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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
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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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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{5cm}|p{7cm}}
1014 Microscopic description of N particle system & \\
1015 \multicolumn{2}{c}{}\\
1016 Numerical integration using Newtons equation of motion as a propagation rule in 6N-dimensional phase space & Velocity Verlet | timestep: \unit[1]{fs} \\
1017 \multicolumn{2}{c}{}\\
1018 Analytical interaction potential & Tersoff-like bond order potential (Erhart/Albe) \\
1019 \multicolumn{2}{c}{}\\
1020 Observables obtained by time and/or ensemble averages & NpT (isothermal-isobaric)\\
1022 %\item Berendsen thermostat:
1023 % $\tau_{\text{T}}=100\text{ fs}$
1024 %\item Berendsen barostat:\\
1025 % $\tau_{\text{P}}=100\text{ fs}$,
1026 % $\beta^{-1}=100\text{ GPa}$
1032 \item Microscopic description of N particle system
1033 \item Analytical interaction potential
1034 \item Numerical integration using Newtons equation of motion\\
1035 as a propagation rule in 6N-dimensional phase space
1036 \item Observables obtained by time and/or ensemble averages
1038 {\bf Details of the simulation:}
1040 \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
1041 \item Ensemble: NpT (isothermal-isobaric)
1043 \item Berendsen thermostat:
1044 $\tau_{\text{T}}=100\text{ fs}$
1045 \item Berendsen barostat:\\
1046 $\tau_{\text{P}}=100\text{ fs}$,
1047 $\beta^{-1}=100\text{ GPa}$
1049 \item Erhart/Albe potential: Tersoff-like bond order potential
1052 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
1053 \pot_{ij} = {\color{red}f_C(r_{ij})}
1054 \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
1058 \begin{picture}(0,0)(-230,-30)
1059 \includegraphics[width=5cm]{tersoff_angle.eps}
1070 Density functional theory (DFT) calculations
1075 Basic ingredients necessary for DFT
1078 \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
1080 \item ... uniquely determines the ground state potential
1082 \item ... minimizes the systems total energy
1084 \item \underline{Born-Oppenheimer}
1085 - $N$ moving electrons in an external potential of static nuclei
1087 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
1088 +\sum_i^N V_{\text{ext}}(r_i)
1089 +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
1091 \item \underline{Effective potential}
1092 - averaged electrostatic potential \& exchange and correlation
1094 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1095 +V_{\text{XC}}[n(r)]
1097 \item \underline{Kohn-Sham system}
1098 - Schr\"odinger equation of N non-interacting particles
1100 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
1101 =\epsilon_i\Phi_i(r)
1105 n(r)=\sum_i^N|\Phi_i(r)|^2
1107 \item \underline{Self-consistent solution}\\
1108 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
1109 which in turn depends on $n(r)$
1110 \item \underline{Variational principle}
1111 - minimize total energy with respect to $n(r)$
1119 Density functional theory (DFT) calculations
1126 Details of applied DFT calculations in this work
1129 \item \underline{Exchange correlation functional}
1130 - approximations for the inhomogeneous electron gas
1132 \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
1133 \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
1135 \item \underline{Plane wave basis set}
1136 - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
1139 \text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
1140 \qquad ({\color{blue}300\text{ eV}})
1142 \item \underline{Brillouin zone sampling} -
1143 {\color{blue}$\Gamma$-point only} calculations
1144 \item \underline{Pseudo potential}
1145 - consider only the valence electrons
1146 \item \underline{Code} - VASP 4.6
1151 MD and structural optimization
1154 \item MD integration: Gear predictor corrector algorithm
1155 \item Pressure control: Parrinello-Rahman pressure control
1156 \item Structural optimization: Conjugate gradient method
1159 \begin{pspicture}(0,0)(0,0)
1160 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
1168 C and Si self-interstitial point defects in silicon
1175 \begin{minipage}{8cm}
1177 \begin{pspicture}(0,0)(7,5)
1178 \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1181 \item Creation of c-Si simulation volume
1182 \item Periodic boundary conditions
1183 \item $T=0\text{ K}$, $p=0\text{ bar}$
1186 \rput(3.5,2.1){\rnode{insert}{\psframebox{
1189 Insertion of interstitial C/Si atoms
