC\\[0.2cm]
763 {\bf Binding energy}\\
767 E_{\text{f}}^{\text{comb}}-
768 E_{\text{f}}^{1^{\text{st}}}-
769 E_{\text{f}}^{2^{\text{nd}}}
773 $E_{\text{b}}<0$: energetically favorable configuration\\
774 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
776 \begin{minipage}[t]{6cm}
778 {\bf Migration barrier}
781 \item Displace diffusing atom
782 \item Constrain relaxation of (diffusing) atoms
783 \item Record configurational energy
785 \begin{picture}(0,0)(-60,-33)
786 \includegraphics[width=4.5cm]{crt_mod.eps}
798 C interstitial point defects in silicon\\
801 \begin{tabular}{l c c c c c c r}
803 $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
804 {\color{black} \cs{} \& \si}\\
806 \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
807 Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
809 \end{tabular}\\[0.1cm]
812 \begin{minipage}{2.8cm}
813 \underline{Hexagonal} \hspace{2pt}
814 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
815 $E_{\text{f}}^*=9.05\text{ eV}$\\
816 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
818 \begin{minipage}{0.4cm}
823 \begin{minipage}{2.8cm}
824 \underline{\hkl<1 0 0>}\\
825 $E_{\text{f}}=3.88\text{ eV}$\\
826 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
829 \begin{minipage}{1.4cm}
832 \begin{minipage}{3.0cm}
834 \underline{Tetrahedral}\\
835 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
840 \begin{minipage}{2.8cm}
841 \underline{Bond-centered}\\
842 $E_{\text{f}}^*=5.59\text{ eV}$\\
843 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
845 \begin{minipage}{0.4cm}
850 \begin{minipage}{2.8cm}
851 \underline{\hkl<1 1 0> dumbbell}\\
852 $E_{\text{f}}=5.18\text{ eV}$\\
853 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
856 \begin{minipage}{1.4cm}
859 \begin{minipage}{3.0cm}
861 \underline{Substitutional}\\
862 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
872 C interstitial migration --- ab initio
879 \begin{minipage}{6.8cm}
880 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
881 \begin{minipage}{2.0cm}
882 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
884 \begin{minipage}{0.2cm}
887 \begin{minipage}{2.0cm}
888 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
890 \begin{minipage}{0.2cm}
893 \begin{minipage}{2.0cm}
894 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
895 \end{minipage}\\[0.1cm]
897 $\Rightarrow$ Sufficient to consider \hkl[00-1] to BC transition\\
898 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
900 \begin{minipage}{5.4cm}
901 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
902 %\end{minipage}\\[0.2cm]
903 \end{minipage}\\[0.4cm]
906 \begin{minipage}{6.8cm}
907 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
908 \begin{minipage}{2.0cm}
909 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
911 \begin{minipage}{0.2cm}
914 \begin{minipage}{2.0cm}
915 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
917 \begin{minipage}{0.2cm}
920 \begin{minipage}{2.0cm}
921 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
922 \end{minipage}\\[0.1cm]
923 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
924 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
925 Note: Change in orientation
927 \begin{minipage}{5.4cm}
928 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
929 \end{minipage}\\[0.1cm]
932 %Reorientation pathway composed of two consecutive processes of the above type
941 C interstitial migration --- analytical potential
948 \begin{minipage}[t]{6.0cm}
949 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
950 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
952 \item Lowermost migration barrier
953 \item $\Delta E \approx \unit[2.2]{eV}$
954 \item 2.4 times higher than ab initio result
955 \item Different pathway
958 \begin{minipage}[t]{0.2cm}
961 \begin{minipage}[t]{6.0cm}
962 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
965 \item Bond-centered configuration unstable\\
966 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
967 \item Minimum of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
968 $\rightarrow$ \ci{} \hkl<1 1 0> DB
971 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
973 \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
974 \item 2.4 -- 3.4 times higher than ab initio result
975 \item After all: Change of the DB orientation
981 {\color{red}\bf Drastically overestimated diffusion barrier}
984 \begin{pspicture}(0,0)(0,0)
985 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
994 Defect combinations --- ab inito
1001 \begin{minipage}{9cm}
1003 Summary of combinations}\\[0.1cm]
1005 \begin{tabular}{l c c c c c c}
1007 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1009 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1010 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1011 \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}\\
