\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
+\usepackage{latexsym}
\usepackage{ae}
\usepackage{calc} % Simple computations with LaTeX variables
\usepackage{fancyvrb} % Fancy verbatim environments
\usepackage{pstricks} % PSTricks with the standard color package
+\usepackage{pstricks}
+\usepackage{pst-node}
+
\usepackage{graphicx}
\graphicspath{{../img/}}
+\usepackage[setpagesize=false]{hyperref}
+
\usepackage{semcolor}
\usepackage{semlayer} % Seminar overlays
\usepackage{slidesec} % Seminar sections and list of slides
\articlemag{1}
+\special{landscape}
+
\begin{document}
\extraslideheight{10in}
-\slideframe{plain}
+\slideframe{none}
+
+\pagestyle{empty}
% specify width and height
\slidewidth 27.7cm
% shift it into visual area properly
\def\slideleftmargin{3.3cm}
-\def\slidetopmargin{0.0cm}
+\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}$\bullet$}}
+
% topic
\begin{slide}
\item Integrator, potential, ensemble control
\item Simulation sequence
\end{itemize}
- \item Results gained by simulation
+ \item Simulation results
\begin{itemize}
- \item Carbon interstitials in silicon
- \item Existence of $SiC$-precipitates
+ \item Interstitials in silicon
+ \item SiC-precipitation experiments
\end{itemize}
\item Conclusion / Outlook
\end{itemize}
% start of contents
+\begin{slide}
+
+ {\large\bf
+ Motivation / Introduction
+ }
+
+ \vspace{16pt}
+
+ Reasons for investigating C in Si:
+
+ \begin{itemize}
+ \item 3C-SiC wide band gap semiconductor formation
+ \item Strained Si (no precipitation wanted!)
+ \end{itemize}
+
+ \vspace{16pt}
+
+ Si / 3C-SiC facts:
+
+ \begin{minipage}{8cm}
+ \begin{itemize}
+ \item Unit cell:
+ \begin{itemize}
+ \item {\color{yellow}fcc} $+$
+ \item {\color{gray}fcc shifted $1/4$ of volume diagonal}
+ \end{itemize}
+ \item Lattice constants: $4a_{Si}\approx5a_{SiC}$
+ \item Silicon density:
+ \[
+ \frac{n_{SiC}}{n_{Si}}=
+ \frac{4/a_{SiC}^3}{8/a_{Si}^3}=
+ \frac{5^3}{2\cdot4^3}={\color{cyan}97,66}\,\%
+ \]
+ \end{itemize}
+ \end{minipage}
+ \hspace{8pt}
+ \begin{minipage}{4cm}
+ \includegraphics[width=4cm]{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 (hkl)-planes identical for Si and SiC
+ \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 control: 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 und 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{20pt}
+
+ Interstitial experiments:
+
+ \vspace{12pt}
+
+ \begin{itemize}
+ \item Initial configuration: $9\times9\times9$ unit cells Si
+ \item Periodic boundary conditions
+ \item $T=0 \, K$
+ \item Insertion of Si / C atom at
+ \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{yellow}110 dumbbell}
+ \item random positions (critical distance check)
+ \end{itemize}
+ \item Relaxation time: $2\, ps$
+ \item Optional heating-up
+ \end{itemize}
+
+ \begin{picture}(0,0)(-210,-45)
+ \includegraphics[width=6cm]{unit_cell.eps}
+ \end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Simulation details
+ }
+
+ \small
+
+ SiC precipitation experiments:
+
+ \begin{pspicture}(0,0)(12,8)
+ % nodes
+ \rput(4.5,6.5){\rnode{init}{\psframebox{\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(4.5,4.5){\rnode{tc1}{\psframebox[fillstyle=solid,fillcolor=red]{
+ $T=450\pm 1\, ^{\circ}C$}}}
+ \rput(7,3.5){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
+ \parbox{3cm}{
+ Insertion of 10 atoms\\
