\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{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
% contents
-\begin{slide}
-
- \begin{center}
- {\bf
- Molecular dynamics simulation study\\
- of the silicon carbide precipitation process
- }
- \end{center}
-
- \vspace{16pt}
-
- {\large\bf
- Outline
- }
-
- \vspace{16pt}
-
- \begin{itemize}
- \item Motivation / Introduction
- \item Molecular dynamics simulation details
- \begin{itemize}
- \item Integrator, potential, ensemble control
- \item Simulation sequence
- \end{itemize}
- \item Simulation results
- \begin{itemize}
- \item Interstitials in silicon
- \item SiC-precipitation experiments
- \end{itemize}
- \item Conclusion / Outlook
- \end{itemize}
-\end{slide}
+% no contents for such a short talk!
% start of contents
\vspace{16pt}
- Reasons for investigating C in Si:
+ Reasons for understanding the SiC precipitation process:
\begin{itemize}
\item 3C-SiC wide band gap semiconductor formation
\begin{itemize}
\item Unit cell:
\begin{itemize}
- \item {\color{yellow}fcc} $+$
+ \item {\color{orange}fcc} $+$
\item {\color{gray}fcc shifted $1/4$ of volume diagonal}
\end{itemize}
- \item Lattice constants: $4a_{Si}\approx5a_{SiC}$
+ \item Lattice constants:
+ \[
+ 4a_{Si}\approx5a_{SiC}
+ \]
\item Silicon density:
\[
- \frac{n_{SiC}}{n_{Si}}=
- \frac{4/a_{SiC}^3}{8/a_{Si}^3}=
- \frac{5^3}{2\cdot4^3}={\color{cyan}97,66}\,\%
- \]
+ \frac{n_{SiC}}{n_{Si}}=97,66\,\%
+ \]
\end{itemize}
\end{minipage}
\hspace{8pt}
\small
\vspace{6pt}
- Supposed mechanism of the conversion of heavily carbon doped Si into SiC:
+ Supposed conversion mechanism of heavily carbon doped Si into SiC:
\vspace{8pt}
Experimentally observed:
\begin{itemize}
\item Minimal diameter of precipitation: 4 - 5 nm
- \item (hkl)-planes identical for Si and SiC
+ \item Equal orientation of Si and SiC (hkl)-planes
\end{itemize}
\end{slide}
Application details:
\begin{itemize}
\item Integrator: Velocity Verlet, timestep: $1\, fs$
- \item Ensemble control: NVT, Berendsen thermostat, $\tau=100.0$
+ \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 und K. Albe. Phys. Rev. B 71 (2005) 035211}
+ {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211}
\end{center}
\end{itemize}
Simulation details
}
- \vspace{20pt}
+ \vspace{8pt}
- Interstitial experiments:
+ Interstitial simulations:
- \vspace{12pt}
+ \vspace{8pt}
- \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{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{slide}
-\begin{slide}
-
- {\large\bf
- Simulation details
- }
-
- \small
-
- SiC precipitation experiments:
- \begin{itemize}
- \item Initial configuration: $31\times31\times31$ unit cells Si
- \item Periodic boundary conditions
- \item $T=450\, ^{\circ}C$
- \item Steady state time: $600\, fs$
- \item C insertion steps:
- \begin{itemize}
- \item If $T=450\pm 1\, ^{\circ}C$:\\
- Insertion of 10 atoms at random positions within $V_{ins}$
- \item Otherwise: Annealing for another $100\, fs$
- \end{itemize}
- \item Annealing: ($T_a: 450\rightarrow 20 \, ^{\circ}C$)
- \begin{itemize}
- \item If $T=T_a$: Decrease $T_a$ by $1\, ^{\circ}C$
- \item Otherwise: Annealing for another $50\, fs$
- \end{itemize}
- \end{itemize}
-
- Szenarios:
- \begin{enumerate}
- \item $V_{ins}$: total simulation volume $V$
- \item $V_{ins}$: $12\times12\times12$ SiC unit cells
- ($\sim$ volume of minimal SiC precipitation)
- \item $V_{ins}$: $9\times9\times9$ SiC unit cells
- ($\sim$ volume of necessary amount of Si)
- \end{enumerate}
-
-\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}
+ } - Si self-interstitial runs
\small
- \begin{minipage}[t]{4.0cm}
- \underline{Tetrahedral}
- \begin{itemize}
- \item $E_F=3.41\, eV$
- \item essentialy tetrahedral\\
- bonds
- \end{itemize}
+ \begin{minipage}[t]{4.3cm}
+ \underline{Tetrahedral}\\
+ $E_f=3.41\, eV$\\
+ \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
\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}
+ \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}
- \hspace{0.3cm}
- \begin{minipage}[t]{4.0cm}
- \underline{Hexagonal}
- \begin{itemize}
- \item $E_F^{\star}\approx4.48\, eV$
- \item unstable!
- \end{itemize}
+ \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}
- \vspace{8pt}
+ \underline{Random insertion}
\begin{minipage}{4.3cm}
- \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
+ $E_f=3.97\, eV$\\
+ \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
\end{minipage}
\begin{minipage}{4.3cm}
- \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
+ $E_f=3.75\, eV$\\
+ \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
\end{minipage}
\begin{minipage}{4.3cm}
- \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
+ $E_f=3.56\, eV$\\
+ \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
\end{minipage}
\end{slide}
{\large\bf
Results
- }
-
- \vspace{8pt}
+ } - Carbon interstitial runs
- Si self-interstitial \underline{random insertion} experiments:
+ \small
- \vspace{8pt}
+ \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}
- foo
+ \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
- Results
+ Simulation details
}
- Carbon interstitial experiments:
+ \small
\vspace{8pt}
- \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}
+ SiC precipitation simulations:
\vspace{8pt}
- \begin{minipage}{4.3cm}
- \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
- \end{minipage}
- \begin{minipage}{4.3cm}
- \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
- \end{minipage}
- \begin{minipage}{4.3cm}
- \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
- \end{minipage}
+ \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
- Results
+ Very first results of the SiC precipitation runs
}
- \vspace{8pt}
-
- Carbon \underline{random insertion} experiments:
+ \footnotesize
- \vspace{8pt}
-
- bar
+ \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
- Results
+ Very first results of the SiC precipitation runs
}
- SiC-precipitation experiments:
+ \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
- Conclusion / Outlook
+ 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}
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