1012 \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}\\
1013 \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}\\
1014 \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}\\
1016 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1017 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1024 $E_{\text{b}}$ explainable by stress compensation / increase
1028 \begin{minipage}{3cm}
1029 \includegraphics[width=3.5cm]{comb_pos.eps}
1034 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1035 \begin{minipage}[t]{3.2cm}
1036 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1037 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1039 \begin{minipage}[t]{3.0cm}
1040 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1041 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1043 \begin{minipage}[t]{6.1cm}
1046 \item \ci{} agglomeration energetically favorable
1047 \item Most favorable: C clustering\\
1048 {\color{red}However \ldots}\\
1049 \ldots high migration barrier ($>4\,\text{eV}$)\\
1051 $4\times{\color{cyan}[-2.25]}$ versus
1052 $2\times{\color{orange}[-2.39]}$
1055 {\color{blue}\ci{} agglomeration / no C clustering}
1065 Defect combinations --- ab inito
1072 \begin{minipage}{9cm}
1074 Summary of combinations}\\[0.1cm]
1076 \begin{tabular}{l c c c c c c}
1078 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1080 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1081 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1082 \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}\\
1083 \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}\\
1084 \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}\\
1085 \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}\\
1087 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1088 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1095 $E_{\text{b}}$ explainable by stress compensation / increase
1099 \begin{minipage}{3cm}
1100 \includegraphics[width=3.5cm]{comb_pos.eps}
1105 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1106 \begin{minipage}[t]{3.2cm}
1107 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1108 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1110 \begin{minipage}[t]{3.0cm}
1111 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1112 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1114 \begin{minipage}[t]{6.1cm}
1117 \item \ci{} agglomeration energetically favorable
1118 \item Most favorable: C clustering\\
1119 {\color{red}However \ldots}\\
1120 \ldots high migration barrier ($>4\,\text{eV}$)\\
1122 $4\times{\color{cyan}[-2.25]}$ versus
1123 $2\times{\color{orange}[-2.39]}$
1126 {\color{blue}\ci{} agglomeration / no C clustering}
1131 \begin{pspicture}(0,0)(0,0)
1132 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1133 \begin{minipage}{14cm}
1138 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1139 \begin{minipage}{8cm}
1143 Interaction along \hkl[1 1 0]
1144 \includegraphics[width=7cm]{db_along_110_cc.ps}
1156 Defect combinations of C-Si dimers and vacancies
1162 \begin{minipage}[b]{2.6cm}
1164 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1165 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1168 \begin{minipage}[b]{7cm}
1171 \begin{minipage}[b]{2.6cm}
1173 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1174 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1176 \end{minipage}\\[0.2cm]
1178 \begin{minipage}{6.5cm}
1179 \includegraphics[width=6.0cm]{059-539.ps}
1181 \begin{minipage}{5.7cm}
1182 \includegraphics[width=6.0cm]{314-539.ps}
1185 \begin{pspicture}(0,0)(0,0)
1186 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1188 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1189 \begin{minipage}{6.5cm}
1191 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1192 Low migration barrier towards C$_{\text{sub}}$\\
1194 High barrier for reverse process\\[0.3cm]
1196 High probability of stable C$_{\text{sub}}$ configuration
1209 Combinations of substitutional C and Si self-interstitials
1216 \begin{minipage}{6.2cm}
1218 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1220 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1221 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1222 \item Interaction drops quickly to zero\\
1223 $\rightarrow$ low capture radius
1227 \begin{minipage}{0.2cm}
1230 \begin{minipage}{6.0cm}
1232 {\bf Transition from the ground state}
1234 \item Low transition barrier
1235 \item Barrier smaller than \ci{} migration barrier
1236 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1237 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1240 \end{minipage}\\[0.3cm]
1242 \begin{minipage}{6.0cm}
1243 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1245 \begin{minipage}{0.4cm}
