X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fmpi_app.tex;h=f588e1d46a4248e8e52a74e2bfb1f30e89ac949f;hb=246b317e6fcfc986641a3c20cf8722f40ae131ac;hp=27a048cd7f010dc5bda01bdfa371e0c0b79e889a;hpb=04db9a9e98884d0da3a895d3be58e7f8a85f139c;p=lectures%2Flatex.git

diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex
index 27a048c..f588e1d 100644
--- a/posic/talks/mpi_app.tex
+++ b/posic/talks/mpi_app.tex
@@ -7,6 +7,7 @@
 \usepackage[latin1]{inputenc}
 \usepackage[T1]{fontenc}
 \usepackage{amsmath}
+\usepackage{stmaryrd}
 \usepackage{latexsym}
 \usepackage{ae}
 
@@ -670,8 +671,6 @@ by simulation!
 
 \end{slide}
 
-\fi
-
 \begin{slide}
 
 \headphd
@@ -733,66 +732,69 @@ by simulation!
 
 \end{slide}
 
-
-\end{document}
-
-\ifnum1=0
-
-% continue here
-%\fi
-
 \begin{slide}
 
+\headphd
 {\large\bf
- Model displaying the formation of ordered lamellae
-}
-
-
-\end{slide}
-
-\begin{slide}
-
- {\large\bf
   Supposed precipitation mechanism of SiC in Si
- }
+}
 
  \scriptsize
 
  \vspace{0.1cm}
 
- \begin{minipage}{3.8cm}
- Si \& SiC lattice structure\\[0.2cm]
- \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
- \hrule
+ \framebox{
+ \begin{minipage}{3.6cm}
+ \begin{center}
+ Si \& SiC lattice structure\\[0.1cm]
+ \includegraphics[width=2.3cm]{sic_unit_cell.eps}
+ \end{center}
+{\tiny
+ \begin{minipage}{1.7cm}
+\underline{Silicon}\\
+{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
+$a=\unit[5.429]{\\A}$\\
+$\rho^*_{\text{Si}}=\unit[100]{\%}$
+ \end{minipage}
+ \begin{minipage}{1.7cm}
+\underline{Silicon carbide}\\
+{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
+$a=\unit[4.359]{\\A}$\\
+$\rho^*_{\text{Si}}=\unit[97]{\%}$
+ \end{minipage}
+}
  \end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ }
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
  \begin{center}
  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
  \end{center}
  \end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
  \begin{center}
  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
  \end{center}
  \end{minipage}
 
- \begin{minipage}{4cm}
+ \vspace{0.1cm}
+
+ \begin{minipage}{4.0cm}
  \begin{center}
  C-Si dimers (dumbbells)\\[-0.1cm]
  on Si interstitial sites
  \end{center}
  \end{minipage}
- \hspace{0.2cm}
- \begin{minipage}{4.2cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
  \begin{center}
  Agglomeration of C-Si dumbbells\\[-0.1cm]
  $\Rightarrow$ dark contrasts
  \end{center}
  \end{minipage}
- \hspace{0.2cm}
- \begin{minipage}{4cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
  \begin{center}
  Precipitation of 3C-SiC in Si\\[-0.1cm]
  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
@@ -800,37 +802,39 @@ by simulation!
  \end{center}
  \end{minipage}
 
- \begin{minipage}{3.8cm}
+ \vspace{0.1cm}
+
+ \begin{minipage}{4.0cm}
  \begin{center}
  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
  \end{center}
  \end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
  \begin{center}
  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
  \end{center}
  \end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
  \begin{center}
  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
  \end{center}
  \end{minipage}
 
 \begin{pspicture}(0,0)(0,0)
-\psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
-\psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
-\rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
-\psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
-\rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
+\psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
+\rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
+\psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
+\rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
  $4a_{\text{Si}}=5a_{\text{SiC}}$
  }}}
-\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 \hkl(h k l) planes match
  }}}
-\rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
-r = 2 - 4 nm
+\rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+r = \unit[2--4]{nm}
  }}}
 \end{pspicture}
 
@@ -838,47 +842,67 @@ r = 2 - 4 nm
 
 \begin{slide}
 
- {\large\bf
-  Supposed precipitation mechanism of SiC in Si
- }
+\headphd
+{\large\bf
+ Supposed precipitation mechanism of SiC in Si
+}
 
