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
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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 \newcommand{\headdiplom}{
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61 \rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{
62 \begin{minipage}{14cm}
70 \newcommand{\headphd}{
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73 \begin{minipage}{14cm}
83 \extraslideheight{10in}
88 % specify width and height
93 \def\slidetopmargin{-0.15cm}
95 \newcommand{\ham}{\mathcal{H}}
96 \newcommand{\pot}{\mathcal{V}}
97 \newcommand{\foo}{\mathcal{U}}
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101 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
104 \renewcommand{\phi}{\varphi}
107 \newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
110 \newrgbcolor{si-yellow}{.6 .6 0}
111 \newrgbcolor{hb}{0.75 0.77 0.89}
112 \newrgbcolor{lbb}{0.75 0.8 0.88}
113 \newrgbcolor{hlbb}{0.825 0.88 0.968}
114 \newrgbcolor{lachs}{1.0 .93 .81}
117 \newcommand{\si}{Si$_{\text{i}}${}}
118 \newcommand{\ci}{C$_{\text{i}}${}}
119 \newcommand{\cs}{C$_{\text{sub}}${}}
120 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
121 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
122 \newcommand{\dista}[1]{\unit[#1]{\AA}{}}
123 \newcommand{\perc}[1]{\unit[#1]{\%}{}}
125 % no vertical centering
136 A B C D E F G H G F E D C B A
151 Atomistic simulation studies\\[0.2cm]
157 \textsc{Frank Zirkelbach}
161 Application talk at the Max Planck Institute for Solid State Research
165 Stuttgart, November 2011
170 % no vertical centering
180 % Phase diagram of the C/Si system\\
185 \begin{minipage}{6.5cm}
186 \includegraphics[width=6.5cm]{si-c_phase.eps}
189 R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959)
192 \begin{pspicture}(0,0)(0,0)
193 \psellipse[linecolor=blue,linewidth=0.1cm](3.55,4.0)(0.5,2.9)
196 \begin{minipage}{6cm}
197 {\bf Phase diagram of the C/Si system}\\[0.2cm]
198 {\color{blue}Stoichiometric composition}
200 \item only chemical stable compound
201 \item wide band gap semiconductor\\
202 \underline{silicon carbide}, SiC
208 % motivation / properties / applications of silicon carbide
216 \begin{pspicture}(0,0)(13.5,5)
218 \psframe*[linecolor=hb](-0.2,0)(12.9,5)
220 \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.2,1)(6.5,1)(6.5,3)(5.2,3)
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223 \rput[lt](0,4.6){\color{gray}PROPERTIES}
225 \rput[lt](0.3,4){wide band gap}
226 \rput[lt](0.3,3.5){high electric breakdown field}
227 \rput[lt](0.3,3){good electron mobility}
228 \rput[lt](0.3,2.5){high electron saturation drift velocity}
229 \rput[lt](0.3,2){high thermal conductivity}
231 \rput[lt](0.3,1.5){hard and mechanically stable}
232 \rput[lt](0.3,1){chemically inert}
234 \rput[lt](0.3,0.5){radiation hardness}
236 \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
238 \rput[rt](12.5,3.85){high-temperature, high power}
239 \rput[rt](12.5,3.5){and high-frequency}
240 \rput[rt](12.5,3.15){electronic and optoelectronic devices}
242 \rput[rt](12.5,2.35){material suitable for extreme conditions}
243 \rput[rt](12.5,2){microelectromechanical systems}
244 \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
246 \rput[rt](12.5,0.85){first wall reactor material, detectors}
247 \rput[rt](12.5,0.5){and electronic devices for space}
251 \begin{picture}(0,0)(5,-162)
252 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
254 \begin{picture}(0,0)(-120,-162)
255 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
257 \begin{picture}(0,0)(-270,-162)
258 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
261 \begin{picture}(0,0)(10,65)
262 \includegraphics[height=2.8cm]{sic_switch.eps}
264 %\begin{picture}(0,0)(-243,65)
265 \begin{picture}(0,0)(-110,65)
266 \includegraphics[height=2.8cm]{ise_99.eps}
268 %\begin{picture}(0,0)(-135,65)
269 \begin{picture}(0,0)(-100,65)
270 \includegraphics[height=1.2cm]{infineon_schottky.eps}
272 \begin{picture}(0,0)(-233,65)
273 \includegraphics[height=2.8cm]{solar_car.eps}
283 Polytypes of SiC\\[0.4cm]
286 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
287 \begin{minipage}{1.9cm}
288 {\tiny cubic (twist)}
290 \begin{minipage}{2.9cm}
291 {\tiny hexagonal (no twist)}
294 \begin{picture}(0,0)(-150,0)
295 \includegraphics[width=7cm]{polytypes.eps}
302 \begin{tabular}{l c c c c c c}
304 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
306 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
307 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
308 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
309 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
310 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
311 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
312 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
316 \begin{pspicture}(0,0)(0,0)
317 \psellipse[linecolor=green](5.7,2.10)(0.4,0.5)
319 \begin{pspicture}(0,0)(0,0)
320 \psellipse[linecolor=green](5.6,0.92)(0.4,0.2)
322 \begin{pspicture}(0,0)(0,0)
323 \psellipse[linecolor=red](10.45,0.45)(0.4,0.2)
333 Fabrication of silicon carbide
342 \emph{Silicon carbide --- Born from the stars, perfected on earth.}
348 SiC thin films by MBE \& CVD
350 \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
351 \item \underline{Commercially available} semiconductor power devices based on
352 \underline{\foreignlanguage{greek}{a}-SiC}
353 \item Production of favored \underline{3C-SiC} material
354 \underline{less advanced}
355 \item Quality and size not yet sufficient
357 \begin{picture}(0,0)(-310,-20)
358 \includegraphics[width=2.0cm]{cree.eps}
363 Alternative approach:
364 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
371 \begin{minipage}{3.15cm}
373 \includegraphics[width=3cm]{imp.eps}\\
379 \begin{minipage}{3.15cm}
381 \includegraphics[width=3cm]{annealing.eps}\\
383 \unit[12]{h} annealing at \degc{1200}
388 \begin{minipage}{5.5cm}
389 \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
392 XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
404 Systematic investigation of C implantations into Si
410 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
426 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
429 \begin{pspicture}(0,0)(0,0)
430 \rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
