--- /dev/null
+\pdfoutput=0
+%\documentclass[landscape,semhelv,draft]{seminar}
+\documentclass[landscape,semhelv]{seminar}
+
+\usepackage{verbatim}
+\usepackage[greek,german]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{latexsym}
+\usepackage{ae}
+
+\usepackage{calc} % Simple computations with LaTeX variables
+\usepackage{caption} % Improved captions
+\usepackage{fancybox} % To have several backgrounds
+
+\usepackage{fancyhdr} % Headers and footers definitions
+\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{miller}
+
+\usepackage[setpagesize=false]{hyperref}
+
+\usepackage{semcolor}
+\usepackage{semlayer} % Seminar overlays
+\usepackage{slidesec} % Seminar sections and list of slides
+
+\input{seminar.bug} % Official bugs corrections
+\input{seminar.bg2} % Unofficial bugs corrections
+
+\articlemag{1}
+
+\special{landscape}
+
+% font
+%\usepackage{cmbright}
+%\renewcommand{\familydefault}{\sfdefault}
+%\usepackage{mathptmx}
+
+\usepackage{upgreek}
+
+\begin{document}
+
+\extraslideheight{10in}
+\slideframe{none}
+
+\pagestyle{empty}
+
+% specify width and height
+\slidewidth 27.7cm
+\slideheight 19.1cm
+
+% shift it into visual area properly
+\def\slideleftmargin{3.3cm}
+\def\slidetopmargin{0.6cm}
+
+\newcommand{\ham}{\mathcal{H}}
+\newcommand{\pot}{\mathcal{V}}
+\newcommand{\foo}{\mathcal{U}}
+\newcommand{\vir}{\mathcal{W}}
+
+% itemize level ii
+\renewcommand\labelitemii{{\color{gray}$\bullet$}}
+
+% nice phi
+\renewcommand{\phi}{\varphi}
+
+% roman letters
+\newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
+
+% colors
+\newrgbcolor{si-yellow}{.6 .6 0}
+\newrgbcolor{hb}{0.75 0.77 0.89}
+\newrgbcolor{lbb}{0.75 0.8 0.88}
+\newrgbcolor{hlbb}{0.825 0.88 0.968}
+\newrgbcolor{lachs}{1.0 .93 .81}
+
+% topic
+
+\begin{slide}
+\begin{center}
+
+ \vspace{16pt}
+
+ {\LARGE\bf
+ Atomistic simulation study on the silicon carbide precipitation
+ in silicon
+ }
+
+ \vspace{48pt}
+
+ \textsc{F. Zirkelbach}
+
+ \vspace{48pt}
+
+Yet another seminar contribution
+
+ \vspace{08pt}
+
+ Augsburg am 26. Mai 2011
+
+\end{center}
+\end{slide}
+
+% motivation / properties / applications of silicon carbide
+\begin{slide}
+
+\small
+
+\begin{pspicture}(0,0)(13.5,5)
+
+
+
+ \psframe*[linecolor=hb](0,0)(13.5,5)
+
+ \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.5,1)(7,1)(7,3)(5.5,3)
+ \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.75,0.5)(8,2)(8,2)(6.75,3.5)
+
+ \rput[lt](0.2,4.6){\color{gray}PROPERTIES}
+
+ \rput[lt](0.5,4){wide band gap}
+ \rput[lt](0.5,3.5){high electric breakdown field}
+ \rput[lt](0.5,3){good electron mobility}
+ \rput[lt](0.5,2.5){high electron saturation drift velocity}
+ \rput[lt](0.5,2){high thermal conductivity}
+
+ \rput[lt](0.5,1.5){hard and mechanically stable}
+ \rput[lt](0.5,1){chemically inert}
+
+ \rput[lt](0.5,0.5){radiation hardness}
+
+ \rput[rt](13.3,4.6){\color{gray}APPLICATIONS}
+
+ \rput[rt](13,3.85){high-temperature, high power}
+ \rput[rt](13,3.5){and high-frequency}
+ \rput[rt](13,3.15){electronic and optoelectronic devices}
+
+ \rput[rt](13,2.35){material suitable for extreme conditions}
+ \rput[rt](13,2){microelectromechanical systems}
+ \rput[rt](13,1.65){abrasives, cutting tools, heating elements}
+
+ \rput[rt](13,0.85){first wall reactor material, detectors}
+ \rput[rt](13,0.5){and electronic devices for space}
+
+\end{pspicture}
+
+\begin{picture}(0,0)(-3,68)
+\includegraphics[width=2.6cm]{wide_band_gap.eps}
+\end{picture}
+\begin{picture}(0,0)(-285,-162)
+\includegraphics[width=3.38cm]{sic_led.eps}
+\end{picture}
+\begin{picture}(0,0)(-195,-162)
+\includegraphics[width=2.8cm]{6h-sic_3c-sic.eps}
