X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fseminar_2010.tex;h=5fe206d7d781e026aaae74b576584bda1ecaa399;hb=3e0cf069d29304120c01c063368bfa4d04365e57;hp=fd742bb16a7af6f81c6f1b287771f32ea9bb6208;hpb=3d5577359a78be2b7cf1f2fa6ab2db587f749f8f;p=lectures%2Flatex.git

diff --git a/posic/talks/seminar_2010.tex b/posic/talks/seminar_2010.tex
index fd742bb..5fe206d 100644
--- a/posic/talks/seminar_2010.tex
+++ b/posic/talks/seminar_2010.tex
@@ -26,6 +26,8 @@
 \usepackage{graphicx}
 \graphicspath{{../img/}}
 
+\usepackage{miller}
+
 \usepackage[setpagesize=false]{hyperref}
 
 \usepackage{semcolor}
@@ -172,15 +174,16 @@
 }
 
  \begin{itemize}
-  \item Fabrication of silicon carbide
-  \item Precipitation model
+  \item Polyteps and fabrication of silicon carbide
+  \item Supposed precipitation mechanism of SiC in Si
   \item Utilized simulation techniques
         \begin{itemize}
          \item Molecular dynamics (MD) simulations
          \item Density functional theory (DFT) calculations
         \end{itemize}
-  \item Point defects in silicon
-  \item Precipitation simulations
+  \item C and Si self-interstitial point defects in silicon
+  \item Silicon carbide precipitation simulations
+  \item Investigation of a silicon carbide precipitate in silicon
   \item Summary / Conclusion / Outlook
  \end{itemize}
 
@@ -191,51 +194,674 @@
 \begin{slide}
 
  {\large\bf
-  Motivation
+  Polytypes of SiC
  }
+
+ \vspace{4cm}
+
+ \small
+
+\begin{tabular}{l c c c c c c}
+\hline
+ & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
+\hline
+Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
+Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
+Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
+Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
+Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
+Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
+Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
+\hline
+\end{tabular}
+
+{\tiny
+ Values for $T=300$ K
+}
+
+\begin{picture}(0,0)(-160,-155)
+ \includegraphics[width=7cm]{polytypes.eps}
+\end{picture}
+\begin{picture}(0,0)(-10,-185)
+ \includegraphics[width=3.8cm]{cubic_hex.eps}\\
+\end{picture}
+\begin{picture}(0,0)(-10,-175)
+ {\tiny cubic (twist)}
+\end{picture}
+\begin{picture}(0,0)(-60,-175)
+ {\tiny hexagonal (no twist)}
+\end{picture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=green](5.7,3.03)(0.4,0.5)
+\end{pspicture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=green](5.6,1.68)(0.4,0.2)
+\end{pspicture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=red](10.7,1.13)(0.4,0.2)
+\end{pspicture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Fabrication of silicon carbide
+ }
+
+ \small
  