431 \begin{minipage}{11cm}
432 {\color{black}Diploma thesis}\\
433 \underline{Monte Carlo} simulation modeling the selforganization process\\
434 leading to periodic arrays of nanometric amorphous SiC precipitates
438 \begin{pspicture}(0,0)(0,0)
439 \rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=blue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
440 \begin{minipage}{11cm}
441 {\color{black}Doctoral studies}\\
442 Classical potential \underline{molecular dynamics} simulations \ldots\\
443 \underline{Density functional theory} calculations \ldots\\[0.2cm]
444 \ldots on defect formation and SiC precipitation in Si
448 \begin{pspicture}(0,0)(0,0)
449 \psellipse[linecolor=red,linewidth=0.05cm](5,3.0)(0.8,1.0)
451 \begin{pspicture}(0,0)(0,0)
452 \psellipse[linecolor=blue,linewidth=0.05cm](8.2,3.2)(1.5,1.6)
461 Selforganization of nanometric amorphous SiC lamellae
469 \item Regularly spaced, nanometric spherical\\
470 and lamellar amorphous inclusions\\
471 at the upper a/c interface
472 \item Carbon accumulation\\
478 \begin{minipage}{12cm}
479 \includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\
481 XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si,
482 {\color{red}\underline{\degc{150}}},
483 Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$}
487 \begin{picture}(0,0)(-182,-215)
488 \begin{minipage}{6.5cm}
490 \includegraphics[width=6.5cm]{../../nlsop/img/eftem.eps}\\[-0.2cm]
492 XTEM bright-field and respective EFTEM C map
504 Model displaying the formation of ordered lamellae
510 \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps}
516 \item Supersaturation of C in c-Si\\
517 $\rightarrow$ {\bf Carbon induced} nucleation of spherical
519 \item High interfacial energy between 3C-SiC and c-Si\\
520 $\rightarrow$ {\bf Amorphous} precipitates
521 \item \unit[20-- 30]{\%} lower silicon density of a-SiC$_x$ compared to c-Si\\
522 $\rightarrow$ {\bf Lateral strain} (black arrows)
523 \item Implantation range near surface\\
524 $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component}
525 \item Reduction of the carbon supersaturation in c-Si\\
526 $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina
528 \item Remaining lateral strain\\
529 $\rightarrow$ {\bf Strain enhanced} lateral amorphisation
530 \item Absence of crystalline neighbours (structural information)\\
531 $\rightarrow$ {\bf Stabilization} of amorphous inclusions
532 {\bf against recrystallization}
541 Implementation of the Monte Carlo code
547 \item \underline{Amorphization / Recrystallization}\\
548 Ion collision in discretized target determined by random numbers
549 distributed according to nuclear energy loss.
550 Amorphization/recrystallization probability:
552 p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
555 \item {\color{green} $p_b$} normal `ballistic' amorphization
556 \item {\color{blue} $p_c$} carbon induced amorphization
557 \item {\color{red} $p_s$} stress enhanced amorphization
560 p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
563 \delta (\vec r) = \left\{
565 1 & \textrm{if volume at position $\vec r$ is amorphous} \\
566 0 & \textrm{otherwise} \\
570 \item \underline{Carbon incorporation}\\
571 Incorporation volume determined according to implantation profile
572 \item \underline{Diffusion / Sputtering}
574 \item Transfer fraction of C atoms
575 of crystalline into neighbored amorphous volumes
576 \item Remove surface layer
584 \begin{minipage}{3.7cm}
585 \begin{pspicture}(0,0)(0,0)
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587 \begin{minipage}{3.7cm}
601 Evolution of the \ldots
606 \item lamellar precipitates
608 \ldots reproduced!\\[1.4cm]
612 Experiment \& simulation\\
613 in good agreement\\[1.0cm]
615 Simulation is able to model the whole depth region\\[1.2cm]
620 \begin{minipage}{0.5cm}
623 \begin{minipage}{8.0cm}
625 \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\
626 \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps}
635 Structural \& compositional details
638 \begin{minipage}[t]{7.5cm}
639 \includegraphics[height=6.5cm]{../../nlsop/img/ac_cconc_ver2_e.eps}\\
641 \begin{minipage}[t]{5.0cm}
642 \includegraphics[height=6.5cm]{../../nlsop/img/97_98_e.eps}
650 \item Fluctuation of C concentration in lamellae region
651 \item \unit[8--10]{at.\%} C saturation limit
652 within the respective conditions
653 \item Complementarily arranged and alternating sequence of layers\\
654 with a high and low amount of amorphous regions
655 \item C accumulation in the amorphous phase / Origin of stress
658 \begin{picture}(0,0)(-260,-50)
660 \begin{minipage}{3cm}
663 Precipitation process\\
678 Formation of epitaxial single crystalline 3C-SiC
687 \item \underline{Implantation step 1}\\[0.1cm]
688 Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
689 $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
690 {\color{blue}precipitates}
691 \item \underline{Implantation step 2}\\[0.1cm]
692 Little remaining dose | \unit[180]{keV} | \degc{250}\\
694 Destruction/Amorphization of precipitates at layer interface
695 \item \underline{Annealing}\\[0.1cm]
696 \unit[10]{h} at \degc{1250}\\
697 $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
701 \begin{minipage}{7cm}
702 \includegraphics[width=7cm]{ibs_3c-sic.eps}
704 \begin{minipage}{5cm}
705 \begin{pspicture}(0,0)(0,0)
707 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
708 \begin{minipage}{5.3cm}
711 3C-SiC precipitation\\
712 not yet fully understood
716 \renewcommand\labelitemi{$\Rightarrow$}
717 Details of the SiC precipitation
719 \item significant technological progress\\
720 in SiC thin film formation
721 \item perspectives for processes relying\\
722 upon prevention of SiC precipitation
726 \rput(-6.8,5.4){\pnode{h0}}
727 \rput(-3.0,5.4){\pnode{h1}}
728 \ncline[linecolor=blue]{-}{h0}{h1}
729 \ncline[linecolor=blue]{->}{h1}{box}
739 Supposed precipitation mechanism of SiC in Si
747 \begin{minipage}{3.6cm}
749 Si \& SiC lattice structure\\[0.1cm]
750 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
753 \begin{minipage}{1.7cm}
754 \underline{Silicon}\\
755 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
756 $a=\unit[5.429]{\\A}$\\
757 $\rho^*_{\text{Si}}=\unit[100]{\%}$
759 \begin{minipage}{1.7cm}
760 \underline{Silicon carbide}\\
761 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
