X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fmpi_app.tex;h=e4cdd485901ab5dbde0bc2bf829d7f9e861eaf1f;hp=9931ba16bb1a0f2d05c7b3f9147e1c6a6b0ec785;hb=ab8104bce0b6ea93877f9a5102a9fa933c4bf17f;hpb=448bf217190b3d815e3d749631af50cbcbd21834

diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex
index 9931ba1..e4cdd48 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}
 
@@ -20,6 +21,7 @@
 
 \usepackage{pstricks}
 \usepackage{pst-node}
+\usepackage{pst-grad}
 
 %\usepackage{epic}
 %\usepackage{eepic}
@@ -54,6 +56,28 @@
 
 \usepackage{upgreek}
 
+\newcommand{\headdiplom}{
+\begin{pspicture}(0,0)(0,0)
+\rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{
+\begin{minipage}{14cm}
+\hfill
+\vspace{0.7cm}
+\end{minipage}
+}}
+\end{pspicture}
+}
+
+\newcommand{\headphd}{
+\begin{pspicture}(0,0)(0,0)
+\rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=blue,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{
+\begin{minipage}{14cm}
+\hfill
+\vspace{0.7cm}
+\end{minipage}
+}}
+\end{pspicture}
+}
+
 \begin{document}
 
 \extraslideheight{10in}
@@ -143,6 +167,9 @@ E\\
 \end{center}
 \end{slide}
 
+% no vertical centering
+\centerslidesfalse
+
 \ifnum1=0
 
 % intro
@@ -182,6 +209,8 @@ R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959)
 
 \begin{slide}
 
+\vspace*{1.8cm}
+
 \small
 
 \begin{pspicture}(0,0)(13.5,5)
@@ -296,7 +325,6 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 
 \end{slide}
 
-\fi
 % fabrication
 
 \begin{slide}
@@ -317,7 +345,7 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 
 \vspace{2pt}
 
-SiC thin film by MBE \& CVD
+SiC thin films by MBE \& CVD
 \begin{itemize}
  \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
  \item \underline{Commercially available} semiconductor power devices based on
@@ -330,33 +358,33 @@ SiC thin film by MBE \& CVD
   \includegraphics[width=2.0cm]{cree.eps}
 \end{picture}
 
-\vspace{-0.4cm}
+\vspace{-0.2cm}
 
 Alternative approach:
 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
 
+\vspace{0.2cm}
+
 \scriptsize
 
-\begin{minipage}{6.5cm}
- \begin{itemize}
-  \item \underline{Implantation step 1}\\
-        180 keV C$^+$, $D=7.9\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=500\,^{\circ}\mathrm{C}$\\[0.1cm]
-        Box-like distribution of equally sized \&\\
-        epitaxially oriented SiC precipitates
-                       
-  \item \underline{Implantation step 2}\\
-        180 keV C$^+$, $D=0.6\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=250\,^{\circ}\mathrm{C}$\\[0.1cm]
-        Destruction of SiC nanocrystals\\
-        in growing amorphous interface layers
-  \item \underline{Annealing}\\
-        $T=1250\,^{\circ}\mathrm{C}$, $t=10\,\text{h}$\\[0.1cm]
-        Homogeneous, stoichiometric SiC layer\\
-        with sharp interfaces
- \end{itemize}
+\framebox{
+\begin{minipage}{3.15cm}
+ \begin{center}
+\includegraphics[width=3cm]{imp.eps}\\
+ {\tiny
+  Carbon implantation
+ }
+ \end{center}
 \end{minipage}
-\begin{minipage}{0.3cm}
-\hfill
+\begin{minipage}{3.15cm}
+ \begin{center}
+\includegraphics[width=3cm]{annealing.eps}\\
+ {\tiny
+  \unit[12]{h} annealing at \degc{1200}
+ }
+ \end{center}
 \end{minipage}
+}
 \begin{minipage}{5.5cm}
  \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
  \begin{center}
@@ -366,26 +394,25 @@ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
  \end{center}
 \end{minipage}
 
-\framebox{
- \begin{minipage}{6.3cm}
- \begin{center}
- {\color{blue}
-  Precipitation mechanism not yet fully understood!
- }
- \renewcommand\labelitemi{$\Rightarrow$}
- \small
- \underline{Understanding the SiC precipitation}
- \begin{itemize}
-  \item significant technological progress in SiC thin film formation
-  \item perspectives for processes relying upon prevention of SiC precipitation
- \end{itemize}
- \end{center}
- \end{minipage}
+\end{slide}
+
+% contents
+
+\begin{slide}
+
+{\large\bf
+ Systematic investigation of C implantations into Si
 }
 