+\end{picture}
+\begin{picture}(0,0)(-313,65)
+\includegraphics[width=2.2cm]{infineon_schottky.eps}
+\end{picture}
+\begin{picture}(0,0)(-220,65)
+\includegraphics[width=2.9cm]{sic_wechselrichter_ise.eps}
+\end{picture}
+\begin{picture}(0,0)(0,-160)
+\includegraphics[width=3.0cm]{sic_proton.eps}
+\end{picture}
+\begin{picture}(0,0)(-60,65)
+\includegraphics[width=3.4cm]{sic_switch.eps}
+\end{picture}
+
+\end{slide}
+
+% start of contents
+
+\begin{slide}
+
+ {\large\bf
+ 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}
+
+ Conventional thin film SiC growth:
+ \begin{itemize}
+ \item \underline{Sublimation growth using the modified Lely method}
+ \begin{itemize}
+ \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 \underline{Homoepitaxial growth using CVD}
+ \begin{itemize}
+ \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
+ \end{itemize}
+ \item \underline{Heteroepitaxial growth of 3C-SiC on Si using CVD/MBE}
+ \begin{itemize}
+ \item Two steps: carbonization and growth
+ \item $T=650-1050 \, ^{\circ} \text{C}$
+ \item SiC/Si lattice mismatch $\approx$ 20 \%
+ \item Quality and size not yet sufficient
+ \end{itemize}
+ \end{itemize}
+
+ \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)(-333,-175)
+ \begin{minipage}{5cm}
+ {\tiny
+ 1. Lid\\[-7pt]
+ 2. Heating\\[-7pt]
+ 3. Source\\[-7pt]
+ 4. Crucible\\[-7pt]
+ 5. Insulation\\[-7pt]
+ 6. Seed crystal
+ }
+ \end{minipage}
+ \end{picture}
+ \begin{picture}(0,0)(-230,-35)
+ \framebox{
+ {\footnotesize\color{blue}\bf Hex: micropipes along c-axis}
+ }
+ \end{picture}
+ \begin{picture}(0,0)(-230,-10)
+ \framebox{
+ \begin{minipage}{3cm}
+ {\footnotesize\color{blue}\bf 3C-SiC fabrication\\
+ less advanced}
+ \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}
+\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
+ Outline
+}
+
+ \begin{itemize}
+ \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 C and Si self-interstitial point defects in silicon
+ \item Silicon carbide precipitation simulations
+ \item Summary / Conclusion / Outlook
+ \end{itemize}
+
+\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)
+\rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+ $4a_{\text{Si}}=5a_{\text{SiC}}$
+ }}}
+\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\hkl(h k l) planes match
+ }}}
+\rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+r = 2 - 4 nm
+ }}}
+\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 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}
+
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
+\end{pspicture}
+
+\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 [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
+\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 [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
+\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 [nm]& $a$ & $b$ & $|a|+|b|$ \\
+\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}
+
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
+\psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
+\psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
+\psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
+\end{pspicture}
+
+\end{slide}
+
+\begin{slide}
+
+\small
+
+\begin{minipage}{8.5cm}
+
+ {\large\bf
+ Bond-centered interstitial configuration\\[-0.1cm]
+ }
+
+\begin{minipage}{3.0cm}
+\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
+\end{minipage}
+\begin{minipage}{5.2cm}
+\begin{itemize}
+ \item Linear Si-C-Si bond
+ \item Si: one C \& 3 Si neighbours
+ \item Spin polarized calculations
+ \item No saddle point!\\
+ Real local minimum!