762 $a=\unit[4.359]{\\A}$\\
763 $\rho^*_{\text{Si}}=\unit[97]{\%}$
769 \begin{minipage}{4.1cm}
771 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
775 \begin{minipage}{4.0cm}
777 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
783 \begin{minipage}{4.0cm}
785 C-Si dimers (dumbbells)\\[-0.1cm]
786 on Si interstitial sites
790 \begin{minipage}{4.1cm}
792 Agglomeration of C-Si dumbbells\\[-0.1cm]
793 $\Rightarrow$ dark contrasts
797 \begin{minipage}{4.0cm}
799 Precipitation of 3C-SiC in Si\\[-0.1cm]
800 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
801 \& release of Si self-interstitials
807 \begin{minipage}{4.0cm}
809 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
813 \begin{minipage}{4.1cm}
815 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
819 \begin{minipage}{4.0cm}
821 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
825 \begin{pspicture}(0,0)(0,0)
826 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
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828 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
829 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
830 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
831 $4a_{\text{Si}}=5a_{\text{SiC}}$
833 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
834 \hkl(h k l) planes match
836 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
847 Supposed precipitation mechanism of SiC in Si
855 \begin{minipage}{3.6cm}
857 Si \& SiC lattice structure\\[0.1cm]
858 \includegraphics[width=2.3cm]{sic_unit_cell.eps}
861 \begin{minipage}{1.7cm}
862 \underline{Silicon}\\
863 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
864 $a=\unit[5.429]{\\A}$\\
865 $\rho^*_{\text{Si}}=\unit[100]{\%}$
867 \begin{minipage}{1.7cm}
868 \underline{Silicon carbide}\\
869 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
870 $a=\unit[4.359]{\\A}$\\
871 $\rho^*_{\text{Si}}=\unit[97]{\%}$
877 \begin{minipage}{4.1cm}
879 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
883 \begin{minipage}{4.0cm}
885 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
891 \begin{minipage}{4.0cm}
893 C-Si dimers (dumbbells)\\[-0.1cm]
894 on Si interstitial sites
898 \begin{minipage}{4.1cm}
900 Agglomeration of C-Si dumbbells\\[-0.1cm]
901 $\Rightarrow$ dark contrasts
905 \begin{minipage}{4.0cm}
907 Precipitation of 3C-SiC in Si\\[-0.1cm]
908 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
909 \& release of Si self-interstitials
915 \begin{minipage}{4.0cm}
917 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
921 \begin{minipage}{4.1cm}
923 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
927 \begin{minipage}{4.0cm}
929 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
933 \begin{pspicture}(0,0)(0,0)
934 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
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936 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
937 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
938 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
939 $4a_{\text{Si}}=5a_{\text{SiC}}$
941 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
942 \hkl(h k l) planes match
944 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
947 % controversial view!
948 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
949 \begin{minipage}{14cm}
954 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
955 \begin{minipage}{10cm}
959 {\color{gray}\bf Controversial findings}
962 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
964 \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
965 \item \si{} reacting with further C in cleared volume
967 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
969 \item Room temperature implantation $\rightarrow$ high C diffusion
970 \item Elevated temperature implantation $\rightarrow$ no C redistribution
972 $\Rightarrow$ mobile {\color{red}\ci} opposed to
973 stable {\color{blue}\cs{}} configurations
974 \item Strained silicon \& Si/SiC heterostructures
975 {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
977 \item {\color{blue}Coherent} SiC precipitates (tensile strain)
978 \item Incoherent SiC (strain relaxation)
983 {\Huge${\lightning}$} \hspace{0.3cm}
984 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
985 {\Huge${\lightning}$}
1001 Utilized computational methods
1008 {\bf Molecular dynamics (MD)}\\
1010 \begin{tabular}{p{4.5cm} p{7.5cm}}
1014 System of $N$ particles &
1015 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
1017 Phase space propagation &
1018 Velocity Verlet | timestep: \unit[1]{fs} \\
1020 Analytical interaction potential &
1021 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
1024 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
1025 \pot_{ij} = {\color{red}f_C(r_{ij})}
1026 \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
1029 %\multicolumn{2}{c}{}\\
1030 Observables: time/ensemble averages &
1031 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
1033 %\item Berendsen thermostat:
1034 % $\tau_{\text{T}}=100\text{ fs}$
1035 %\item Berendsen barostat:\\
1036 % $\tau_{\text{P}}=100\text{ fs}$,
1037 % $\beta^{-1}=100\text{ GPa}$
1046 {\bf Density functional theory (DFT)}
1050 \begin{minipage}[t]{6cm}
1053 \item Born-Oppenheimer approximation:\\
1054 Decouple electronic \& ionic motion
1055 \item Hohenberg-Kohn theorem:\\
1056 $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$
1057 $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$}
1061 \item Code: \textsc{vasp}
1062 \item Plane wave basis set $\{\phi_j\}$\\[0.1cm]
1064 \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r)
1067 E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
1069 \item Ultrasoft pseudopotential
1070 \item Brillouin zone sampling: $\Gamma$-point
1073 \begin{minipage}[t]{6cm}
1085 Density functional theory (DFT) calculations
1088 Basic ingredients necessary for DFT
1091 \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
1093 \item ... uniquely determines the ground state potential
1095 \item ... minimizes the systems total energy
1097 \item \underline{Born-Oppenheimer}
1098 - $N$ moving electrons in an external potential of static nuclei
1100 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
1101 +\sum_i^N V_{\text{ext}}(r_i)
1102 +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