+\vspace{1.7cm}
+\begin{center}
+\hspace{-1.0cm}
+\includegraphics[width=0.75\textwidth]{imp_inv.eps}
+\end{center}
+
 \end{slide}
 
-% contents
+% outline
 
 \begin{slide}
 
@@ -393,75 +420,381 @@ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
  Outline
 }
 
- \begin{itemize}
-  \item Implantation of C in Si --- Overview of experimental observations
-  \item Utilized simulation techniques and modeled problems
-        \begin{itemize}
-         \item {\color{blue}Diploma thesis}\\
-               \underline{Monte Carlo} simulations
-               modeling the selforganization process
-               leading to periodic arrays of nanometric amorphous SiC
-               precipitates
-         \item {\color{blue}Doctoral studies}\\
-               Classical potential \underline{molecular dynamics} simulations
-               \ldots\\
-               \underline{Density functional theory} calculations
-               \ldots\\[0.2cm]
-               \ldots on defects and SiC precipitation in Si
-        \end{itemize}
-  \item Summary / Conclusion / Outlook
- \end{itemize}
+\vspace{1.7cm}
+\begin{center}
+\hspace{-1.0cm}
+\includegraphics[width=0.75\textwidth]{imp_inv.eps}
+\end{center}
+
+\begin{pspicture}(0,0)(0,0)
+\rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
+\begin{minipage}{11cm}
+{\color{black}Diploma thesis}\\
+ \underline{Monte Carlo} simulation modeling the selforganization process\\
+ leading to periodic arrays of nanometric amorphous SiC precipitates
+\end{minipage}
+}}}
+\end{pspicture}
+\begin{pspicture}(0,0)(0,0)
+\rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=blue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
+\begin{minipage}{11cm}
+{\color{black}Doctoral studies}\\
+ Classical potential \underline{molecular dynamics} simulations \ldots\\
+ \underline{Density functional theory} calculations \ldots\\[0.2cm]
+ \ldots on defect formation and SiC precipitation in Si
+\end{minipage}
+}}}
+\end{pspicture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=red,linewidth=0.05cm](5,3.0)(0.8,1.0)
+\end{pspicture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=blue,linewidth=0.05cm](8.2,3.2)(1.5,1.6)
+\end{pspicture}
 
 \end{slide}
 
+\begin{slide}
 
-\end{document}
-\ifnum1=0
+\headdiplom
+{\large\bf
+ Selforganization of nanometric amorphous SiC lamellae
+}
+
+\small
+
+\vspace{0.2cm}
+
+\begin{itemize}
+ \item Regularly spaced, nanometric spherical\\
+       and lamellar amorphous inclusions\\
+       at the upper a/c interface
+ \item Carbon accumulation\\
+       in amorphous volumes
+\end{itemize}
+
+\vspace{0.4cm}
+
+\begin{minipage}{12cm}
+\includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\
+{\scriptsize
+XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si,
+{\color{red}\underline{\degc{150}}},
+Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$}
+}
+\end{minipage}
+
+\begin{picture}(0,0)(-182,-215)
+\begin{minipage}{6.5cm}
+\begin{center}
+\includegraphics[width=6.5cm]{../../nlsop/img/eftem.eps}\\[-0.2cm]
+{\scriptsize
+XTEM bright-field and respective EFTEM C map
+}
+\end{center}
+\end{minipage}
+\end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+\headdiplom
+{\large\bf
+ Model displaying the formation of ordered lamellae
+}
+
+\vspace{0.1cm}
+
+\begin{center}
+ \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps}
+\end{center}
+
+\footnotesize
+
+\begin{itemize}
+\item Supersaturation of C in c-Si\\
+      $\rightarrow$ {\bf Carbon induced} nucleation of spherical
+      SiC$_x$-precipitates
+\item High interfacial energy between 3C-SiC and c-Si\\
+      $\rightarrow$ {\bf Amorphous} precipitates
+\item \unit[20-- 30]{\%} lower silicon density of a-SiC$_x$ compared to c-Si\\
+      $\rightarrow$ {\bf Lateral strain} (black arrows)
+\item Implantation range near surface\\
+      $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component}
+\item Reduction of the carbon supersaturation in c-Si\\
+      $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina
+      (white arrows)
+\item Remaining lateral strain\\
+      $\rightarrow$ {\bf Strain enhanced} lateral amorphisation
+\item Absence of crystalline neighbours (structural information)\\
+      $\rightarrow$ {\bf Stabilization} of amorphous inclusions 
+      {\bf against recrystallization}
+\end{itemize}
 