+\end{itemize}
+\end{minipage}
+
+\framebox{
+ \tiny
+ \begin{minipage}[t]{6.5cm}
+ \begin{minipage}[t]{1.2cm}
+ {\color{red}Si}\\
+ {\tiny sp$^3$}\\[0.8cm]
+ \underline{${\color{black}\uparrow}$}
+ \underline{${\color{black}\uparrow}$}
+ \underline{${\color{black}\uparrow}$}
+ \underline{${\color{red}\uparrow}$}\\
+ sp$^3$
+ \end{minipage}
+ \begin{minipage}[t]{1.4cm}
+ \begin{center}
+ {\color{red}M}{\color{blue}O}\\[0.8cm]
+ \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+ $\sigma_{\text{ab}}$\\[0.5cm]
+ \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+ $\sigma_{\text{b}}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{1.0cm}
+ \begin{center}
+ {\color{blue}C}\\
+ {\tiny sp}\\[0.2cm]
+ \underline{${\color{white}\uparrow\uparrow}$}
+ \underline{${\color{white}\uparrow\uparrow}$}\\
+ 2p\\[0.4cm]
+ \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
+ \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
+ sp
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{1.4cm}
+ \begin{center}
+ {\color{blue}M}{\color{green}O}\\[0.8cm]
+ \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+ $\sigma_{\text{ab}}$\\[0.5cm]
+ \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
+ $\sigma_{\text{b}}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{1.2cm}
+ \begin{flushright}
+ {\color{green}Si}\\
+ {\tiny sp$^3$}\\[0.8cm]
+ \underline{${\color{green}\uparrow}$}
+ \underline{${\color{black}\uparrow}$}
+ \underline{${\color{black}\uparrow}$}
+ \underline{${\color{black}\uparrow}$}\\
+ sp$^3$
+ \end{flushright}
+ \end{minipage}
+ \end{minipage}
+}\\[0.1cm]
+
+\framebox{
+\begin{minipage}{4.5cm}
+\includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
+\end{minipage}
+\begin{minipage}{3.5cm}
+{\color{gray}$\bullet$} Spin up\\
+{\color{green}$\bullet$} Spin down\\
+{\color{blue}$\bullet$} Resulting spin up\\
+{\color{yellow}$\bullet$} Si atoms\\
+{\color{red}$\bullet$} C atom
+\end{minipage}
+}
+
+\end{minipage}
+\begin{minipage}{4.2cm}
+\begin{flushright}
+\includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
+{\color{green}$\Box$} {\tiny unoccupied}\\
+{\color{red}$\bullet$} {\tiny occupied}
+\end{flushright}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Migration of the C \hkl<1 0 0> dumbbell interstitial
+ }
+
+\scriptsize
+
+ {\small Investigated pathways}
+
+\begin{minipage}{8.5cm}
+\begin{minipage}{8.3cm}
+\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
+\end{minipage}
+\end{minipage}\\
+\begin{minipage}{8.3cm}
+\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
+\end{minipage}
+\end{minipage}\\
+\begin{minipage}{8.3cm}
+\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
+\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}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Migration of the C \hkl<1 0 0> dumbbell interstitial
+ }
+
+\scriptsize
+
+\framebox{
+\begin{minipage}{5.9cm}
+\begin{flushleft}
+\includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
+\end{flushleft}
+\begin{center}
+\begin{picture}(0,0)(60,0)
+\includegraphics[width=1cm]{vasp_mig/00-1.eps}
+\end{picture}
+\begin{picture}(0,0)(-5,0)
+\includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
+\end{picture}
+\begin{picture}(0,0)(-55,0)
+\includegraphics[width=1cm]{vasp_mig/bc.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,10)
+\includegraphics[width=1cm]{110_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,0)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\vspace*{0.35cm}
+\end{minipage}
+}
+\begin{minipage}{0.3cm}
+\hfill
+\end{minipage}
+\framebox{
+\begin{minipage}{5.9cm}
+\begin{flushright}
+\includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
+\end{flushright}
+\begin{center}
+\begin{picture}(0,0)(60,0)
+\includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
+\end{picture}
+\begin{picture}(0,0)(5,0)
+\includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
+\end{picture}
+\begin{picture}(0,0)(-55,0)
+\includegraphics[width=1cm]{vasp_mig/0-10.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,10)
+\includegraphics[width=1cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,0)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\vspace*{0.3cm}
+\end{minipage}\\
+}
+
+\vspace*{0.05cm}
+
+\framebox{
+\begin{minipage}{5.9cm}
+\begin{flushleft}
+\includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
+\end{flushleft}
+\begin{center}
+\begin{picture}(0,0)(60,0)
+\includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
+\end{picture}
+\begin{picture}(0,0)(10,0)
+\includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
+\end{picture}
+\begin{picture}(0,0)(-60,0)
+\includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,10)
+\includegraphics[width=1cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,0)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\vspace*{0.3cm}
+\end{minipage}
+}
+\begin{minipage}{0.3cm}
+\hfill
+\end{minipage}
+\begin{minipage}{6.5cm}
+VASP results
+\begin{itemize}
+ \item Energetically most favorable path
+ \begin{itemize}
+ \item Path 2
+ \item Activation energy: $\approx$ 0.9 eV
+ \item Experimental values: 0.73 ... 0.87 eV
+ \end{itemize}
+ $\Rightarrow$ {\color{blue}Diffusion} path identified!