1248 \begin{minipage}{6.0cm}
1250 \includegraphics[width=6.0cm]{162-097.ps}
1254 \begin{pspicture}(0,0)(0,0)
1255 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1256 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1257 \begin{minipage}{8cm}
1261 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1262 IBS --- process far from equilibrium\\
1275 Combinations of substitutional C and Si self-interstitials
1282 \begin{minipage}{6.2cm}
1284 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1286 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1287 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1288 \item Interaction drops quickly to zero\\
1289 $\rightarrow$ low capture radius
1293 \begin{minipage}{0.2cm}
1296 \begin{minipage}{6.0cm}
1298 {\bf Transition from the ground state}
1300 \item Low transition barrier
1301 \item Barrier smaller than \ci{} migration barrier
1302 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1303 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1306 \end{minipage}\\[0.3cm]
1308 \begin{minipage}{6.0cm}
1309 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1311 \begin{minipage}{0.4cm}
1314 \begin{minipage}{6.0cm}
1316 \includegraphics[width=6.0cm]{162-097.ps}
1320 \begin{pspicture}(0,0)(0,0)
1321 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1322 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1323 \begin{minipage}{8cm}
1327 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1328 IBS --- process far from equilibrium\\
1336 \begin{pspicture}(0,0)(0,0)
1337 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1338 \begin{minipage}{14cm}
1343 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1344 \begin{minipage}{11cm}
1348 Ab initio MD at \degc{900}\\[0.4cm]
1349 \begin{minipage}{5.4cm}
1351 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1354 \begin{minipage}{5.4cm}
1356 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1358 \end{minipage}\\[0.5cm]
1360 Contribution of entropy to structural formation\\[0.1cm]
1373 Silicon carbide precipitation simulations
1383 \begin{pspicture}(0,0)(12,6.5)
1385 \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1388 \item Create c-Si volume
1389 \item Periodc boundary conditions
1390 \item Set requested $T$ and $p=0\text{ bar}$
1391 \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1394 \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1396 Insertion of C atoms at constant T
1398 \item total simulation volume {\pnode{in1}}
1399 \item volume of minimal SiC precipitate size {\pnode{in2}}
1400 \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1404 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1406 Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1408 \ncline[]{->}{init}{insert}
1409 \ncline[]{->}{insert}{cool}
1410 \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
1411 \rput(7.6,6){\footnotesize $V_1$}
1412 \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
1413 \rput(8.9,4.85){\tiny $V_2$}
1414 \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
1415 \rput(9.25,4.45){\footnotesize $V_3$}
1416 \rput(7.9,3.2){\pnode{ins1}}
1417 \rput(8.92,2.8){\pnode{ins2}}
1418 \rput(10.8,2.4){\pnode{ins3}}
1419 \ncline[]{->}{in1}{ins1}
1420 \ncline[]{->}{in2}{ins2}
1421 \ncline[]{->}{in3}{ins3}
1431 \begin{minipage}{5.7cm}
1433 \item Amount of C atoms: 6000\\
1434 ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
1435 \item Simulation volume: $31^3$ Si unit cells\\
1439 \begin{minipage}{0.3cm}
1443 \begin{minipage}{6.0cm}
1444 Restricted to classical potential caclulations\\
1445 $\rightarrow$ Low C diffusion / overestimated barrier\\
1446 $\rightarrow$ Consider $V_2$ and $V_3$
1448 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
1459 Silicon carbide precipitation simulations at \degc{450} as in IBS
1464 \begin{minipage}{6.3cm}
1465 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1466 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1469 \begin{minipage}{6.1cm}
1471 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1472 \ci{} \hkl<1 0 0> dumbbell dominated structure
1474 \item Si-C bumbs around \unit[0.19]{nm}
1475 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1476 concatenated differently oriented \ci{} DBs
1477 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1479 \begin{pspicture}(0,0)(6.0,1.0)
1480 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1481 \begin{minipage}{6cm}
1483 Formation of \ci{} dumbbells\\
1484 C atoms separated as expected in 3C-SiC
1487 \end{pspicture}\\[0.1cm]
1488 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1490 \item High amount of strongly bound C-C bonds
1491 \item Increased defect \& damage density\\
1492 $\rightarrow$ Arrangements hard to categorize and trace
