2 %\documentclass[landscape,semhelv,draft]{seminar}
3 \documentclass[landscape,semhelv]{seminar}
6 \usepackage[greek,german]{babel}
7 \usepackage[latin1]{inputenc}
8 \usepackage[T1]{fontenc}
14 \usepackage{calc} % Simple computations with LaTeX variables
15 \usepackage{caption} % Improved captions
16 \usepackage{fancybox} % To have several backgrounds
18 \usepackage{fancyhdr} % Headers and footers definitions
19 \usepackage{fancyvrb} % Fancy verbatim environments
20 \usepackage{pstricks} % PSTricks with the standard color package
32 \graphicspath{{../img/}}
36 \usepackage[setpagesize=false]{hyperref}
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
53 %\usepackage{cmbright}
54 %\renewcommand{\familydefault}{\sfdefault}
55 %\usepackage{mathptmx}
59 %\newrgbcolor{hred}{0.9 0.13 0.13}
60 %\newrgbcolor{hblue}{0.13 0.13 0.9}
61 \newrgbcolor{hred}{1.0 0.0 0.0}
62 \newrgbcolor{hblue}{0.0 0.0 1.0}
66 \extraslideheight{10in}
71 % specify width and height
76 \def\slidetopmargin{-0.15cm}
78 \newcommand{\ham}{\mathcal{H}}
79 \newcommand{\pot}{\mathcal{V}}
80 \newcommand{\foo}{\mathcal{U}}
81 \newcommand{\vir}{\mathcal{W}}
84 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
87 \renewcommand{\phi}{\varphi}
90 \newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
93 \newrgbcolor{si-yellow}{.6 .6 0}
94 \newrgbcolor{hb}{0.75 0.77 0.89}
95 \newrgbcolor{lbb}{0.75 0.8 0.88}
96 \newrgbcolor{hlbb}{0.825 0.88 0.968}
97 \newrgbcolor{lachs}{1.0 .93 .81}
100 \newcommand{\headphd}{
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}{}}
117 \newcommand{\dista}[1]{\unit[#1]{\AA}{}}
118 \newcommand{\perc}[1]{\unit[#1]{\%}{}}
120 % no vertical centering
131 A B C D E F G H G F E D C B A
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)
187 \psframe*[linecolor=hb](-0.2,0)(12.9,5)
189 \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.2,1)(6.5,1)(6.5,3)(5.2,3)
190 \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.4,0.5)(7.7,2)(7.7,2)(6.4,3.5)
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}
253 Polytypes of SiC\\[0.6cm]
258 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
259 \begin{minipage}{1.9cm}
260 {\tiny cubic (twist)}
262 \begin{minipage}{2.9cm}
263 {\tiny hexagonal (no twist)}
266 \begin{picture}(0,0)(-150,0)
267 \includegraphics[width=7cm]{polytypes.eps}
274 \begin{tabular}{l c c c c c c}
276 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
278 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
279 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
280 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
281 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
282 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
283 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
284 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
288 \begin{pspicture}(0,0)(0,0)
289 \psellipse[linecolor=green](5.7,2.05)(0.4,0.50)
291 \begin{pspicture}(0,0)(0,0)
292 \psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
294 \begin{pspicture}(0,0)(0,0)
295 \psellipse[linecolor=red](10.45,0.42)(0.4,0.20)
306 Fabrication of silicon carbide
315 \emph{Silicon carbide --- Born from the stars, perfected on earth.}
321 SiC thin films by MBE \& CVD
323 \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
324 \item \underline{Commercially available} semiconductor power devices based on
325 \underline{\foreignlanguage{greek}{a}-SiC}
326 \item Production of favored \underline{3C-SiC} material
327 \underline{less advanced}
328 \item Quality and size not yet sufficient
330 \begin{picture}(0,0)(-310,-20)
331 \includegraphics[width=2.0cm]{cree.eps}
339 {\footnotesize\color{black}
340 Mismatch in \underline{thermal expansion coeefficient}
341 and \underline{lattice parameter} w.r.t. substrate
348 {\bf Alternative approach}\\
349 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
356 \begin{minipage}{3.15cm}
358 \includegraphics[width=3cm]{imp.eps}\\
364 \begin{minipage}{3.15cm}
366 \includegraphics[width=3cm]{annealing.eps}\\
368 Postannealing at $>$ \degc{1200}
373 \begin{minipage}{5.5cm}
376 No surface bending effects\\
377 High areal homogenity\\[0.1cm]
378 $\Downarrow$\\[0.1cm]
379 Synthesis of large area SiC films possible
390 IBS of epitaxial single crystalline 3C-SiC
399 \item \underline{Implantation step 1}\\[0.1cm]
400 Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
401 $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
402 {\color{blue}precipitates}
403 \item \underline{Implantation step 2}\\[0.1cm]
404 Little remaining dose | \unit[180]{keV} | \degc{250}\\
406 Destruction/Amorphization of precipitates at layer interface