1192 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1195 Relaxation / structural energy minimization
1198 \ncline[]{->}{init}{insert}
1199 \ncline[]{->}{insert}{cool}
1202 \begin{minipage}{5cm}
1203 \includegraphics[width=5cm]{unit_cell_e.eps}\\
1206 \begin{minipage}{9cm}
1207 \begin{tabular}{l c c}
1209 & size [unit cells] & \# atoms\\
1211 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
1212 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
1216 \begin{minipage}{4cm}
1217 {\color{red}$\bullet$} Tetrahedral\\
1218 {\color{green}$\bullet$} Hexagonal\\
1219 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
1220 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
1221 {\color{cyan}$\bullet$} Bond-centered\\
1222 {\color{black}$\bullet$} Vacancy / Substitutional
1231 \begin{minipage}{9.5cm}
1234 Si self-interstitial point defects in silicon\\
1237 \begin{tabular}{l c c c c c}
1239 $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1241 VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1242 Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1244 \end{tabular}\\[0.2cm]
1246 \begin{minipage}{4.7cm}
1247 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
1249 \begin{minipage}{4.7cm}
1251 {\tiny nearly T $\rightarrow$ T}\\
1253 \includegraphics[width=4.7cm]{nhex_tet.ps}
1256 \underline{Hexagonal} \hspace{2pt}
1257 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1259 \begin{minipage}{2.7cm}
1260 $E_{\text{f}}^*=4.48\text{ eV}$\\
1261 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
1263 \begin{minipage}{0.4cm}
1268 \begin{minipage}{2.7cm}
1269 $E_{\text{f}}=3.96\text{ eV}$\\
1270 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
1273 \begin{minipage}{2.9cm}
1275 \underline{Vacancy}\\
1276 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
1281 \begin{minipage}{3.5cm}
1284 \underline{\hkl<1 1 0> dumbbell}\\
1285 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
1286 \underline{Tetrahedral}\\
1287 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
1288 \underline{\hkl<1 0 0> dumbbell}\\
1289 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
1301 C interstitial point defects in silicon\\[-0.1cm]
1304 \begin{tabular}{l c c c c c c r}
1306 $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
1308 VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1309 Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1311 \end{tabular}\\[0.1cm]
1314 \begin{minipage}{2.7cm}
1315 \underline{Hexagonal} \hspace{2pt}
1316 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1317 $E_{\text{f}}^*=9.05\text{ eV}$\\
1318 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
1320 \begin{minipage}{0.4cm}
1325 \begin{minipage}{2.7cm}
1326 \underline{\hkl<1 0 0>}\\
1327 $E_{\text{f}}=3.88\text{ eV}$\\
1328 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
1331 \begin{minipage}{2cm}
1334 \begin{minipage}{3cm}
1336 \underline{Tetrahedral}\\
1337 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
1342 \begin{minipage}{2.7cm}
1343 \underline{Bond-centered}\\
1344 $E_{\text{f}}^*=5.59\text{ eV}$\\
1345 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
1347 \begin{minipage}{0.4cm}
1352 \begin{minipage}{2.7cm}
1353 \underline{\hkl<1 1 0> dumbbell}\\
1354 $E_{\text{f}}=5.18\text{ eV}$\\
1355 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
1358 \begin{minipage}{2cm}
1361 \begin{minipage}{3cm}
1363 \underline{Substitutional}\\
1364 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
1375 C \hkl<1 0 0> dumbbell interstitial configuration\\
1379 \begin{tabular}{l c c c c c c c c}
1381 Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
1383 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
1384 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
1386 \end{tabular}\\[0.2cm]
1387 \begin{tabular}{l c c c c }
1389 Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
1391 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
1392 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
1394 \end{tabular}\\[0.2cm]
1395 \begin{tabular}{l c c c}
1397 Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
1399 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
1400 VASP & 0.109 & -0.065 & 0.174 \\
1402 \end{tabular}\\[0.6cm]
1405 \begin{minipage}{3.0cm}
1407 \underline{Erhart/Albe}
1408 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
1411 \begin{minipage}{3.0cm}
1414 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
1418 \begin{picture}(0,0)(-185,10)
1419 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
1421 \begin{picture}(0,0)(-280,-150)
