X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fdpg_2008.tex;h=483f760d62bb05491b787a15b3cff0c3e487fc77;hp=5349eac542dd8b8afd6ffa09fdb8e8ddd6cb642a;hb=f14aef6d5395a7e3ec537b6025aa36a1490464d9;hpb=49f1ea0ef08a54fb99739f04a420e689daef7c4f

diff --git a/posic/talks/dpg_2008.tex b/posic/talks/dpg_2008.tex
index 5349eac..483f760 100644
--- a/posic/talks/dpg_2008.tex
+++ b/posic/talks/dpg_2008.tex
@@ -6,6 +6,7 @@
 \usepackage[latin1]{inputenc}
 \usepackage[T1]{fontenc}
 \usepackage{amsmath}
+\usepackage{latexsym}
 \usepackage{ae}
 
 \usepackage{calc}               % Simple computations with LaTeX variables
@@ -16,9 +17,17 @@
 \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
@@ -33,7 +42,9 @@
 \begin{document}
 
 \extraslideheight{10in}
-\slideframe{plain}
+\slideframe{none}
+
+\pagestyle{empty}
 
 % specify width and height
 \slidewidth 27.7cm 
@@ -41,7 +52,7 @@
 
 % 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}}
@@ -111,41 +122,54 @@
 
 % contents
 
+% no contents for such a short talk!
+
+% start of contents
+
 \begin{slide}
 
- \begin{center}
- {\bf
-  Molecular dynamics simulation study\\
-  of the silicon carbide precipitation process
+ {\large\bf
+  Motivation / Introduction
  }
- \end{center}
 
  \vspace{16pt}
 
- {\large\bf
-  Outline
- }
+ Reasons for understanding the SiC precipitation process:
+
+ \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 Motivation / Introduction
-  \item Molecular dynamics simulation details
+  \item Unit cell:
         \begin{itemize}
-	 \item Integrator, potential, ensemble control
-	 \item Simulation sequence
+         \item {\color{orange}fcc} $+$
+         \item {\color{gray}fcc shifted $1/4$ of volume diagonal}
 	\end{itemize}
-  \item Results gained by simulation
-        \begin{itemize}
-         \item Interstitials in silicon
-         \item SiC-precipitation experiments
-	\end{itemize}
-  \item Conclusion / Outlook
+  \item Lattice constants:
+        \[
+	4a_{Si}\approx5a_{SiC}
+	\]
+  \item Silicon density: 
+        \[
+        \frac{n_{SiC}}{n_{Si}}=97,66\,\%
+	\]
  \end{itemize}
-\end{slide}
+ \end{minipage}
+ \hspace{8pt}
+ \begin{minipage}{4cm}
+ \includegraphics[width=4cm]{sic_unit_cell.eps}
+ \end{minipage}
 
-% start of contents
+\end{slide}
 
+ \small
 \begin{slide}
 
  {\large\bf
@@ -155,7 +179,7 @@
  \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}
 
@@ -185,16 +209,13 @@
  Precipitation of 3C-SiC + Creation of interstitials\\
  \end{minipage}
 
- \begin{center}
- \[
-   \textrm{Silicon density: } \quad
-   5a_{SiC}=4a_{Si} \quad \Rightarrow \quad
-   \frac{n_{SiC}}{n_{Si}}=\frac{\frac{4}{a_{SiC}^3}}{\frac{8}{a_{Si}^3}}=
-                          \frac{5^3}{2\cdot4^3}={\color{cyan}97,66}\,\%
- \]
- \end{center}
+ \vspace{12pt}
 
- Experimentally observed minimal diameter of precipitation: 4 - 5 nm
+ 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}
 
@@ -204,31 +225,37 @@
   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-dimemnsional phase space
+        in 6N-dimensional phase space
   \item Observables obtained by time average
  \end{itemize}
 
- \vspace{4pt}
+ \vspace{12pt}
 
  Application details:
  \begin{itemize}
-  \item Integrator: velocity verlet, timestep: $1\, fs$
-  \item Ensemble control: NVT, Berendsen thermostat, $\tau=100.0$
+  \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 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}
 
+ \begin{picture}(0,0)(-240,-70)
+  \includegraphics[width=5cm]{tersoff_angle.eps} 
+ \end{picture}
+
 \end{slide}
 
 \begin{slide}
@@ -237,127 +264,84 @@
   Simulation details
  }
 
- \vspace{20pt}
-
- Interstitial experiments:
+ \vspace{8pt}
 
- \vspace{12pt}
+ Interstitial simulations:
 
- \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}
+ \vspace{8pt}
 
- \begin{picture}(0,0)(-210,-85)
+ \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
-  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 $E_F^{\star}=4.48\, eV$
-  \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}
@@ -366,100 +350,170 @@
 
  {\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 $E_F\sim5.6\, eV$
-  \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:
-
- \vspace{8pt}
+ \footnotesize
 
- 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}