+\end{slide}
 
 \begin{slide}
 
- {\large\bf
-  Supposed precipitation mechanism of SiC in Si
+\headdiplom
+{\large\bf
+ Implementation of the Monte Carlo code
+}
+
+\small
+
+\begin{enumerate}
+ \item \underline{Amorphization / Recrystallization}\\
+       Ion collision in discretized target determined by random numbers
+       distributed according to nuclear energy loss.
+       Amorphization/recrystallization probability:
+\[
+p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
+\]
+\begin{itemize}
+ \item {\color{green} $p_b$} normal `ballistic' amorphization
+ \item {\color{blue} $p_c$} carbon induced amorphization
+ \item {\color{red} $p_s$} stress enhanced amorphization
+\end{itemize}
+\[
+p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
+\]
+\[
+\delta (\vec r) = \left\{
+\begin{array}{ll}
+        1 & \textrm{if volume at position $\vec r$ is amorphous} \\
+        0 & \textrm{otherwise} \\
+\end{array}
+\right.
+\]
+ \item \underline{Carbon incorporation}\\
+       Incorporation volume determined according to implantation profile
+ \item \underline{Diffusion / Sputtering}
+       \begin{itemize}
+        \item Transfer fraction of C atoms
+              of crystalline into neighbored amorphous volumes
+        \item Remove surface layer
+       \end{itemize}
+\end{enumerate}
+
+\end{slide}
+
+\begin{slide}
+
+\begin{minipage}{3.7cm}
+\begin{pspicture}(0,0)(0,0)
+\rput(1.7,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradangle=10,gradmidpoint=1,linestyle=none]{
+\begin{minipage}{3.7cm}
+\hfill
+\vspace{0.7cm}
+\end{minipage}
+}}
+\end{pspicture}
+{\large\bf
+ Results
+}
+
+\footnotesize
+
+\vspace{1.2cm}
+
+Evolution of the \ldots
+\begin{itemize}
+ \item continuous\\
+       amorphous layer
+ \item a/c interface
+ \item lamellar precipitates
+\end{itemize}
+\ldots reproduced!\\[1.4cm]
+
+{\color{blue}
+\begin{center}
+Experiment \& simulation\\
+in good agreement\\[1.0cm]
+
+Simulation is able to model the whole depth region\\[1.2cm]
+\end{center}
+}
+
+\end{minipage}
+\begin{minipage}{0.5cm}
+\vfill
+\end{minipage}
+\begin{minipage}{8.0cm}
+ \vspace{-0.3cm}
+ \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\
+ \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+\headdiplom
+{\large\bf
+ Structural \& compositional details
+}
+
+\begin{minipage}[t]{7.5cm}
+\includegraphics[height=6.5cm]{../../nlsop/img/ac_cconc_ver2_e.eps}\\
+\end{minipage}
+\begin{minipage}[t]{5.0cm}
+\includegraphics[height=6.5cm]{../../nlsop/img/97_98_e.eps}
+\end{minipage}
+
+\footnotesize
+
+\vspace{-0.1cm}
+
+\begin{itemize}
+ \item Fluctuation of C concentration in lamellae region
+ \item \unit[8--10]{at.\%} C saturation limit
+       within the respective conditions
+ \item Complementarily arranged and alternating sequence of layers\\
+       with a high and low amount of amorphous regions
+ \item C accumulation in the amorphous phase / Origin of stress
+\end{itemize}
+
+\begin{picture}(0,0)(-260,-50)
+\framebox{
+\begin{minipage}{3cm}
+\begin{center}
+{\color{blue}
+Precipitation process\\
+gets traceable\\
+by simulation!
+}
+\end{center}
+\end{minipage}
+}
+\end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+\headphd
+{\large\bf
+ Formation of epitaxial single crystalline 3C-SiC
+}
+
+\footnotesize
+
+\vspace{0.2cm}
+
+\begin{center}
+\begin{itemize}
+ \item \underline{Implantation step 1}\\[0.1cm]
+        Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
+        $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
+        {\color{blue}precipitates}
+ \item \underline{Implantation step 2}\\[0.1cm]
+        Little remaining dose | \unit[180]{keV} | \degc{250}\\
+        $\Rightarrow$
+        Destruction/Amorphization of precipitates at layer interface
+ \item \underline{Annealing}\\[0.1cm]
+       \unit[10]{h} at \degc{1250}\\
+       $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
+\end{itemize}
+\end{center}
+
+\begin{minipage}{7cm}
+\includegraphics[width=7cm]{ibs_3c-sic.eps}
+\end{minipage}
+\begin{minipage}{5cm}
+\begin{pspicture}(0,0)(0,0)
+\rnode{box}{
+\psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
+\begin{minipage}{5.3cm}
+ \begin{center}
+ {\color{blue}
+  3C-SiC precipitation\\
+  not yet fully understood
  }
+ \end{center}
+ \vspace*{0.1cm}
+ \renewcommand\labelitemi{$\Rightarrow$}
+ Details of the SiC precipitation
+ \begin{itemize}
+  \item significant technological progress\\
+        in SiC thin film formation
+  \item perspectives for processes relying\\
+        upon prevention of SiC precipitation
+ \end{itemize}
+\end{minipage}
+}}
+\rput(-6.8,5.4){\pnode{h0}}
+\rput(-3.0,5.4){\pnode{h1}}
+\ncline[linecolor=blue]{-}{h0}{h1}
+\ncline[linecolor=blue]{->}{h1}{box}
+\end{pspicture}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+\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]
@@ -469,37 +802,39 @@ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
  \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}
 
