From: hackbard Date: Sat, 31 Dec 2011 16:33:54 +0000 (+0100) Subject: initial checkin of defense talk X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=3f65cf44692d94497ff4a2ac366cb91b97ac3012;p=lectures%2Flatex.git initial checkin of defense talk --- diff --git a/posic/talks/defense.tex b/posic/talks/defense.tex new file mode 100644 index 0000000..a8062e8 --- /dev/null +++ b/posic/talks/defense.tex @@ -0,0 +1,2279 @@ +\pdfoutput=0 +%\documentclass[landscape,semhelv,draft]{seminar} +\documentclass[landscape,semhelv]{seminar} + +\usepackage{verbatim} +\usepackage[greek,german]{babel} +\usepackage[latin1]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{amsmath} +\usepackage{stmaryrd} +\usepackage{latexsym} +\usepackage{ae} + +\usepackage{calc} % Simple computations with LaTeX variables +\usepackage{caption} % Improved captions +\usepackage{fancybox} % To have several backgrounds + +\usepackage{fancyhdr} % Headers and footers definitions +\usepackage{fancyvrb} % Fancy verbatim environments +\usepackage{pstricks} % PSTricks with the standard color package + +\usepackage{pstricks} +\usepackage{pst-node} +\usepackage{pst-grad} + +%\usepackage{epic} +%\usepackage{eepic} + +\usepackage{layout} + +\usepackage{graphicx} +\graphicspath{{../img/}} + +\usepackage{miller} + +\usepackage[setpagesize=false]{hyperref} + +% units +\usepackage{units} + +\usepackage{semcolor} +\usepackage{semlayer} % Seminar overlays +\usepackage{slidesec} % Seminar sections and list of slides + +\input{seminar.bug} % Official bugs corrections +\input{seminar.bg2} % Unofficial bugs corrections + +\articlemag{1} + +\special{landscape} + +% font +%\usepackage{cmbright} +%\renewcommand{\familydefault}{\sfdefault} +%\usepackage{mathptmx} + +\usepackage{upgreek} + +%\newrgbcolor{hred}{0.9 0.13 0.13} +%\newrgbcolor{hblue}{0.13 0.13 0.9} +\newrgbcolor{hred}{1.0 0.0 0.0} +\newrgbcolor{hblue}{0.0 0.0 1.0} + +\begin{document} + +\extraslideheight{10in} +\slideframe{plain} + +\pagestyle{empty} + +% specify width and height +\slidewidth 26.3cm +\slideheight 19.9cm + +% margin +\def\slidetopmargin{-0.15cm} + +\newcommand{\ham}{\mathcal{H}} +\newcommand{\pot}{\mathcal{V}} +\newcommand{\foo}{\mathcal{U}} +\newcommand{\vir}{\mathcal{W}} + +% itemize level ii +\renewcommand\labelitemii{{\color{gray}$\bullet$}} + +% nice phi +\renewcommand{\phi}{\varphi} + +% roman letters +\newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}} + +% colors +\newrgbcolor{si-yellow}{.6 .6 0} +\newrgbcolor{hb}{0.75 0.77 0.89} +\newrgbcolor{lbb}{0.75 0.8 0.88} +\newrgbcolor{hlbb}{0.825 0.88 0.968} +\newrgbcolor{lachs}{1.0 .93 .81} + +% head +\newcommand{\headphd}{ +\begin{pspicture}(0,0)(0,0) +\rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=hb,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{ +\begin{minipage}{14cm} +\hfill +\vspace{0.7cm} +\end{minipage} +}} +\end{pspicture} +} + +% shortcuts +\newcommand{\si}{Si$_{\text{i}}${}} +\newcommand{\ci}{C$_{\text{i}}${}} +\newcommand{\cs}{C$_{\text{sub}}${}} +\newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}} +\newcommand{\distn}[1]{\unit[#1]{nm}{}} +\newcommand{\dista}[1]{\unit[#1]{\AA}{}} +\newcommand{\perc}[1]{\unit[#1]{\%}{}} + +% no vertical centering +%\centerslidesfalse + +% layout check +%\layout +\begin{slide} +\center +{\Huge +E\\ +F\\ +G\\ +A B C D E F G H G F E D C B A +G\\ +F\\ +E\\ +} +\end{slide} + +% topic + +\begin{slide} +\begin{center} + + \vspace{16pt} + + {\LARGE\bf + Atomistic simulation study\\[0.2cm] + on silicon carbide precipitation\\[0.2cm] + in silicon + } + + \vspace{48pt} + + \textsc{Frank Zirkelbach} + + \vspace{48pt} + + Defense of doctor's thesis + + \vspace{08pt} + + Augsburg, 10. Jan. 2012 + +\end{center} +\end{slide} + +% no vertical centering +\centerslidesfalse + +% intro + +% motivation / properties / applications of silicon carbide + +\begin{slide} + +\vspace*{1.8cm} + +\small + +\begin{pspicture}(0,0)(13.5,5) + + \psframe*[linecolor=hb](-0.2,0)(12.9,5) + + \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.2,1)(6.5,1)(6.5,3)(5.2,3) + \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.4,0.5)(7.7,2)(7.7,2)(6.4,3.5) + + \rput[lt](0,4.6){\color{gray}PROPERTIES} + + \rput[lt](0.3,4){wide band gap} + \rput[lt](0.3,3.5){high electric breakdown field} + \rput[lt](0.3,3){good electron mobility} + \rput[lt](0.3,2.5){high electron saturation drift velocity} + \rput[lt](0.3,2){high thermal conductivity} + + \rput[lt](0.3,1.5){hard and mechanically stable} + \rput[lt](0.3,1){chemically inert} + + \rput[lt](0.3,0.5){radiation hardness} + + \rput[rt](12.7,4.6){\color{gray}APPLICATIONS} + + \rput[rt](12.5,3.85){high-temperature, high power} + \rput[rt](12.5,3.5){and high-frequency} + \rput[rt](12.5,3.15){electronic and optoelectronic devices} + + \rput[rt](12.5,2.35){material suitable for extreme conditions} + \rput[rt](12.5,2){microelectromechanical systems} + \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements} + + \rput[rt](12.5,0.85){first wall reactor material, detectors} + \rput[rt](12.5,0.5){and electronic devices for space} + +\end{pspicture} + +\begin{picture}(0,0)(5,-162) +\includegraphics[height=2.2cm]{3C_SiC_bs.eps} +\end{picture} +\begin{picture}(0,0)(-120,-162) +\includegraphics[height=2.2cm]{nasa_600c_led.eps} +\end{picture} +\begin{picture}(0,0)(-270,-162) +\includegraphics[height=2.2cm]{6h-sic_3c-sic.eps} +\end{picture} +%%%% +\begin{picture}(0,0)(10,65) +\includegraphics[height=2.8cm]{sic_switch.eps} +\end{picture} +%\begin{picture}(0,0)(-243,65) +\begin{picture}(0,0)(-110,65) +\includegraphics[height=2.8cm]{ise_99.eps} +\end{picture} +%\begin{picture}(0,0)(-135,65) +\begin{picture}(0,0)(-100,65) +\includegraphics[height=1.2cm]{infineon_schottky.eps} +\end{picture} +\begin{picture}(0,0)(-233,65) +\includegraphics[height=2.8cm]{solar_car.eps} +\end{picture} + +\end{slide} + +% motivation + +\begin{slide} + + {\large\bf + Polytypes of SiC\\[0.4cm] + } + +\includegraphics[width=3.8cm]{cubic_hex.eps}\\ +\begin{minipage}{1.9cm} +{\tiny cubic (twist)} +\end{minipage} +\begin{minipage}{2.9cm} +{\tiny hexagonal (no twist)} +\end{minipage} + +\begin{picture}(0,0)(-150,0) + \includegraphics[width=7cm]{polytypes.eps} +\end{picture} + +\vspace{0.6cm} + +\footnotesize + +\begin{tabular}{l c c c c c c} +\hline + & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\ +\hline +Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\ +Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\ +Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\ +Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\ +Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\ +Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\ +Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ +\hline +\end{tabular} + +\begin{pspicture}(0,0)(0,0) +\psellipse[linecolor=green](5.7,2.10)(0.4,0.5) +\end{pspicture} +\begin{pspicture}(0,0)(0,0) +\psellipse[linecolor=green](5.6,0.92)(0.4,0.2) +\end{pspicture} +\begin{pspicture}(0,0)(0,0) +\psellipse[linecolor=red](10.45,0.45)(0.4,0.2) +\end{pspicture} + +\end{slide} + +% fabrication + +\begin{slide} + +\headphd + {\large\bf + Fabrication of silicon carbide + } + + \small + + \vspace{2pt} + +\begin{center} + {\color{gray} + \emph{Silicon carbide --- Born from the stars, perfected on earth.