  \scriptsize
 
  \vspace{0.1cm}
 
- \begin{minipage}{3.8cm}
- Si \& SiC lattice structure\\[0.2cm]
- \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
- \hrule
+ \framebox{
+ \begin{minipage}{3.6cm}
+ \begin{center}
+ Si \& SiC lattice structure\\[0.1cm]
+ \includegraphics[width=2.3cm]{sic_unit_cell.eps}
+ \end{center}
+{\tiny
+ \begin{minipage}{1.7cm}
+\underline{Silicon}\\
+{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
+$a=\unit[5.429]{\\A}$\\
+$\rho^*_{\text{Si}}=\unit[100]{\%}$
+ \end{minipage}
+ \begin{minipage}{1.7cm}
+\underline{Silicon carbide}\\
+{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
+$a=\unit[4.359]{\\A}$\\
+$\rho^*_{\text{Si}}=\unit[97]{\%}$
+ \end{minipage}
+}
  \end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ }
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
  \begin{center}
  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
  \end{center}
  \end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
  \begin{center}
  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
  \end{center}
  \end{minipage}
 
- \begin{minipage}{4cm}
+ \vspace{0.1cm}
+
+ \begin{minipage}{4.0cm}
  \begin{center}
  C-Si dimers (dumbbells)\\[-0.1cm]
  on Si interstitial sites
  \end{center}
  \end{minipage}
- \hspace{0.2cm}
- \begin{minipage}{4.2cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
  \begin{center}
  Agglomeration of C-Si dumbbells\\[-0.1cm]
  $\Rightarrow$ dark contrasts
  \end{center}
  \end{minipage}
- \hspace{0.2cm}
- \begin{minipage}{4cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
  \begin{center}
  Precipitation of 3C-SiC in Si\\[-0.1cm]
  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
@@ -886,118 +910,181 @@ r = 2 - 4 nm
  \end{center}
  \end{minipage}
 
- \begin{minipage}{3.8cm}
+ \vspace{0.1cm}
+
+ \begin{minipage}{4.0cm}
  \begin{center}
  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
  \end{center}
  \end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
  \begin{center}
  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
  \end{center}
  \end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
  \begin{center}
  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
  \end{center}
  \end{minipage}
 
 \begin{pspicture}(0,0)(0,0)
-\psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
-\psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
-\rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
-\psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
-\rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
+\psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
+\rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
+\psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
+\rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
  $4a_{\text{Si}}=5a_{\text{SiC}}$
  }}}
-\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 \hkl(h k l) planes match
  }}}
-\rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
-r = 2 - 4 nm
+\rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+r = \unit[2--4]{nm}
  }}}
-\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
+% controversial view!
+\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
+\begin{minipage}{14cm}
+\hfill
+\vspace{12cm}
+\end{minipage}
+}}
+\rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
 \begin{minipage}{10cm}
 \small
-{\color{red}\bf Controversial views}
+\vspace*{0.2cm}
+\begin{center}
+{\color{gray}\bf Controversial findings}
+\end{center}
 \begin{itemize}
-\item Implantations at high T (Nejim et al.)
+\item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
  \begin{itemize}
-  \item Topotactic transformation based on \cs
-  \item \si{} as supply reacting with further C in cleared volume
+  \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
+  \item \si{} reacting with further C in cleared volume
  \end{itemize}
-\item Annealing behavior (Serre et al.)
+\item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
  \begin{itemize}
-  \item Room temperature implants $\rightarrow$ highly mobile C
-  \item Elevated T implants $\rightarrow$ no/low C redistribution/migration\\
-        (indicate stable \cs{} configurations)
+  \item Room temperature implantation $\rightarrow$ high C diffusion
+  \item Elevated temperature implantation $\rightarrow$ no C redistribution
  \end{itemize}
+ $\Rightarrow$ mobile {\color{red}\ci} opposed to
+ stable {\color{blue}\cs{}} configurations
 \item Strained silicon \& Si/SiC heterostructures
+      {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
  \begin{itemize}
-  \item Coherent SiC precipitates (tensile strain)
+  \item {\color{blue}Coherent} SiC precipitates (tensile strain)
   \item Incoherent SiC (strain relaxation)
  \end{itemize}
 \end{itemize}
+\vspace{0.1cm}
+\begin{center}
+{\Huge${\lightning}$} \hspace{0.3cm}
+{\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
+{\Huge${\lightning}$}
+\end{center}
+\vspace{0.2cm}
 \end{minipage}
  }}}
 \end{pspicture}
 