@@ -507,47 +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]
@@ -555,60 +910,81 @@ 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}
@@ -617,160 +993,110 @@ r = 2 - 4 nm
 
 \begin{slide}
 
- {\large\bf
-  Molecular dynamics (MD) simulations
- }
-
- \vspace{12pt}
+\headphd
+{\large\bf
+ Utilized computational methods
+}
 
- \small
+\vspace{0.3cm}
 
- {\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}
+\small
 
- \begin{picture}(0,0)(-230,-30)
-  \includegraphics[width=5cm]{tersoff_angle.eps} 
- \end{picture}
- 
-\end{slide}
+{\bf Molecular dynamics (MD)}\\[0.1cm]
+\scriptsize
+\begin{tabular}{| p{4.5cm} | p{7.5cm} |}
+\hline
+System of $N$ particles &
+$N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
+Phase space propagation &
+Velocity Verlet | timestep: \unit[1]{fs} \\
+Analytical interaction potential &
+Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
+(Erhart/Albe)
+$\displaystyle
+E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
+    \pot_{ij} = {\color{red}f_C(r_{ij})}
+    \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
+$\\
+Observables: time/ensemble averages &
+NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
+\hline
+\end{tabular}
 
-\begin{slide}
+\small
 
- {\large\bf
-  Density functional theory (DFT) calculations
- }
+\vspace{0.3cm}
 
- \small
+{\bf Density functional theory (DFT)}
 
- Basic ingredients necessary for DFT
+\scriptsize
 
- \begin{itemize}
-  \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
-        \begin{itemize}
-         \item ... uniquely determines the ground state potential
-               / wavefunctions
-         \item ... minimizes the systems total energy
-        \end{itemize}
-  \item \underline{Born-Oppenheimer}
-        - $N$ moving electrons in an external potential of static nuclei
-\[
-H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
-              +\sum_i^N V_{\text{ext}}(r_i)
-              +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
-\]
-  \item \underline{Effective potential}
-        - averaged electrostatic potential \& exchange and correlation
-\[
+\begin{minipage}[t]{6cm}
+\begin{itemize}
+ \item Hohenberg-Kohn theorem:\\
+       $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
+ \item Kohn-Sham approach:\\
+       Single-particle effective theory
+\end{itemize}
+\hrule
+\begin{itemize}
+\item Code: \textsc{vasp}
+\item Plane wave basis set
+%$\displaystyle
+%\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
+%$\\
+%$\displaystyle
+%E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
+%$
+\item Ultrasoft pseudopotential
+\item Exchange \& correlation: GGA
+\item Brillouin zone sampling: $\Gamma$-point
+\item Supercell: $N=216\pm2$
+\end{itemize}
+\end{minipage}
+\begin{minipage}{6cm}
+\begin{pspicture}(0,0)(0,0)
+\pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
+\rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
+\left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
+$
+}}
+\rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
+n(r)=\sum_i^N|\Phi_i(r)|^2
+$
+}}
+\rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
                  +V_{\text{XC}}[n(r)]
-\]
-  \item \underline{Kohn-Sham system}
-        - Schr\"odinger equation of N non-interacting particles