1422 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
1425 \begin{pspicture}(0,0)(0,0)
1426 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
1427 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
1428 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
1429 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
1438 \begin{minipage}{8.5cm}
1441 Bond-centered interstitial configuration\\[-0.1cm]
1444 \begin{minipage}{3.0cm}
1445 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1447 \begin{minipage}{5.2cm}
1449 \item Linear Si-C-Si bond
1450 \item Si: one C \& 3 Si neighbours
1451 \item Spin polarized calculations
1452 \item No saddle point!\\
1459 \begin{minipage}[t]{6.5cm}
1460 \begin{minipage}[t]{1.2cm}
1462 {\tiny sp$^3$}\\[0.8cm]
1463 \underline{${\color{black}\uparrow}$}
1464 \underline{${\color{black}\uparrow}$}
1465 \underline{${\color{black}\uparrow}$}
1466 \underline{${\color{red}\uparrow}$}\\
1469 \begin{minipage}[t]{1.4cm}
1471 {\color{red}M}{\color{blue}O}\\[0.8cm]
1472 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1473 $\sigma_{\text{ab}}$\\[0.5cm]
1474 \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1478 \begin{minipage}[t]{1.0cm}
1482 \underline{${\color{white}\uparrow\uparrow}$}
1483 \underline{${\color{white}\uparrow\uparrow}$}\\
1485 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1486 \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1490 \begin{minipage}[t]{1.4cm}
1492 {\color{blue}M}{\color{green}O}\\[0.8cm]
1493 \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1494 $\sigma_{\text{ab}}$\\[0.5cm]
1495 \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1499 \begin{minipage}[t]{1.2cm}
1502 {\tiny sp$^3$}\\[0.8cm]
1503 \underline{${\color{green}\uparrow}$}
1504 \underline{${\color{black}\uparrow}$}
1505 \underline{${\color{black}\uparrow}$}
1506 \underline{${\color{black}\uparrow}$}\\
1514 \begin{minipage}{4.5cm}
1515 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
1517 \begin{minipage}{3.5cm}
1518 {\color{gray}$\bullet$} Spin up\\
1519 {\color{green}$\bullet$} Spin down\\
1520 {\color{blue}$\bullet$} Resulting spin up\\
1521 {\color{yellow}$\bullet$} Si atoms\\
1522 {\color{red}$\bullet$} C atom
1527 \begin{minipage}{4.2cm}
1529 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
1530 {\color{green}$\Box$} {\tiny unoccupied}\\
1531 {\color{red}$\bullet$} {\tiny occupied}
1540 Migration of the C \hkl<1 0 0> dumbbell interstitial
1545 {\small Investigated pathways}
1547 \begin{minipage}{8.5cm}
1548 \begin{minipage}{8.3cm}
1549 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1550 \begin{minipage}{2.4cm}
1551 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1553 \begin{minipage}{0.4cm}
1556 \begin{minipage}{2.4cm}
1557 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1559 \begin{minipage}{0.4cm}
1562 \begin{minipage}{2.4cm}
1563 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1566 \begin{minipage}{8.3cm}
1567 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1568 \begin{minipage}{2.4cm}
1569 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1571 \begin{minipage}{0.4cm}
1574 \begin{minipage}{2.4cm}
1575 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1577 \begin{minipage}{0.4cm}
1580 \begin{minipage}{2.4cm}
1581 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1584 \begin{minipage}{8.3cm}
1585 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1586 \begin{minipage}{2.4cm}
1587 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1589 \begin{minipage}{0.4cm}
1592 \begin{minipage}{2.4cm}
1593 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1595 \begin{minipage}{0.4cm}
1598 \begin{minipage}{2.4cm}
1599 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1604 \begin{minipage}{4.2cm}
1605 {\small Constrained relaxation\\
1606 technique (CRT) method}\\
1607 \includegraphics[width=4cm]{crt_orig.eps}
1609 \item Constrain diffusing atom
1610 \item Static constraints
1613 {\small Modifications}\\
1614 \includegraphics[width=4cm]{crt_mod.eps}
1616 \item Constrain all atoms
1617 \item Update individual\\
1628 Migration of the C \hkl<1 0 0> dumbbell interstitial
1634 \begin{minipage}{5.9cm}
1636 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1639 \begin{picture}(0,0)(60,0)
1640 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1642 \begin{picture}(0,0)(-5,0)
1643 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1645 \begin{picture}(0,0)(-55,0)
1646 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1648 \begin{picture}(0,0)(12.5,10)
1649 \includegraphics[width=1cm]{110_arrow.eps}
1651 \begin{picture}(0,0)(90,0)