407 \item \underline{Annealing}\\[0.1cm]
408 \unit[10]{h} at \degc{1250}\\
409 $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
413 \begin{minipage}{6.9cm}
414 \includegraphics[width=7cm]{ibs_3c-sic.eps}\\[-0.4cm]
417 XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
421 \begin{minipage}{5cm}
422 \begin{pspicture}(0,0)(0,0)
424 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
425 \begin{minipage}{5.3cm}
428 3C-SiC precipitation\\
429 not yet fully understood
433 \renewcommand\labelitemi{$\Rightarrow$}
434 Details of the SiC precipitation
436 \item significant technological progress\\
437 in SiC thin film formation
438 \item perspectives for processes relying\\
439 upon prevention of SiC precipitation
443 \rput(-6.8,5.5){\pnode{h0}}
444 \rput(-3.0,5.5){\pnode{h1}}
445 \ncline[linecolor=blue]{-}{h0}{h1}
446 \ncline[linecolor=blue]{->}{h1}{box}
462 Supposed precipitation mechanism of SiC in Si
470 \begin{minipage}{3.6cm}
472 Si \& SiC lattice structure\\[0.1cm]
473 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
476 \begin{minipage}{1.7cm}
477 \underline{Silicon}\\
478 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
479 $a=\unit[5.429]{\\A}$\\
480 $\rho^*_{\text{Si}}=\unit[100]{\%}$
482 \begin{minipage}{1.7cm}
483 \underline{Silicon carbide}\\
484 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
485 $a=\unit[4.359]{\\A}$\\
486 $\rho^*_{\text{Si}}=\unit[97]{\%}$
492 \begin{minipage}{4.1cm}
494 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
498 \begin{minipage}{4.0cm}
500 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
506 \begin{minipage}{4.0cm}
508 C-Si dimers (dumbbells)\\[-0.1cm]
513 \begin{minipage}{4.1cm}
515 Agglomeration of C-Si dumbbells\\[-0.1cm]
516 $\Rightarrow$ dark contrasts
520 \begin{minipage}{4.0cm}
522 Precipitation of 3C-SiC in Si\\[-0.1cm]
523 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
524 \& release of Si self-interstitials
530 \begin{minipage}{4.0cm}
532 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
536 \begin{minipage}{4.1cm}
538 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
542 \begin{minipage}{4.0cm}
544 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
548 \begin{pspicture}(0,0)(0,0)
549 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
550 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
551 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
552 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
553 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
554 $4a_{\text{Si}}=5a_{\text{SiC}}$
556 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
557 \hkl(h k l) planes match
559 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
570 Supposed precipitation mechanism of SiC in Si
578 \begin{minipage}{3.6cm}
580 Si \& SiC lattice structure\\[0.1cm]
581 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
584 \begin{minipage}{1.7cm}
585 \underline{Silicon}\\
586 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
587 $a=\unit[5.429]{\\A}$\\
588 $\rho^*_{\text{Si}}=\unit[100]{\%}$
590 \begin{minipage}{1.7cm}
591 \underline{Silicon carbide}\\
592 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
593 $a=\unit[4.359]{\\A}$\\
594 $\rho^*_{\text{Si}}=\unit[97]{\%}$
600 \begin{minipage}{4.1cm}
602 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
606 \begin{minipage}{4.0cm}
608 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
614 \begin{minipage}{4.0cm}
616 C-Si dimers (dumbbells)\\[-0.1cm]
617 on Si interstitial sites
621 \begin{minipage}{4.1cm}
623 Agglomeration of C-Si dumbbells\\[-0.1cm]
624 $\Rightarrow$ dark contrasts
628 \begin{minipage}{4.0cm}
630 Precipitation of 3C-SiC in Si\\[-0.1cm]
631 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
632 \& release of Si self-interstitials
638 \begin{minipage}{4.0cm}
640 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
644 \begin{minipage}{4.1cm}
646 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
650 \begin{minipage}{4.0cm}
652 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
656 \begin{pspicture}(0,0)(0,0)
657 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
658 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
659 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
660 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
661 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
662 $4a_{\text{Si}}=5a_{\text{SiC}}$
664 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
665 \hkl(h k l) planes match
667 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
670 % controversial view!
