X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fdpg_2008.tex;h=8f01390bebef7c6073dbd8b327758945c8271df3;hb=37e509f4b9ae7e0a0edd38317dd38bfca9bacce4;hp=1f6bce4cc820951f3fb19b86d22b89e49661f974;hpb=aa5433fe4c9c534360371ed7489d64c3f9e22c3f;p=lectures%2Flatex.git

diff --git a/posic/talks/dpg_2008.tex b/posic/talks/dpg_2008.tex
index 1f6bce4..8f01390 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}}
@@ -135,10 +146,10 @@
 	 \item Integrator, potential, ensemble control
 	 \item Simulation sequence
 	\end{itemize}
-  \item Results gained by simulation
+  \item Simulation results
         \begin{itemize}
          \item Interstitials in silicon
-         \item $SiC$-precipitation experiments
+         \item SiC-precipitation experiments
 	\end{itemize}
   \item Conclusion / Outlook
  \end{itemize}
@@ -146,6 +157,49 @@
 
 % 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
@@ -155,7 +209,7 @@
  \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}
 
@@ -185,14 +239,13 @@
  Precipitation of 3C-SiC + Creation of interstitials\\
  \end{minipage}
 
- \begin{center}
- \[5a_{SiC}=4a_{Si} \quad \Rightarrow \quad
-   \frac{n_{SiC}}{n_{Si}}=\frac{\frac{4}{a_{SiC}^3}}{\frac{8}{a_{Si}^3}}=
-                          \frac{5^3}{2\cdot4^3}=97,66\%
- \]
- \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 (hkl)-planes identical for Si and SiC
+ \end{itemize}
 
 \end{slide}
 
@@ -202,20 +255,22 @@
   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 Integrator: Velocity Verlet, timestep: $1\, fs$
   \item Ensemble control: NVT, Berendsen thermostat, $\tau=100.0$
   \item Potential: Tersoff-like bond order potential\\
         \[
@@ -227,6 +282,10 @@
 	\end{center}
  \end{itemize}
 
+ \begin{picture}(0,0)(-240,-70)
+  \includegraphics[width=5cm]{tersoff_angle.eps} 
+ \end{picture}
+
 \end{slide}
 
 \begin{slide}
@@ -235,7 +294,7 @@
   Simulation details
  }
 
- \vspace{16pt}
+ \vspace{20pt}
 
  Interstitial experiments:
 
@@ -249,14 +308,15 @@
         \begin{itemize}
          \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
          \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
-         \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$
+         \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,-65)
+ \begin{picture}(0,0)(-210,-45)
   \includegraphics[width=6cm]{unit_cell.eps}
  \end{picture}
 
@@ -271,32 +331,96 @@
  \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}
+ \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}
 
@@ -308,6 +432,14 @@
 
  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
@@ -315,37 +447,41 @@
  \begin{minipage}[t]{4.0cm}
  \underline{Tetrahedral}
  \begin{itemize}
-  \item $E_F=3.41\, eV$
-  \item $r_{cutoff}^{Si-Si}=2.96>\frac{5.43}{2}$
+  \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 Small bond strength
+  \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 $E_F=4.48\, eV$
-  \item unstable for $T\ne 0\,K$
+  \item $E_f^{\star}\approx4.48\, eV$
+  \item unstable!
  \end{itemize}
  \end{minipage}
 
  \vspace{8pt}
 
- \begin{minipage}{4.3cm}
+ \begin{minipage}[t]{4.3cm}
  \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
  \end{minipage}
- \begin{minipage}{4.3cm}
+ \begin{minipage}[t]{4.3cm}
  \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
  \end{minipage}
- \begin{minipage}{4.3cm}
+ \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}
@@ -356,6 +492,59 @@
   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}
@@ -364,45 +553,125 @@
   Results
  }
 
+ \vspace{8pt}
+
  Carbon interstitial experiments:
 