1652 \includegraphics[height=0.9cm]{001_arrow.eps}
1658 \begin{minipage}{0.3cm}
1662 \begin{minipage}{5.9cm}
1664 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1667 \begin{picture}(0,0)(60,0)
1668 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1670 \begin{picture}(0,0)(5,0)
1671 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1673 \begin{picture}(0,0)(-55,0)
1674 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1676 \begin{picture}(0,0)(12.5,10)
1677 \includegraphics[width=1cm]{100_arrow.eps}
1679 \begin{picture}(0,0)(90,0)
1680 \includegraphics[height=0.9cm]{001_arrow.eps}
1690 \begin{minipage}{5.9cm}
1692 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1695 \begin{picture}(0,0)(60,0)
1696 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1698 \begin{picture}(0,0)(10,0)
1699 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1701 \begin{picture}(0,0)(-60,0)
1702 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1704 \begin{picture}(0,0)(12.5,10)
1705 \includegraphics[width=1cm]{100_arrow.eps}
1707 \begin{picture}(0,0)(90,0)
1708 \includegraphics[height=0.9cm]{001_arrow.eps}
1714 \begin{minipage}{0.3cm}
1717 \begin{minipage}{6.5cm}
1720 \item Energetically most favorable path
1723 \item Activation energy: $\approx$ 0.9 eV
1724 \item Experimental values: 0.73 ... 0.87 eV
1726 $\Rightarrow$ {\color{blue}Diffusion} path identified!
1727 \item Reorientation (path 3)
1729 \item More likely composed of two consecutive steps of type 2
1730 \item Experimental values: 0.77 ... 0.88 eV
1732 $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1741 Migration of the C \hkl<1 0 0> dumbbell interstitial
1748 \begin{minipage}{6.5cm}
1751 \begin{minipage}[t]{5.9cm}
1753 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1756 \begin{pspicture}(0,0)(0,0)
1757 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1759 \begin{picture}(0,0)(60,-50)
1760 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1762 \begin{picture}(0,0)(5,-50)
1763 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1765 \begin{picture}(0,0)(-55,-50)
1766 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1768 \begin{picture}(0,0)(12.5,-40)
1769 \includegraphics[width=1cm]{110_arrow.eps}
1771 \begin{picture}(0,0)(90,-45)
1772 \includegraphics[height=0.9cm]{001_arrow.eps}
1774 \begin{pspicture}(0,0)(0,0)
1775 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1777 \begin{picture}(0,0)(60,-15)
1778 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1780 \begin{picture}(0,0)(35,-15)
1781 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1783 \begin{picture}(0,0)(-5,-15)
1784 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1786 \begin{picture}(0,0)(-55,-15)
1787 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1789 \begin{picture}(0,0)(12.5,-5)
1790 \includegraphics[width=1cm]{100_arrow.eps}
1792 \begin{picture}(0,0)(90,-15)
1793 \includegraphics[height=0.9cm]{010_arrow.eps}
1799 \begin{minipage}{5.9cm}
1802 \item Lowest activation energy: $\approx$ 2.2 eV
1803 \item 2.4 times higher than VASP
1804 \item Different pathway
1809 \begin{minipage}{6.5cm}
1812 \begin{minipage}{5.9cm}
1814 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1817 %\begin{pspicture}(0,0)(0,0)
1818 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1820 %\begin{picture}(0,0)(60,-5)
1821 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1823 %\begin{picture}(0,0)(0,-5)
1824 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1826 %\begin{picture}(0,0)(-55,-5)
1827 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1829 %\begin{picture}(0,0)(12.5,5)
1830 %\includegraphics[width=1cm]{100_arrow.eps}
1832 %\begin{picture}(0,0)(90,0)
1833 %\includegraphics[height=0.9cm]{001_arrow.eps}
1841 %\begin{minipage}{5.9cm}
1842 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1846 \begin{minipage}{5.9cm}
1847 Transition involving \ci{} \hkl<1 1 0>
1849 \item Bond-centered configuration unstable\\
1850 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1851 \item Transition minima of path 2 \& 3\\
1852 $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1853 \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1854 \item 2.4 - 3.4 times higher than VASP
1855 \item Rotation of dumbbell orientation
1859 {\color{blue}Overestimated diffusion barrier}
1870 Combinations with a C-Si \hkl<1 0 0>-type interstitial
1880 E_{\text{f}}^{\text{defect combination}}-
1881 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1882 E_{\text{f}}^{\text{2nd defect}}
1888 \begin{tabular}{l c c c c c c}