} + } +\end{center} + +\vspace{2pt} + +SiC thin films by MBE \& CVD +\begin{itemize} + \item Much progress achieved in homo/heteroepitaxial SiC thin film growth + \item \underline{Commercially available} semiconductor power devices based on + \underline{\foreignlanguage{greek}{a}-SiC} + \item Production of favored \underline{3C-SiC} material + \underline{less advanced} + \item Quality and size not yet sufficient +\end{itemize} +\begin{picture}(0,0)(-310,-20) + \includegraphics[width=2.0cm]{cree.eps} +\end{picture} + +\vspace{-0.2cm} + +Alternative approach: +Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) + +\vspace{0.2cm} + +\scriptsize + +\framebox{ +\begin{minipage}{3.15cm} + \begin{center} +\includegraphics[width=3cm]{imp.eps}\\ + {\tiny + Carbon implantation + } + \end{center} +\end{minipage} +\begin{minipage}{3.15cm} + \begin{center} +\includegraphics[width=3cm]{annealing.eps}\\ + {\tiny + Postannealing at $>$ \degc{1200} + } + \end{center} +\end{minipage} +} +\begin{minipage}{5.5cm} + \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm] + \begin{center} + {\tiny + XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0) + } + \end{center} +\end{minipage} + +\end{slide} + +% contents + +\begin{slide} + +\headphd +{\large\bf + Outline +} + + \begin{itemize} + \item Supposed precipitation mechanism of SiC in Si + \item Utilized simulation techniques + \begin{itemize} + \item Molecular dynamics (MD) simulations + \item Density functional theory (DFT) calculations + \end{itemize} + \item C and Si self-interstitial point defects in silicon + \item Silicon carbide precipitation simulations + \item Summary / Conclusion / Outlook + \end{itemize} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Formation of epitaxial single crystalline 3C-SiC +} + +\footnotesize + +\vspace{0.2cm} + +\begin{center} +\begin{itemize} + \item \underline{Implantation step 1}\\[0.1cm] + Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\ + $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \& + {\color{blue}precipitates} + \item \underline{Implantation step 2}\\[0.1cm] + Little remaining dose | \unit[180]{keV} | \degc{250}\\ + $\Rightarrow$ + Destruction/Amorphization of precipitates at layer interface + \item \underline{Annealing}\\[0.1cm] + \unit[10]{h} at \degc{1250}\\ + $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces +\end{itemize} +\end{center} + +\begin{minipage}{7cm} +\includegraphics[width=7cm]{ibs_3c-sic.eps} +\end{minipage} +\begin{minipage}{5cm} +\begin{pspicture}(0,0)(0,0) +\rnode{box}{ +\psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{ +\begin{minipage}{5.3cm} + \begin{center} + {\color{blue} + 3C-SiC precipitation\\ + not yet fully understood + } + \end{center} + \vspace*{0.1cm} + \renewcommand\labelitemi{$\Rightarrow$} + Details of the SiC precipitation + \begin{itemize} + \item significant technological progress\\ + in SiC thin film formation + \item perspectives for processes relying\\ + upon prevention of SiC precipitation + \end{itemize} +\end{minipage} +}} +\rput(-6.8,5.4){\pnode{h0}} +\rput(-3.0,5.4){\pnode{h1}} +\ncline[linecolor=blue]{-}{h0}{h1} +\ncline[linecolor=blue]{->}{h1}{box} +\end{pspicture} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Supposed precipitation mechanism of SiC in Si +} + + \scriptsize + + \vspace{0.1cm} + + \framebox{ + \begin{minipage}{3.6cm} + \begin{center} + Si \& SiC lattice structure\\[0.1cm] + \includegraphics[width=2.3cm]{sic_unit_cell.eps} + \end{center} +{\tiny + \begin{minipage}{1.7cm} +\underline{Silicon}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\ +$a=\unit[5.429]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[100]{\%}$ + \end{minipage} + \begin{minipage}{1.7cm} +\underline{Silicon carbide}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\ +$a=\unit[4.359]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[97]{\%}$ + \end{minipage} +} + \end{minipage} + } + \hspace{0.1cm} + \begin{minipage}{4.1cm} + \begin{center} + \includegraphics[width=3.3cm]{tem_c-si-db.eps} + \end{center} + \end{minipage} + \hspace{0.1cm} + \begin{minipage}{4.0cm} + \begin{center} + \includegraphics[width=3.3cm]{tem_3c-sic.eps} + \end{center} + \end{minipage} + + \vspace{0.1cm} + + \begin{minipage}{4.0cm} + \begin{center} + C-Si dimers (dumbbells)\\[-0.1cm] + on Si interstitial sites + \end{center} + \end{minipage} + \hspace{0.1cm} + \begin{minipage}{4.1cm} + \begin{center} + Agglomeration of C-Si dumbbells\\[-0.1cm] + $\Rightarrow$ dark contrasts + \end{center} + \end{minipage} + \hspace{0.1cm} + \begin{minipage}{4.0cm} + \begin{center} + Precipitation of 3C-SiC in Si\\[-0.1cm] + $\Rightarrow$ Moir\'e fringes\\[-0.1cm] + \& release of Si self-interstitials + \end{center} + \end{minipage} + + \vspace{0.1cm} + + \begin{minipage}{4.0cm} + \begin{center} + \includegraphics[width=3.3cm]{sic_prec_seq_01.eps} + \end{center} + \end{minipage} + \hspace{0.1cm} + \begin{minipage}{4.1cm} + \begin{center} + \includegraphics[width=3.3cm]{sic_prec_seq_02.eps} + \end{center} + \end{minipage} + \hspace{0.1cm} + \begin{minipage}{4.0cm} + \begin{center} + \includegraphics[width=3.3cm]{sic_prec_seq_03.eps} + \end{center} + \end{minipage} + +\begin{pspicture}(0,0)(0,0) +\psline[linewidth=2pt]{->}(8.3,2)(8.8,2) +\psellipse[linecolor=blue](11.1,6.0)(0.3,0.5) +\rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)} +\psline[linewidth=2pt]{->}(3.9,2)(4.4,2) +\rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ + $4a_{\text{Si}}=5a_{\text{SiC}}$ + }}} +\rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\hkl(h k l) planes match + }}} +\rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +r = \unit[2--4]{nm} + }}} +\end{pspicture} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Supposed precipitation mechanism of SiC in Si +} + + \scriptsize + + \vspace{0.1cm} + + \framebox{ + \begin{minipage}{3.6cm} + \begin{center} + Si \& SiC lattice structure\\[0.1cm] + \includegraphics[width=2.3cm]{sic_unit_cell.eps} + \end{center} +{\tiny + \begin{minipage}{1.7cm} +\underline{Silicon}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\ +$a=\unit[5.429]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[100]{\%}$ + \end{minipage} + \begin{minipage}{1.7cm} +\underline{Silicon carbide}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\ +$a=\unit[4.359]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[97]{\%}$ + \end{minipage} +} + \end{minipage} + } + \hspace{0.1cm} + \begin{minipage}{4.1cm} + \begin{center} + \includegraphics[width=3.3cm]{tem_c-si-db.eps} + \end{center} + \end{minipage} + \hspace{0.1cm} + \begin{minipage}{4.0cm} + \begin{center} + \includegraphics[width=3.3cm]{tem_3c-sic.eps} + \end{center} + \end{minipage} + + \vspace{0.1cm} + + \begin{minipage}{4.0cm} + \begin{center} + C-Si dimers (dumbbells)\\[-0.1cm] + on Si interstitial sites + \end{center} + \end{minipage} + \hspace{0.1cm} + \begin{minipage}{4.1cm} + \begin{center} + Agglomeration of C-Si dumbbells\\[-0.1cm] + $\Rightarrow$ dark contrasts + \end{center} + \end{minipage} + \hspace{0.1cm} + \begin{minipage}{4.0cm} + \begin{center} + Precipitation of 3C-SiC in Si\\[-0.1cm] + $\Rightarrow$ Moir\'e fringes\\[-0.1cm] + \& release of Si self-interstitials + \end{center} + \end{minipage} + + \vspace{0.1cm} + + \begin{minipage}{4.0cm} + \begin{center} + \includegraphics[width=3.3cm]{sic_prec_seq_01.eps} + \end{center} + \end{minipage} + \hspace{0.1cm} + \begin{minipage}{4.1cm} + \begin{center} + \includegraphics[width=3.3cm]{sic_prec_seq_02.eps} + \end{center} + \end{minipage} + \hspace{0.1cm} + \begin{minipage}{4.0cm} + \begin{center} + \includegraphics[width=3.3cm]{sic_prec_seq_03.eps} + \end{center} + \end{minipage} + +\begin{pspicture}(0,0)(0,0) +\psline[linewidth=2pt]{->}(8.3,2)(8.8,2) +\psellipse[linecolor=blue](11.1,6.0)(0.3,0.5) +\rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)} +\psline[linewidth=2pt]{->}(3.9,2)(4.4,2) +\rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ + $4a_{\text{Si}}=5a_{\text{SiC}}$ + }}} +\rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\hkl(h k l) planes match + }}} +\rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +r = \unit[2--4]{nm} + }}} +% controversial view! +\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{ +\begin{minipage}{14cm} +\hfill +\vspace{12cm} +\end{minipage} +}} +\rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{ +\begin{minipage}{10cm} +\small +\vspace*{0.2cm} +\begin{center} +{\color{gray}\bf Controversial findings} +\end{center} +\begin{itemize} +\item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./} + \begin{itemize} + \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites + \item \si{} reacting with further C in cleared volume + \end{itemize} +\item Annealing behavior {\tiny\color{gray}/Serre~et~al./} + \begin{itemize} + \item Room temperature implantation $\rightarrow$ high C diffusion + \item Elevated temperature implantation $\rightarrow$ no C redistribution + \end{itemize} + $\Rightarrow$ mobile {\color{red}\ci} opposed to + stable {\color{blue}\cs{}} configurations +\item Strained silicon \& Si/SiC heterostructures + {\tiny\color{gray}/Strane~et~al./Guedj~et~al./} + \begin{itemize} + \item {\color{blue}Coherent} SiC precipitates (tensile strain) + \item Incoherent SiC (strain relaxation) + \end{itemize} +\end{itemize} +\vspace{0.1cm} +\begin{center} +{\Huge${\lightning}$} \hspace{0.3cm} +{\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm} +{\Huge${\lightning}$} +\end{center} +\vspace{0.2cm} +\end{minipage} + }}} +\end{pspicture} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Utilized computational methods +} + +\vspace{0.3cm} + +\small + +{\bf Molecular dynamics (MD)}\\[0.1cm] +\scriptsize +\begin{tabular}{| p{4.5cm} | p{7.5cm} |} +\hline +System of $N$ particles & +$N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\ +Phase space propagation & +Velocity Verlet | timestep: \unit[1]{fs} \\ +Analytical interaction potential & +Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential +(Erhart/Albe) +$\displaystyle +E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad + \pot_{ij} = {\color{red}f_C(r_{ij})} + \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right] +$\\ +Observables: time/ensemble averages & +NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\ +\hline +\end{tabular} + +\small + +\vspace{0.3cm} + +{\bf Density functional theory (DFT)} + +\scriptsize + +\begin{minipage}[t]{6cm} +\begin{itemize} + \item Hohenberg-Kohn theorem:\\ + $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$ + \item Kohn-Sham approach:\\ + Single-particle effective theory +\end{itemize} +\hrule +\begin{itemize} +\item Code: \textsc{vasp} +\item Plane wave basis set +%$\displaystyle +%\Phi_i=\sum_{|G+k|}(3.5,-2.0){2.5}{130}{15} +\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165} +\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310} + +\end{pspicture} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headphd + {\large\bf + Point defects \& defect migration + } + + \small + + \vspace{0.2cm} + +\begin{minipage}[b]{7.5cm} +{\bf Defect structure}\\ + \begin{pspicture}(0,0)(7,4.4) + \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ + \parbox{7cm}{ + \begin{itemize} + \item Creation of c-Si simulation volume + \item Periodic boundary conditions + \item $T=0\text{ K}$, $p=0\text{ bar}$ + \end{itemize} + }}}} +\rput(3.5,1.3){\rnode{insert}{\psframebox{ + \parbox{7cm}{ + \begin{center} + Insertion of interstitial C/Si atoms + \end{center} + }}}} + \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{ + \parbox{7cm}{ + \begin{center} + Relaxation / structural energy minimization + \end{center} + }}}} + \ncline[]{->}{init}{insert} + \ncline[]{->}{insert}{cool} + \end{pspicture} +\end{minipage} +\begin{minipage}[b]{4.5cm} +\begin{center} +\includegraphics[width=3.8cm]{unit_cell_e.eps}\\ +\end{center} +\begin{minipage}{2.21cm} +{\scriptsize +{\color{red}$\bullet$} Tetrahedral\\[-0.1cm] +{\color{green}$\bullet$} Hexagonal\\[-0.1cm] +{\color{yellow}$\bullet$} \hkl<1 0 0> DB +} +\end{minipage} +\begin{minipage}{2.21cm} +{\scriptsize +{\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm] +{\color{cyan}$\bullet$} Bond-centered\\[-0.1cm] +{\color{black}$\bullet$} Vac. / Sub. +} +\end{minipage} +\end{minipage} + +\vspace{0.2cm} + +\begin{minipage}[b]{6cm} +{\bf Defect formation energy}\\ +\framebox{ +$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm] +Particle reservoir: Si \& SiC\\[0.2cm] +{\bf Binding energy}\\ +\framebox{ +$ +E_{\text{b}}= +E_{\text{f}}^{\text{comb}}- +E_{\text{f}}^{1^{\text{st}}}- +E_{\text{f}}^{2^{\text{nd}}} +$ +}\\[0.1cm] +\footnotesize +$E_{\text{b}}<0$: energetically favorable configuration\\ +$E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\ +\end{minipage} +\begin{minipage}[b]{6cm} +{\bf Migration barrier} +\footnotesize +\begin{itemize} + \item Displace diffusing atom + \item Constrain relaxation of (diffusing) atoms + \item Record configurational energy +\end{itemize} +\begin{picture}(0,0)(-60,-33) +\includegraphics[width=4.5cm]{crt_mod.eps} +\end{picture} +\end{minipage} + +\end{slide} + +\begin{slide} + +\footnotesize + +\headphd +{\large\bf + Si self-interstitial point defects in silicon\\[0.1cm] +} + +\begin{center} +\begin{tabular}{l c c c c c} +\hline + $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\ +\hline + \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\ + Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\ +\hline +\end{tabular}\\[0.4cm] +\end{center} + +\begin{minipage}{3cm} +\begin{center} +\underline{Vacancy}\\ +\includegraphics[width=2.8cm]{si_pd_albe/vac.eps} +\end{center} +\end{minipage} +\begin{minipage}{3cm} +\begin{center} +\underline{\hkl<1 1 0> DB}\\ +\includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps} +\end{center} +\end{minipage} +\begin{minipage}{3cm} +\begin{center} +\underline{\hkl<1 0 0> DB}\\ +\includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps} +\end{center} +\end{minipage} +\begin{minipage}{3cm} +\begin{center} +\underline{Tetrahedral}\\ +\includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps} +\end{center} +\end{minipage}\\ + +\underline{Hexagonal} \hspace{2pt} +\href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm] +\framebox{ +\begin{minipage}{2.7cm} +$E_{\text{f}}^*=4.48\text{ eV}$\\ +\includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps} +\end{minipage} +\begin{minipage}{0.4cm} +\begin{center} +$\Rightarrow$ +\end{center} +\end{minipage} +\begin{minipage}{2.7cm} +$E_{\text{f}}=3.96\text{ eV}$\\ +\includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps} +\end{minipage} +} +\begin{minipage}{5.5cm} +\begin{center} +{\tiny nearly T $\rightarrow$ T}\\ +\end{center} +\includegraphics[width=6.0cm]{nhex_tet.ps} +\end{minipage} + +\end{slide} + +\begin{slide} + +\footnotesize + +\headphd +{\large\bf + C interstitial point defects in silicon\\ +} + +\begin{tabular}{l c c c c c c r} +\hline + $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & + {\color{black} \cs{} \& \si}\\ +\hline + \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\ + Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\ +\hline +\end{tabular}\\[0.1cm] + +\framebox{ +\begin{minipage}{2.8cm} +\underline{Hexagonal} \hspace{2pt} +\href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\ +$E_{\text{f}}^*=9.05\text{ eV}$\\ +\includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps} +\end{minipage} +\begin{minipage}{0.4cm} +\begin{center} +$\Rightarrow$ +\end{center} +\end{minipage} +\begin{minipage}{2.8cm} +\underline{\hkl<1 0 0>}\\ +$E_{\text{f}}=3.88\text{ eV}$\\ +\includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps} +\end{minipage} +} +\begin{minipage}{1.4cm} +\hfill +\end{minipage} +\begin{minipage}{3.0cm} +\begin{flushright} +\underline{Tetrahedral}\\ +\includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps} +\end{flushright} +\end{minipage} + +\framebox{ +\begin{minipage}{2.8cm} +\underline{Bond-centered}\\ +$E_{\text{f}}^*=5.59\text{ eV}$\\ +\includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps} +\end{minipage} +\begin{minipage}{0.4cm} +\begin{center} +$\Rightarrow$ +\end{center} +\end{minipage} +\begin{minipage}{2.8cm} +\underline{\hkl<1 1 0> dumbbell}\\ +$E_{\text{f}}=5.18\text{ eV}$\\ +\includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps} +\end{minipage} +} +\begin{minipage}{1.4cm} +\hfill +\end{minipage} +\begin{minipage}{3.0cm} +\begin{flushright} +\underline{Substitutional}\\ +\includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps} +\end{flushright} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf\boldmath + C-Si dimer \& bond-centered interstitial configuration +} + +\footnotesize + +\vspace{0.1cm} + +\begin{minipage}[t]{4.1cm} +{\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm] +\begin{minipage}{2.0cm} +\begin{center} +\underline{Erhart/Albe} +\includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps} +\end{center} +\end{minipage} +\begin{minipage}{2.0cm} +\begin{center} +\underline{\textsc{vasp}} +\includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps} +\end{center} +\end{minipage}\\[0.2cm] +Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\ +$\Rightarrow$ $sp$ hybridization\\[0.1cm] +Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\ +$\Rightarrow$ $sp^2$ hybridization +\begin{center} +\includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm] +{\tiny Charge density isosurface} +\end{center} +\end{minipage} +\begin{minipage}{0.2cm} +\hfill +\end{minipage} +\begin{minipage}[t]{8.1cm} +\begin{flushright} +{\bf Bond-centered interstitial}\\[0.1cm] +\begin{minipage}{4.4cm} +%\scriptsize +\begin{itemize} + \item Linear Si-C-Si bond + \item Si: one C \& 3 Si neighbours + \item Spin polarized calculations + \item No saddle point!\\ + Real local minimum! +\end{itemize} +\end{minipage} +\begin{minipage}{2.7cm} +%\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\ +\vspace{0.2cm} +\includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\ +\end{minipage} + +\framebox{ + \tiny + \begin{minipage}[t]{6.5cm} + \begin{minipage}[t]{1.2cm} + {\color{red}Si}\\ + {\tiny sp$^3$}\\[0.8cm] + \underline{${\color{black}\uparrow}$} + \underline{${\color{black}\uparrow}$} + \underline{${\color{black}\uparrow}$} + \underline{${\color{red}\uparrow}$}\\ + sp$^3$ + \end{minipage} + \begin{minipage}[t]{1.4cm} + \begin{center} + {\color{red}M}{\color{blue}O}\\[0.8cm] + \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\ + $\sigma_{\text{ab}}$\\[0.5cm] + \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\ + $\sigma_{\text{b}}$ + \end{center} + \end{minipage} + \begin{minipage}[t]{1.0cm} + \begin{center} + {\color{blue}C}\\ + {\tiny sp}\\[0.2cm] + \underline{${\color{white}\uparrow\uparrow}$} + \underline{${\color{white}\uparrow\uparrow}$}\\ + 2p\\[0.4cm] + \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$} + \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\ + sp + \end{center} + \end{minipage} + \begin{minipage}[t]{1.4cm} + \begin{center} + {\color{blue}M}{\color{green}O}\\[0.8cm] + \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\ + $\sigma_{\text{ab}}$\\[0.5cm] + \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\ + $\sigma_{\text{b}}$ + \end{center} + \end{minipage} + \begin{minipage}[t]{1.2cm} + \begin{flushright} + {\color{green}Si}\\ + {\tiny sp$^3$}\\[0.8cm] + \underline{${\color{green}\uparrow}$} + \underline{${\color{black}\uparrow}$} + \underline{${\color{black}\uparrow}$} + \underline{${\color{black}\uparrow}$}\\ + sp$^3$ + \end{flushright} + \end{minipage} + \end{minipage} +}\\[0.4cm] + +%\framebox{ +\begin{minipage}{3.0cm} +%\scriptsize +\underline{Charge density}\\ +{\color{gray}$\bullet$} Spin up\\ +{\color{green}$\bullet$} Spin down\\ +{\color{blue}$\bullet$} Resulting spin up\\ +{\color{yellow}$\bullet$} Si atoms\\ +{\color{red}$\bullet$} C atom +\end{minipage} +\begin{minipage}{3.6cm} +\includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps} +\end{minipage} +%} + +\end{flushright} + +\end{minipage} +\begin{pspicture}(0,0)(0,0) +\psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0) +\end{pspicture} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf\boldmath + C interstitial migration --- ab initio +} + +\scriptsize + +\vspace{0.1cm} + +\begin{minipage}{6.8cm} +\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\ +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps} +\end{minipage} +\begin{minipage}{0.2cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps} +\end{minipage} +\begin{minipage}{0.2cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps} +\end{minipage}\\[0.1cm] +Spin polarization\\ +$\Rightarrow$ BC configuration constitutes local minimum\\ +$\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$ +\end{minipage} +\begin{minipage}{5.4cm} +\includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps} +\end{minipage}\\[0.2cm] +%\hrule +% +\begin{minipage}{6.8cm} +\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\ +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps} +\end{minipage} +\begin{minipage}{0.2cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps} +\end{minipage} +\begin{minipage}{0.2cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps} +\end{minipage}\\[0.1cm] +$\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\ +$\Rightarrow$ {\color{red}Migration mechanism identified!