-\[
-\left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
-=\epsilon_i\Phi_i(r)
-\quad
-\Rightarrow
-\quad
-n(r)=\sum_i^N|\Phi_i(r)|^2
-\]
-  \item \underline{Self-consistent solution}\\
-$n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
-which in turn depends on $n(r)$
-  \item \underline{Variational principle}
-        - minimize total energy with respect to $n(r)$
- \end{itemize}
-
-\end{slide}
-
-\begin{slide}
-
- {\large\bf
-  Density functional theory (DFT) calculations
- }
-
- \small
-
- \vspace*{0.2cm}
-
- Details of applied DFT calculations in this work
-
- \begin{itemize}
-  \item \underline{Exchange correlation functional}
-        - approximations for the inhomogeneous electron gas
-        \begin{itemize}
-         \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
-         \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
-        \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} 
-        - consider only the valence electrons
-  \item \underline{Code} - VASP 4.6
- \end{itemize}
-
- \vspace*{0.2cm}
-
- MD and structural optimization
-
- \begin{itemize}
-  \item MD integration: Gear predictor corrector algorithm
-  \item Pressure control: Parrinello-Rahman pressure control
-  \item Structural optimization: Conjugate gradient method
- \end{itemize}
+$
+}}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
 
-\begin{pspicture}(0,0)(0,0)
-\psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
 \end{pspicture}
+\end{minipage}
 
 \end{slide}
 
 \begin{slide}
 
+\headphd
  {\large\bf
-  C and Si self-interstitial point defects in silicon
+  Point defects \& defect migration
  }
 
  \small
 
- \vspace*{0.3cm}
+ \vspace{0.2cm}
 
-\begin{minipage}{8cm}
-Procedure:\\[0.3cm]
-  \begin{pspicture}(0,0)(7,5)
-  \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\begin{minipage}[b]{7.5cm}
+{\bf Defect structure}\\
+  \begin{pspicture}(0,0)(7,4.4)
+  \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
    \parbox{7cm}{
    \begin{itemize}
     \item Creation of c-Si simulation volume
@@ -778,13 +1104,13 @@ Procedure:\\[0.3cm]
     \item $T=0\text{ K}$, $p=0\text{ bar}$
    \end{itemize}
   }}}}
-\rput(3.5,2.1){\rnode{insert}{\psframebox{
+\rput(3.5,1.3){\rnode{insert}{\psframebox{
  \parbox{7cm}{
   \begin{center}
   Insertion of interstitial C/Si atoms
   \end{center}
   }}}}
-  \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
+  \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
    \parbox{7cm}{
    \begin{center}
    Relaxation / structural energy minimization
@@ -794,49 +1120,83 @@ Procedure:\\[0.3cm]
   \ncline[]{->}{insert}{cool}
  \end{pspicture}
 \end{minipage}
-\begin{minipage}{5cm}
-  \includegraphics[width=5cm]{unit_cell_e.eps}\\
+\begin{minipage}[b]{4.5cm}
+\begin{center}
+\includegraphics[width=3.8cm]{unit_cell_e.eps}\\
+\end{center}
+\begin{minipage}{2.21cm}
+{\scriptsize
+{\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
+{\color{green}$\bullet$} Hexagonal\\[-0.1cm]
+{\color{yellow}$\bullet$} \hkl<1 0 0> DB
+}
+\end{minipage}
+\begin{minipage}{2.21cm}
+{\scriptsize
+{\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
+{\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
+{\color{black}$\bullet$} Vac. / Sub.
+}
+\end{minipage}
 \end{minipage}
 