671 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
672 \begin{minipage}{14cm}
677 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
678 \begin{minipage}{10cm}
682 {\color{gray}\bf Controversial findings}
685 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
687 \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
688 \item \si{} reacting with further C in cleared volume
690 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
692 \item Room temperature implantation $\rightarrow$ high C diffusion
693 \item Elevated temperature implantation $\rightarrow$ no C redistribution
695 $\Rightarrow$ mobile {\color{red}\ci} opposed to
696 stable {\color{blue}\cs{}} configurations
697 \item Strained silicon \& Si/SiC heterostructures
698 {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
700 \item {\color{blue}Coherent} SiC precipitates (tensile strain)
701 \item Incoherent SiC (strain relaxation)
706 {\Huge${\lightning}$} \hspace{0.3cm}
707 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
708 {\Huge${\lightning}$}
728 \item Introduction / Motivation
729 \item Assumed SiC precipitation mechanisms / Controversy
731 \item Utilized simulation techniques
733 \item Molecular dynamics (MD) simulations
734 \item Density functional theory (DFT) calculations
736 \item Simulation results
738 \item C and Si self-interstitial point defects in silicon
739 \item Silicon carbide precipitation simulations
741 \item Summary / Conclusion
750 Utilized computational methods
757 {\bf Molecular dynamics (MD)}\\[0.1cm]
759 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
761 System of $N$ particles &
762 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
763 Phase space propagation &
764 Velocity Verlet | timestep: \unit[1]{fs} \\
765 Analytical interaction potential &
766 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
769 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
770 \pot_{ij} = {\color{red}f_C(r_{ij})}
771 \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
773 Observables: time/ensemble averages &
774 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
782 {\bf Density functional theory (DFT)}
786 \begin{minipage}[t]{6cm}
788 \item Hohenberg-Kohn theorem:\\
789 $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
790 \item Kohn-Sham approach:\\
791 Single-particle effective theory
795 \item Code: \textsc{vasp}
796 \item Plane wave basis set | $E_{\text{cut}}=\unit[300]{eV}$
798 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
801 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
803 \item Ultrasoft pseudopotential
804 \item Exchange \& correlation: GGA
805 \item Brillouin zone sampling: $\Gamma$-point
806 \item Supercell: $N=216\pm2$
809 \begin{minipage}{6cm}
810 \begin{pspicture}(0,0)(0,0)
811 \pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
812 \rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
814 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
817 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
819 n(r)=\sum_i^N|\Phi_i(r)|^2
822 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
824 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
828 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
829 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
830 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
841 Point defects \& defect migration
848 \begin{minipage}[b]{7.5cm}
849 {\bf Defect structure}\\
850 \begin{pspicture}(0,0)(7,4.4)
851 \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
854 \item Creation of c-Si simulation volume
855 \item Periodic boundary conditions
856 \item $T=0\text{ K}$, $p=0\text{ bar}$
859 \rput(3.5,1.3){\rnode{insert}{\psframebox{
862 Insertion of interstitial C/Si atoms
865 \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
868 Relaxation / structural energy minimization
871 \ncline[]{->}{init}{insert}
872 \ncline[]{->}{insert}{cool}
875 \begin{minipage}[b]{4.5cm}
877 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
879 \begin{minipage}{2.21cm}
881 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
882 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
883 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
886 \begin{minipage}{2.21cm}
888 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
889 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
890 {\color{black}$\bullet$} Vac. / Sub.
897 \begin{minipage}[b]{6cm}
898 {\bf Defect formation energy}\\
900 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
901 Particle reservoir: Si \& SiC\\[0.2cm]
902 {\bf Binding energy}\\
906 E_{\text{f}}^{\text{comb}}-
907 E_{\text{f}}^{1^{\text{st}}}-
908 E_{\text{f}}^{2^{\text{nd}}}
912 $E_{\text{b}}<0$: energetically favorable configuration\\
913 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
915 \begin{minipage}[b]{6cm}
916 {\bf Migration barrier}
919 \item Displace diffusing atom
920 \item Constrain relaxation of (diffusing) atoms
921 \item Record configurational energy
923 \begin{picture}(0,0)(-60,-33)
924 \includegraphics[width=4.5cm]{crt_mod.eps}
936 Si self-interstitial point defects in silicon\\[0.1cm]
940 \begin{tabular}{l c c c c c}
942 $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