+ \item Reorientation (path 3)
+ \begin{itemize}
+ \item More likely composed of two consecutive steps of type 2
+ \item Experimental values: 0.77 ... 0.88 eV
+ \end{itemize}
+ $\Rightarrow$ {\color{blue}Reorientation} transition identified!
+\end{itemize}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Migration of the C \hkl<1 0 0> dumbbell interstitial
+ }
+
+\scriptsize
+
+\begin{minipage}{6.5cm}
+
+\framebox{
+\begin{minipage}{5.9cm}
+\begin{flushleft}
+\includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
+\end{flushleft}
+\begin{center}
+\begin{pspicture}(0,0)(0,0)
+\psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
+\end{pspicture}
+\begin{picture}(0,0)(60,-50)
+\includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
+\end{picture}
+\begin{picture}(0,0)(5,-50)
+\includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
+\end{picture}
+\begin{picture}(0,0)(-55,-50)
+\includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,-40)
+\includegraphics[width=1cm]{110_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,-45)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}\\
+\begin{pspicture}(0,0)(0,0)
+\psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
+\end{pspicture}
+\begin{picture}(0,0)(60,-15)
+\includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
+\end{picture}
+\begin{picture}(0,0)(35,-15)
+\includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
+\end{picture}
+\begin{picture}(0,0)(-5,-15)
+\includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
+\end{picture}
+\begin{picture}(0,0)(-55,-15)
+\includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,-5)
+\includegraphics[width=1cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,-15)
+\includegraphics[height=0.9cm]{010_arrow.eps}
+\end{picture}
+\end{center}
+\end{minipage}
+}\\[0.1cm]
+
+\begin{minipage}{5.9cm}
+Erhart/Albe results
+\begin{itemize}
+ \item Lowest activation energy: $\approx$ 2.2 eV
+ \item 2.4 times higher than VASP
+ \item Different pathway
+ \item Transition minima ($\rightarrow$ \hkl<1 1 0> dumbbell)
+\end{itemize}
+\end{minipage}
+
+\end{minipage}
+\begin{minipage}{6.5cm}
+
+\framebox{
+\begin{minipage}{5.9cm}
+\begin{flushright}
+\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
+\end{flushright}
+\begin{center}
+\begin{pspicture}(0,0)(0,0)
+\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
+\end{pspicture}
+\begin{picture}(0,0)(60,-5)
+\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
+\end{picture}
+\begin{picture}(0,0)(0,-5)
+\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
+\end{picture}
+\begin{picture}(0,0)(-55,-5)
+\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,5)
+\includegraphics[width=1cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,0)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\vspace{0.2cm}
+\end{minipage}
+}\\[0.2cm]
+
+\framebox{
+\begin{minipage}{5.9cm}
+\includegraphics[width=5.9cm]{00-1_ip0-10.ps}
+\end{minipage}
+}
+
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combinations with a C-Si \hkl<1 0 0>-type interstitial
+ }
+
+\small
+
+\vspace*{0.1cm}
+
+Binding energy:
+$
+E_{\text{b}}=
+E_{\text{f}}^{\text{defect combination}}-
+E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
+E_{\text{f}}^{\text{2nd defect}}
+$
+
+\vspace*{0.1cm}
+
+{\scriptsize
+\begin{tabular}{l c c c c c c}
+\hline
+ $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
+ \hline
+ \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
+ \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
+ \hkl<0 -1 0> & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl<0 1 0> & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hkl<-1 0 0> & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl<1 0 0> & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hline
+ C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
+ Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
+\hline
+\end{tabular}
+}
+
+\vspace*{0.3cm}
+
+\footnotesize
+
+\begin{minipage}[t]{3.8cm}
+\underline{\hkl<1 0 0> at position 1}\\[0.1cm]
+\includegraphics[width=3.5cm]{00-1dc/2-25.eps}
+\end{minipage}
+\begin{minipage}[t]{3.5cm}
+\underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
+\includegraphics[width=3.2cm]{00-1dc/2-39.eps}
+\end{minipage}
+\begin{minipage}[t]{5.5cm}
+\begin{itemize}
+ \item Restricted to VASP simulations
+ \item $E_{\text{b}}=0$ for isolated non-interacting defects
+ \item $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
+ \item Stress compensation / increase
+ \item Most favorable: C clustering
+ \item Unfavored: antiparallel orientations
