From 310e93282535b42f7ae2e3cd167776cc6249171a Mon Sep 17 00:00:00 2001 From: hackbard Date: Mon, 14 May 2012 21:50:15 +0200 Subject: [PATCH] almostr finished --- posic/talks/emrs2012.tex | 2054 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 2054 insertions(+) create mode 100644 posic/talks/emrs2012.tex diff --git a/posic/talks/emrs2012.tex b/posic/talks/emrs2012.tex new file mode 100644 index 0000000..b437eb1 --- /dev/null +++ b/posic/talks/emrs2012.tex @@ -0,0 +1,2054 @@ +\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 +\ifnum1=0 +\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} +\fi + +% topic + +\begin{slide} + + \small + + \vspace{16pt} + + {\LARGE\bf + %\hrule + %\vspace{5pt} + First-principles and empirical\\[0.2cm] + potential simulation study of intrinsic\\[0.2cm] + and carbon-related defects in silicon + %\vspace{10pt} + %\hrule + } + + \vspace{30pt} + + {\bf\small + \underline{F. Zirkelbach} $\color{gray}\bullet$ B. Stritzker\\ + } + {\color{gray} + Experimentalphysik IV, Universit\"at Augsburg, 86135 Augsburg, Germany + }\\[0.3cm] + {\bf\small + K. Nordlund\\ + } + {\color{gray} + Department of Physics, University of Helsinki, 00014 Helsinki, Finland + }\\[0.3cm] + {\bf\small + W. G. Schmidt $\color{gray}\bullet$ E. Rauls $\color{gray}\bullet$ + J. K. N. Lindner\\ + } + {\color{gray} + Department Physik, Universit\"at Paderborn, 33095 Paderborn, Germany + } + + \vspace{30pt} + + { + E-MRS Spring Meeting, Strasbourg, 17.05.2012 + } + +\end{slide} + +% no vertical centering +\centerslidesfalse + +% skip for preparation +\ifnum1=0 + +% intro + +\begin{slide} + +\headphd +{\large\bf + Motivation \& Outline +} + +\vspace{0.1cm} + +{\bf + Ion beam synthesis (IBS) of epitaxial single crystalline 3C-SiC +} + +\vspace{0.1cm} + +\begin{minipage}{7.0cm} +\small +\begin{itemize} + \item \underline{Implantation}\\[0.1cm] + Stoichiometric dose | \unit[180]{keV} | \degc{500}\\ + $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \& + {\color{blue}precipitates} + \item \underline{Annealing}\\[0.1cm] + \unit[10]{h} at \degc{1250}\\ + $\Rightarrow$ Homogeneous 3C-SiC layer +\end{itemize} +\begin{center} +{\color{blue} +\framebox{ +\begin{minipage}{4.5cm} + \color{black} + \centering + 3C-SiC precipitation\\ + not yet fully understood +\end{minipage} +} +} +\end{center} +\end{minipage} +\begin{minipage}{5.0cm} +\includegraphics[width=5.5cm]{ibs_3c-sic.eps}\\[-0.4cm] +\begin{center} +{\tiny + XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0) +} +\end{center} +\end{minipage}\\[0.2cm] + +{\bf + Outline +} + +\begin{itemize} + \item Assumed SiC precipitation mechanisms / Controversy + \item Utilized simulation techniques + \item C and Si self-interstitial point defects in silicon + \item Silicon carbide precipitation simulations +\end{itemize} + +\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 lattice 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 {\color{blue}Substitutionally} incorporated C 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 Si$_{1-y}$C$_y$/Si heterostructures + {\tiny\color{gray}/Strane~et~al./Guedj~et~al./} + \begin{itemize} + \item Initial {\color{blue}coherent} SiC structures (tensile strain) + \item Incoherent SiC nanocrystals (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 | $E_{\text{cut}}=\unit[300]{eV}$ +%$\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{0.3cm} + +\begin{minipage}[t]{6cm} +{\bf Defect formation energy}\\ +\framebox{ +$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.5cm] +%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}[t]{6cm} +\vspace{1.4cm} +{\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 + 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 interstitial migration +} + +\scriptsize + +\vspace{0.3cm} + +\begin{minipage}{6.8cm} +{\bf\underline{First-principles}} $\quad$ \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{blue}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}\\[0.4cm] +\begin{minipage}{6.8cm} +{\bf\underline{Empirical potential}} $\quad$ +\hkl[0 0 -1] $\rightarrow$ \hkl[1 1 0] $\rightarrow$ \hkl[0 -1 0]\\ +\begin{itemize} + \item Transition involving \hkl[1 1 0] DB\\ + (instability of BC configuration) + \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} +\vspace{0.1cm} +\begin{center} +{\color{red}Drastically overestimated diffusion barrier} +\end{center} +\end{minipage} +\begin{minipage}{5.4cm} +\includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf\boldmath + Defect combinations --- ab inito +} + +\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} +} +\end{minipage} +\begin{minipage}{3cm} +\includegraphics[width=3.5cm]{comb_pos.eps} +\end{minipage} + +\vspace{0.5cm} + +{\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm] +\begin{minipage}{6.1cm} +\begin{itemize} + \item \ci{} agglomeration energetically favorable + \item Reduction of strain + \item Capture radius exceeding \unit[1]{nm} + \item Disappearance of attractive forces\\ + between two lowest separations. +\end{itemize} +\begin{center} +{\color{blue}\ci{} agglomeration / no C clustering} +\end{center} +\end{minipage} + +\begin{picture}(0,0)(-180,-40) +\begin{minipage}{6.0cm} +\scriptsize\centering +Interaction along \hkl[1 1 0]\\ +\includegraphics[width=6.2cm]{db_along_110_cc.ps} +\end{minipage} +\end{picture} + +\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} + +\fi + +\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}}\\ + \item volume containing 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 + Silicon carbide precipitation simulations +} + +\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]{tot_pc_thesis.ps} +\hfill +\end{minipage} +\begin{minipage}{6.1cm} +\scriptsize +\underline{Temperature as used in IBS (\degc{450})}\\[0.2cm] +\ci{} \hkl<1 0 0> dumbbell dominated structure\\ +\begin{pspicture}(0,0)(6.0,1.0) +\rput(2.75,0.4){\psframebox[linewidth=0.05cm,linecolor=black]{ +\begin{minipage}{5cm} +\vspace{0.1cm} +\centering +{\color{blue}Formation of \ci{} DBs}\\ +{\color{red}No agllomeration / precipitation} +\end{minipage} +}} +\end{pspicture}\\[0.1cm] +Limitations: +\begin{itemize} + \item Time scale problem of MD\\ + $\Rightarrow$ slow phase space propagation + \item Short range potential\\ + $\Rightarrow$ overestimated diffusion barrier +\end{itemize} +\vspace{0.6cm} +\underline{Increased temperatures}\\[0.2cm] +\cs{} dominated structure\\ +\begin{pspicture}(0,0)(6.0,1.0) +\rput(2.75,0.4){\psframebox[linewidth=0.05cm,linecolor=black]{ +\begin{minipage}{5cm} +\vspace{0.1cm} +\centering +Si-{\color{blue}C$_{\text{sub}}$}-Si along \hkl<1 1 0>\\ +{\color{blue}\cs}-Si-{\color{blue}\cs} \& nearby \si +\end{minipage} +}} +\end{pspicture}\\[0.1cm] +Conclusions: +\begin{itemize} + \item Stretched coherent SiC structures\\ + $\Rightarrow$ \cs{} involved in precipitation mechanism + \item High T $\leftrightarrow$ non-equilibrium IBS conditions +\end{itemize} +\vspace{0.3cm} + +\end{minipage} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Summary and Conclusions +} + +Summary + +\begin{itemize} + \item First-principles investigation of defect combinations + and mobilities in Si + \item Empirical potential MD simulations on SiC prcipitation in Si +\end{itemize} + + +% conclusions +\rput(6.5,-4.0){\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 directly observed\\ +\psframebox[linecolor=blue,linewidth=0.05cm]{ +\begin{minipage}{7cm} +\centering +\cs{} involved in the precipitation mechanism\\ +\end{minipage} +} +\item Emission of \si{} serves several needs: + \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} +\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} +\psframebox[linecolor=blue,linewidth=0.05cm]{ +\begin{minipage}{7cm} +\centering +High T $\leftrightarrow$ IBS conditions far from equilibrium\\ +\end{minipage} +} +\end{itemize} +\end{minipage} +\vspace{0.2cm} +}} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Acknowledgements +} + + \vspace{0.1cm} + + \small + + Thanks to \ldots + +\begin{minipage}[t]{6cm} + \underline{Augsburg} + \begin{itemize} + \item Prof. B. Stritzker + \end{itemize} + + \underline{Helsinki} + \begin{itemize} + \item Prof. K. Nordlund + \end{itemize} + + \underline{Munich} + \begin{itemize} + \item Bayerische Forschungsstiftung + \end{itemize} +\end{minipage} +\begin{minipage}[t]{6cm} + \underline{Paderborn} + \begin{itemize} + \item Prof. J. Lindner + \item Prof. G. Schmidt + \item Dr. E. Rauls + \end{itemize} +\end{minipage} + +\vspace{2.5cm} + +\begin{center} +\framebox{ +\LARGE\bf Thank you for your attention! +} +\end{center} + +\end{slide} + + + + + + + +\ifnum1=0 + +\begin{slide} + +\headphd + {\large\bf + Polytypes of SiC\\[0.6cm] + } + +\vspace{0.6cm} + +\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](5.7,2.05)(0.4,0.50) +\end{pspicture} +\begin{pspicture}(0,0)(0,0) +\psellipse[linecolor=green](5.6,0.89)(0.4,0.20) +\end{pspicture} +\begin{pspicture}(0,0)(0,0) +\psellipse[linecolor=red](10.45,0.42)(0.4,0.20) +\end{pspicture} + +\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} + +\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} + + {\large\bf + Increased temperature simulations at high C concentration + } + +\footnotesize + +\begin{minipage}{6.0cm} +\includegraphics[width=6.4cm]{12_pc_thesis.ps} +\end{minipage} +\begin{minipage}{6.0cm} +\includegraphics[width=6.4cm]{12_pc_c_thesis.ps} +\end{minipage} + +\vspace{0.1cm} + +\scriptsize + +\framebox{ +\begin{minipage}[t]{5.5cm} +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}{0.1cm} +\hfill +\end{minipage} +\framebox{ +\begin{minipage}[t]{5.9cm} +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} + +\begin{center} +{\color{blue} +\framebox{ +{\color{black} +High C \& small $V$ \& short $t$ +$\Rightarrow$ +} +\begin{minipage}{4cm} +\begin{center} +Slow structural evolution due to strong C-C bonds +\end{center} +\end{minipage} +{\color{black} +$\Leftarrow$ +High C \& low T implants +} +} +} +\end{center} + +\end{slide} + + + +\begin{slide} + + {\large\bf + Valuation of a practicable temperature limit + } + + \small + +\vspace{0.1cm} + +\begin{center} +\framebox{ +{\color{blue} +Recrystallization is a hard task! +$\Rightarrow$ Avoid melting! +} +} +\end{center} + +\vspace{0.1cm} + +\footnotesize + +\begin{minipage}{6.4cm} +\includegraphics[width=6.4cm]{fe_and_t.ps} +\end{minipage} +\begin{minipage}{5.7cm} +\underline{Melting does not occur instantly after}\\ +\underline{exceeding the melting point $T_{\text{m}}=2450\text{ K}$} +\begin{itemize} +\item required transition enthalpy +\item hysterisis behaviour +\end{itemize} +\underline{Heating up c-Si by 1 K/ps} +\begin{itemize} +\item transition occurs at $\approx$ 3125 K +\item $\Delta E=0.58\text{ eV/atom}=55.7\text{ kJ/mole}$\\ + (literature: 50.2 kJ/mole) +\end{itemize} +\end{minipage} + +\vspace{0.1cm} + +\framebox{ +\begin{minipage}{4cm} +Initially chosen temperatures:\\ +$1.0 - 1.2 \cdot