944 \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
945 Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
947 \end{tabular}\\[0.4cm]
950 \begin{minipage}{3cm}
952 \underline{Vacancy}\\
953 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
956 \begin{minipage}{3cm}
958 \underline{\hkl<1 1 0> DB}\\
959 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
962 \begin{minipage}{3cm}
964 \underline{\hkl<1 0 0> DB}\\
965 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
968 \begin{minipage}{3cm}
970 \underline{Tetrahedral}\\
971 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
975 \underline{Hexagonal} \hspace{2pt}
976 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
978 \begin{minipage}{2.7cm}
979 $E_{\text{f}}^*=4.48\text{ eV}$\\
980 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
982 \begin{minipage}{0.4cm}
987 \begin{minipage}{2.7cm}
988 $E_{\text{f}}=3.96\text{ eV}$\\
989 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
992 \begin{minipage}{5.5cm}
994 {\tiny nearly T $\rightarrow$ T}\\
996 \includegraphics[width=6.0cm]{nhex_tet.ps}
1007 C interstitial point defects in silicon\\
1010 \begin{tabular}{l c c c c c c r}
1012 $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
1013 {\color{black} \cs{} \& \si}\\
1015 \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1016 Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1018 \end{tabular}\\[0.1cm]
1021 \begin{minipage}{2.8cm}
1022 \underline{Hexagonal} \hspace{2pt}
1023 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1024 $E_{\text{f}}^*=9.05\text{ eV}$\\
1025 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
1027 \begin{minipage}{0.4cm}
1032 \begin{minipage}{2.8cm}
1033 \underline{\hkl<1 0 0>}\\
1034 $E_{\text{f}}=3.88\text{ eV}$\\
1035 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
1038 \begin{minipage}{1.4cm}
1041 \begin{minipage}{3.0cm}
1043 \underline{Tetrahedral}\\
1044 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
1049 \begin{minipage}{2.8cm}
1050 \underline{Bond-centered}\\
1051 $E_{\text{f}}^*=5.59\text{ eV}$\\
1052 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
1054 \begin{minipage}{0.4cm}
1059 \begin{minipage}{2.8cm}
1060 \underline{\hkl<1 1 0> dumbbell}\\
1061 $E_{\text{f}}=5.18\text{ eV}$\\
1062 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
1065 \begin{minipage}{1.4cm}
1068 \begin{minipage}{3.0cm}
1070 \underline{Substitutional}\\
1071 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
1084 C-Si dimer \& bond-centered interstitial configuration
1091 \begin{minipage}[t]{4.1cm}
1092 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
1093 \begin{minipage}{2.0cm}
1095 \underline{Erhart/Albe}
1096 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
1099 \begin{minipage}{2.0cm}
1101 \underline{\textsc{vasp}}
1102 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
1104 \end{minipage}\\[0.2cm]
1105 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
1106 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
1107 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
1108 $\Rightarrow$ $sp^2$ hybridization
1110 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
1111 {\tiny Charge density isosurface}
1114 \begin{minipage}{0.2cm}
1117 \begin{minipage}[t]{8.1cm}
1119 {\bf Bond-centered interstitial}\\[0.1cm]
1120 \begin{minipage}{4.4cm}
1123 \item Linear Si-C-Si bond
1124 \item Si: one C \& 3 Si neighbours
1125 \item Spin polarized calculations
1126 \item No saddle point!\\
1130 \begin{minipage}{2.7cm}
1131 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1133 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
1138 \begin{minipage}[t]{6.5cm}
1139 \begin{minipage}[t]{1.2cm}
1141 {\tiny sp$^3$}\\[0.8cm]
1142 \underline{${\color{black}\uparrow}$}
1143 \underline{${\color{black}\uparrow}$}
1144 \underline{${\color{black}\uparrow}$}
1145 \underline{${\color{red}\uparrow}$}\\
1148 \begin{minipage}[t]{1.4cm}
1150 {\color{red}M}{\color{blue}O}\\[0.8cm]
1151 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1152 $\sigma_{\text{ab}}$\\[0.5cm]
1153 \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1157 \begin{minipage}[t]{1.0cm}
1161 \underline{${\color{white}\uparrow\uparrow}$}
1162 \underline{${\color{white}\uparrow\uparrow}$}\\
1164 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1165 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1169 \begin{minipage}[t]{1.4cm}
1171 {\color{blue}M}{\color{green}O}\\[0.8cm]
1172 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1173 $\sigma_{\text{ab}}$\\[0.5cm]
1174 \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1178 \begin{minipage}[t]{1.2cm}
1181 {\tiny sp$^3$}\\[0.8cm]
1182 \underline{${\color{green}\uparrow}$}
1183 \underline{${\color{black}\uparrow}$}
1184 \underline{${\color{black}\uparrow}$}
1185 \underline{${\color{black}\uparrow}$}\\
1193 \begin{minipage}{3.0cm}
1195 \underline{Charge density}\\
1196 {\color{gray}$\bullet$} Spin up\\
1197 {\color{green}$\bullet$} Spin down\\
1198 {\color{blue}$\bullet$} Resulting spin up\\
1199 {\color{yellow}$\bullet$} Si atoms\\
1200 {\color{red}$\bullet$} C atom
1202 \begin{minipage}{3.6cm}
1203 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