  \vspace{4pt}
 
  SiC - \emph{Born from the stars, perfected on earth.}
-
+ 
  \vspace{4pt}
 
- Herstellung d"unner SiC-Filme:
+ Conventional thin film SiC growth:
  \begin{itemize}
-  \item modifizierter Lely-Prozess
+  \item \underline{Sublimation growth using the modified Lely method}
         \begin{itemize}
-         \item Impfkristall mit $T=2200 \, ^{\circ} \text{C}$
-         \item umgeben von polykristallinen SiC mit
-               $T=2400 \, ^{\circ} \text{C}$
+         \item SiC single-crystalline seed at $T=1800 \, ^{\circ} \text{C}$
+         \item Surrounded by polycrystalline SiC in a graphite crucible\\
+               at $T=2100-2400 \, ^{\circ} \text{C}$
+         \item Deposition of supersaturated vapor on cooler seed crystal
         \end{itemize}
-  \item CVD Homoepitaxie
+  \item \underline{Homoepitaxial growth using CVD}
         \begin{itemize}
-         \item 'step controlled epitaxy' auf 6H-SiC-Substrat
-         \item C$_3$H$_8$/SiH$_4$/H$_2$ bei $1500 \, ^{\circ} \text{C}$
-         \item Winkel $\rightarrow$ 3C/6H/4H-SiC
-         \item hohe Qualit"at aber limitiert durch\\
-               Substratgr"o"se
+         \item Step-controlled epitaxy on off-oriented 6H-SiC substrates
+         \item C$_3$H$_8$/SiH$_4$/H$_2$ at $1100-1500 \, ^{\circ} \text{C}$
+         \item Angle, temperature $\rightarrow$ 3C/6H/4H-SiC
+         \item High quality but limited in size of substrates
         \end{itemize}
-  \item CVD/MBE Heteroepitaxie von 3C-SiC auf Si
+  \item \underline{Heteroepitaxial growth of 3C-SiC on Si using CVD/MBE}
         \begin{itemize}
-         \item 2 Schritte: Karbonisierung und Wachstum
+         \item Two steps: carbonization and growth
          \item $T=650-1050 \, ^{\circ} \text{C}$
-         \item Qualit"at/Gr"o"se noch nicht ausreichend
+         \item Quality and size not yet sufficient
         \end{itemize}
  \end{itemize}
 
- \begin{picture}(0,0)(-245,-50)
-  \includegraphics[width=5cm]{6h-sic_3c-sic.eps}
+ \begin{picture}(0,0)(-280,-65)
+  \includegraphics[width=3.8cm]{6h-sic_3c-sic.eps}
+ \end{picture}
+ \begin{picture}(0,0)(-280,-55)
+  \begin{minipage}{5cm}
+  {\tiny
+   NASA: 6H-SiC and 3C-SiC LED\\[-7pt]
+   on 6H-SiC substrate
+  }
+  \end{minipage}
+ \end{picture}
+ \begin{picture}(0,0)(-265,-150)
+  \includegraphics[width=2.4cm]{m_lely.eps}
  \end{picture}
- \begin{picture}(0,0)(-240,-35)
+ \begin{picture}(0,0)(-333,-175)
   \begin{minipage}{5cm}
-  {\scriptsize
-   NASA: 6H-SiC LED und 3C-SiC LED\\[-6pt]
-   nebeneinander auf 6H-SiC-Substrat
+  {\tiny
+   1. Lid\\[-7pt]
+   2. Heating\\[-7pt]
+   3. Source\\[-7pt]
+   4. Crucible\\[-7pt]
+   5. Insulation\\[-7pt]
+   6. Seed crystal
   }
   \end{minipage}
  \end{picture}
 
