From 93bfd5e9849fe87eb9004f6ba5c2081b1fed2c70 Mon Sep 17 00:00:00 2001 From: hackbard Date: Sun, 17 Aug 2008 15:51:10 +0200 Subject: [PATCH] added helsinki 2008 tex file --- posic/talks/helsinki_2008.tex | 546 ++++++++++++++++++++++++++++++++++ 1 file changed, 546 insertions(+) create mode 100644 posic/talks/helsinki_2008.tex diff --git a/posic/talks/helsinki_2008.tex b/posic/talks/helsinki_2008.tex new file mode 100644 index 0000000..5a5ceda --- /dev/null +++ b/posic/talks/helsinki_2008.tex @@ -0,0 +1,546 @@ +\pdfoutput=0 +\documentclass[landscape,semhelv]{seminar} + +\usepackage{verbatim} +\usepackage[german]{babel} +\usepackage[latin1]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{amsmath} +\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{epic} +%\usepackage{eepic} + +\usepackage{graphicx} +\graphicspath{{../img/}} + +\usepackage[setpagesize=false]{hyperref} + +\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} + +\begin{document} + +\extraslideheight{10in} +\slideframe{none} + +\pagestyle{empty} + +% specify width and height +\slidewidth 27.7cm +\slideheight 19.1cm + +% shift it into visual area properly +\def\slideleftmargin{3.3cm} +\def\slidetopmargin{0.6cm} + +\newcommand{\ham}{\mathcal{H}} +\newcommand{\pot}{\mathcal{V}} +\newcommand{\foo}{\mathcal{U}} +\newcommand{\vir}{\mathcal{W}} + +% itemize level ii +\renewcommand\labelitemii{{\color{gray}$\bullet$}} + +% colors +\newrgbcolor{si-yellow}{.6 .6 0} +\newrgbcolor{hb}{0.75 0.77 0.89} +\newrgbcolor{lbb}{0.75 0.8 0.88} +\newrgbcolor{lachs}{1.0 .93 .81} + +% topic + +\begin{slide} +\begin{center} + + \vspace{16pt} + + {\LARGE\bf + Molecular dynamics simulation study\\ + of the silicon carbide precipitation process + } + + \vspace{24pt} + + \textsc{\small \underline{F. Zirkelbach}$^1$, J. K. N. Lindner$^1$, + K. Nordlund$^2$, B. Stritzker$^1$}\\ + + \vspace{32pt} + + \begin{minipage}{2.0cm} + \begin{center} + \includegraphics[height=1.6cm]{uni-logo.eps} + \end{center} + \end{minipage} + \begin{minipage}{8.0cm} + \begin{center} + {\footnotesize + $^1$ Experimentalphysik IV, Institut f"ur Physik,\\ + Universit"at Augsburg, Universit"atsstr. 1,\\ + D-86135 Augsburg, Germany + } + \end{center} + \end{minipage} + \begin{minipage}{2.3cm} + \begin{center} + \includegraphics[height=1.5cm]{Lehrstuhl-Logo.eps} + \end{center} + \end{minipage} + + \vspace{16pt} + + \begin{minipage}{4.0cm} + \begin{center} + \includegraphics[height=1.6cm]{logo_eng.eps} + \end{center} + \end{minipage} + \begin{minipage}{8.0cm} + \begin{center} + {\footnotesize + $^2$ Accelerator Laboratory, Department of Physical Sciences,\\ + University of Helsinki, Pietari Kalmink. 2,\\ + 00014 Helsinki, Finland + } + \end{center} + \end{minipage} +\end{center} +\end{slide} + +% contents + +% no contents for such a short talk! + +% start of contents + +\begin{slide} + + {\large\bf + Motivation + } + + \vspace{16pt} + + Reasons for understanding the SiC precipitation process: + + \vspace{16pt} + + \begin{itemize} + \item 3C-SiC is a promising wide band gap material for high-temperature, + high-power, high-frequency semiconductor devices [1] + \item 3C-SiC epitaxial thin film formation on Si requires detailed + knowledge of SiC nucleation + \item Fabrication of high carbon doped, strained pseudomorphic + $\text{Si}_{1-y}\text{C}_y$ layers requires suppression of + 3C-SiC nucleation [2] + \end{itemize} + + \vspace{16pt} + + {\tiny + [1] J. H. Edgar, J. Mater. Res. 7 (1992) 235.}\\ + {\tiny + [2] J. W. Strane, S. R. Lee, H. J. Stein, S. T. Picraux, + J. K. Watanabe, J. W. Mayer, J. Appl. Phys. 79 (1996) 637.