1493 \item Only short range order observable
1495 \begin{pspicture}(0,0)(6.0,0.8)
1496 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1497 \begin{minipage}{6cm}
1499 Amorphous SiC-like phase
1502 \end{pspicture}\\[0.3cm]
1503 \begin{pspicture}(0,0)(6.0,2.0)
1504 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
1505 \begin{minipage}{6cm}
1519 Silicon carbide precipitation simulations at \degc{450} as in IBS
1524 \begin{minipage}{6.3cm}
1525 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1526 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1529 \begin{minipage}{6.1cm}
1531 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1532 \ci{} \hkl<1 0 0> dumbbell dominated structure
1534 \item Si-C bumbs around \unit[0.19]{nm}
1535 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1536 concatenated differently oriented \ci{} DBs
1537 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1539 \begin{pspicture}(0,0)(6.0,1.0)
1540 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1541 \begin{minipage}{6cm}
1543 Formation of \ci{} dumbbells\\
1544 C atoms separated as expected in 3C-SiC
1547 \end{pspicture}\\[0.1cm]
1548 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1550 \item High amount of strongly bound C-C bonds
1551 \item Increased defect \& damage density\\
1552 $\rightarrow$ Arrangements hard to categorize and trace
1553 \item Only short range order observable
1555 \begin{pspicture}(0,0)(6.0,0.8)
1556 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1557 \begin{minipage}{6cm}
1559 Amorphous SiC-like phase
1562 \end{pspicture}\\[0.3cm]
1563 \begin{pspicture}(0,0)(6.0,2.0)
1564 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
1565 \begin{minipage}{6cm}
1568 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
1569 \begin{minipage}{0.8cm}
1570 {\bf\boldmath $V_1$:}
1572 \begin{minipage}{5.1cm}
1573 Formation of \ci{} indeed occurs\\
1574 Agllomeration not observed
1575 \end{minipage}\\[0.3cm]
1576 \begin{minipage}{0.8cm}
1577 {\bf\boldmath $V_{2,3}$:}
1579 \begin{minipage}{5.1cm}
1580 Amorphous SiC-like structure\\
1581 (not expected at \degc{450})\\[0.05cm]
1582 No rearrangement/transition into 3C-SiC
1583 \end{minipage}\\[0.1cm]
1595 Limitations of MD and short range potentials
1602 {\bf Time scale problem of MD}\\[0.2cm]
1603 Minimize integration error \& precise thermodynamic sampling\\
1604 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
1605 $\omega$: vibrational mode\\
1606 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
1607 Several local minima separated by large energy barriers\\
1608 $\Rightarrow$ Transition event corresponds to a multiple
1609 of vibrational periods\\
1610 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
1611 infrequent transition events\\[0.2cm]
1612 {\color{blue}Accelerated methods:}
1613 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1617 {\bf Limitations related to the short range potential}\\[0.2cm]
1618 Cut-off function limits interaction to next neighbours\\
1619 $\Rightarrow$ Overestimated diffusion barrier (factor: 2.4--3.4)
1623 {\bf Approach to the (twofold) problem}\\[0.2cm]
1624 Increased temperature simulations without TAD corrections\\
1625 Accelerated methods or higher time scales exclusively not sufficient!
1627 \begin{pspicture}(0,0)(0,0)
1628 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
1629 \begin{minipage}{7.5cm}
1632 Potential enhanced slow phase space propagation
1635 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1636 \begin{minipage}{2.7cm}
1640 thermodynamic sampling
1643 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
1644 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
1645 \begin{minipage}{3.6cm}
1648 \underline{IBS}\\[0.1cm]
1649 3C-SiC also observed for higher T\\[0.1cm]
1650 Higher T inside sample\\[0.1cm]
1651 Structural evolution vs.\\
1652 equilibrium properties
1655 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
1664 Increased temperature simulations --- $V_1$
1669 \begin{minipage}{6.2cm}
1670 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1673 \begin{minipage}{6.2cm}
1674 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
1677 \begin{minipage}{6.2cm}
1678 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
1681 \begin{minipage}{6.3cm}
1683 \underline{Si-C bonds:}
1685 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1686 \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$
1689 \underline{Si-Si bonds:}
1690 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1691 ($\rightarrow$ 0.325 nm)\\[0.1cm]
1692 \underline{C-C bonds:}
1694 \item C-C next neighbour pairs reduced (mandatory)
1695 \item Peak at 0.3 nm slightly shifted\\[0.05cm]
1696 $\searrow$ \ci{} combinations (dashed arrows)\\
1697 $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