+ \item Indication of energetically favored\\
+ agglomeration
+\end{itemize}
+\end{minipage}
+
+\begin{picture}(0,0)(-295,-130)
+\includegraphics[width=3.5cm]{comb_pos.eps}
+\end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combinations of C-Si \hkl<1 0 0>-type interstitials
+ }
+
+\small
+
+\vspace*{0.1cm}
+
+Energetically most favorable combinations along \hkl<1 1 0>
+
+\vspace*{0.1cm}
+
+{\scriptsize
+\begin{tabular}{l c c c c c c}
+\hline
+ & 1 & 2 & 3 & 4 & 5 & 6\\
+\hline
+$E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
+C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
+Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\
+\hline
+\end{tabular}
+}
+
+\vspace*{0.3cm}
+
+\begin{minipage}{7.0cm}
+\includegraphics[width=7cm]{db_along_110_cc.ps}
+\end{minipage}
+\begin{minipage}{6.0cm}
+\begin{center}
+{\color{blue}
+ Interaction proportional to reciprocal cube of C-C distance
+}\\[0.2cm]
+ Saturation in the immediate vicinity
+\end{center}
+\end{minipage}
+
+\vspace{0.2cm}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
+ }
+
+ \scriptsize
+
+\begin{center}
+\begin{minipage}{3.2cm}
+\includegraphics[width=3cm]{sub_110_combo.eps}
+\end{minipage}
+\begin{minipage}{7.8cm}
+\begin{tabular}{l c c c c c c}
+\hline
+C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
+ \hkl<1 0 1> & \hkl<-1 0 1> \\
+\hline
+1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
+2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
+3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
+4 & \RM{4} & B & D & E & E & D \\
+5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
+\hline
+\end{tabular}
+\end{minipage}
+\end{center}
+
+\begin{center}
+\begin{tabular}{l c c c c c c c c c c}
+\hline
+Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
+\hline
+$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
+$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
+$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
+\hline
+\end{tabular}
+\end{center}
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=5.8cm]{c_sub_si110.ps}
+\end{minipage}
+\begin{minipage}{7cm}
+\small
+\begin{itemize}
+ \item IBS: C may displace Si\\
+ $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
+ \item Assumption:\\
+ \hkl<1 1 0>-type $\rightarrow$ favored combination
+ \renewcommand\labelitemi{$\Rightarrow$}
+ \item Less favorable than C-Si \hkl<1 0 0> dumbbell\\
+ ($E_{\text{f}}=3.88\text{ eV}$)
+ \item Interaction drops quickly to zero\\
+ (low interaction capture radius)
+\end{itemize}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Migration in C-Si \hkl<1 0 0> and vacancy combinations
+ }
+
+ \footnotesize
+
+\vspace{0.1cm}
+
+\begin{minipage}[t]{3cm}
+\underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
+\includegraphics[width=2.8cm]{00-1dc/0-59.eps}
+\end{minipage}
+\begin{minipage}[t]{7cm}
+\vspace{0.2cm}
+\begin{center}
+ Low activation energies\\
+ High activation energies for reverse processes\\
+ $\Downarrow$\\
+ {\color{blue}C$_{\text{sub}}$ very stable}\\
+\vspace*{0.1cm}
+ \hrule
+\vspace*{0.1cm}
+ Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
+ $\Downarrow$\\
+ {\color{blue}Formation of SiC by successive substitution by C}
+
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{3cm}
+\underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
+\includegraphics[width=2.8cm]{00-1dc/3-14.eps}
+\end{minipage}
+
+
+\framebox{
+\begin{minipage}{5.9cm}
+\includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
+\begin{center}
+\begin{picture}(0,0)(70,0)
+\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
+\end{picture}
+\begin{picture}(0,0)(30,0)
+\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
+\end{picture}
+\begin{picture}(0,0)(-10,0)
+\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
+\end{picture}
+\begin{picture}(0,0)(-48,0)
+\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,5)
+\includegraphics[width=1cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(97,-10)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\vspace{0.1cm}
+\end{minipage}
+}
+\begin{minipage}{0.3cm}
+\hfill
+\end{minipage}
+\framebox{
+\begin{minipage}{5.9cm}
+\includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
+\begin{center}
+\begin{picture}(0,0)(60,0)
+\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
+\end{picture}
+\begin{picture}(0,0)(25,0)
+\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
+\end{picture}
+\begin{picture}(0,0)(-20,0)
+\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
+\end{picture}
+\begin{picture}(0,0)(-55,0)
+\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,5)