T_{\text{m}}$ +\end{minipage} +} +\begin{minipage}{2cm} +\begin{center} +$\Longrightarrow$ +\end{center} +\end{minipage} +\framebox{ +\begin{minipage}{5cm} +Introduced C (defects)\\ +$\rightarrow$ reduction of transition point\\ +$\rightarrow$ melting already at $T_{\text{m}}$ +\end{minipage} +} + +\vspace{0.4cm} + +\begin{center} +\framebox{ +{\color{blue} +Maximum temperature used: $0.95\cdot T_{\text{m}}$ +} +} +\end{center} + +\end{slide} + +\begin{slide} + + {\large\bf + Long time scale simulations at maximum temperature + } + +\small + +\vspace{0.1cm} + +\underline{Differences} +\begin{itemize} + \item Temperature set to $0.95 \cdot T_{\text{m}}$ + \item Cubic insertion volume $\Rightarrow$ spherical insertion volume + \item Amount of C atoms: 6000 $\rightarrow$ 5500 + $\Leftrightarrow r_{\text{prec}}=0.3\text{ nm}$ + \item Simulation volume: 21 unit cells of c-Si in each direction +\end{itemize} + +\footnotesize + +\vspace{0.3cm} + +\begin{minipage}[t]{4.3cm} +\begin{center} +\underline{Low C concentration, Si-C} +\includegraphics[width=4.3cm]{c_in_si_95_v1_si-c.ps}\\ +Sharper peaks! +\end{center} +\end{minipage} +\begin{minipage}[t]{4.3cm} +\begin{center} +\underline{Low C concentration, C-C} +\includegraphics[width=4.3cm]{c_in_si_95_v1_c-c.ps}\\ +Sharper peaks!\\ +No C agglomeration! +\end{center} +\end{minipage} +\begin{minipage}[t]{3.4cm} +\begin{center} +\underline{High C concentration} +\includegraphics[width=4.3cm]{c_in_si_95_v2.ps}\\ +No significant changes\\ +iC-Si-Si $\uparrow$\\ +C-Si-C $\downarrow$ +\end{center} +\end{minipage} + +\begin{center} +\framebox{ +Long time scales and high temperatures most probably not sufficient enough! +} +\end{center} + +\end{slide} + +\begin{slide} + + {\large\bf + Investigation of a silicon carbide precipitate in silicon + } + + \scriptsize + +\vspace{0.2cm} + +\framebox{ +\scriptsize +\begin{minipage}{5.3cm} +\[ +\frac{8}{a_{\text{Si}}^3}( +\underbrace{21^3 a_{\text{Si}}^3}_{=V} +-\frac{4}{3}\pi x^3)+ +\underbrace{\frac{4}{y^3}\frac{4}{3}\pi x^3}_{\stackrel{!}{=}5500} +=21^3\cdot 8 +\] +\[ +\Downarrow +\] +\[ +\frac{8}{a_{\text{Si}}^3}\frac{4}{3}\pi x^3=5500 +\Rightarrow x = \left(\frac{5500 \cdot 3}{32 \pi} \right)^{1/3}a_{\text{Si}} +\] +\[ +y=\left(\frac{1}{2} \right)^{1/3}a_{\text{Si}} +\] +\end{minipage} +} +\begin{minipage}{0.1cm} +\hfill +\end{minipage} +\begin{minipage}{6.3cm} +\underline{Construction} +\begin{itemize} + \item Simulation volume: 21$^3$ unit cells of c-Si + \item Spherical topotactically aligned precipitate\\ + $r=3.0\text{ nm}$ $\Leftrightarrow$ $\approx$ 5500 C atoms + \item Create c-Si but skipped inside sphere\\ + of radius $x$ + \item Create 3C-SiC inside sphere of radius $x$\\ + and lattice constant $y$ + \item Strong coupling to heat bath ($T=20\,^{\circ}\mathrm{C}$) +\end{itemize} +\end{minipage} + +\vspace{0.3cm} + +\begin{minipage}{6.0cm} +\includegraphics[width=6cm]{pc_0.ps} +\end{minipage} +\begin{minipage}{6.1cm} +\underline{Results} +\begin{itemize} + \item Slight increase of c-Si lattice constant! + \item C-C peaks\\ + (imply same distanced Si-Si peaks) + \begin{itemize} + \item New peak at 0.307 nm: 2$^{\text{nd}}$ NN in 3C-SiC + \item Bumps ({\color{green}$\downarrow$}): + 4$^{\text{th}}$ and 6$^{\text{th}}$ NN + \end{itemize} + \item 3C-SiC lattice constant: 4.34 \AA (bulk: 4.36 \AA)\\ + $\rightarrow$ compressed precipitate + \item Interface tension:\\ + 20.15 eV/nm$^2$ or $3.23 \times 10^{-4}$ J/cm$^2$\\ + (literature: $2 - 8 \times 10^{-4}$ J/cm$^2$) +\end{itemize} +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + Investigation of a silicon carbide precipitate in silicon + } + + \footnotesize + +\begin{minipage}{7cm} +\underline{Appended annealing steps} +\begin{itemize} + \item artificially constructed interface\\ + $\rightarrow$ allow for rearrangement of interface atoms + \item check SiC stability +\end{itemize} +\underline{Temperature schedule} +\begin{itemize} + \item rapidly heat up structure up to $2050\,^{\circ}\mathrm{C}$\\ + (75 K/ps) + \item slow heating up to $1.2\cdot T_{\text{m}}=2940\text{ K}$ + by 1 K/ps\\ + $\rightarrow$ melting at around 2840 K + (\href{../video/sic_prec_120.avi}{$\rhd$}) + \item cooling down structure at 100 \% $T_{\text{m}}$ (1 K/ps)\\ + $\rightarrow$ no energetically more favorable struture +\end{itemize} +\end{minipage} +\begin{minipage}{5cm} +\includegraphics[width=5.5cm]{fe_and_t_sic.ps} +\end{minipage} + +\begin{minipage}{4cm} +\includegraphics[width=4cm]{sic_prec/melt_01.eps} +\end{minipage} +\begin{minipage}{0.2cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{4cm} +\includegraphics[width=4cm]{sic_prec/melt_02.eps} +\end{minipage} +\begin{minipage}{0.2cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{3.7cm} +\includegraphics[width=4cm]{sic_prec/melt_03.eps} +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + DFT parameters + } + +\scriptsize + +\vspace{0.1cm} + +Equilibrium lattice constants and cohesive energies + +\begin{tabular}{l r c c c c c} +\hline +\hline + & & USPP, LDA & USPP, GGA & PAW, LDA & PAW, GGA & Exp. \\ +\hline +Si (dia) & $a$ [\AA] & 5.389 & 5.455 & - & - & 5.429 \\ + & $\Delta_a$ [\%] & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - & - & - \\ + & $E_{\text{coh}}$ [eV] & -5.277 & -4.591 & - & - & -4.63 \\ + & $\Delta_E$ [\%] & \unit[{\color{red}14.0}]{\%} & \unit[{\color{green}0.8}]{\%} & - & - & - \\ +\hline +C (dia) & $a$ [\AA] & 3.527 & 3.567 & - & - & 3.567 \\ + & $\Delta_a$ [\%] & \unit[{\color{green}1.1}]{\%} & \unit[{\color{green}0.01}]{\%} & - & - & - \\ + & $E_{\text{coh}}$ [eV] & -8.812 & -7.703 & - & - & -7.374 \\ + & $\Delta_E$ [\%] & \unit[{\color{red}19.5}]{\%} & \unit[{\color{orange}4.5}]{\%} & - & - & - \\ +\hline +3C-SiC & $a$ [\AA] & 4.319 & 4.370 & 4.330 & 4.379 & 4.359 \\ + & $\Delta_a$ [\%] & \unit[{\color{green}0.9}]{\%} & \unit[{\color{green}0.3}]{\%} & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - \\ + & $E_{\text{coh}}$ [eV] & -7.318 & -6.426 & -7.371 & -6.491 & -6.340 \\ + & $\Delta_E$ [\%] & \unit[{\color{red}15.4}]{\%} & \unit[{\color{green}1.4}]{\%} & \unit[{\color{red}16.3}]{\%} & \unit[{\color{orange}2.4}]{\%} & - \\ +\hline +\hline +\end{tabular} + +\vspace{0.3cm} + +\begin{minipage}{7cm} +\begin{center} +\begin{tabular}{l c c c} +\hline +\hline + & Si (dia) & C (dia) & 3C-SiC \\ +\hline +$a$ [\AA] & 5.458 & 3.562 & 4.365 \\ +$\Delta_a$ [\%] & 0.5 & 0.1 & 0.1 \\ +\hline +$E_{\text{coh}}$ [eV] & -4.577 & -7.695 & -6.419 \\ +$\Delta_E$ [\%] & 1.1 & 4.4 & 1.2 \\ +\hline +\hline +\end{tabular} +\end{center} +\end{minipage} +\begin{minipage}{5cm} +$\leftarrow$ entire parameter set +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + DFT parameters\\ + } + +\footnotesize + +\begin{minipage}{6cm} +\begin{center} +\includegraphics[width=6cm]{sic_32pc_gamma_cutoff_lc.ps} +\end{center} +\end{minipage} +\begin{minipage}{6cm} +\begin{center} +Lattice constants with respect to the PW cut-off energy +\end{center} +\end{minipage} + +\begin{minipage}{6cm} +\begin{center} +\includegraphics[width=6cm]{si_self_int_thesis.ps} +\end{center} +\end{minipage} +\begin{minipage}{6cm} +\begin{center} +Defect formation energy with respect to the size of the supercell\\[0.1cm] +\end{center} + +\end{minipage} + +\end{slide} + +\fi + +\end{document} + -- 2.20.1