1698 $\nearrow$ \ci{} pure \cs{} combinations ($\downarrow$)\\[0.05cm]
1699 Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
1709 Increased temperature simulations --- $V_1$
1714 \begin{minipage}{6.2cm}
1715 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1718 \begin{minipage}{6.2cm}
1719 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
1722 \begin{minipage}{6.2cm}
1723 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
1726 \begin{minipage}{6.3cm}
1728 \underline{Si-C bonds:}
1730 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1731 \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$
1734 \underline{Si-Si bonds:}
1735 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1736 ($\rightarrow$ 0.325 nm)\\[0.1cm]
1737 \underline{C-C bonds:}
1739 \item C-C next neighbour pairs reduced (mandatory)
1740 \item Peak at 0.3 nm slightly shifted\\[0.05cm]
1741 $\searrow$ \ci{} combinations (dashed arrows)\\
1742 $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
1743 $\nearrow$ \ci{} pure \cs{} combinations ($\downarrow$)\\[0.05cm]
1744 Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
1749 \begin{pspicture}(0,0)(0,0)
1750 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1751 \begin{minipage}{14cm}
1756 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1757 \begin{minipage}{9cm}
1761 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
1762 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
1765 \item Stretched coherent SiC structures directly observed\\
1766 \psframebox[linecolor=blue,linewidth=0.05cm]{
1767 \begin{minipage}{7cm}
1769 \cs{} involved in the precipitation mechanism\\
1772 \item Emission of \si{} serves several needs:
1774 \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
1775 \item Building block for surrounding Si host \& further SiC
1776 \item Strain compensation \ldots\\
1777 \ldots Si/SiC interface\\
1778 \ldots within stretched coherent SiC structure
1780 \item Explains annealing behavior of high/low T C implantations
1782 \item Low T: highly mobile {\color{red}\ci}
1783 \item High T: stable configurations of {\color{blue}\cs}
1785 \psframebox[linecolor=blue,linewidth=0.05cm]{
1786 \begin{minipage}{7cm}
1788 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
1799 % skip high c conc results
1805 Increased temperature simulations at high C concentration
1810 \begin{minipage}{6.0cm}
1811 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
1813 \begin{minipage}{6.0cm}
1814 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
1822 \begin{minipage}[t]{6.0cm}
1823 0.186 nm: Si-C pairs $\uparrow$\\
1824 (as expected in 3C-SiC)\\[0.2cm]
1825 0.282 nm: Si-C-C\\[0.2cm]
1826 $\approx$0.35 nm: C-Si-Si
1829 \begin{minipage}{0.2cm}
1833 \begin{minipage}[t]{6.0cm}
1834 0.15 nm: C-C pairs $\uparrow$\\
1835 (as expected in graphite/diamond)\\[0.2cm]
1836 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
1837 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
1842 \item Decreasing cut-off artifact
1843 \item {\color{red}Amorphous} SiC-like phase remains
1844 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
1845 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
1854 High C \& small $V$ \& short $t$
1857 Slow restructuring due to strong C-C bonds
1860 High C \& low T implants
1875 Summary and Conclusions
1883 \begin{minipage}{12.3cm}
1888 \item Point defects excellently / fairly well described
1890 \item Identified \ci{} migration path
1891 \item EA drastically overestimates the diffusion barrier
1893 \item Combinations of defects (DFT)
1895 \item Agglomeration of point defects energetically favorable
1896 \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
1897 \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
1898 Low barrier (\unit[0.77]{eV}) \& low capture radius
1905 \begin{minipage}[t]{12.3cm}
1906 \underline{Pecipitation simulations}
1908 \item Problem of potential enhanced slow phase space propagation
1909 \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
1910 \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
1911 \item High T necessary to simulate IBS conditions (far from equilibrium)
1912 \item \cs{} involved in the precipitation process at elevated temperatures
1913 \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
1914 (stretched SiC, interface)
1921 \framebox{IBS: 3C-SiC precipitation occurs by successive agglomeration of \cs{}}
1940 \begin{minipage}[t]{6cm}
1941 \underline{Augsburg}
1943 \item Prof. B. Stritzker
1948 \underline{Helsinki}
1950 \item Prof. K. Nordlund
1955 \item Bayerische Forschungsstiftung
1958 \underline{Paderborn}
1960 \item Prof. J. Lindner
1961 \item Prof. G. Schmidt
1965 \begin{minipage}[t]{6cm}
1966 \underline{Referees}
1969 \item Prof. F. Haider
1976 \Large\bf Thank you for your attention!