1210 \begin{pspicture}(0,0)(0,0)
1211 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
1220 C interstitial migration --- ab initio
1227 \begin{minipage}{6.8cm}
1228 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
1229 \begin{minipage}{2.0cm}
1230 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1232 \begin{minipage}{0.2cm}
1235 \begin{minipage}{2.0cm}
1236 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
1238 \begin{minipage}{0.2cm}
1241 \begin{minipage}{2.0cm}
1242 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
1243 \end{minipage}\\[0.1cm]
1245 $\Rightarrow$ BC configuration constitutes local minimum\\
1246 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
1248 \begin{minipage}{5.4cm}
1249 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
1250 \end{minipage}\\[0.2cm]
1253 \begin{minipage}{6.8cm}
1254 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
1255 \begin{minipage}{2.0cm}
1256 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1258 \begin{minipage}{0.2cm}
1261 \begin{minipage}{2.0cm}
1262 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
1264 \begin{minipage}{0.2cm}
1267 \begin{minipage}{2.0cm}
1268 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
1269 \end{minipage}\\[0.1cm]
1270 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
1271 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
1272 Note: Change in orientation
1274 \begin{minipage}{5.4cm}
1275 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
1276 \end{minipage}\\[0.1cm]
1279 Reorientation pathway composed of two consecutive processes of the above type
1288 C interstitial migration --- analytical potential
1295 \begin{minipage}[t]{6.0cm}
1296 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
1297 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
1299 \item Lowermost migration barrier
1300 \item $\Delta E \approx \unit[2.2]{eV}$
1301 \item 2.4 times higher than ab initio result
1302 \item Different pathway
1305 \begin{minipage}[t]{0.2cm}
1308 \begin{minipage}[t]{6.0cm}
1309 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
1312 \item Bond-centered configuration unstable\\
1313 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1314 \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
1315 $\rightarrow$ \ci{} \hkl<1 1 0> DB
1318 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
1320 \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
1321 \item 2.4 -- 3.4 times higher than ab initio result
1322 \item After all: Change of the DB orientation
1328 {\color{red}\bf Drastically overestimated diffusion barrier}
1331 \begin{pspicture}(0,0)(0,0)
1332 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
1348 \begin{minipage}{9cm}
1350 Summary of combinations}\\[0.1cm]
1352 \begin{tabular}{l c c c c c c}
1354 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1356 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1357 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1358 \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}\\
1359 \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}\\
1360 \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}\\
1361 \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}\\
1363 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1364 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1371 $E_{\text{b}}$ explainable by stress compensation / increase
1375 \begin{minipage}{3cm}
1376 \includegraphics[width=3.5cm]{comb_pos.eps}
1381 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1382 \begin{minipage}[t]{3.2cm}
1383 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1384 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1386 \begin{minipage}[t]{3.0cm}
1387 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1388 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1390 \begin{minipage}[t]{6.1cm}
1393 \item \ci{} agglomeration energetically favorable
1394 \item Most favorable: C clustering\\
1395 {\color{red}However \ldots}\\
1396 \ldots high migration barrier ($>4\,\text{eV}$)\\
1398 $4\times{\color{cyan}[-2.25]}$ versus
1399 $2\times{\color{orange}[-2.39]}$
1402 {\color{blue}\ci{} agglomeration / no C clustering}
1419 \begin{minipage}{9cm}
1421 Summary of combinations}\\[0.1cm]
1423 \begin{tabular}{l c c c c c c}
1425 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1427 \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1428 \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1429 \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}\\
1430 \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}\\
1431 \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}\\
1432 \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}\\
1434 C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1435 Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1442 $E_{\text{b}}$ explainable by stress compensation / increase
1446 \begin{minipage}{3cm}
1447 \includegraphics[width=3.5cm]{comb_pos.eps}
1452 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1453 \begin{minipage}[t]{3.2cm}
1454 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1455 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1457 \begin{minipage}[t]{3.0cm}