1104 \item \underline{Effective potential}
1105 - averaged electrostatic potential \& exchange and correlation
1107 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1108 +V_{\text{XC}}[n(r)]
1110 \item \underline{Kohn-Sham system}
1111 - Schr\"odinger equation of N non-interacting particles
1113 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
1114 =\epsilon_i\Phi_i(r)
1118 n(r)=\sum_i^N|\Phi_i(r)|^2
1120 \item \underline{Self-consistent solution}\\
1121 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
1122 which in turn depends on $n(r)$
1123 \item \underline{Variational principle}
1124 - minimize total energy with respect to $n(r)$
1132 Density functional theory (DFT) calculations
1139 Details of applied DFT calculations in this work
1142 \item \underline{Exchange correlation functional}
1143 - approximations for the inhomogeneous electron gas
1145 \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
1146 \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
1148 \item \underline{Plane wave basis set}
1149 - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
1150 \item \underline{Brillouin zone sampling} -
1151 {\color{blue}$\Gamma$-point only} calculations
1152 \item \underline{Pseudo potential}
1153 - consider only the valence electrons
1154 \item \underline{Code} - VASP 4.6
1159 MD and structural optimization
1162 \item MD integration: Gear predictor corrector algorithm
1163 \item Pressure control: Parrinello-Rahman pressure control
1164 \item Structural optimization: Conjugate gradient method
1167 \begin{pspicture}(0,0)(0,0)
1168 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
1176 C and Si self-interstitial point defects in silicon
1183 \begin{minipage}{8cm}
1185 \begin{pspicture}(0,0)(7,5)
1186 \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1189 \item Creation of c-Si simulation volume
1190 \item Periodic boundary conditions
1191 \item $T=0\text{ K}$, $p=0\text{ bar}$
1194 \rput(3.5,2.1){\rnode{insert}{\psframebox{
1197 Insertion of interstitial C/Si atoms
1200 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1203 Relaxation / structural energy minimization
1206 \ncline[]{->}{init}{insert}
1207 \ncline[]{->}{insert}{cool}
1210 \begin{minipage}{5cm}
1211 \includegraphics[width=5cm]{unit_cell_e.eps}\\
1214 \begin{minipage}{9cm}
1215 \begin{tabular}{l c c}
1217 & size [unit cells] & \# atoms\\
1219 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
1220 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
1224 \begin{minipage}{4cm}
1225 {\color{red}$\bullet$} Tetrahedral\\
1226 {\color{green}$\bullet$} Hexagonal\\
1227 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
1228 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
1229 {\color{cyan}$\bullet$} Bond-centered\\
1230 {\color{black}$\bullet$} Vacancy / Substitutional
1239 \begin{minipage}{9.5cm}
1242 Si self-interstitial point defects in silicon\\
1245 \begin{tabular}{l c c c c c}
1247 $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1249 VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1250 Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1252 \end{tabular}\\[0.2cm]
1254 \begin{minipage}{4.7cm}
1255 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
1257 \begin{minipage}{4.7cm}
1259 {\tiny nearly T $\rightarrow$ T}\\
1261 \includegraphics[width=4.7cm]{nhex_tet.ps}
1264 \underline{Hexagonal} \hspace{2pt}
1265 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1267 \begin{minipage}{2.7cm}
1268 $E_{\text{f}}^*=4.48\text{ eV}$\\
1269 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
1271 \begin{minipage}{0.4cm}
1276 \begin{minipage}{2.7cm}
1277 $E_{\text{f}}=3.96\text{ eV}$\\
1278 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
1281 \begin{minipage}{2.9cm}
1283 \underline{Vacancy}\\
1284 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
1289 \begin{minipage}{3.5cm}
1292 \underline{\hkl<1 1 0> dumbbell}\\
1293 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
1294 \underline{Tetrahedral}\\
1295 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
1296 \underline{\hkl<1 0 0> dumbbell}\\
1297 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
1309 C interstitial point defects in silicon\\[-0.1cm]
1312 \begin{tabular}{l c c c c c c r}
1314 $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
1316 VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1317 Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1319 \end{tabular}\\[0.1cm]
1322 \begin{minipage}{2.7cm}
1323 \underline{Hexagonal} \hspace{2pt}
1324 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1325 $E_{\text{f}}^*=9.05\text{ eV}$\\
1326 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
1328 \begin{minipage}{0.4cm}
1333 \begin{minipage}{2.7cm}
1334 \underline{\hkl<1 0 0>}\\
1335 $E_{\text{f}}=3.88\text{ eV}$\\
1336 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
1339 \begin{minipage}{2cm}
1342 \begin{minipage}{3cm}
1344 \underline{Tetrahedral}\\
1345 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
1350 \begin{minipage}{2.7cm}
1351 \underline{Bond-centered}\\
1352 $E_{\text{f}}^*=5.59\text{ eV}$\\
1353 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
1355 \begin{minipage}{0.4cm}
1360 \begin{minipage}{2.7cm}
1361 \underline{\hkl<1 1 0> dumbbell}\\
1362 $E_{\text{f}}=5.18\text{ eV}$\\
1363 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
1366 \begin{minipage}{2cm}
1369 \begin{minipage}{3cm}
1371 \underline{Substitutional}\\
1372 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
1383 C \hkl<1 0 0> dumbbell interstitial configuration\\
1387 \begin{tabular}{l c c c c c c c c}
1389 Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
1391 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
1392 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
1394 \end{tabular}\\[0.2cm]
1395 \begin{tabular}{l c c c c }
1397 Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
1399 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
1400 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
1402 \end{tabular}\\[0.2cm]
1403 \begin{tabular}{l c c c}
1405 Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
1407 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
1408 VASP & 0.109 & -0.065 & 0.174 \\
1410 \end{tabular}\\[0.6cm]
1413 \begin{minipage}{3.0cm}