+\includegraphics[width=1cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(95,0)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\vspace{0.1cm}
+\end{minipage}
+}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Conclusion of defect / migration / combined defect simulations
+ }
+
+ \small
+
+\vspace*{0.1cm}
+
+Defect structures
+\begin{itemize}
+ \item Accurately described by quantum-mechanical simulations
+ \item Less accurate description by classical potential simulations
+\end{itemize}
+\vspace*{0.2cm}
+\begin{itemize}
+ \item \hkl<1 0 0> C-Si dumbbell interstitial ground state configuration
+ \item Consistent with reorientation and diffusion experiments
+ \item C migration pathway in Si identified
+\end{itemize}
+
+Concerning the precipitation mechanism
+\begin{itemize}
+ \item Agglomeration of C-Si dumbbells energetically favorable
+ \item C-Si indeed favored compared to
+ C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
+ \item Possible low interaction capture radius of
+ C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
+ \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
+ C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
+\end{itemize}
+\begin{center}
+{\color{blue}Some results point to a different precipitation mechanism!}
+\end{center}
+In progress ...
+\begin{itemize}
+ \item \hkl<1 0 0> C-Si $\rightarrow$
+ C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
+ \item \hkl<1 0 0> C-Si combinations: C-C $\rightarrow$ C-...-C
+\end{itemize}
+
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Silicon carbide precipitation simulations
+ }
+
+ \small
+
+{\scriptsize
+ \begin{pspicture}(0,0)(12,6.5)
+ % nodes
+ \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+ \parbox{7cm}{
+ \begin{itemize}
+ \item Create c-Si volume
+ \item Periodc boundary conditions
+ \item Set requested $T$ and $p=0\text{ bar}$
+ \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
+ \end{itemize}
+ }}}}
+ \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
+ \parbox{7cm}{
+ Insertion of C atoms at constant T
+ \begin{itemize}
+ \item total simulation volume {\pnode{in1}}
+ \item volume of minimal SiC precipitate {\pnode{in2}}
+ \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
+ precipitate
+ \end{itemize}
+ }}}}
+ \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
+ \parbox{7.0cm}{
+ Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
+ }}}}
+ \ncline[]{->}{init}{insert}
+ \ncline[]{->}{insert}{cool}
+ \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
+ \rput(7.8,6){\footnotesize $V_1$}
+ \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
+ \rput(9.2,4.85){\tiny $V_2$}
+ \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
+ \rput(9.55,4.45){\footnotesize $V_3$}
+ \rput(7.9,3.2){\pnode{ins1}}
+ \rput(9.22,2.8){\pnode{ins2}}
+ \rput(11.0,2.4){\pnode{ins3}}
+ \ncline[]{->}{in1}{ins1}
+ \ncline[]{->}{in2}{ins2}
+ \ncline[]{->}{in3}{ins3}
+ \end{pspicture}
+}
+
+\begin{itemize}
+ \item Restricted to classical potential simulations
+ \item $V_2$ and $V_3$ considered due to low diffusion
+ \item Amount of C atoms: 6000
+ ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
+ \item Simulation volume: $31\times 31\times 31$ unit cells
+ (238328 Si atoms)
+\end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
+ }
+
+ \small
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
+\end{minipage}
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\scriptsize
+\underline{Low C concentration ($V_1$)}\\
+\hkl<1 0 0> C-Si dumbbell dominated structure
+\begin{itemize}
+ \item Si-C bumbs around 0.19 nm
+ \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
+ concatenated dumbbells of various orientation
+ \item Si-Si NN distance stretched to 0.3 nm
+\end{itemize}
+{\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
+\underline{High C concentration ($V_2$, $V_3$)}\\
+High amount of strongly bound C-C bonds\\
+Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
+Only short range order observable\\
+{\color{blue}$\Rightarrow$ amorphous SiC-like phase}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Limitations of molecular dynamics and short range potentials
+ }
+
+\footnotesize
+
+\vspace{0.2cm}
+
+\underline{Time scale problem of MD}\\[0.2cm]
+Minimize integration error\\
+$\Rightarrow$ discretization considerably smaller than
+ reciprocal of fastest vibrational mode\\[0.1cm]
+Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
+$\Rightarrow$ suitable choice of time step:
+ $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
+$\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