1458 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1459 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1461 \begin{minipage}[t]{6.1cm}
1464 \item \ci{} agglomeration energetically favorable
1465 \item Most favorable: C clustering\\
1466 {\color{red}However \ldots}\\
1467 \ldots high migration barrier ($>4\,\text{eV}$)\\
1469 $4\times{\color{cyan}[-2.25]}$ versus
1470 $2\times{\color{orange}[-2.39]}$
1473 {\color{blue}\ci{} agglomeration / no C clustering}
1478 \begin{pspicture}(0,0)(0,0)
1479 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1480 \begin{minipage}{14cm}
1485 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1486 \begin{minipage}{8cm}
1490 Interaction along \hkl[1 1 0]
1491 \includegraphics[width=7cm]{db_along_110_cc.ps}
1503 Defect combinations of C-Si dimers and vacancies
1509 \begin{minipage}[b]{2.6cm}
1511 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1512 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1515 \begin{minipage}[b]{7cm}
1518 \begin{minipage}[b]{2.6cm}
1520 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1521 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1523 \end{minipage}\\[0.2cm]
1525 \begin{minipage}{6.5cm}
1526 \includegraphics[width=6.0cm]{059-539.ps}
1528 \begin{minipage}{5.7cm}
1529 \includegraphics[width=6.0cm]{314-539.ps}
1532 \begin{pspicture}(0,0)(0,0)
1533 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1535 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1536 \begin{minipage}{6.5cm}
1538 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1539 Low migration barrier towards C$_{\text{sub}}$\\
1541 High barrier for reverse process\\[0.3cm]
1543 High probability of stable C$_{\text{sub}}$ configuration
1556 Combinations of substitutional C and Si self-interstitials
1563 \begin{minipage}{6.2cm}
1565 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1567 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1568 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1569 \item Interaction drops quickly to zero\\
1570 $\rightarrow$ low capture radius
1574 \begin{minipage}{0.2cm}
1577 \begin{minipage}{6.0cm}
1579 {\bf Transition from the ground state}
1581 \item Low transition barrier
1582 \item Barrier smaller than \ci{} migration barrier
1583 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1584 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1587 \end{minipage}\\[0.3cm]
1589 \begin{minipage}{6.0cm}
1590 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1592 \begin{minipage}{0.4cm}
1595 \begin{minipage}{6.0cm}
1597 \includegraphics[width=6.0cm]{162-097.ps}
1601 \begin{pspicture}(0,0)(0,0)
1602 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1603 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1604 \begin{minipage}{8cm}
1608 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1609 IBS --- process far from equilibrium\\
1622 Combinations of substitutional C and Si self-interstitials
1629 \begin{minipage}{6.2cm}
1631 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1633 \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1634 \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1635 \item Interaction drops quickly to zero\\
1636 $\rightarrow$ low capture radius
1640 \begin{minipage}{0.2cm}
1643 \begin{minipage}{6.0cm}
1645 {\bf Transition from the ground state}
1647 \item Low transition barrier
1648 \item Barrier smaller than \ci{} migration barrier
1649 \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1650 $\rightarrow$ Separation of \cs{} \& \si{} most probable
1653 \end{minipage}\\[0.3cm]
1655 \begin{minipage}{6.0cm}
1656 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1658 \begin{minipage}{0.4cm}
1661 \begin{minipage}{6.0cm}
1663 \includegraphics[width=6.0cm]{162-097.ps}
1667 \begin{pspicture}(0,0)(0,0)
1668 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1669 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1670 \begin{minipage}{8cm}
1674 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1675 IBS --- process far from equilibrium\\
1683 \begin{pspicture}(0,0)(0,0)
1684 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1685 \begin{minipage}{14cm}
1690 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1691 \begin{minipage}{11cm}
1695 Ab initio MD at \degc{900}\\[0.4cm]
1696 \begin{minipage}{5.4cm}
1698 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1701 \begin{minipage}{5.4cm}
1703 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1705 \end{minipage}\\[0.5cm]
1707 Contribution of entropy to structural formation\\[0.1cm]
1720 Silicon carbide precipitation simulations
1730 \begin{pspicture}(0,0)(12,6.5)
1732 \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1735 \item Create c-Si volume
1736 \item Periodc boundary conditions
1737 \item Set requested $T$ and $p=0\text{ bar}$
1738 \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1741 \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1743 Insertion of C atoms at constant T
1745 \item total simulation volume {\pnode{in1}}
1746 \item volume of minimal SiC precipitate size {\pnode{in2}}
1747 \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1751 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1753 Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1755 \ncline[]{->}{init}{insert}