}\\ +Note: Change in orientation +\end{minipage} +\begin{minipage}{5.4cm} +\includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps} +\end{minipage}\\[0.1cm] +% +\begin{center} +Reorientation pathway composed of two consecutive processes of the above type +\end{center} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf\boldmath + C interstitial migration --- analytical potential +} + +\scriptsize + +\vspace{0.3cm} + +\begin{minipage}[t]{6.0cm} +{\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm] +\includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\ +\begin{itemize} + \item Lowermost migration barrier + \item $\Delta E \approx \unit[2.2]{eV}$ + \item 2.4 times higher than ab initio result + \item Different pathway +\end{itemize} +\end{minipage} +\begin{minipage}[t]{0.2cm} +\hfill +\end{minipage} +\begin{minipage}[t]{6.0cm} +{\bf\boldmath Transition involving a \hkl<1 1 0> configuration} +\vspace{0.1cm} +\begin{itemize} + \item Bond-centered configuration unstable\\ + $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell + \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\ + $\rightarrow$ \ci{} \hkl<1 1 0> DB +\end{itemize} +\vspace{0.1cm} +\includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps} +\begin{itemize} + \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$ + \item 2.4 -- 3.4 times higher than ab initio result + \item After all: Change of the DB orientation +\end{itemize} +\end{minipage} + +\vspace{0.5cm} +\begin{center} +{\color{red}\bf Drastically overestimated diffusion barrier} +\end{center} + +\begin{pspicture}(0,0)(0,0) +\psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3) +\end{pspicture} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf\boldmath + Defect combinations +} + +\footnotesize + +\vspace{0.3cm} + +\begin{minipage}{9cm} +{\bf + Summary of combinations}\\[0.1cm] +{\scriptsize +\begin{tabular}{l c c c c c c} +\hline + $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\ + \hline + \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\ + \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\ + \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}\\ + \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}\\ + \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}\\ + \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}\\ + \hline + C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\ + Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\ +\hline +\end{tabular} +} +\vspace{0.2cm} +\begin{center} +{\color{blue} + $E_{\text{b}}$ explainable by stress compensation / increase +} +\end{center} +\end{minipage} +\begin{minipage}{3cm} +\includegraphics[width=3.5cm]{comb_pos.eps} +\end{minipage} + +\vspace{0.2cm} + +{\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm] +\begin{minipage}[t]{3.2cm} +\underline{\hkl[1 0 0] at position 1}\\[0.1cm] +\includegraphics[width=2.8cm]{00-1dc/2-25.eps} +\end{minipage} +\begin{minipage}[t]{3.0cm} +\underline{\hkl[0 -1 0] at position 1}\\[0.1cm] +\includegraphics[width=2.8cm]{00-1dc/2-39.eps} +\end{minipage} +\begin{minipage}[t]{6.1cm} +\vspace{0.7cm} +\begin{itemize} + \item \ci{} agglomeration energetically favorable + \item Most favorable: C clustering\\ + {\color{red}However \ldots}\\ + \ldots high migration barrier ($>4\,\text{eV}$)\\ + \ldots entropy: + $4\times{\color{cyan}[-2.25]}$ versus + $2\times{\color{orange}[-2.39]}$ +\end{itemize} +\begin{center} +{\color{blue}\ci{} agglomeration / no C clustering} +\end{center} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf\boldmath + Defect combinations +} + +\footnotesize + +\vspace{0.3cm} + +\begin{minipage}{9cm} +{\bf + Summary of combinations}\\[0.1cm] +{\scriptsize +\begin{tabular}{l c c c c c c} +\hline + $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\ + \hline + \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\ + \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\ + \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}\\ + \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}\\ + \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}\\ + \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}\\ + \hline + C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\ + Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\ +\hline +\end{tabular} +} +\vspace{0.2cm} +\begin{center} +{\color{blue} + $E_{\text{b}}$ explainable by stress compensation / increase +} +\end{center} +\end{minipage} +\begin{minipage}{3cm} +\includegraphics[width=3.5cm]{comb_pos.eps} +\end{minipage} + +\vspace{0.2cm} + +{\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm] +\begin{minipage}[t]{3.2cm} +\underline{\hkl[1 0 0] at position 1}\\[0.1cm] +\includegraphics[width=2.8cm]{00-1dc/2-25.eps} +\end{minipage} +\begin{minipage}[t]{3.0cm} +\underline{\hkl[0 -1 0] at position 1}\\[0.1cm] +\includegraphics[width=2.8cm]{00-1dc/2-39.eps} +\end{minipage} +\begin{minipage}[t]{6.1cm} +\vspace{0.7cm} +\begin{itemize} + \item \ci{} agglomeration energetically favorable + \item Most favorable: C clustering\\ + {\color{red}However \ldots}\\ + \ldots high migration barrier ($>4\,\text{eV}$)\\ + \ldots entropy: + $4\times{\color{cyan}[-2.25]}$ versus + $2\times{\color{orange}[-2.39]}$ +\end{itemize} +\begin{center} +{\color{blue}\ci{} agglomeration / no C clustering} +\end{center} +\end{minipage} + +% insert graph ... +\begin{pspicture}(0,0)(0,0) +\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{ +\begin{minipage}{14cm} +\hfill +\vspace{12cm} +\end{minipage} +}} +\rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{ +\begin{minipage}{8cm} +\begin{center} +\vspace{0.2cm} +\scriptsize +Interaction along \hkl[1 1 0] +\includegraphics[width=7cm]{db_along_110_cc.ps} +\end{center} +\end{minipage} +}}} +\end{pspicture} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Defect combinations of C-Si dimers and vacancies +} +\footnotesize + +\vspace{0.2cm} + +\begin{minipage}[b]{2.6cm} +\begin{flushleft} +\underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm] +\includegraphics[width=2.5cm]{00-1dc/0-59.eps} +\end{flushleft} +\end{minipage} +\begin{minipage}[b]{7cm} +\hfill +\end{minipage} +\begin{minipage}[b]{2.6cm} +\begin{flushright} +\underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm] +\includegraphics[width=2.5cm]{00-1dc/3-14.eps} +\end{flushright} +\end{minipage}\\[0.2cm] + +\begin{minipage}{6.5cm} +\includegraphics[width=6.0cm]{059-539.ps} +\end{minipage} +\begin{minipage}{5.7cm} +\includegraphics[width=6.0cm]{314-539.ps} +\end{minipage} + +\begin{pspicture}(0,0)(0,0) +\psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0) + +\rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{ +\begin{minipage}{6.5cm} +\begin{center} +IBS: Impinging C creates V \& far away \si\\[0.3cm] +Low migration barrier towards C$_{\text{sub}}$\\ +\&\\ +High barrier for reverse process\\[0.3cm] +{\color{blue} +High probability of stable C$_{\text{sub}}$ configuration +} +\end{center} +\end{minipage} +}}} +\end{pspicture} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Combinations of substitutional C and Si self-interstitials +} + +\scriptsize + +\vspace{0.3cm} + +\begin{minipage}{6.2cm} +\begin{center} +{\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction} +\begin{itemize} + \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{} + \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB + \item Interaction drops quickly to zero\\ + $\rightarrow$ low capture radius +\end{itemize} +\end{center} +\end{minipage} +\begin{minipage}{0.2cm} +\hfill +\end{minipage} +\begin{minipage}{6.0cm} +\begin{center} +{\bf Transition from the ground state} +\begin{itemize} + \item Low transition barrier + \item Barrier smaller than \ci{} migration barrier + \item Low \si{} migration barrier (\unit[0.67]{eV})\\ + $\rightarrow$ Separation of \cs{} \& \si{} most probable +\end{itemize} +\end{center} +\end{minipage}\\[0.3cm] + +\begin{minipage}{6.0cm} +\includegraphics[width=6.0cm]{c_sub_si110.ps} +\end{minipage} +\begin{minipage}{0.4cm} +\hfill +\end{minipage} +\begin{minipage}{6.0cm} +\begin{flushright} +\includegraphics[width=6.0cm]{162-097.ps} +\end{flushright} +\end{minipage} + +\begin{pspicture}(0,0)(0,0) +\psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5) +\rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{ +\begin{minipage}{8cm} +\begin{center} +\vspace{0.1cm} +{\color{black} +\cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm] +IBS --- process far from equilibrium\\ +} +\end{center} +\end{minipage} +}}} +\end{pspicture} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Combinations of substitutional C and Si self-interstitials +} + +\scriptsize + +\vspace{0.3cm} + +\begin{minipage}{6.2cm} +\begin{center} +{\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction} +\begin{itemize} + \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{} + \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB + \item Interaction drops quickly to zero\\ + $\rightarrow$ low capture radius +\end{itemize} +\end{center} +\end{minipage} +\begin{minipage}{0.2cm} +\hfill +\end{minipage} +\begin{minipage}{6.0cm} +\begin{center} +{\bf Transition from the ground state} +\begin{itemize} + \item Low transition barrier + \item Barrier smaller than \ci{} migration barrier + \item Low \si{} migration barrier (\unit[0.67]{eV})\\ + $\rightarrow$ Separation of \cs{} \& \si{} most probable +\end{itemize} +\end{center} +\end{minipage}\\[0.3cm] + +\begin{minipage}{6.0cm} +\includegraphics[width=6.0cm]{c_sub_si110.ps} +\end{minipage} +\begin{minipage}{0.4cm} +\hfill +\end{minipage} +\begin{minipage}{6.0cm} +\begin{flushright} +\includegraphics[width=6.0cm]{162-097.ps} +\end{flushright} +\end{minipage} + +\begin{pspicture}(0,0)(0,0) +\psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5) +\rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{ +\begin{minipage}{8cm} +\begin{center} +\vspace{0.1cm} +{\color{black} +\cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm] +IBS --- process far from equilibrium\\ +} +\end{center} +\end{minipage} +}}} +\end{pspicture} + +% md support +\begin{pspicture}(0,0)(0,0) +\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{ +\begin{minipage}{14cm} +\hfill +\vspace{14cm} +\end{minipage} +}} +\rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{ +\begin{minipage}{11cm} +\begin{center} +\vspace{0.2cm} +\scriptsize +Ab initio MD at \degc{900}\\[0.4cm] +\begin{minipage}{5.4cm} +\centering +\includegraphics[width=4.3cm]{md01_bonds.eps}\\ +$t=\unit[2230]{fs}$ +\end{minipage} +\begin{minipage}{5.4cm} +\centering +\includegraphics[width=4.3cm]{md02_bonds.eps}\\ +$t=\unit[2900]{fs}$ +\end{minipage}\\[0.5cm] +{\color{blue} +Contribution of entropy to structural formation\\[0.1cm] +} +\end{center} +\end{minipage} +}}} +\end{pspicture} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Silicon carbide precipitation simulations +} + +\small + +\vspace{0.2cm} + +{\bf Procedure} + +{\scriptsize + \begin{pspicture}(0,0)(12,6.5) + % nodes + \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ + \parbox{7cm}{ + \begin{itemize} + \item Create c-Si volume + \item Periodc boundary conditions + \item Set requested $T$ and $p=0\text{ bar}$ + \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$ + \end{itemize} + }}}} + \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{ + \parbox{7cm}{ + Insertion of C atoms at constant T + \begin{itemize} + \item total simulation volume {\pnode{in1}} + \item volume of minimal SiC precipitate size {\pnode{in2}} + \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\ + precipitate + \end{itemize} + }}}} + \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{ + \parbox{7.0cm}{ + Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$ + }}}} + \ncline[]{->}{init}{insert} + \ncline[]{->}{insert}{cool} + \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3) + \rput(7.6,6){\footnotesize $V_1$} + \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5) + \rput(8.9,4.85){\tiny $V_2$} + \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75) + \rput(9.25,4.45){\footnotesize $V_3$} + \rput(7.9,3.2){\pnode{ins1}} + \rput(8.92,2.8){\pnode{ins2}} + \rput(10.8,2.4){\pnode{ins3}} + \ncline[]{->}{in1}{ins1} + \ncline[]{->}{in2}{ins2} + \ncline[]{->}{in3}{ins3} + \end{pspicture} +} + +\vspace{-0.5cm} + +{\bf Note} + +\footnotesize + +\begin{minipage}{5.7cm} +\begin{itemize} + \item Amount of C atoms: 6000\\ + ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm}) + \item Simulation volume: $31^3$ Si unit cells\\ + (238328 Si atoms) +\end{itemize} +\end{minipage} +\begin{minipage}{0.3cm} +\hfill +\end{minipage} +\framebox{ +\begin{minipage}{6.0cm} +Restricted to classical potential caclulations\\ +$\rightarrow$ Low C diffusion / overestimated barrier\\ +$\rightarrow$ Consider $V_2$ and $V_3$ +%\begin{itemize} +% \item $V_2$ and $V_3$ considered due to expected low C diffusion +%\end{itemize} +\end{minipage} +} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf\boldmath + Silicon carbide precipitation simulations at \degc{450} as in IBS +} + +\small + +\begin{minipage}{6.3cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\ +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps} +\hfill +\end{minipage} +\begin{minipage}{6.1cm} +\scriptsize +\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm] +\hkl<1 0 0> C-Si dumbbell dominated structure +\begin{itemize} + \item Si-C bumbs around \unit[0.19]{nm} + \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\ + concatenated differently oriented \ci{} DBs + \item Si-Si NN distance stretched to \unit[0.3]{nm} +\end{itemize} +\begin{pspicture}(0,0)(6.0,1.0) +\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{6cm} +\centering +Formation of \ci{} dumbbells\\ +C atoms in proper 3C-SiC distance first +\end{minipage} +}} +\end{pspicture}\\[0.1cm] +\underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}} +\begin{itemize} +\item High amount of strongly bound C-C bonds +\item Increased defect \& damage density\\ + $\rightarrow$ Arrangements hard to categorize and trace +\item Only short range order observable +\end{itemize} +\begin{pspicture}(0,0)(6.0,0.8) +\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{6cm} +\centering +Amorphous SiC-like phase +\end{minipage} +}} +\end{pspicture}\\[0.3cm] +\begin{pspicture}(0,0)(6.0,2.0) +\rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{ +\begin{minipage}{6cm} +\hfill +\vspace{2.5cm} +\end{minipage} +}} +\end{pspicture} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf\boldmath + Silicon carbide precipitation simulations at \degc{450} as in IBS +} + +\small + +\begin{minipage}{6.3cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\ +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps} +\hfill +\end{minipage} +\begin{minipage}{6.1cm} +\scriptsize +\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm] +\hkl<1 0 0> C-Si dumbbell dominated structure +\begin{itemize} + \item Si-C bumbs around \unit[0.19]{nm} + \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\ + concatenated differently oriented \ci{} DBs + \item Si-Si NN distance stretched to \unit[0.3]{nm} +\end{itemize} +\begin{pspicture}(0,0)(6.0,1.0) +\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{6cm} +\centering +Formation of \ci{} dumbbells\\ +C atoms in proper 3C-SiC distance first +\end{minipage} +}} +\end{pspicture}\\[0.1cm] +\underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}} +\begin{itemize} +\item High amount of strongly bound C-C bonds +\item Increased defect \& damage density\\ + $\rightarrow$ Arrangements hard to categorize and trace +\item Only short range order observable +\end{itemize} +\begin{pspicture}(0,0)(6.0,0.8) +\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{6cm} +\centering +Amorphous SiC-like phase +\end{minipage} +}} +\end{pspicture}\\[0.3cm] +\begin{pspicture}(0,0)(6.0,2.0) +\rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{ +\begin{minipage}{6cm} +\vspace{0.1cm} +\centering +{\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm] +\begin{minipage}{0.8cm} +{\bf\boldmath $V_1$:} +\end{minipage} +\begin{minipage}{5.1cm} +Formation of \ci{} indeed occurs\\ +Agllomeration not observed +\end{minipage}\\[0.3cm] +\begin{minipage}{0.8cm} +{\bf\boldmath $V_{2,3}$:} +\end{minipage} +\begin{minipage}{5.1cm} +Amorphous SiC-like structure\\ +(not expected at \degc{450})\\[0.05cm] +No rearrangement/transition into 3C-SiC +\end{minipage}\\[0.1cm] +\end{minipage} +}} +\end{pspicture} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Limitations of MD and short range potentials +} + +\small + +\vspace{0.2cm} + +{\bf Time scale problem of MD}\\[0.2cm] +Precise integration \& thermodynamic sampling\\ +$\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$, + $\omega$: vibrational mode\\ +$\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm] +Several local minima separated by large energy barriers\\ +$\Rightarrow$ Transition event corresponds to a multiple + of vibrational periods\\ +$\Rightarrow$ Phase transition consists of {\color{red}\underline{many}} + infrequent transition events\\[0.2cm] +{\color{blue}Accelerated methods:} +\underline{Temperature accelerated} MD (TAD), self-guided MD \ldots + +\vspace{0.2cm} + +{\bf Limitations related to the short range potential}\\[0.2cm] +Cut-off function limits interaction to next neighbours\\ +$\Rightarrow$ Overestimated unphysical high forces of next neighbours + (factor: 2.4--3.4) + +\vspace{1.4cm} + +{\bf Approach to the (twofold) problem}\\[0.2cm] +Increased temperature simulations without TAD corrections\\ +Accelerated methods or higher time scales exclusively not sufficient! + +\begin{pspicture}(0,0)(0,0) +\rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{ +\begin{minipage}{7.5cm} +\centering +\vspace{0.05cm} +Potential enhanced slow phase space propagation +\end{minipage} +}} +\rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{2.7cm} +\tiny +\centering +retain proper\\ +thermodynamic sampling +\end{minipage} +}} +\psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7) +\rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{3.6cm} +\tiny +\centering +\underline{IBS}\\[0.1cm] +3C-SiC also observed for higher T\\[0.1cm] +Higher T inside sample\\[0.1cm] +Structural evolution vs.\\ +equilibrium properties +\end{minipage} +}} +\psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0) +\end{pspicture} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf\boldmath + Increased temperature simulations --- $V_1$ +} + +\small + +\begin{minipage}{6.2cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps} +\hfill +\end{minipage} +\begin{minipage}{6.2cm} +\includegraphics[width=6.5cm]{tot_pc3_thesis.ps} +\end{minipage} + +\begin{minipage}{6.2cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps} +\hfill +\end{minipage} +\begin{minipage}{6.3cm} +\scriptsize + \underline{Si-C bonds:} + \begin{itemize} + \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$) + \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$ + \end{itemize} + \underline{Si-Si bonds:} + {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0> + ($\rightarrow$ 0.325 nm)\\[0.1cm] + \underline{C-C bonds:} + \begin{itemize} + \item C-C next neighbour pairs reduced (mandatory) + \item Peak at 0.3 nm slightly shifted + \begin{itemize} + \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\ + $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$ + combinations (|)\\ + $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations} + ($\downarrow$) + \item Range [|-$\downarrow$]: + {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$ + with nearby Si$_{\text{I}}$} + \end{itemize} + \end{itemize} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf\boldmath + Increased temperature