1890 $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1892 \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1893 \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1894 \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}\\
1895 \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}\\
1896 \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}\\
1897 \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}\\
1899 C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1900 Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1909 \begin{minipage}[t]{3.8cm}
1910 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1911 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1913 \begin{minipage}[t]{3.5cm}
1914 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1915 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1917 \begin{minipage}[t]{5.5cm}
1919 \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1920 $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1921 \item Stress compensation / increase
1922 \item Unfavored: antiparallel orientations
1923 \item Indication of energetically favored\\
1925 \item Most favorable: C clustering
1926 \item However: High barrier ($>4\,\text{eV}$)
1927 \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1932 \begin{picture}(0,0)(-295,-130)
1933 \includegraphics[width=3.5cm]{comb_pos.eps}
1941 Combinations of C-Si \hkl<1 0 0>-type interstitials
1948 Energetically most favorable combinations along \hkl<1 1 0>
1953 \begin{tabular}{l c c c c c c}
1955 & 1 & 2 & 3 & 4 & 5 & 6\\
1957 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1958 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1959 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>\\
1966 \begin{minipage}{7.0cm}
1967 \includegraphics[width=7cm]{db_along_110_cc.ps}
1969 \begin{minipage}{6.0cm}
1971 \item Interaction proportional to reciprocal cube of C-C distance
1972 \item Saturation in the immediate vicinity
1973 \renewcommand\labelitemi{$\Rightarrow$}
1974 \item Agglomeration of \ci{} expected
1975 \item Absence of C clustering
1979 Consisten with initial precipitation model
1991 Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1997 %\begin{minipage}{3.2cm}
1998 %\includegraphics[width=3cm]{sub_110_combo.eps}
2000 %\begin{minipage}{7.8cm}
2001 %\begin{tabular}{l c c c c c c}
2003 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
2004 % \hkl<1 0 1> & \hkl<-1 0 1> \\
2006 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
2007 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
2008 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
2009 %4 & \RM{4} & B & D & E & E & D \\
2010 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
2017 %\begin{tabular}{l c c c c c c c c c c}
2019 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
2021 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
2022 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
2023 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
2028 \begin{minipage}{6.0cm}
2029 \includegraphics[width=5.8cm]{c_sub_si110.ps}
2031 \begin{minipage}{7cm}
2034 \item IBS: C may displace Si\\
2035 $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
2037 \hkl<1 1 0>-type $\rightarrow$ favored combination
2038 \renewcommand\labelitemi{$\Rightarrow$}
2039 \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
2040 \item Less favorable than C-Si \hkl<1 0 0> dumbbell
2041 \item Interaction drops quickly to zero\\
2042 $\rightarrow$ low capture radius
2046 IBS process far from equilibrium\\
2047 \cs{} \& \si{} instead of thermodynamic ground state
2052 \begin{minipage}{6.5cm}
2053 \includegraphics[width=6.0cm]{162-097.ps}
2055 \item Low migration barrier
2058 \begin{minipage}{6.5cm}
2060 Ab initio MD at \degc{900}\\
2061 \includegraphics[width=3.3cm]{md_vasp_01.eps}
2062 $t=\unit[2230]{fs}$\\
2063 \includegraphics[width=3.3cm]{md_vasp_02.eps}
2067 Contribution of entropy to structural formation
2076 Migration in C-Si \hkl<1 0 0> and vacancy combinations
2083 \begin{minipage}[t]{3cm}
2084 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
2085 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
2087 \begin{minipage}[t]{7cm}
2090 Low activation energies\\
2091 High activation energies for reverse processes\\
2093 {\color{blue}C$_{\text{sub}}$ very stable}\\
2097 Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
2099 {\color{blue}Formation of SiC by successive substitution by C}
2103 \begin{minipage}[t]{3cm}
2104 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
2105 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
2110 \begin{minipage}{5.9cm}