} + +\end{slide} + +\begin{slide} + + {\large\bf + Crystalline silicon and cubic silicon carbide + } + + {\bf Lattice types and unit cells:} + \begin{itemize} + \item Crystalline silicon (c-Si) has diamond structure\\ + $\Rightarrow {\color{si-yellow}\bullet}$ and + ${\color{gray}\bullet}$ are Si atoms + \item Cubic silicon carbide (3C-SiC) has zincblende structure\\ + $\Rightarrow {\color{si-yellow}\bullet}$ are Si atoms, + ${\color{gray}\bullet}$ are C atoms + \end{itemize} + \begin{minipage}{8cm} + {\bf Lattice constants:} + \[ + 4a_{\text{c-Si}}\approx5a_{\text{3C-SiC}} + \] + {\bf Silicon density:} + \[ + \frac{n_{\text{3C-SiC}}}{n_{\text{c-Si}}}=97,66\,\% + \] + \end{minipage} + \begin{minipage}{5cm} + \includegraphics[width=5cm]{sic_unit_cell.eps} + \end{minipage} + +\end{slide} + + \small +\begin{slide} + + {\large\bf + Motivation / Introduction + } + + \small + \vspace{6pt} + + Supposed conversion mechanism of heavily carbon doped Si into SiC: + + \vspace{8pt} + + \begin{minipage}{3.8cm} + \includegraphics[width=3.7cm]{sic_prec_seq_01.eps} + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + \includegraphics[width=3.7cm]{sic_prec_seq_02.eps} + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + \includegraphics[width=3.7cm]{sic_prec_seq_03.eps} + \end{minipage} + + \vspace{8pt} + + \begin{minipage}{3.8cm} + Formation of C-Si dumbbells on regular c-Si lattice sites + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + Agglomeration into large clusters (embryos)\\ + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + Precipitation of 3C-SiC + Creation of interstitials\\ + \end{minipage} + + \vspace{12pt} + + Experimentally observed: + \begin{itemize} + \item Minimal diameter of precipitation: 4 - 5 nm + \item Equal orientation of Si and SiC (hkl)-planes + \end{itemize} + +\end{slide} + +\begin{slide} + + {\large\bf + Simulation details + } + + \vspace{12pt} + + MD basics: + \begin{itemize} + \item Microscopic description of N particle system + \item Analytical interaction potential + \item Hamilton's equations of motion as propagation rule\\ + in 6N-dimensional phase space + \item Observables obtained by time average + \end{itemize} + + \vspace{12pt} + + Application details: + \begin{itemize} + \item Integrator: Velocity Verlet, timestep: $1\, fs$ + \item Ensemble: NVT, Berendsen thermostat, $\tau=100.0$ + \item Potential: Tersoff-like bond order potential\\ + \[ + E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad + \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] + \] + \begin{center} + {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211} + \end{center} + \end{itemize} + + \begin{picture}(0,0)(-240,-70) + \includegraphics[width=5cm]{tersoff_angle.eps} + \end{picture} + +\end{slide} + +\begin{slide} + + {\large\bf + Simulation details + } + + \vspace{8pt} + + Interstitial simulations: + + \vspace{8pt} + + \begin{pspicture}(0,0)(7,8) + \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{ + \parbox{7cm}{ + \begin{itemize} + \item Initial configuration: $9\times9\times9$ unit cells Si + \item Periodic boundary conditions + \item $T=0 \, K$ + \end{itemize} + }}}} +\rput(3.5,3.5){\rnode{insert}{\psframebox{ + \parbox{7cm}{ + Insertion of C / Si atom: + \begin{itemize} + \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral} + \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal} + \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\ + $\rightarrow$ {\color{magenta}110 dumbbell} + \item random positions (critical distance check) + \end{itemize} + }}}} + \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{ + \parbox{3.5cm}{ + Relaxation time: $2\, ps$ + }}}} + \ncline[]{->}{init}{insert} + \ncline[]{->}{insert}{cool} + \end{pspicture} + + \begin{picture}(0,0)(-210,-45) + \includegraphics[width=6cm]{unit_cell.eps} + \end{picture} + +\end{slide} + +\begin{slide} + + {\large\bf + Results + } - Si self-interstitial runs + + \small + + \begin{minipage}[t]{4.3cm} + \underline{Tetrahedral}\\ + $E_f=3.41\, eV$\\ + \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps} + \end{minipage} + \begin{minipage}[t]{4.3cm} + \underline{110 dumbbell}\\ + $E_f=4.39\, eV$\\ + \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps} + \end{minipage} + \begin{minipage}[t]{4.3cm} + \underline{Hexagonal} \hspace{4pt} + \href{../video/si_self_int_hexa.avi}{$\rhd$}\\ + $E_f^{\star}\approx4.48\, eV$ (unstable!)