+ at random positions}}}}
+ \rput(2,3.5){\rnode{adj1}{\psframebox[fillstyle=solid,fillcolor=red]{
+ \parbox{3.5cm}{
+ Adjusting temperature\\
+ for another $100\, fs$}}}}
+ \rput(7,2.5){\rnode{nc}{\psframebox[fillstyle=solid,fillcolor=red]{
+ $N_{atoms}=6000$}}}
+ \rput(4.5,2){\rnode{tc2}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ $T=T_{set}$}}}
+ \rput(7,1){\rnode{td}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ $T_{set}:=T_{set}-1\, ^{\circ}C$}}}
+ \rput(2,1){\rnode{adj2}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ \parbox{3.5cm}{
+ Adjusting temperature\\
+ for another $50\, fs$}}}}
+ \rput(7,0){\rnode{tc3}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ $T_{set}=20\, ^{\circ}C$}}}
+ \rput(10,0){\rnode{end}{\psframebox{End}}}
+ % help nodes
+ \rput(7,4.5){\pnode{tc1-h}}
+ \rput(2,4.5){\pnode{tc1-hh}}
+ \rput(4.5,2.5){\pnode{nc-h}}
+ \rput(9,2.5){\pnode{nc-hh}}
+ \rput(9,2){\pnode{tc2-h}}
+ \rput(2,2){\pnode{tc2-hh}}
+ \rput(4.5,0){\pnode{tc3-h}}
+ % direct lines
+ \ncline[]{->}{init}{tc1}
+ \ncline[]{->}{adj1}{tc1}
+ \ncline[]{->}{insert}{nc}
+ \ncline[]{->}{adj2}{tc2}
+ \ncline[]{->}{tc2}{td}
+ \lput*{0}{yes}
+ \ncline[]{->}{td}{tc3}
+ \ncline[]{->}{tc3}{end}
+ \lput*{0}{yes}
+ % lines using help nodes
+ \ncline[]{tc1}{tc1-h}
+ \lput*{0}{yes}
+ \ncline[]{->}{tc1-h}{insert}
+ \ncline[]{tc1}{tc1-hh}
+ \lput*{0}{no}
+ \ncline[]{->}{tc1-hh}{adj1}
+ \ncline[]{nc}{nc-h}
+ \lput*{0}{no}
+ \ncline[]{->}{nc-h}{tc1}
+ \ncline[]{nc}{nc-hh}
+ \ncline[]{-}{nc-hh}{tc2-h}
+ \ncline[]{->}{tc2-h}{tc2}
+ \lput*{0}{yes, {\footnotesize $T_{set}:=450\, ^{\circ}C$}}
+ \ncline[]{tc2}{tc2-hh}
+ \lput*{0}{no}
+ \ncline[]{->}{tc2-hh}{adj2}
+ \ncline[]{tc3}{tc3-h}
+ \lput*{0}{no}
+ \ncline[]{->}{tc3-h}{tc2}
+ % insertion volumes
+ \psframe[fillstyle=solid,fillcolor=white](9.5,1.3)(13.5,5.3)
+ \psframe[fillstyle=solid,fillcolor=lightgray](10,1.8)(13,4.8)
+ \psframe[fillstyle=solid,fillcolor=gray](10.5,2.3)(12.5,4.3)
+ \rput(9.75,3){\pnode{ins1}}
+ \rput(10.25,3.3){\pnode{ins2}}
+ \rput(10.75,3.6){\pnode{ins3}}
+ \ncline[]{-}{insert}{ins1}
+ \ncline[]{-}{insert}{ins2}
+ \ncline[]{-}{insert}{ins3}
+ \psframe[fillstyle=solid,fillcolor=white](9.5,7.6)(13.5,8.1)
+ \psframe[fillstyle=solid,fillcolor=lightgray](9.5,6.8)(13.5,7.3)
+ \psframe[fillstyle=solid,fillcolor=gray](9.5,6)(13.5,6.5)
+ \rput(11.5,7.85){{\tiny Simulation volume:
+ $31\times31\times31\, a^3_{Si}$}}
+ \rput(11.5,7.05){{\tiny Volume of minimal SiC precipitation}}
+ \rput(11.5,6.25){{\tiny Volume of necessary amount of Si}}
+ \end{pspicture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Results
+ }
+
+ Si self-interstitial experiments:
+
+ {\footnotesize
+ {\bf Note:}
+ \begin{itemize}
+ \item $r_{cutoff}^{Si-Si}=2.96>\frac{5.43}{2}$
+ \item Bond length near $r_{cutoff} \Rightarrow$ small bond strength
+ \end{itemize}
+ }
+
+ \vspace{8pt}
+
+ \small
+
+ \begin{minipage}[t]{4.0cm}
+ \underline{Tetrahedral}
+ \begin{itemize}
+ \item $E_f=3.41\, eV$
+ \item essentialy tetrahedral\\
+ bonds
+ \end{itemize}
+ \end{minipage}
+ \hspace{0.3cm}
+ \begin{minipage}[t]{4.0cm}
+ \underline{110 dumbbell}
+ \begin{itemize}
+ \item $E_f=4.39\, eV$
+ \item essentially 4 bonds
+ \end{itemize}
+ \end{minipage}
+ \hspace{0.3cm}
+ \begin{minipage}[t]{4.0cm}
+ \underline{Hexagonal}
+ \begin{itemize}
+ \item $E_f^{\star}\approx4.48\, eV$
+ \item unstable!