2111 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
2113 \begin{picture}(0,0)(70,0)
2114 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
2116 \begin{picture}(0,0)(30,0)
2117 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
2119 \begin{picture}(0,0)(-10,0)
2120 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
2122 \begin{picture}(0,0)(-48,0)
2123 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
2125 \begin{picture}(0,0)(12.5,5)
2126 \includegraphics[width=1cm]{100_arrow.eps}
2128 \begin{picture}(0,0)(97,-10)
2129 \includegraphics[height=0.9cm]{001_arrow.eps}
2135 \begin{minipage}{0.3cm}
2139 \begin{minipage}{5.9cm}
2140 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
2142 \begin{picture}(0,0)(60,0)
2143 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2145 \begin{picture}(0,0)(25,0)
2146 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2148 \begin{picture}(0,0)(-20,0)
2149 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2151 \begin{picture}(0,0)(-55,0)
2152 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2154 \begin{picture}(0,0)(12.5,5)
2155 \includegraphics[width=1cm]{100_arrow.eps}
2157 \begin{picture}(0,0)(95,0)
2158 \includegraphics[height=0.9cm]{001_arrow.eps}
2170 Conclusion of defect / migration / combined defect simulations
2179 \item Accurately described by quantum-mechanical simulations
2180 \item Less accurate description by classical potential simulations
2181 \item Underestimated formation energy of \cs{} by classical approach
2182 \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2187 \item C migration pathway in Si identified
2188 \item Consistent with reorientation and diffusion experiments
2191 \item Different path and ...
2192 \item overestimated barrier by classical potential calculations
2195 Concerning the precipitation mechanism
2197 \item Agglomeration of C-Si dumbbells energetically favorable
2198 (stress compensation)
2199 \item C-Si indeed favored compared to
2200 C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2201 \item Possible low interaction capture radius of
2202 C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2203 \item Low barrier for
2204 \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2205 \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2206 C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2209 {\color{blue}Results suggest increased participation of \cs}
2217 Silicon carbide precipitation simulations
2223 \begin{pspicture}(0,0)(12,6.5)
2225 \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2228 \item Create c-Si volume
2229 \item Periodc boundary conditions
2230 \item Set requested $T$ and $p=0\text{ bar}$
2231 \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2234 \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2236 Insertion of C atoms at constant T
2238 \item total simulation volume {\pnode{in1}}
2239 \item volume of minimal SiC precipitate {\pnode{in2}}
2240 \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2244 \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2246 Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2248 \ncline[]{->}{init}{insert}
2249 \ncline[]{->}{insert}{cool}
2250 \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2251 \rput(7.8,6){\footnotesize $V_1$}
2252 \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2253 \rput(9.2,4.85){\tiny $V_2$}
2254 \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2255 \rput(9.55,4.45){\footnotesize $V_3$}
2256 \rput(7.9,3.2){\pnode{ins1}}
2257 \rput(9.22,2.8){\pnode{ins2}}
2258 \rput(11.0,2.4){\pnode{ins3}}
2259 \ncline[]{->}{in1}{ins1}
2260 \ncline[]{->}{in2}{ins2}
2261 \ncline[]{->}{in3}{ins3}
2266 \item Restricted to classical potential simulations
2267 \item $V_2$ and $V_3$ considered due to low diffusion
2268 \item Amount of C atoms: 6000
2269 ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2270 \item Simulation volume: $31\times 31\times 31$ unit cells
2279 Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2284 \begin{minipage}{6.5cm}
2285 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2287 \begin{minipage}{6.5cm}
2288 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2291 \begin{minipage}{6.5cm}
2292 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2294 \begin{minipage}{6.5cm}
2296 \underline{Low C concentration ($V_1$)}\\
2297 \hkl<1 0 0> C-Si dumbbell dominated structure
2299 \item Si-C bumbs around 0.19 nm
2300 \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2301 concatenated dumbbells of various orientation
2302 \item Si-Si NN distance stretched to 0.3 nm
