X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fdpg_2008.tex;h=483f760d62bb05491b787a15b3cff0c3e487fc77;hp=d518610b1ae605960cef1ba7cb87b63d9c93195b;hb=5ae918a991fba3555ed19d642568f3c9cfcd9c95;hpb=9991d2da9e3c1ff1239bfcb9362e77d99451010b

diff --git a/posic/talks/dpg_2008.tex b/posic/talks/dpg_2008.tex
index d518610..483f760 100644
--- a/posic/talks/dpg_2008.tex
+++ b/posic/talks/dpg_2008.tex
@@ -20,6 +20,9 @@
 \usepackage{pstricks}
 \usepackage{pst-node}
 
+%\usepackage{epic}
+%\usepackage{eepic}
+
 \usepackage{graphicx}
 \graphicspath{{../img/}}
 
@@ -119,38 +122,7 @@
 
 % 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
 
@@ -162,7 +134,7 @@
 
  \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
@@ -177,16 +149,17 @@
  \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}
@@ -241,7 +214,7 @@
  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}
@@ -268,14 +241,14 @@
  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}
 
@@ -291,346 +264,256 @@
   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
- }
+ \vspace{8pt}
 
- \small
+ Interstitial simulations:
 
- SiC precipitation experiments:
+ \vspace{8pt}
 
- \begin{pspicture}(0,0)(12,8)
-  % nodes
-  \rput(4.5,6.5){\rnode{init}{\psframebox{\parbox{7cm}{
+ \begin{pspicture}(0,0)(7,8)
+  \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
+   \parbox{7cm}{
    \begin{itemize}
-    \item Initial configuration: $31\times31\times31$ unit cells Si
+    \item Initial configuration: $9\times9\times9$ unit cells Si
     \item Periodic boundary conditions
-    \item $T=450\, ^{\circ}C$
-    \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
+    \item $T=0 \, K$
    \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}}
+\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 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}
- \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}
+ \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}
- \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}
+ \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}
 
- \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}
+ } - Carbon interstitial runs
 
  \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}
+ \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}
- \begin{center}
- \href{../video/c_in_si_int_hexa.avi}{$\rhd$}
- \end{center}
  \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
-  Results
+  Simulation details
  }
 
+ \small
+
  \vspace{8pt}
 
- Carbon \underline{random insertion} experiments:
+ SiC precipitation simulations:
 
  \vspace{8pt}
 
- bar
+ \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
-  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}