simulations --- $V_1$ +} + +\small + +\begin{minipage}{6.2cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps} +\hfill +\end{minipage} +\begin{minipage}{6.2cm} +\includegraphics[width=6.5cm]{tot_pc3_thesis.ps} +\end{minipage} + +\begin{minipage}{6.2cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps} +\hfill +\end{minipage} +\begin{minipage}{6.3cm} +\scriptsize + \underline{Si-C bonds:} + \begin{itemize} + \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$) + \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$ + \end{itemize} + \underline{Si-Si bonds:} + {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0> + ($\rightarrow$ 0.325 nm)\\[0.1cm] + \underline{C-C bonds:} + \begin{itemize} + \item C-C next neighbour pairs reduced (mandatory) + \item Peak at 0.3 nm slightly shifted + \begin{itemize} + \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\ + $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$ + combinations (|)\\ + $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations} + ($\downarrow$) + \item Range [|-$\downarrow$]: + {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$ + with nearby Si$_{\text{I}}$} + \end{itemize} + \end{itemize} +\end{minipage} + +% conclusions +\begin{pspicture}(0,0)(0,0) +\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{ +\begin{minipage}{14cm} +\hfill +\vspace{14cm} +\end{minipage} +}} +\rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{ +\begin{minipage}{9cm} +\vspace{0.2cm} +\small +\begin{center} +{\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm] +{\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\ +\end{center} +\begin{itemize} +\item Stretched coherent SiC structures\\ +$\Rightarrow$ Precipitation process involves {\color{blue}\cs} +\item Explains annealing behavior of high/low T C implantations + \begin{itemize} + \item Low T: highly mobile {\color{red}\ci} + \item High T: stable configurations of {\color{blue}\cs} + \end{itemize} +\item Role of \si{} + \begin{itemize} + \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci] + \item Building block for surrounding Si host \& further SiC + \item Strain compensation \ldots\\ + \ldots Si/SiC interface\\ + \ldots within stretched coherent SiC structure + \end{itemize} +\end{itemize} +\vspace{0.2cm} +\centering +\psframebox[linecolor=blue,linewidth=0.05cm]{ +\begin{minipage}{7cm} +\centering +Precipitation mechanism involving \cs\\ +High T $\leftrightarrow$ IBS conditions far from equilibrium\\ +\end{minipage} +} +\end{minipage} +\vspace{0.2cm} +}} +\end{pspicture} + +\end{slide} + +% skip high T / C conc ... only here! +\ifnum1=0 + +\begin{slide} + + {\large\bf + Increased temperature simulations at high C concentration + } + +\footnotesize + +\begin{minipage}{6.5cm} +\includegraphics[width=6.4cm]{12_pc_thesis.ps} +\end{minipage} +\begin{minipage}{6.5cm} +\includegraphics[width=6.4cm]{12_pc_c_thesis.ps} +\end{minipage} + +\vspace{0.1cm} + +\scriptsize + +\framebox{ +\begin{minipage}[t]{6.0cm} +0.186 nm: Si-C pairs $\uparrow$\\ +(as expected in 3C-SiC)\\[0.2cm] +0.282 nm: Si-C-C\\[0.2cm] +$\approx$0.35 nm: C-Si-Si +\end{minipage} +} +\begin{minipage}{0.2cm} +\hfill +\end{minipage} +\framebox{ +\begin{minipage}[t]{6.0cm} +0.15 nm: C-C pairs $\uparrow$\\ +(as expected in graphite/diamond)\\[0.2cm] +0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm] +0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C +\end{minipage} +} + +\begin{itemize} +\item Decreasing cut-off artifact +\item {\color{red}Amorphous} SiC-like phase remains +\item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost +\item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature +\end{itemize} + +\vspace{-0.1cm} + +\begin{center} +{\color{blue} +\framebox{ +{\color{black} +High C \& small $V$ \& short $t$ +$\Rightarrow$ +} +Slow restructuring due to strong C-C bonds +{\color{black} +$\Leftarrow$ +High C \& low T implants +} +} +} +\end{center} + +\end{slide} + +% skipped high T / C conc +\fi + +\begin{slide} + +{\large\bf + Summary / Outlook +} + +\small + +\begin{pspicture}(0,0)(12,1.0) +\psframebox[fillstyle=gradient,gradbegin=hred,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{ +\begin{minipage}{11cm} +{\color{black}Diploma thesis}\\ + \underline{Monte Carlo} simulation modeling the selforganization process\\ + leading to periodic arrays of nanometric amorphous SiC precipitates +\end{minipage} +} +\end{pspicture}\\[0.4cm] +\begin{pspicture}(0,0)(12,2) +\psframebox[fillstyle=gradient,gradbegin=hblue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{ +\begin{minipage}{11cm} +{\color{black}Doctoral studies}\\ + Classical potential \underline{molecular dynamics} simulations \ldots\\ + \underline{Density functional theory} calculations \ldots\\[0.2cm] + \ldots on defect formation and SiC precipitation in Si +\end{minipage} +} +\end{pspicture}\\[0.5cm] +\begin{pspicture}(0,0)(12,3) +\psframebox[fillstyle=solid,fillcolor=white,linestyle=solid]{ +\begin{minipage}{11cm} +\vspace{0.2cm} +{\color{black}\bf How to proceed \ldots}\\[0.1cm] +MC $\rightarrow$ empirical potential MD $\rightarrow$ Ground-state DFT \ldots +\begin{itemize} + \renewcommand\labelitemi{$\ldots$} + \item beyond LDA/GGA methods \& ground-state DFT +\end{itemize} +Investigation of structure \& structural evolution \ldots +\begin{itemize} + \renewcommand\labelitemi{$\ldots$} + \item electronic/optical properties + \item electronic correlations + \item non-equilibrium systems +\end{itemize} +\end{minipage} +} +\end{pspicture}\\[0.5cm] + +\end{slide} + +\begin{slide} + + {\large\bf + Acknowledgements + } + + \vspace{0.1cm} + + \small + + Thanks to \ldots + + \underline{Augsburg} + \begin{itemize} + \item Prof. B. Stritzker (accomodation at EP \RM{4}) + \item Ralf Utermann (EDV) + \end{itemize} + + \underline{Helsinki} + \begin{itemize} + \item Prof. K. Nordlund (MD) + \end{itemize} + + \underline{Munich} + \begin{itemize} + \item Bayerische Forschungsstiftung (financial support) + \end{itemize} + + \underline{Paderborn} + \begin{itemize} + \item Prof. J. Lindner (SiC) + \item Prof. G. Schmidt (DFT + financial support) + \item Dr. E. Rauls (DFT + SiC) + \end{itemize} + + \underline{Stuttgart} +\begin{center} +\framebox{ +\bf Thank you for your attention / invitation! +} +\end{center} + +\end{slide} + +\end{document} + diff --git a/posic/talks/defense.txt b/posic/talks/defense.txt new file mode 100644 index 0000000..83f618d --- /dev/null +++ b/posic/talks/defense.txt @@ -0,0 +1,24 @@ +slide 1 + +dear examiners, dear colleagues. +welcome everybody to the the defense of my doctor's thesis entitled ... +as usual, i would like to start with a small motivation, +which in this case is a motivation with respect to the materials system, SiC. + +slide 2 + +the semiconductor material SiC ... + +slide 3 +slide 4 +slide 5 +slide 6 +slide 7 +slide 8 +slide 9 +slide 10 +slide 11 +slide 12 +slide 13 +slide 14 +slide 15