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf
+  Fabrication of silicon carbide
+ }
+
+ \small
+
+ Alternative approach:
+ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
+ \begin{itemize}
+  \item \underline{Implantation step 1}\\
+        180 keV C$^+$, $D=7.9\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=500\,^{\circ}\mathrm{C}$\\
+        $\Rightarrow$ box-like distribution of equally sized
+                       and epitactically oriented SiC precipitates
+                       
+  \item \underline{Implantation step 2}\\
+        180 keV C$^+$, $D=0.6\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=250\,^{\circ}\mathrm{C}$\\
+        $\Rightarrow$ destruction of SiC nanocrystals
+                      in growing amorphous interface layers
+  \item \underline{Annealing}\\
+        $T=1250\,^{\circ}\mathrm{C}$, $t=10\,\text{h}$\\
+        $\Rightarrow$ homogeneous, stoichiometric SiC layer
+                      with sharp interfaces
+ \end{itemize}
+
+ \begin{minipage}{6.3cm}
+ \includegraphics[width=6cm]{ibs_3c-sic.eps}\\[-0.2cm]
+ {\tiny
+  XTEM micrograph of single crystalline 3C-SiC in Si\hkl(1 0 0)
+ }
+ \end{minipage}
+ \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}
+
+\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
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \begin{center}
+ \includegraphics[width=3.3cm]{tem_c-si-db.eps}
+ \end{center}
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \begin{center}
+ \includegraphics[width=3.3cm]{tem_3c-sic.eps}
+ \end{center}
+ \end{minipage}
+
+ \begin{minipage}{4cm}
+ \begin{center}
+ C-Si dimers (dumbbells)\\[-0.1cm]
+ on Si interstitial sites
+ \end{center}
+ \end{minipage}
+ \hspace{0.2cm}
+ \begin{minipage}{4.2cm}
+ \begin{center}
+ Agglomeration of C-Si dumbbells\\[-0.1cm]
+ $\Rightarrow$ dark contrasts
+ \end{center}
+ \end{minipage}
+ \hspace{0.2cm}
+ \begin{minipage}{4cm}
+ \begin{center}
+ Precipitation of 3C-SiC in Si\\[-0.1cm]
+ $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
+ \& release of Si self-interstitials
+ \end{center}
+ \end{minipage}
+
+ \begin{minipage}{3.8cm}
+ \begin{center}
+ \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
+ \end{center}
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \begin{center}
+ \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
+ \end{center}
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \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)
+\end{pspicture}
+ 
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Molecular dynamics (MD) simulations
+ }
+
+ \vspace{12pt}
+
+ \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}
+        \[
+        E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
+        \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
+        \]
+ \end{itemize}
+
+ \begin{picture}(0,0)(-230,-30)
+  \includegraphics[width=5cm]{tersoff_angle.eps} 
+ \end{picture}
+ 
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Density functional theory (DFT) calculations
+ }
+
+ \small
+
+ Basic ingredients necessary for DFT
+
+ \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
+\[
+V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
+                 +V_{\text{XC}}[n(r)]
+\]
+  \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 depends 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 $\phi_j$
+\[
+\rightarrow
+\text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
+\]
+  \item \underline{$k$-point sampling} - $\Gamma$-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}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  C and Si self-interstitial point defects in silicon
+ }
+
+ \small
+
+ \vspace*{0.3cm}
+
+\begin{minipage}{8cm}
+Procedure:\\[0.3cm]
+  \begin{pspicture}(0,0)(7,5)
+  \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+   \parbox{7cm}{
+   \begin{itemize}
+    \item Creation of c-Si simulation volume
+    \item Periodic boundary conditions
+    \item $T=0\text{ K}$, $p=0\text{ bar}$
+   \end{itemize}
+  }}}}
+\rput(3.5,2.1){\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]{
+   \parbox{7cm}{
+   \begin{center}
+   Relaxation / structural energy minimization
+   \end{center}
+  }}}}
+  \ncline[]{->}{init}{insert}
+  \ncline[]{->}{insert}{cool}
+ \end{pspicture}
+\end{minipage}
+\begin{minipage}{5cm}
+  \includegraphics[width=5cm]{unit_cell_e.eps}\\
+\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}
+\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
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ \footnotesize
+
+\begin{minipage}{9.5cm}
+
+ {\large\bf
+  Si self-interstitial point defects in silicon\\
+ }
+
+\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 \\
+ Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
+\hline
+\end{tabular}\\[0.2cm]
+
+\begin{minipage}{4.7cm}
+\includegraphics[width=4.7cm]{e_kin_si_hex.ps}
+\end{minipage}
+\begin{minipage}{4.7cm}
+\begin{center}
+{\tiny nearly T $\rightarrow$ T}\\
+\end{center}
+\includegraphics[width=4.7cm]{nhex_tet.ps}
+\end{minipage}\\
+
+\underline{Hexagonal} \hspace{2pt}
+\href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
+\framebox{
+\begin{minipage}{2.7cm}
+$E_{\text{f}}^*=4.48\text{ eV}$\\
+\includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+\begin{center}
+$\Rightarrow$
+\end{center}
+\end{minipage}
+\begin{minipage}{2.7cm}
+$E_{\text{f}}=3.96\text{ eV}$\\
+\includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
+\end{minipage}
+}
+\begin{minipage}{2.9cm}
+\begin{flushright}
+\underline{Vacancy}\\
+\includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
+\end{flushright}
+\end{minipage}
+
+\end{minipage}
+\begin{minipage}{3.5cm}
+
+\begin{flushright}
+\underline{\hkl<1 1 0> dumbbell}\\
+\includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
+\underline{Tetrahedral}\\
+\includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
+\underline{\hkl<1 0 0> dumbbell}\\
+\includegraphics[width=3.0cm]{si_pd_albe/100.eps}
+\end{flushright}
+
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+\footnotesize
+
+ {\large\bf
+  C interstitial point defects in silicon\\[-0.1cm]
+ }
+
+\begin{tabular}{l c c c c c c}
+\hline
+ $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B \\
+\hline
+ VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 \\
+ Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & 0.75 & 5.59$^*$ \\
+\hline
+\end{tabular}\\[0.1cm]
+
+\framebox{
+\begin{minipage}{2.7cm}
+\underline{Hexagonal} \hspace{2pt}
+\href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
+$E_{\text{f}}^*=9.05\text{ eV}$\\
+\includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+\begin{center}
+$\Rightarrow$
+\end{center}
+\end{minipage}
+\begin{minipage}{2.7cm}
+\underline{\hkl<1 0 0>}\\
+$E_{\text{f}}=3.88\text{ eV}$\\
+\includegraphics[width=2.7cm]{c_pd_albe/100.eps}
+\end{minipage}
+}
+\begin{minipage}{2cm}
+\hfill
+\end{minipage}
+\begin{minipage}{3cm}
+\begin{flushright}
+\underline{Tetrahedral}\\
+\includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
+\end{flushright}
+\end{minipage}
+
+\framebox{
+\begin{minipage}{2.7cm}
+\underline{Bond-centered}\\
+$E_{\text{f}}^*=5.59\text{ eV}$\\
+\includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+\begin{center}
+$\Rightarrow$
+\end{center}
+\end{minipage}
+\begin{minipage}{2.7cm}
+\underline{\hkl<1 1 0> dumbbell}\\
+$E_{\text{f}}=5.18\text{ eV}$\\
+\includegraphics[width=2.7cm]{c_pd_albe/110.eps}
+\end{minipage}
+}
+\begin{minipage}{2cm}
+\hfill
+\end{minipage}
+\begin{minipage}{3cm}
+\begin{flushright}
+\underline{Substitutional}\\
+\includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
+\end{flushright}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+\footnotesize
+
+ {\large\bf\boldmath
+  C \hkl<1 0 0> dumbbell interstitial configuration\\
+ }
+
+{\tiny
+\begin{tabular}{l c c c c c c c c}
+\hline
+ Distances & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
+\hline
+Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
+VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
+\hline
+\end{tabular}\\[0.2cm]
+\begin{tabular}{l c c c c }
+\hline
+ Angles & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
+\hline
+Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
+VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
+\hline
+\end{tabular}\\[0.2cm]
+\begin{tabular}{l c c c}
+\hline
+ Displacements & $a$ & $b$ & $|a|+|b|$ \\
+\hline
+Erhart/Albe & 0.084 & -0.091 & 0.175 \\
+VASP & 0.109 & -0.065 & 0.174 \\
+\hline
+\end{tabular}\\[0.6cm]
+}
+
+\begin{minipage}{3.0cm}
+\begin{center}
+\underline{Erhart/Albe}
+\includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{3.0cm}
+\begin{center}
+\underline{VASP}
+\includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
+\end{center}
+\end{minipage}\\
+
+\begin{picture}(0,0)(-185,10)
+\includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
+\end{picture}
+\begin{picture}(0,0)(-280,-150)
+\includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
+\end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+\footnotesize
+
+ {\large\bf
+  Bond-centered interstitial configuration\\
+ }
+
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Silicon carbide precipitation simulations
+ }
+
+ \small
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Investigation of a silicon carbide precipitate in silicon
+ }
+
+ \small
+
+\end{slide}
+
 \end{document}