\\ + \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps} + \end{minipage} + + \underline{Random insertion} + + \begin{minipage}{4.3cm} + $E_f=3.97\, eV$\\ + \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps} + \end{minipage} + \begin{minipage}{4.3cm} + $E_f=3.75\, eV$\\ + \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps} + \end{minipage} + \begin{minipage}{4.3cm} + $E_f=3.56\, eV$\\ + \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps} + \end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + Results + } - Carbon interstitial runs + + \small + + \begin{minipage}[t]{4.3cm} + \underline{Tetrahedral}\\ + $E_f=2.67\, eV$\\ + \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps} + \end{minipage} + \begin{minipage}[t]{4.3cm} + \underline{110 dumbbell}\\ + $E_f=1.76\, eV$\\ + \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps} + \end{minipage} + \begin{minipage}[t]{4.3cm} + \underline{Hexagonal} \hspace{4pt} + \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\ + $E_f^{\star}\approx5.6\, eV$ (unstable!)\\ + \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps} + \end{minipage} + + \underline{Random insertion} + + \footnotesize + +\begin{minipage}[t]{3.3cm} + $E_f=0.47\, eV$\\ + \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps} + \begin{picture}(0,0)(-15,-3) + 001 dumbbell + \end{picture} +\end{minipage} +\begin{minipage}[t]{3.3cm} + $E_f=1.62\, eV$\\ + \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps} +\end{minipage} +\begin{minipage}[t]{3.3cm} + $E_f=2.39\, eV$\\ + \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps} +\end{minipage} +\begin{minipage}[t]{3.0cm} + $E_f=3.41\, eV$\\ + \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps} +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + Simulation details + } + + \small + + \vspace{8pt} + + SiC precipitation simulations: + + \vspace{8pt} + + \begin{pspicture}(0,0)(12,8) + % nodes + \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{ + \parbox{7cm}{ + \begin{itemize} + \item Initial configuration: $31\times31\times31$ unit cells Si + \item Periodic boundary conditions + \item $T=450\, ^{\circ}C$ + \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$ + \end{itemize} + }}}} + \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{ + \parbox{7cm}{ + Insertion of $6000$ carbon atoms at constant\\ + temperature into: + \begin{itemize} + \item Total simulation volume {\pnode{in1}} + \item Volume of minimal SiC precipitation {\pnode{in2}} + \item Volume of necessary amount of Si {\pnode{in3}} + \end{itemize} + }}}} + \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{ + \parbox{3.5cm}{ + Cooling down to $20\, ^{\circ}C$ + }}}} + \ncline[]{->}{init}{insert} + \ncline[]{->}{insert}{cool} + \psframe[fillstyle=solid,fillcolor=white](7.5,1.8)(13.5,7.8) + \psframe[fillstyle=solid,fillcolor=lightgray](9,3.3)(12,6.3) + \psframe[fillstyle=solid,fillcolor=gray](9.25,3.55)(11.75,6.05) + \rput(7.9,4.8){\pnode{ins1}} + \rput(9.22,4.4){\pnode{ins2}} + \rput(10.5,4.8){\pnode{ins3}} + \ncline[]{->}{in1}{ins1} + \ncline[]{->}{in2}{ins2} + \ncline[]{->}{in3}{ins3} + \end{pspicture} + +\end{slide} + +\begin{slide} + + {\large\bf + Very first results of the SiC precipitation runs + } + + \footnotesize + + \begin{minipage}[b]{6.9cm} + \includegraphics[width=6.3cm]{../plot/sic_prec_energy.ps} + \includegraphics[width=6.3cm]{../plot/sic_prec_temp.ps} + \end{minipage} + \begin{minipage}[b]{5.5cm} + \begin{itemize} + \item {\color{red} Total simulation volume} + \item {\color{green} Volume of minimal SiC precipitation} + \item {\color{blue} Volume of necessary amount of Si} + \end{itemize} + \vspace{40pt} + \includegraphics[width=6.3cm]{../plot/foo150.ps} + \end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + Very first results of the SiC precipitation runs + } + + \begin{minipage}[t]{6.9cm} + \includegraphics[width=6.3cm]{../plot/sic_pc.ps} + \includegraphics[width=6.3cm]{../plot/foo_end.ps} + \hspace{12pt} + \end{minipage} + \begin{minipage}[c]{5.5cm} + \includegraphics[width=6.0cm]{sic_si-c-n.eps} + \end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + Summary / Outlook + } + +\vspace{24pt} + +\begin{itemize} + \item Importance of understanding the SiC precipitation mechanism + \item Interstitial configurations in silicon using the Albe potential + \item Indication of SiC precipitation +\end{itemize} + +\vspace{24pt} + +\begin{itemize} + \item Displacement and stress calculations + \item Refinement of simulation sequence to create 3C-SiC + \item Analyzing self-designed Si/SiC interface +\end{itemize} + +\end{slide} + +\end{document} + -- 2.20.1