- \vspace{8pt}
+ \vspace{12pt}
 
  \small
 
  \begin{minipage}[t]{4.0cm}
  \underline{Tetrahedral}
  \begin{itemize}
-  \item $E_F=2.67\, eV$
+  \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 $E_f=1.76\, eV$
+  \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}{4.3cm}
+ \begin{minipage}[t]{4.3cm}
  \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
  \end{minipage}
- \begin{minipage}{4.3cm}
+ \begin{minipage}[t]{4.3cm}
  \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
  \end{minipage}
- \begin{minipage}{4.3cm}
- %\includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
+ \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}
+
+ \footnotesize
+
+ \begin{minipage}[c]{6.3cm}
+  \begin{minipage}{3.4cm}
+   \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
+  \end{minipage}
+  \begin{minipage}{2.5cm}
+   \begin{itemize}
+    \item $E_f=0.47\, eV$
+    \item 001 dumbbell
+   \end{itemize}
+  \end{minipage}
+ \end{minipage}
+ \begin{minipage}[c]{6.3cm}
+  \begin{minipage}{3.4cm}
+   \includegraphics[width=3.3cm]{c_in_si_int_rand_162_0.eps}
+  \end{minipage}
+  \begin{minipage}{2.8cm}
+   \begin{itemize}
+    \item $E_f=1.62\, eV$
+    \item 3 weak + strong bonds
+   \end{itemize}
+  \end{minipage}
+ \end{minipage}
+
+ \begin{minipage}[c]{6.3cm}
+  \begin{minipage}{3.4cm}
+   \includegraphics[width=3.3cm]{c_in_si_int_rand_239_0.eps}
+  \end{minipage}
+  \begin{minipage}{2.5cm}
+   \begin{itemize}
+    \item $E_f=2.39\, eV$
+   \end{itemize}
+   \begin{center}
+    \href{../video/c_in_si_int_rand_239.avi}{$\rhd$}
+   \end{center}
+  \end{minipage}
+ \end{minipage}
+ \begin{minipage}[c]{6.3cm}
+  \begin{minipage}{3.4cm}
+   \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
+  \end{minipage}
+  \begin{minipage}{2.8cm}
+   \begin{itemize}
+    \item $E_f=3.41\, eV$
+   \end{itemize}
+   \begin{center}
+    \href{../video/c_in_si_int_rand_341.avi}{$\rhd$}
+   \end{center}
+  \end{minipage}
  \end{minipage}
 
+ \vspace{4pt}
+
+ \begin{center}
+ {\bf Note:} High probability for 110 dumbbell ($1.76\, eV$) configurations!
+ \end{center}
+
 \end{slide}
 
 \begin{slide}
@@ -413,6 +682,16 @@
 
  SiC-precipitation experiments:
 
+ \begin{minipage}[t]{6.3cm}
+  %\input{../plot/sic_prec}
+  \includegraphics[width=6.0cm]{../plot/sic_prec_energy.ps}
+  \includegraphics[width=6.0cm]{../plot/sic_prec_temp.ps}
+ \end{minipage}
+ \begin{minipage}[t]{6cm}
+  \includegraphics[width=6.0cm]{../plot/sic_pc.ps}
+  \includegraphics[width=6.0cm]{../plot/sic_prec_pc.ps}
+ \end{minipage}
+
 \end{slide}
 
 \begin{slide}
@@ -421,6 +700,23 @@
   Conclusion / Outlook
  }
 
+\vspace{24pt}
+
+\begin{itemize}
+ \item Importance of understanding C in Si
+ \item Interstitial configurations in silicon using the Albe potential
+ \item Indication of SiC precipitation
+\end{itemize}
+
+\vspace{16pt}
+
+\begin{itemize}
+ \item Displacement and stress calculations
+ \item Diffusion dependence of temperature and carbon concentration
+ \item Analyzing results of the precipitation simulation runs
+ \item Analyzing self-designed Si/SiC interface
+\end{itemize}
+
 \end{slide}
 
 \end{document}