+Several local minima in energy surface separated by large energy barriers\\
+$\Rightarrow$ transition event corresponds to a multiple
+ of vibrational periods\\
+$\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
+ infrequent transition events\\[0.1cm]
+{\color{blue}Accelerated methods:}
+\underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
+
+\vspace{0.3cm}
+
+\underline{Limitations related to the short range potential}\\[0.2cm]
+Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
+and 2$^{\text{nd}}$ next neighbours\\
+$\Rightarrow$ overestimated unphysical high forces of next neighbours
+
+\vspace{0.3cm}
+
+\framebox{
+\color{red}
+Potential enhanced problem of slow phase space propagation
+}
+
+\vspace{0.3cm}
+
+\underline{Approach to the (twofold) problem}\\[0.2cm]
+Increased temperature simulations without TAD corrections\\
+(accelerated methods or higher time scales exclusively not sufficient)
+
+\begin{picture}(0,0)(-260,-30)
+\framebox{
+\begin{minipage}{4.2cm}
+\tiny
+\begin{center}
+\vspace{0.03cm}
+\underline{IBS}
+\end{center}
+\begin{itemize}
+\item 3C-SiC also observed for higher T
+\item higher T inside sample
+\item structural evolution vs.\\
+ equilibrium properties
+\end{itemize}
+\end{minipage}
+}
+\end{picture}
+
+\begin{picture}(0,0)(-305,-155)
+\framebox{
+\begin{minipage}{2.5cm}
+\tiny
+\begin{center}
+retain proper\\
+thermodynmic sampling
+\end{center}
+\end{minipage}
+}
+\end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Increased temperature simulations at low C concentration
+ }
+
+\small
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{tot_pc_thesis.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
+\end{minipage}
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\scriptsize
+ \underline{Si-C bonds:}
+ \begin{itemize}
+ \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
+ \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
+ \end{itemize}
+ \underline{Si-Si bonds:}
+ {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
+ ($\rightarrow$ 0.325 nm)\\[0.1cm]
+ \underline{C-C bonds:}
+ \begin{itemize}
+ \item C-C next neighbour pairs reduced (mandatory)
+ \item Peak at 0.3 nm slightly shifted
+ \begin{itemize}
+ \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
+ $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
+ combinations (|)\\
+ $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
+ ($\downarrow$)
+ \item Range [|-$\downarrow$]:
+ {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
+ with nearby Si$_{\text{I}}$}
+ \end{itemize}
+ \end{itemize}
+\end{minipage}
+
+\begin{picture}(0,0)(-330,-74)
+\color{blue}
+\framebox{
+\begin{minipage}{1.6cm}
+\tiny
+\begin{center}
+stretched SiC\\[-0.1cm]
+in c-Si
+\end{center}
+\end{minipage}
+}
+\end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Increased temperature simulations at high C concentration
+ }
+
+\footnotesize
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{12_pc_thesis.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
+\end{minipage}
+
+\begin{center}
+Decreasing cut-off artifact\\
+High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
+$\Rightarrow$ hard to categorize
+\end{center}
+
+\vspace{0.1cm}
+
+\framebox{
+\begin{minipage}[t]{6.0cm}
+0.186 nm: Si-C pairs $\uparrow$\\
+(as expected in 3C-SiC)\\[0.2cm]
+0.282 nm: Si-C-C\\[0.2cm]
+$\approx$0.35 nm: C-Si-Si
+\end{minipage}
+}
+\begin{minipage}{0.2cm}
+\hfill
+\end{minipage}
+\framebox{
+\begin{minipage}[t]{6.0cm}
+0.15 nm: C-C pairs $\uparrow$\\
+(as expected in graphite/diamond)\\[0.2cm]
+0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
+0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
+\end{minipage}
+}
+
+\vspace{0.1cm}
+
+\begin{center}
+{\color{red}Amorphous} SiC-like phase remains\\
+Slightly sharper peaks
+$\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics}
+due to temperature\\[0.1cm]
+\framebox{
+\bf
+Continue with higher temperatures and longer time scales
+}
+\end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Long time scale simulations at maximum temperature
+ }
+
+\small
+
+\vspace{0.1cm}
+
+\underline{Differences}
+\begin{itemize}
+ \item Temperature set to $0.95 \cdot T_{\text{m}}$
+ \item Cubic insertion volume $\Rightarrow$ spherical insertion volume
+ \item Amount of C atoms: 6000 $\rightarrow$ 5500
+ $\Leftrightarrow r_{\text{prec}}=0.3\text{ nm}$
+ \item Simulation volume: 21 unit cells of c-Si in each direction
+\end{itemize}
+
+\footnotesize
+
+\vspace{0.3cm}
+
+\begin{minipage}[t]{4.5cm}
+\begin{center}
+\underline{Low C concentration, Si-C}
+\includegraphics[width=4.5cm]{c_in_si_95_v1_si-c.ps}\\
+Sharper peaks!