-\begin{minipage}{9cm}
- \begin{tabular}{l c c}
- \hline
- & size [unit cells] & \# atoms\\
-\hline
-VASP & $3\times 3\times 3$ & $216\pm 1$ \\
-Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
-\hline
- \end{tabular}
+\vspace{0.2cm}
+
+\begin{minipage}[b]{6cm}
+{\bf Defect formation energy}\\
+\framebox{
+$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
+Particle reservoir: Si \& SiC\\[0.2cm]
+{\bf Binding energy}\\
+\framebox{
+$
+E_{\text{b}}=
+E_{\text{f}}^{\text{comb}}-
+E_{\text{f}}^{1^{\text{st}}}-
+E_{\text{f}}^{2^{\text{nd}}}
+$
+}\\[0.1cm]
+\footnotesize
+$E_{\text{b}}<0$: energetically favorable configuration\\
+$E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
 \end{minipage}
-\begin{minipage}{4cm}
-{\color{red}$\bullet$} Tetrahedral\\
-{\color{green}$\bullet$} Hexagonal\\
-{\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
-{\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
-{\color{cyan}$\bullet$} Bond-centered\\
-{\color{black}$\bullet$} Vacancy / Substitutional
+\begin{minipage}[b]{6cm}
+{\bf Migration barrier}
+\footnotesize
+\begin{itemize}
+ \item Displace diffusing atom
+ \item Constrain relaxation of (diffusing) atoms
+ \item Record configurational energy
+\end{itemize}
+\begin{picture}(0,0)(-60,-33)
+\includegraphics[width=4.5cm]{crt_mod.eps}
+\end{picture}
 \end{minipage}
 
 \end{slide}
 
+% continue here
+\fi
+
 \begin{slide}
 
  \footnotesize
 
 \begin{minipage}{9.5cm}
 
+\headphd
  {\large\bf
-  Si self-interstitial point defects in silicon\\
+  Si self-interstitial point defects in silicon\\[0.1cm]
  }
 
 \begin{tabular}{l c c c c c}
 \hline
  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
 \hline
- VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
+ \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
 \hline
-\end{tabular}\\[0.2cm]
+\end{tabular}\\[0.3cm]
 
 \begin{minipage}{4.7cm}
 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
@@ -846,7 +1206,7 @@ Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
 {\tiny nearly T $\rightarrow$ T}\\
 \end{center}
 \includegraphics[width=4.7cm]{nhex_tet.ps}
-\end{minipage}\\
+\end{minipage}\\[0.1cm]
 
 \underline{Hexagonal} \hspace{2pt}
 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
@@ -873,9 +1233,10 @@ $E_{\text{f}}=3.96\text{ eV}$\\
 \end{minipage}
 
 \end{minipage}
-\begin{minipage}{3.5cm}
+\begin{minipage}{2.5cm}
 
 \begin{flushright}
+\vspace*{0.2cm}
 \underline{\hkl<1 1 0> dumbbell}\\
 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
 \underline{Tetrahedral}\\
@@ -892,18 +1253,21 @@ $E_{\text{f}}=3.96\text{ eV}$\\
 
 \footnotesize
 
+\headphd
  {\large\bf
   C interstitial point defects in silicon\\[-0.1cm]
  }
 
+{\scriptsize
 \begin{tabular}{l c c c c c c r}
 \hline
  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
 \hline
- VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
+ \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
 \hline
-\end{tabular}\\[0.1cm]
+\end{tabular}
+}\\[0.1cm]
 
 \framebox{
 \begin{minipage}{2.7cm}
@@ -962,6 +1326,9 @@ $E_{\text{f}}=5.18\text{ eV}$\\
 
 \end{slide}
 
+\end{document}
+\ifnum1=0
+
 \begin{slide}
 
 \footnotesize
@@ -1195,25 +1562,6 @@ $\rightarrow$
 \end{minipage}
 \end{minipage}
 \end{minipage}
-\framebox{
-\begin{minipage}{4.2cm}
- {\small Constrained relaxation\\
-         technique (CRT) method}\\
-\includegraphics[width=4cm]{crt_orig.eps}
-\begin{itemize}
- \item Constrain diffusing atom
- \item Static constraints 
-\end{itemize}
-\vspace*{0.3cm}
- {\small Modifications}\\
-\includegraphics[width=4cm]{crt_mod.eps}
-\begin{itemize}
- \item Constrain all atoms
- \item Update individual\\
-       constraints
-\end{itemize}
-\end{minipage}
-}
 
 \end{slide}