2304 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2305 \underline{High C concentration ($V_2$, $V_3$)}\\
2306 High amount of strongly bound C-C bonds\\
2307 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2308 Only short range order observable\\
2309 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2317 Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2322 \begin{minipage}{6.5cm}
2323 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2325 \begin{minipage}{6.5cm}
2326 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2329 \begin{minipage}{6.5cm}
2330 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2332 \begin{minipage}{6.5cm}
2334 \underline{Low C concentration ($V_1$)}\\
2335 \hkl<1 0 0> C-Si dumbbell dominated structure
2337 \item Si-C bumbs around 0.19 nm
2338 \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2339 concatenated dumbbells of various orientation
2340 \item Si-Si NN distance stretched to 0.3 nm
2342 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2343 \underline{High C concentration ($V_2$, $V_3$)}\\
2344 High amount of strongly bound C-C bonds\\
2345 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2346 Only short range order observable\\
2347 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2350 \begin{pspicture}(0,0)(0,0)
2351 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2352 \begin{minipage}{10cm}
2354 {\color{red}\bf 3C-SiC formation fails to appear}
2356 \item Low C concentration simulations
2358 \item Formation of \ci{} indeed occurs
2359 \item Agllomeration not observed
2361 \item High C concentration simulations
2363 \item Amorphous SiC-like structure\\
2364 (not expected at prevailing temperatures)
2365 \item Rearrangement and transition into 3C-SiC structure missing
2377 Limitations of molecular dynamics and short range potentials
2384 \underline{Time scale problem of MD}\\[0.2cm]
2385 Minimize integration error\\
2386 $\Rightarrow$ discretization considerably smaller than
2387 reciprocal of fastest vibrational mode\\[0.1cm]
2388 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2389 $\Rightarrow$ suitable choice of time step:
2390 $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2391 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2392 Several local minima in energy surface separated by large energy barriers\\
2393 $\Rightarrow$ transition event corresponds to a multiple
2394 of vibrational periods\\
2395 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2396 infrequent transition events\\[0.1cm]
2397 {\color{blue}Accelerated methods:}
2398 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2402 \underline{Limitations related to the short range potential}\\[0.2cm]
2403 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2404 and 2$^{\text{nd}}$ next neighbours\\
2405 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2411 Potential enhanced problem of slow phase space propagation
2416 \underline{Approach to the (twofold) problem}\\[0.2cm]
2417 Increased temperature simulations without TAD corrections\\
2418 (accelerated methods or higher time scales exclusively not sufficient)
2420 \begin{picture}(0,0)(-260,-30)
2422 \begin{minipage}{4.2cm}
2429 \item 3C-SiC also observed for higher T
2430 \item higher T inside sample
2431 \item structural evolution vs.\\
2432 equilibrium properties
2438 \begin{picture}(0,0)(-305,-155)
2440 \begin{minipage}{2.5cm}
2444 thermodynmic sampling
2455 Increased temperature simulations at low C concentration
2460 \begin{minipage}{6.5cm}
2461 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2463 \begin{minipage}{6.5cm}
2464 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2467 \begin{minipage}{6.5cm}
2468 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2470 \begin{minipage}{6.5cm}
2472 \underline{Si-C bonds:}
2474 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2475 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2477 \underline{Si-Si bonds:}
2478 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2479 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2480 \underline{C-C bonds:}
2482 \item C-C next neighbour pairs reduced (mandatory)
2483 \item Peak at 0.3 nm slightly shifted
2485 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2486 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2488 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2490 \item Range [|-$\downarrow$]:
2491 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2492 with nearby Si$_{\text{I}}$}
2497 \begin{picture}(0,0)(-330,-74)
2500 \begin{minipage}{1.6cm}