 \end{slide}
 
+% continue here
+\fi
+
 \begin{slide}
 
- {\large\bf
-  Molecular dynamics (MD) simulations
- }
+\headphd
+{\large\bf
+ Utilized computational methods
+}
 
- \vspace{12pt}
+\vspace{0.2cm}
 
- \small
+\small
 
- {\bf MD basics:}
- \begin{itemize}
-  \item Microscopic description of N particle system
-  \item Analytical interaction potential
-  \item Numerical integration using Newtons equation of motion\\
-        as a propagation rule in 6N-dimensional phase space
-  \item Observables obtained by time and/or ensemble averages
- \end{itemize}
- {\bf Details of the simulation:}
- \begin{itemize}
-  \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
-  \item Ensemble: NpT (isothermal-isobaric)
-        \begin{itemize}
-         \item Berendsen thermostat:
-               $\tau_{\text{T}}=100\text{ fs}$
-         \item Berendsen barostat:\\
-               $\tau_{\text{P}}=100\text{ fs}$,
-               $\beta^{-1}=100\text{ GPa}$
-        \end{itemize}
-  \item Erhart/Albe potential: Tersoff-like bond order potential
-  \vspace*{12pt}
-        \[
-        E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
-        \pot_{ij} = {\color{red}f_C(r_{ij})}
-        \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
-        \]
- \end{itemize}
+{\bf Molecular dynamics (MD)}\\
+\scriptsize
+\begin{tabular}{p{4.5cm} p{7.5cm}}
+%\hline
+Basics & Details\\
+\hline
+System of $N$ particles &
+$N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
+\hline
+Phase space propagation &
+Velocity Verlet | timestep: \unit[1]{fs} \\
+\hline
+Analytical interaction potential &
+Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
+(Erhart/Albe)
+$\displaystyle
+E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
+    \pot_{ij} = {\color{red}f_C(r_{ij})}
+    \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
+$\\
+\hline
+%\multicolumn{2}{c}{}\\
+Observables: time/ensemble averages &
+NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
+%\begin{itemize}
+%\item Berendsen thermostat:
+%      $\tau_{\text{T}}=100\text{ fs}$
+%\item Berendsen barostat:\\
+%      $\tau_{\text{P}}=100\text{ fs}$,
+%      $\beta^{-1}=100\text{ GPa}$
+%\end{itemize}\\
+\hline
+\end{tabular}
+
+\small
+
+\vspace{0.1cm}
+
+{\bf Density functional theory (DFT)}
+
+\scriptsize
+
+\begin{minipage}[t]{6cm}
+\underline{Basics}
+\begin{itemize}
+ \item Born-Oppenheimer approximation:\\
+       Decouple electronic \& ionic motion
+ \item Hohenberg-Kohn theorem:\\
+       $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$
+       $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$}
+\end{itemize}
+\underline{Details}
+\begin{itemize}
+\item Code: \textsc{vasp}
+\item Plane wave basis set $\{\phi_j\}$\\[0.1cm]
+$\displaystyle
+\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r)
+$\\
+$\displaystyle
+E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
+$
+\item Ultrasoft pseudopotential
+\item Brillouin zone sampling: $\Gamma$-point
+\end{itemize}
+\end{minipage}
+\begin{minipage}[t]{6cm}
+\end{minipage}
 
- \begin{picture}(0,0)(-230,-30)
-  \includegraphics[width=5cm]{tersoff_angle.eps} 
- \end{picture}
- 
 \end{slide}
 
+\end{document}
+\ifnum1=0
+
 \begin{slide}
 
+ \small
  {\large\bf
   Density functional theory (DFT) calculations
  }
 
- \small
-
  Basic ingredients necessary for DFT
 
  \begin{itemize}
@@ -1060,11 +1147,6 @@ which in turn depends on $n(r)$
         \end{itemize}
   \item \underline{Plane wave basis set}
         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
-\[
-\rightarrow
-\text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
-\qquad ({\color{blue}300\text{ eV}})
-\]
   \item \underline{Brillouin zone sampling} -
         {\color{blue}$\Gamma$-point only} calculations
   \item \underline{Pseudo potential}