1415 \underline{Erhart/Albe}
1416 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
1419 \begin{minipage}{3.0cm}
1422 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
1426 \begin{picture}(0,0)(-185,10)
1427 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
1429 \begin{picture}(0,0)(-280,-150)
1430 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
1433 \begin{pspicture}(0,0)(0,0)
1434 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
1435 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
1436 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
1437 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
1446 \begin{minipage}{8.5cm}
1449 Bond-centered interstitial configuration\\[-0.1cm]
1452 \begin{minipage}{3.0cm}
1453 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1455 \begin{minipage}{5.2cm}
1457 \item Linear Si-C-Si bond
1458 \item Si: one C \& 3 Si neighbours
1459 \item Spin polarized calculations
1460 \item No saddle point!\\
1467 \begin{minipage}[t]{6.5cm}
1468 \begin{minipage}[t]{1.2cm}
1470 {\tiny sp$^3$}\\[0.8cm]
1471 \underline{${\color{black}\uparrow}$}
1472 \underline{${\color{black}\uparrow}$}
1473 \underline{${\color{black}\uparrow}$}
1474 \underline{${\color{red}\uparrow}$}\\
1477 \begin{minipage}[t]{1.4cm}
1479 {\color{red}M}{\color{blue}O}\\[0.8cm]
1480 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1481 $\sigma_{\text{ab}}$\\[0.5cm]
1482 \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1486 \begin{minipage}[t]{1.0cm}
1490 \underline{${\color{white}\uparrow\uparrow}$}
1491 \underline{${\color{white}\uparrow\uparrow}$}\\
1493 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1494 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1498 \begin{minipage}[t]{1.4cm}
1500 {\color{blue}M}{\color{green}O}\\[0.8cm]
1501 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1502 $\sigma_{\text{ab}}$\\[0.5cm]
1503 \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1507 \begin{minipage}[t]{1.2cm}
1510 {\tiny sp$^3$}\\[0.8cm]
1511 \underline{${\color{green}\uparrow}$}
1512 \underline{${\color{black}\uparrow}$}
1513 \underline{${\color{black}\uparrow}$}
1514 \underline{${\color{black}\uparrow}$}\\
1522 \begin{minipage}{4.5cm}
1523 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
1525 \begin{minipage}{3.5cm}
1526 {\color{gray}$\bullet$} Spin up\\
1527 {\color{green}$\bullet$} Spin down\\
1528 {\color{blue}$\bullet$} Resulting spin up\\
1529 {\color{yellow}$\bullet$} Si atoms\\
1530 {\color{red}$\bullet$} C atom
1535 \begin{minipage}{4.2cm}
1537 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
1538 {\color{green}$\Box$} {\tiny unoccupied}\\
1539 {\color{red}$\bullet$} {\tiny occupied}
1548 Migration of the C \hkl<1 0 0> dumbbell interstitial
1553 {\small Investigated pathways}
1555 \begin{minipage}{8.5cm}
1556 \begin{minipage}{8.3cm}
1557 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1558 \begin{minipage}{2.4cm}
1559 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1561 \begin{minipage}{0.4cm}
1564 \begin{minipage}{2.4cm}
1565 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1567 \begin{minipage}{0.4cm}
1570 \begin{minipage}{2.4cm}
1571 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1574 \begin{minipage}{8.3cm}
1575 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1576 \begin{minipage}{2.4cm}
1577 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1579 \begin{minipage}{0.4cm}
1582 \begin{minipage}{2.4cm}
1583 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1585 \begin{minipage}{0.4cm}
1588 \begin{minipage}{2.4cm}
1589 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1592 \begin{minipage}{8.3cm}
1593 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1594 \begin{minipage}{2.4cm}
1595 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1597 \begin{minipage}{0.4cm}
1600 \begin{minipage}{2.4cm}
1601 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1603 \begin{minipage}{0.4cm}
1606 \begin{minipage}{2.4cm}
1607 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1612 \begin{minipage}{4.2cm}
1613 {\small Constrained relaxation\\
1614 technique (CRT) method}\\
1615 \includegraphics[width=4cm]{crt_orig.eps}
1617 \item Constrain diffusing atom
1618 \item Static constraints
1621 {\small Modifications}\\
1622 \includegraphics[width=4cm]{crt_mod.eps}
1624 \item Constrain all atoms
1625 \item Update individual\\
1636 Migration of the C \hkl<1 0 0> dumbbell interstitial
1642 \begin{minipage}{5.9cm}
1644 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1647 \begin{picture}(0,0)(60,0)
1648 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1650 \begin{picture}(0,0)(-5,0)
1651 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1653 \begin{picture}(0,0)(-55,0)
1654 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1656 \begin{picture}(0,0)(12.5,10)
1657 \includegraphics[width=1cm]{110_arrow.eps}
1659 \begin{picture}(0,0)(90,0)
1660 \includegraphics[height=0.9cm]{001_arrow.eps}
1666 \begin{minipage}{0.3cm}
1670 \begin{minipage}{5.9cm}
1672 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1675 \begin{picture}(0,0)(60,0)
1676 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1678 \begin{picture}(0,0)(5,0)
1679 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1681 \begin{picture}(0,0)(-55,0)
1682 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1684 \begin{picture}(0,0)(12.5,10)
1685 \includegraphics[width=1cm]{100_arrow.eps}
1687 \begin{picture}(0,0)(90,0)
1688 \includegraphics[height=0.9cm]{001_arrow.eps}
1698 \begin{minipage}{5.9cm}
1700 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1703 \begin{picture}(0,0)(60,0)
1704 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1706 \begin{picture}(0,0)(10,0)
1707 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1709 \begin{picture}(0,0)(-60,0)
1710 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1712 \begin{picture}(0,0)(12.5,10)
1713 \includegraphics[width=1cm]{100_arrow.eps}
1715 \begin{picture}(0,0)(90,0)
1716 \includegraphics[height=0.9cm]{001_arrow.eps}
1722 \begin{minipage}{0.3cm}
1725 \begin{minipage}{6.5cm}
1728 \item Energetically most favorable path
1731 \item Activation energy: $\approx$ 0.9 eV
1732 \item Experimental values: 0.73 ... 0.87 eV
1734 $\Rightarrow$ {\color{blue}Diffusion} path identified!