2503 stretched SiC\\[-0.1cm]
2515 Increased temperature simulations at low C concentration
2520 \begin{minipage}{6.5cm}
2521 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2523 \begin{minipage}{6.5cm}
2524 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2527 \begin{minipage}{6.5cm}
2528 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2530 \begin{minipage}{6.5cm}
2532 \underline{Si-C bonds:}
2534 \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2535 \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2537 \underline{Si-Si bonds:}
2538 {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2539 ($\rightarrow$ 0.325 nm)\\[0.1cm]
2540 \underline{C-C bonds:}
2542 \item C-C next neighbour pairs reduced (mandatory)
2543 \item Peak at 0.3 nm slightly shifted
2545 \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2546 $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2548 $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2550 \item Range [|-$\downarrow$]:
2551 {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2552 with nearby Si$_{\text{I}}$}
2557 %\begin{picture}(0,0)(-330,-74)
2560 %\begin{minipage}{1.6cm}
2563 %stretched SiC\\[-0.1cm]
2570 \begin{pspicture}(0,0)(0,0)
2571 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2572 \begin{minipage}{10cm}
2574 {\color{blue}\bf Stretched SiC in c-Si}
2576 \item Consistent to precipitation model involving \cs{}
2577 \item Explains annealing behavior of high/low T C implants
2579 \item Low T: highly mobiel \ci{}
2580 \item High T: stable configurations of \cs{}
2583 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2584 $\Rightarrow$ Precipitation mechanism involving \cs{}
2594 Increased temperature simulations at high C concentration
2599 \begin{minipage}{6.5cm}
2600 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2602 \begin{minipage}{6.5cm}
2603 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2611 \begin{minipage}[t]{6.0cm}
2612 0.186 nm: Si-C pairs $\uparrow$\\
2613 (as expected in 3C-SiC)\\[0.2cm]
2614 0.282 nm: Si-C-C\\[0.2cm]
2615 $\approx$0.35 nm: C-Si-Si
2618 \begin{minipage}{0.2cm}
2622 \begin{minipage}[t]{6.0cm}
2623 0.15 nm: C-C pairs $\uparrow$\\
2624 (as expected in graphite/diamond)\\[0.2cm]
2625 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2626 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2631 \item Decreasing cut-off artifact
2632 \item {\color{red}Amorphous} SiC-like phase remains
2633 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2634 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2643 High C \& small $V$ \& short $t$
2646 Slow restructuring due to strong C-C bonds
2649 High C \& low T implants
2660 Summary and Conclusions
2668 \begin{minipage}[t]{12.9cm}
2669 \underline{Pecipitation simulations}
2671 \item High C concentration $\rightarrow$ amorphous SiC like phase
2672 \item Problem of potential enhanced slow phase space propagation
2673 \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2674 \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2675 \item High T necessary to simulate IBS conditions (far from equilibrium)
2676 \item Precipitation by successive agglomeration of \cs (epitaxy)
2677 \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2678 (stretched SiC, interface)
2686 \begin{minipage}{12.9cm}
2691 \item Point defects excellently / fairly well described
2693 \item C$_{\text{sub}}$ drastically underestimated by EA
2694 \item EA predicts correct ground state:
2695 C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2696 \item Identified migration path explaining
2697 diffusion and reorientation experiments by DFT
2698 \item EA fails to describe \ci{} migration:
2699 Wrong path \& overestimated barrier
2701 \item Combinations of defects
2703 \item Agglomeration of point defects energetically favorable
2704 by compensation of stress
2705 \item Formation of C-C unlikely
2706 \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2707 \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2708 Low barrier (\unit[0.77]{eV}) \& low capture radius
2716 \framebox{Precipitation by successive agglomeration of \cs{}}
2734 \underline{Augsburg}
2736 \item Prof. B. Stritzker (accomodation at EP \RM{4})
2737 \item Ralf Utermann (EDV)
2740 \underline{Helsinki}
2742 \item Prof. K. Nordlund (MD)
2747 \item Bayerische Forschungsstiftung (financial support)
2750 \underline{Paderborn}
2752 \item Prof. J. Lindner (SiC)
2753 \item Prof. G. Schmidt (DFT + financial support)
2754 \item Dr. E. Rauls (DFT + SiC)
2755 \item Dr. S. Sanna (VASP)
2762 \bf Thank you for your attention!