1756 \ncline[]{->}{insert}{cool}
1757 \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
1758 \rput(7.6,6){\footnotesize $V_1$}
1759 \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
1760 \rput(8.9,4.85){\tiny $V_2$}
1761 \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
1762 \rput(9.25,4.45){\footnotesize $V_3$}
1763 \rput(7.9,3.2){\pnode{ins1}}
1764 \rput(8.92,2.8){\pnode{ins2}}
1765 \rput(10.8,2.4){\pnode{ins3}}
1766 \ncline[]{->}{in1}{ins1}
1767 \ncline[]{->}{in2}{ins2}
1768 \ncline[]{->}{in3}{ins3}
1778 \begin{minipage}{5.7cm}
1780 \item Amount of C atoms: 6000\\
1781 ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
1782 \item Simulation volume: $31^3$ Si unit cells\\
1786 \begin{minipage}{0.3cm}
1790 \begin{minipage}{6.0cm}
1791 Restricted to classical potential caclulations\\
1792 $\rightarrow$ Low C diffusion / overestimated barrier\\
1793 $\rightarrow$ Consider $V_2$ and $V_3$
1795 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
1806 Silicon carbide precipitation simulations at \degc{450} as in IBS
1811 \begin{minipage}{6.3cm}
1812 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1813 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1816 \begin{minipage}{6.1cm}
1818 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1819 \hkl<1 0 0> C-Si dumbbell dominated structure
1821 \item Si-C bumbs around \unit[0.19]{nm}
1822 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1823 concatenated differently oriented \ci{} DBs
1824 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1826 \begin{pspicture}(0,0)(6.0,1.0)
1827 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1828 \begin{minipage}{6cm}
1830 Formation of \ci{} dumbbells\\
1831 C atoms in proper 3C-SiC distance first
1834 \end{pspicture}\\[0.1cm]
1835 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1837 \item High amount of strongly bound C-C bonds
1838 \item Increased defect \& damage density\\
1839 $\rightarrow$ Arrangements hard to categorize and trace
1840 \item Only short range order observable
1842 \begin{pspicture}(0,0)(6.0,0.8)
1843 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1844 \begin{minipage}{6cm}
1846 Amorphous SiC-like phase
1849 \end{pspicture}\\[0.3cm]
1850 \begin{pspicture}(0,0)(6.0,2.0)
1851 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
1852 \begin{minipage}{6cm}
1866 Silicon carbide precipitation simulations at \degc{450} as in IBS
1871 \begin{minipage}{6.3cm}
1872 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1873 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1876 \begin{minipage}{6.1cm}
1878 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1879 \hkl<1 0 0> C-Si dumbbell dominated structure
1881 \item Si-C bumbs around \unit[0.19]{nm}
1882 \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1883 concatenated differently oriented \ci{} DBs
1884 \item Si-Si NN distance stretched to \unit[0.3]{nm}
1886 \begin{pspicture}(0,0)(6.0,1.0)
1887 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1888 \begin{minipage}{6cm}
1890 Formation of \ci{} dumbbells\\
1891 C atoms in proper 3C-SiC distance first
1894 \end{pspicture}\\[0.1cm]
1895 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1897 \item High amount of strongly bound C-C bonds
1898 \item Increased defect \& damage density\\
1899 $\rightarrow$ Arrangements hard to categorize and trace
1900 \item Only short range order observable
1902 \begin{pspicture}(0,0)(6.0,0.8)
1903 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1904 \begin{minipage}{6cm}
1906 Amorphous SiC-like phase
1909 \end{pspicture}\\[0.3cm]
1910 \begin{pspicture}(0,0)(6.0,2.0)
1911 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
1912 \begin{minipage}{6cm}
1915 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
1916 \begin{minipage}{0.8cm}
1917 {\bf\boldmath $V_1$:}
1919 \begin{minipage}{5.1cm}
1920 Formation of \ci{} indeed occurs\\
1921 Agllomeration not observed
1922 \end{minipage}\\[0.3cm]
1923 \begin{minipage}{0.8cm}
1924 {\bf\boldmath $V_{2,3}$:}
1926 \begin{minipage}{5.1cm}
1927 Amorphous SiC-like structure\\
1928 (not expected at \degc{450})\\[0.05cm]
1929 No rearrangement/transition into 3C-SiC
1930 \end{minipage}\\[0.1cm]
1942 Limitations of MD and short range potentials
1949 {\bf Time scale problem of MD}\\[0.2cm]
1950 Precise integration \& thermodynamic sampling\\
1951 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
1952 $\omega$: vibrational mode\\
1953 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
1954 Several local minima separated by large energy barriers\\
1955 $\Rightarrow$ Transition event corresponds to a multiple
1956 of vibrational periods\\
1957 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
1958 infrequent transition events\\[0.2cm]
1959 {\color{blue}Accelerated methods:}
1960 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1964 {\bf Limitations related to the short range potential}\\[0.2cm]
1965 Cut-off function limits interaction to next neighbours\\
1966 $\Rightarrow$ Overestimated unphysical high forces of next neighbours
1971 {\bf Approach to the (twofold) problem}\\[0.2cm]