1735 \item Reorientation (path 3)
1737 \item More likely composed of two consecutive steps of type 2
1738 \item Experimental values: 0.77 ... 0.88 eV
1740 $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1749 Migration of the C \hkl<1 0 0> dumbbell interstitial
1756 \begin{minipage}{6.5cm}
1759 \begin{minipage}[t]{5.9cm}
1761 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1764 \begin{pspicture}(0,0)(0,0)
1765 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1767 \begin{picture}(0,0)(60,-50)
1768 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1770 \begin{picture}(0,0)(5,-50)
1771 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1773 \begin{picture}(0,0)(-55,-50)
1774 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1776 \begin{picture}(0,0)(12.5,-40)
1777 \includegraphics[width=1cm]{110_arrow.eps}
1779 \begin{picture}(0,0)(90,-45)
1780 \includegraphics[height=0.9cm]{001_arrow.eps}
1782 \begin{pspicture}(0,0)(0,0)
1783 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1785 \begin{picture}(0,0)(60,-15)
1786 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1788 \begin{picture}(0,0)(35,-15)
1789 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1791 \begin{picture}(0,0)(-5,-15)
1792 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1794 \begin{picture}(0,0)(-55,-15)
1795 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1797 \begin{picture}(0,0)(12.5,-5)
1798 \includegraphics[width=1cm]{100_arrow.eps}
1800 \begin{picture}(0,0)(90,-15)
1801 \includegraphics[height=0.9cm]{010_arrow.eps}
1807 \begin{minipage}{5.9cm}
1810 \item Lowest activation energy: $\approx$ 2.2 eV
1811 \item 2.4 times higher than VASP
1812 \item Different pathway
1817 \begin{minipage}{6.5cm}
1820 \begin{minipage}{5.9cm}
1822 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1825 %\begin{pspicture}(0,0)(0,0)
1826 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1828 %\begin{picture}(0,0)(60,-5)
1829 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1831 %\begin{picture}(0,0)(0,-5)
1832 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1834 %\begin{picture}(0,0)(-55,-5)
1835 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1837 %\begin{picture}(0,0)(12.5,5)
1838 %\includegraphics[width=1cm]{100_arrow.eps}
1840 %\begin{picture}(0,0)(90,0)
1841 %\includegraphics[height=0.9cm]{001_arrow.eps}
1849 %\begin{minipage}{5.9cm}
1850 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1854 \begin{minipage}{5.9cm}
1855 Transition involving \ci{} \hkl<1 1 0>
1857 \item Bond-centered configuration unstable\\
1858 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1859 \item Transition minima of path 2 \& 3\\
1860 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1861 \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1862 \item 2.4 - 3.4 times higher than VASP
1863 \item Rotation of dumbbell orientation
1867 {\color{blue}Overestimated diffusion barrier}
1878 Combinations with a C-Si \hkl<1 0 0>-type interstitial
1888 E_{\text{f}}^{\text{defect combination}}-
1889 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1890 E_{\text{f}}^{\text{2nd defect}}
1896 \begin{tabular}{l c c c c c c}
1898 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1900 \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1901 \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1902 \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}\\
1903 \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}\\
1904 \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}\\
1905 \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}\\
1907 C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1908 Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1917 \begin{minipage}[t]{3.8cm}
1918 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1919 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1921 \begin{minipage}[t]{3.5cm}
1922 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1923 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1925 \begin{minipage}[t]{5.5cm}
1927 \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1928 $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1929 \item Stress compensation / increase
1930 \item Unfavored: antiparallel orientations
1931 \item Indication of energetically favored\\
1933 \item Most favorable: C clustering
1934 \item However: High barrier ($>4\,\text{eV}$)
1935 \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1940 \begin{picture}(0,0)(-295,-130)
1941 \includegraphics[width=3.5cm]{comb_pos.eps}
1949 Combinations of C-Si \hkl<1 0 0>-type interstitials
1956 Energetically most favorable combinations along \hkl<1 1 0>
1961 \begin{tabular}{l c c c c c c}
1963 & 1 & 2 & 3 & 4 & 5 & 6\\
1965 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1966 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1967 Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\
1974 \begin{minipage}{7.0cm}
1975 \includegraphics[width=7cm]{db_along_110_cc.ps}
1977 \begin{minipage}{6.0cm}
1979 \item Interaction proportional to reciprocal cube of C-C distance
1980 \item Saturation in the immediate vicinity
1981 \renewcommand\labelitemi{$\Rightarrow$}
1982 \item Agglomeration of \ci{} expected
1983 \item Absence of C clustering
1987 Consisten with initial precipitation model
1999 Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
2005 %\begin{minipage}{3.2cm}
2006 %\includegraphics[width=3cm]{sub_110_combo.eps}
2008 %\begin{minipage}{7.8cm}
2009 %\begin{tabular}{l c c c c c c}
2011 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
2012 % \hkl<1 0 1> & \hkl<-1 0 1> \\
2014 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
2015 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
2016 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
2017 %4 & \RM{4} & B & D & E & E & D \\
2018 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
2025 %\begin{tabular}{l c c c c c c c c c c}
2027 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
2029 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
2030 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
2031 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
2036 \begin{minipage}{6.0cm}
2037 \includegraphics[width=5.8cm]{c_sub_si110.ps}
2039 \begin{minipage}{7cm}
2042 \item IBS: C may displace Si\\
2043 $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
2045 \hkl<1 1 0>-type $\rightarrow$ favored combination
2046 \renewcommand\labelitemi{$\Rightarrow$}
2047 \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
2048 \item Less favorable than C-Si \hkl<1 0 0> dumbbell
2049 \item Interaction drops quickly to zero\\
2050 $\rightarrow$ low capture radius
2054 IBS process far from equilibrium\\
2055 \cs{} \& \si{} instead of thermodynamic ground state
2060 \begin{minipage}{6.5cm}
2061 \includegraphics[width=6.0cm]{162-097.ps}
2063 \item Low migration barrier
2066 \begin{minipage}{6.5cm}
2068 Ab initio MD at \degc{900}\\
2069 \includegraphics[width=3.3cm]{md_vasp_01.eps}
2070 $t=\unit[2230]{fs}$\\
2071 \includegraphics[width=3.3cm]{md_vasp_02.eps}
2075 Contribution of entropy to structural formation
2084 Migration in C-Si \hkl<1 0 0> and vacancy combinations