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{4.5cm}
+\begin{center}
+\underline{Low C concentration, C-C}
+\includegraphics[width=4.5cm]{c_in_si_95_v1_c-c.ps}\\
+Sharper peaks!\\
+No C agglomeration!
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{4cm}
+\begin{center}
+\underline{High C concentration}
+\includegraphics[width=4.5cm]{c_in_si_95_v2.ps}\\
+No significant changes\\
+C-Si-Si $\uparrow$\\
+C-Si-C $\downarrow$
+\end{center}
+\end{minipage}
+
+\begin{center}
+\framebox{
+Long time scales and high temperatures most probably not sufficient enough!
+}
+\end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Summary / Conclusion / Outlook
+ }
+
+ \scriptsize
+
+\vspace{0.1cm}
+
+\framebox{
+\begin{minipage}{12.9cm}
+ \underline{Defects}
+ \begin{itemize}
+ \item Summary \& conclusion
+ \begin{itemize}
+ \item Point defects excellently / fairly well described
+ by QM / classical potential simulations
+ \item Identified migration path explaining
+ diffusion and reorientation experiments
+ \item Agglomeration of point defects energetically favorable
+ \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
+ \end{itemize}
+ \item In progress
+ \begin{itemize}
+ \item Migrations separating C-C bond in \hkl<1 0 0> C-Si dumbbell
+ interstitial combination
+ \item Migration: \hkl<1 0 0> C-Si $\rightarrow$
+ C$_{\text{sub}}$ \& Si \hkl<1 1 0> interstitial
+ \end{itemize}
+ \item Todo
+ \begin{itemize}
+ \item Discussions concerning interpretation of QM results (Paderborn)
+ \item Compare migration barrier of
+ \hkl<1 1 0> Si and C-Si \hkl<1 0 0> dumbbell
+ \item Combination: Vacancy \& \hkl<1 1 0> Si self-interstitial \&
+ C-Si \hkl<1 0 0> dumbbell (IBS)
+ \end{itemize}
+ \end{itemize}
+\end{minipage}
+}
+
+\vspace{0.2cm}
+
+\framebox{
+\begin{minipage}[t]{12.9cm}
+ \underline{Pecipitation simulations}
+ \begin{itemize}
+ \item Summary \& conclusion
+ \begin{itemize}
+ \item Low T
+ $\rightarrow$ C-Si \hkl<1 0 0> dumbbell
+ dominated structure
+ \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
+ \item High C concentration
+ $\rightarrow$ amorphous SiC like phase
+ \end{itemize}
+ \item Todo
+ \begin{itemize}
+ \item Accelerated method: self-guided MD
+ \item Activation relaxation technique
+ \item Constrainted transition path
+ \end{itemize}
+ \end{itemize}
+\end{minipage}
+}
+
+ \small
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Acknowledgements
+ }
+
+ \vspace{0.1cm}
+
+ \small
+
+ Thanks to \ldots
+
+ \underline{Augsburg}
+ \begin{itemize}
+ \item Prof. B. Stritzker (accepting a simulator at EP \RM{4})
+ \item Ralf Utermann (EDV)
+ \end{itemize}
+
+ \underline{Helsinki}
+ \begin{itemize}
+ \item Prof. K. Nordlund (MD)
+ \end{itemize}
+
+ \underline{Munich}
+ \begin{itemize}
+ \item Bayerische Forschungsstiftung (financial support)
+ \end{itemize}
+
+ \underline{Paderborn}
+ \begin{itemize}
+ \item Prof. J. Lindner (SiC)
+ \item Prof. G. Schmidt (DFT + financial support)
+ \item Dr. E. Rauls (DFT + SiC)
+ \item Dr. S. Sanna (VASP)
+ \end{itemize}
+
+\vspace{0.2cm}
+
+\begin{center}
+\framebox{
+\bf Thank you for your attention!
+}
+\end{center}
+
+\end{slide}
+
+\end{document}
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