1992 Polytypes of SiC\\[0.6cm]
1997 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
1998 \begin{minipage}{1.9cm}
1999 {\tiny cubic (twist)}
2001 \begin{minipage}{2.9cm}
2002 {\tiny hexagonal (no twist)}
2005 \begin{picture}(0,0)(-150,0)
2006 \includegraphics[width=7cm]{polytypes.eps}
2013 \begin{tabular}{l c c c c c c}
2015 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
2017 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
2018 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
2019 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
2020 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
2021 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
2022 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
2023 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
2027 \begin{pspicture}(0,0)(0,0)
2028 \psellipse[linecolor=green](5.7,2.05)(0.4,0.50)
2030 \begin{pspicture}(0,0)(0,0)
2031 \psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
2033 \begin{pspicture}(0,0)(0,0)
2034 \psellipse[linecolor=red](10.45,0.42)(0.4,0.20)
2045 Si self-interstitial point defects in silicon\\[0.1cm]
2049 \begin{tabular}{l c c c c c}
2051 $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
2053 \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
2054 Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
2056 \end{tabular}\\[0.4cm]
2059 \begin{minipage}{3cm}
2061 \underline{Vacancy}\\
2062 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
2065 \begin{minipage}{3cm}
2067 \underline{\hkl<1 1 0> DB}\\
2068 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
2071 \begin{minipage}{3cm}
2073 \underline{\hkl<1 0 0> DB}\\
2074 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
2077 \begin{minipage}{3cm}
2079 \underline{Tetrahedral}\\
2080 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
2084 \underline{Hexagonal} \hspace{2pt}
2085 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
2087 \begin{minipage}{2.7cm}
2088 $E_{\text{f}}^*=4.48\text{ eV}$\\
2089 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
2091 \begin{minipage}{0.4cm}
2096 \begin{minipage}{2.7cm}
2097 $E_{\text{f}}=3.96\text{ eV}$\\
2098 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
2101 \begin{minipage}{5.5cm}
2103 {\tiny nearly T $\rightarrow$ T}\\
2105 \includegraphics[width=6.0cm]{nhex_tet.ps}
2114 C-Si dimer \& bond-centered interstitial configuration
2121 \begin{minipage}[t]{4.1cm}
2122 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
2123 \begin{minipage}{2.0cm}
2125 \underline{Erhart/Albe}
2126 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
2129 \begin{minipage}{2.0cm}
2131 \underline{\textsc{vasp}}
2132 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
2134 \end{minipage}\\[0.2cm]
2135 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
2136 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
2137 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
2138 $\Rightarrow$ $sp^2$ hybridization
2140 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
2141 {\tiny Charge density isosurface}
2144 \begin{minipage}{0.2cm}
2147 \begin{minipage}[t]{8.1cm}
2149 {\bf Bond-centered interstitial}\\[0.1cm]
2150 \begin{minipage}{4.4cm}
2153 \item Linear Si-C-Si bond
2154 \item Si: one C \& 3 Si neighbours
2155 \item Spin polarized calculations
2156 \item No saddle point!\\
2160 \begin{minipage}{2.7cm}
2161 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
2163 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
2168 \begin{minipage}[t]{6.5cm}
2169 \begin{minipage}[t]{1.2cm}
2171 {\tiny sp$^3$}\\[0.8cm]
2172 \underline{${\color{black}\uparrow}$}
2173 \underline{${\color{black}\uparrow}$}
2174 \underline{${\color{black}\uparrow}$}
2175 \underline{${\color{red}\uparrow}$}\\
2178 \begin{minipage}[t]{1.4cm}
2180 {\color{red}M}{\color{blue}O}\\[0.8cm]
2181 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
2182 $\sigma_{\text{ab}}$\\[0.5cm]
2183 \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
2187 \begin{minipage}[t]{1.0cm}
2191 \underline{${\color{white}\uparrow\uparrow}$}
2192 \underline{${\color{white}\uparrow\uparrow}$}\\
2194 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
2195 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
2199 \begin{minipage}[t]{1.4cm}
2201 {\color{blue}M}{\color{green}O}\\[0.8cm]
2202 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
2203 $\sigma_{\text{ab}}$\\[0.5cm]
2204 \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
2208 \begin{minipage}[t]{1.2cm}
2211 {\tiny sp$^3$}\\[0.8cm]
2212 \underline{${\color{green}\uparrow}$}
2213 \underline{${\color{black}\uparrow}$}
2214 \underline{${\color{black}\uparrow}$}
2215 \underline{${\color{black}\uparrow}$}\\
2223 \begin{minipage}{3.0cm}
2225 \underline{Charge density}\\
2226 {\color{gray}$\bullet$} Spin up\\
2227 {\color{green}$\bullet$} Spin down\\
2228 {\color{blue}$\bullet$} Resulting spin up\\
2229 {\color{yellow}$\bullet$} Si atoms\\
2230 {\color{red}$\bullet$} C atom
2232 \begin{minipage}{3.6cm}
2233 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
2240 \begin{pspicture}(0,0)(0,0)
2241 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)