2091 \begin{minipage}[t]{3cm}
2092 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
2093 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
2095 \begin{minipage}[t]{7cm}
2098 Low activation energies\\
2099 High activation energies for reverse processes\\
2101 {\color{blue}C$_{\text{sub}}$ very stable}\\
2105 Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
2107 {\color{blue}Formation of SiC by successive substitution by C}
2111 \begin{minipage}[t]{3cm}
2112 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
2113 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
2118 \begin{minipage}{5.9cm}
2119 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
2121 \begin{picture}(0,0)(70,0)
2122 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
2124 \begin{picture}(0,0)(30,0)
2125 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
2127 \begin{picture}(0,0)(-10,0)
2128 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
2130 \begin{picture}(0,0)(-48,0)
2131 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
2133 \begin{picture}(0,0)(12.5,5)
2134 \includegraphics[width=1cm]{100_arrow.eps}
2136 \begin{picture}(0,0)(97,-10)
2137 \includegraphics[height=0.9cm]{001_arrow.eps}
2143 \begin{minipage}{0.3cm}
2147 \begin{minipage}{5.9cm}
2148 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
2150 \begin{picture}(0,0)(60,0)
2151 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2153 \begin{picture}(0,0)(25,0)
2154 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2156 \begin{picture}(0,0)(-20,0)
2157 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2159 \begin{picture}(0,0)(-55,0)
2160 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2162 \begin{picture}(0,0)(12.5,5)
2163 \includegraphics[width=1cm]{100_arrow.eps}
2165 \begin{picture}(0,0)(95,0)
2166 \includegraphics[height=0.9cm]{001_arrow.eps}
2178 Conclusion of defect / migration / combined defect simulations
2187 \item Accurately described by quantum-mechanical simulations
2188 \item Less accurate description by classical potential simulations
2189 \item Underestimated formation energy of \cs{} by classical approach
2190 \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2195 \item C migration pathway in Si identified
2196 \item Consistent with reorientation and diffusion experiments
2199 \item Different path and ...
2200 \item overestimated barrier by classical potential calculations
2203 Concerning the precipitation mechanism
2205 \item Agglomeration of C-Si dumbbells energetically favorable
2206 (stress compensation)
2207 \item C-Si indeed favored compared to
2208 C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2209 \item Possible low interaction capture radius of
2210 C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2211 \item Low barrier for
2212 \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2213 \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2214 C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2217 {\color{blue}Results suggest increased participation of \cs}
2225 Silicon carbide precipitation simulations
2231 \begin{pspicture}(0,0)(12,6.5)
2233 \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2236 \item Create c-Si volume
2237 \item Periodc boundary conditions
2238 \item Set requested $T$ and $p=0\text{ bar}$
2239 \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2242 \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2244 Insertion of C atoms at constant T
2246 \item total simulation volume {\pnode{in1}}
2247 \item volume of minimal SiC precipitate {\pnode{in2}}
2248 \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2252 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2254 Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2256 \ncline[]{->}{init}{insert}
2257 \ncline[]{->}{insert}{cool}
2258 \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2259 \rput(7.8,6){\footnotesize $V_1$}
2260 \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2261 \rput(9.2,4.85){\tiny $V_2$}
2262 \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2263 \rput(9.55,4.45){\footnotesize $V_3$}
2264 \rput(7.9,3.2){\pnode{ins1}}
2265 \rput(9.22,2.8){\pnode{ins2}}
2266 \rput(11.0,2.4){\pnode{ins3}}
2267 \ncline[]{->}{in1}{ins1}
2268 \ncline[]{->}{in2}{ins2}
2269 \ncline[]{->}{in3}{ins3}
2274 \item Restricted to classical potential simulations
2275 \item $V_2$ and $V_3$ considered due to low diffusion
2276 \item Amount of C atoms: 6000
2277 ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2278 \item Simulation volume: $31\times 31\times 31$ unit cells
2287 Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2292 \begin{minipage}{6.5cm}
2293 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2295 \begin{minipage}{6.5cm}
2296 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2299 \begin{minipage}{6.5cm}
2300 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2302 \begin{minipage}{6.5cm}
2304 \underline{Low C concentration ($V_1$)}\\
2305 \hkl<1 0 0> C-Si dumbbell dominated structure
2307 \item Si-C bumbs around 0.19 nm
2308 \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2309 concatenated dumbbells of various orientation
2310 \item Si-Si NN distance stretched to 0.3 nm
2312 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2313 \underline{High C concentration ($V_2$, $V_3$)}\\
2314 High amount of strongly bound C-C bonds\\
2315 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2316 Only short range order observable\\
2317 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2325 Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2330 \begin{minipage}{6.5cm}
2331 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2333 \begin{minipage}{6.5cm}
2334 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2337 \begin{minipage}{6.5cm}
2338 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2340 \begin{minipage}{6.5cm}
2342 \underline{Low C concentration ($V_1$)}\\
2343 \hkl<1 0 0> C-Si dumbbell dominated structure
2345 \item Si-C bumbs around 0.19 nm
2346 \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2347 concatenated dumbbells of various orientation
2348 \item Si-Si NN distance stretched to 0.3 nm
2350 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2351 \underline{High C concentration ($V_2$, $V_3$)}\\
2352 High amount of strongly bound C-C bonds\\
2353 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2354 Only short range order observable\\
2355 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2358 \begin{pspicture}(0,0)(0,0)
2359 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2360 \begin{minipage}{10cm}
2362 {\color{red}\bf 3C-SiC formation fails to appear}
2364 \item Low C concentration simulations
2366 \item Formation of \ci{} indeed occurs
2367 \item Agllomeration not observed
2369 \item High C concentration simulations
2371 \item Amorphous SiC-like structure\\
2372 (not expected at prevailing temperatures)
2373 \item Rearrangement and transition into 3C-SiC structure missing
2385 Limitations of molecular dynamics and short range potentials
2392 \underline{Time scale problem of MD}\\[0.2cm]
2393 Minimize integration error\\
2394 $\Rightarrow$ discretization considerably smaller than