1972 Increased temperature simulations without TAD corrections\\
1973 Accelerated methods or higher time scales exclusively not sufficient!
1975 \begin{pspicture}(0,0)(0,0)
1976 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
1977 \begin{minipage}{7.5cm}
1980 Potential enhanced slow phase space propagation
1983 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1984 \begin{minipage}{2.7cm}
1988 thermodynamic sampling
1991 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
1992 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
1993 \begin{minipage}{3.6cm}
1996 \underline{IBS}\\[0.1cm]
1997 3C-SiC also observed for higher T\\[0.1cm]
1998 Higher T inside sample\\[0.1cm]
1999 Structural evolution vs.\\
2000 equilibrium properties
2003 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
2012 Increased temperature simulations --- $V_1$
2017 \begin{minipage}{6.2cm}
2018 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2021 \begin{minipage}{6.2cm}
2022 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2025 \begin{minipage}{6.2cm}
2026 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2029 \begin{minipage}{6.3cm}
2031 \underline{Si-C bonds:}
2033 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2034 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2036 \underline{Si-Si bonds:}
2037 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2038 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2039 \underline{C-C bonds:}
2041 \item C-C next neighbour pairs reduced (mandatory)
2042 \item Peak at 0.3 nm slightly shifted
2044 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2045 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2047 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2049 \item Range [|-$\downarrow$]:
2050 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2051 with nearby Si$_{\text{I}}$}
2062 Increased temperature simulations --- $V_1$
2067 \begin{minipage}{6.2cm}
2068 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2071 \begin{minipage}{6.2cm}
2072 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2075 \begin{minipage}{6.2cm}
2076 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2079 \begin{minipage}{6.3cm}
2081 \underline{Si-C bonds:}
2083 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2084 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2086 \underline{Si-Si bonds:}
2087 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2088 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2089 \underline{C-C bonds:}
2091 \item C-C next neighbour pairs reduced (mandatory)
2092 \item Peak at 0.3 nm slightly shifted
2094 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2095 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2097 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2099 \item Range [|-$\downarrow$]:
2100 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2101 with nearby Si$_{\text{I}}$}
2107 \begin{pspicture}(0,0)(0,0)
2108 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
2109 \begin{minipage}{14cm}
2114 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
2115 \begin{minipage}{9cm}
2119 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
2120 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
2123 \item Stretched coherent SiC structures\\
2124 $\Rightarrow$ Precipitation process involves {\color{blue}\cs}
2125 \item Explains annealing behavior of high/low T C implantations
2127 \item Low T: highly mobile {\color{red}\ci}
2128 \item High T: stable configurations of {\color{blue}\cs}
2132 \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
2133 \item Building block for surrounding Si host \& further SiC
2134 \item Strain compensation \ldots\\
2135 \ldots Si/SiC interface\\
2136 \ldots within stretched coherent SiC structure
2141 \psframebox[linecolor=blue,linewidth=0.05cm]{
2142 \begin{minipage}{7cm}
2144 Precipitation mechanism involving \cs\\
2145 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2155 % skip high T / C conc ... only here!
2161 Increased temperature simulations at high C concentration
2166 \begin{minipage}{6.5cm}
2167 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2169 \begin{minipage}{6.5cm}
2170 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2178 \begin{minipage}[t]{6.0cm}
2179 0.186 nm: Si-C pairs $\uparrow$\\
2180 (as expected in 3C-SiC)\\[0.2cm]
2181 0.282 nm: Si-C-C\\[0.2cm]
2182 $\approx$0.35 nm: C-Si-Si
2185 \begin{minipage}{0.2cm}
2189 \begin{minipage}[t]{6.0cm}
2190 0.15 nm: C-C pairs $\uparrow$\\
2191 (as expected in graphite/diamond)\\[0.2cm]
2192 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2193 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2198 \item Decreasing cut-off artifact
2199 \item {\color{red}Amorphous} SiC-like phase remains
2200 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2201 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2210 High C \& small $V$ \& short $t$
2213 Slow restructuring due to strong C-C bonds
2216 High C \& low T implants
2224 % skipped high T / C conc
2235 \begin{pspicture}(0,0)(12,1.0)
2236 \psframebox[fillstyle=gradient,gradbegin=hred,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
2237 \begin{minipage}{11cm}
2238 {\color{black}Diploma thesis}\\
2239 \underline{Monte Carlo} simulation modeling the selforganization process\\
2240 leading to periodic arrays of nanometric amorphous SiC precipitates
2243 \end{pspicture}\\[0.4cm]
2244 \begin{pspicture}(0,0)(12,2)
2245 \psframebox[fillstyle=gradient,gradbegin=hblue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
2246 \begin{minipage}{11cm}
2247 {\color{black}Doctoral studies}\\
2248 Classical potential \underline{molecular dynamics} simulations \ldots\\
2249 \underline{Density functional theory} calculations \ldots\\[0.2cm]
2250 \ldots on defect formation and SiC precipitation in Si
2253 \end{pspicture}\\[0.5cm]
2254 \begin{pspicture}(0,0)(12,3)
2255 \psframebox[fillstyle=solid,fillcolor=white,linestyle=solid]{
2256 \begin{minipage}{11cm}
2258 {\color{black}\bf How to proceed \ldots}\\[0.1cm]
2259 MC $\rightarrow$ empirical potential MD $\rightarrow$ Ground-state DFT \ldots
2261 \renewcommand\labelitemi{$\ldots$}
2262 \item beyond LDA/GGA methods \& ground-state DFT
2264 Investigation of structure \& structural evolution \ldots
2266 \renewcommand\labelitemi{$\ldots$}
2267 \item electronic/optical properties
2268 \item electronic correlations
2269 \item non-equilibrium systems
2273 \end{pspicture}\\[0.5cm]
2289 \underline{Augsburg}
2291 \item Prof. B. Stritzker (accomodation at EP \RM{4})
2292 \item Ralf Utermann (EDV)
2295 \underline{Helsinki}
2297 \item Prof. K. Nordlund (MD)
2302 \item Bayerische Forschungsstiftung (financial support)
2305 \underline{Paderborn}
2307 \item Prof. J. Lindner (SiC)
2308 \item Prof. G. Schmidt (DFT + financial support)
2309 \item Dr. E. Rauls (DFT + SiC)
2312 \underline{Stuttgart}
2315 \bf Thank you for your attention / invitation!