+ \end{itemize}
+ \end{minipage}
+
+ \vspace{8pt}
+
+ \begin{minipage}[t]{4.3cm}
+ \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.3cm}
+ \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.3cm}
+ \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
+ \begin{center}
+ \href{../video/si_self_int_hexa.avi}{$\rhd$}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Results
+ }
+
+ \vspace{8pt}
+
+ Si self-interstitial \underline{random insertion} experiments:
+
+ \small
+
+ \vspace{8pt}
+
+ \begin{minipage}[t]{4.0cm}
+ \begin{itemize}
+ \item $E_f=3.97\, eV$
+ \item 3 identical weak bonds
+ \item displaced in volume\\ diagonal
+ \end{itemize}
+ \end{minipage}
+ \hspace{0.3cm}
+ \begin{minipage}[t]{4.0cm}
+ \begin{itemize}
+ \item $E_f=3.75\, eV$
+ \item 4 identical weak bonds
+ \item displaced in plane\\ diagonal
+ \end{itemize}
+ \end{minipage}
+ \hspace{0.3cm}
+ \begin{minipage}[t]{4.0cm}
+ \begin{itemize}
+ \item $E_f=3.56\, eV$
+ \item single weak bond
+ \item displaced along\\ $x$-direction
+ \item closest to tetrahedral\\ configuration
+ \end{itemize}
+ \end{minipage}
+
+ \vspace{8pt}
+
+ \begin{minipage}{4.3cm}
+ \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+ \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+ \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
+ \end{minipage}
+
+ \vspace{8pt}
+
+ \begin{center}
+ {\footnotesize
+ {\bf Note:} Displacements relative to tetrahedral configuration
+ }
+ \end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Results
+ }
+
+ \vspace{8pt}
+
+ Carbon interstitial experiments:
+
+ \vspace{12pt}
+
+ \small
+
+ \begin{minipage}[t]{4.0cm}
+ \underline{Tetrahedral}
+ \begin{itemize}
+ \item $E_f=2.67\, eV$
+ \item tetrahedral bond
+ \end{itemize}
+ \end{minipage}
+ \hspace{0.3cm}
+ \begin{minipage}[t]{4.0cm}
+ \underline{110 dumbbell}
+ \begin{itemize}
+ \item $E_f=1.76\, eV$
+ \item C forms 3 bonds
+ \end{itemize}
+ \end{minipage}
+ \hspace{0.3cm}
+ \begin{minipage}[t]{4.0cm}
+ \underline{Hexagonal}
+ \begin{itemize}
+ \item $E_f^{\star}\approx5.6\, eV$
+ \item unstable!
+ \end{itemize}
+ \end{minipage}
+
+ \vspace{8pt}
+
+ \begin{minipage}[t]{4.3cm}
+ \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.3cm}
+ \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.3cm}
+ \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
+ \begin{center}
+ \href{../video/c_in_si_int_hexa.avi}{$\rhd$}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Results
+ }
+
+ \vspace{8pt}
+
+ Carbon \underline{random insertion} experiments:
+
+ \vspace{8pt}
+
+ High probability for dumbbell configurations!\\
+ Others:\\
+ \includegraphics[width=3.0cm]{c_in_si_int_001db_0.eps}
+ \includegraphics[width=3.0cm]{c_in_si_int_rand_162_0.eps}
+ \includegraphics[width=3.0cm]{c_in_si_int_rand_239_0.eps}
+ \includegraphics[width=3.0cm]{c_in_si_int_rand_341_0.eps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Results
+ }
+
+ SiC-precipitation experiments:
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Conclusion / Outlook
+ }
+
+\end{slide}
+
\end{document}
projects / lectures / latex.git / blobdiff