2395 reciprocal of fastest vibrational mode\\[0.1cm]
2396 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2397 $\Rightarrow$ suitable choice of time step:
2398 $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2399 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2400 Several local minima in energy surface separated by large energy barriers\\
2401 $\Rightarrow$ transition event corresponds to a multiple
2402 of vibrational periods\\
2403 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2404 infrequent transition events\\[0.1cm]
2405 {\color{blue}Accelerated methods:}
2406 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2410 \underline{Limitations related to the short range potential}\\[0.2cm]
2411 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2412 and 2$^{\text{nd}}$ next neighbours\\
2413 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2419 Potential enhanced problem of slow phase space propagation
2424 \underline{Approach to the (twofold) problem}\\[0.2cm]
2425 Increased temperature simulations without TAD corrections\\
2426 (accelerated methods or higher time scales exclusively not sufficient)
2428 \begin{picture}(0,0)(-260,-30)
2430 \begin{minipage}{4.2cm}
2437 \item 3C-SiC also observed for higher T
2438 \item higher T inside sample
2439 \item structural evolution vs.\\
2440 equilibrium properties
2446 \begin{picture}(0,0)(-305,-155)
2448 \begin{minipage}{2.5cm}
2452 thermodynmic sampling
2463 Increased temperature simulations at low C concentration
2468 \begin{minipage}{6.5cm}
2469 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2471 \begin{minipage}{6.5cm}
2472 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2475 \begin{minipage}{6.5cm}
2476 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2478 \begin{minipage}{6.5cm}
2480 \underline{Si-C bonds:}
2482 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2483 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2485 \underline{Si-Si bonds:}
2486 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2487 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2488 \underline{C-C bonds:}
2490 \item C-C next neighbour pairs reduced (mandatory)
2491 \item Peak at 0.3 nm slightly shifted
2493 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2494 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2496 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2498 \item Range [|-$\downarrow$]:
2499 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2500 with nearby Si$_{\text{I}}$}
2505 \begin{picture}(0,0)(-330,-74)
2508 \begin{minipage}{1.6cm}
2511 stretched SiC\\[-0.1cm]
2523 Increased temperature simulations at low C concentration
2528 \begin{minipage}{6.5cm}
2529 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2531 \begin{minipage}{6.5cm}
2532 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2535 \begin{minipage}{6.5cm}
2536 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2538 \begin{minipage}{6.5cm}
2540 \underline{Si-C bonds:}
2542 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2543 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2545 \underline{Si-Si bonds:}
2546 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2547 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2548 \underline{C-C bonds:}
2550 \item C-C next neighbour pairs reduced (mandatory)
2551 \item Peak at 0.3 nm slightly shifted
2553 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2554 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2556 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2558 \item Range [|-$\downarrow$]:
2559 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2560 with nearby Si$_{\text{I}}$}
2565 %\begin{picture}(0,0)(-330,-74)
2568 %\begin{minipage}{1.6cm}
2571 %stretched SiC\\[-0.1cm]
2578 \begin{pspicture}(0,0)(0,0)
2579 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2580 \begin{minipage}{10cm}
2582 {\color{blue}\bf Stretched SiC in c-Si}
2584 \item Consistent to precipitation model involving \cs{}
2585 \item Explains annealing behavior of high/low T C implants
2587 \item Low T: highly mobiel \ci{}
2588 \item High T: stable configurations of \cs{}
2591 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2592 $\Rightarrow$ Precipitation mechanism involving \cs{}
2602 Increased temperature simulations at high C concentration
2607 \begin{minipage}{6.5cm}
2608 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2610 \begin{minipage}{6.5cm}
2611 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2619 \begin{minipage}[t]{6.0cm}
2620 0.186 nm: Si-C pairs $\uparrow$\\
2621 (as expected in 3C-SiC)\\[0.2cm]
2622 0.282 nm: Si-C-C\\[0.2cm]
2623 $\approx$0.35 nm: C-Si-Si
2626 \begin{minipage}{0.2cm}
2630 \begin{minipage}[t]{6.0cm}
2631 0.15 nm: C-C pairs $\uparrow$\\
2632 (as expected in graphite/diamond)\\[0.2cm]
2633 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2634 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2639 \item Decreasing cut-off artifact
2640 \item {\color{red}Amorphous} SiC-like phase remains
2641 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2642 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2651 High C \& small $V$ \& short $t$
2654 Slow restructuring due to strong C-C bonds
2657 High C \& low T implants
2668 Summary and Conclusions
2676 \begin{minipage}[t]{12.9cm}
2677 \underline{Pecipitation simulations}
2679 \item High C concentration $\rightarrow$ amorphous SiC like phase
2680 \item Problem of potential enhanced slow phase space propagation
2681 \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2682 \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2683 \item High T necessary to simulate IBS conditions (far from equilibrium)
2684 \item Precipitation by successive agglomeration of \cs (epitaxy)
2685 \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2686 (stretched SiC, interface)
2694 \begin{minipage}{12.9cm}
2699 \item Point defects excellently / fairly well described
2701 \item C$_{\text{sub}}$ drastically underestimated by EA
2702 \item EA predicts correct ground state:
2703 C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2704 \item Identified migration path explaining
2705 diffusion and reorientation experiments by DFT
2706 \item EA fails to describe \ci{} migration:
2707 Wrong path \& overestimated barrier
2709 \item Combinations of defects
2711 \item Agglomeration of point defects energetically favorable
2712 by compensation of stress
2713 \item Formation of C-C unlikely
2714 \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2715 \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2716 Low barrier (\unit[0.77]{eV}) \& low capture radius
2724 \framebox{Precipitation by successive agglomeration of \cs{}}
2742 \underline{Augsburg}
2744 \item Prof. B. Stritzker (accomodation at EP \RM{4})
2745 \item Ralf Utermann (EDV)
2748 \underline{Helsinki}
2750 \item Prof. K. Nordlund (MD)
2755 \item Bayerische Forschungsstiftung (financial support)
2758 \underline{Paderborn}
2760 \item Prof. J. Lindner (SiC)
2761 \item Prof. G. Schmidt (DFT + financial support)
2762 \item Dr. E. Rauls (DFT + SiC)
2763 \item Dr. S. Sanna (VASP)
2770 \bf Thank you for your attention!