+
+
+
+
+
+\begin{slide}
+
+\headphd
+ {\large\bf
+ Polytypes of SiC\\[0.6cm]
+ }
+
+\vspace{0.6cm}
+
+\includegraphics[width=3.8cm]{cubic_hex.eps}\\
+\begin{minipage}{1.9cm}
+{\tiny cubic (twist)}
+\end{minipage}
+\begin{minipage}{2.9cm}
+{\tiny hexagonal (no twist)}
+\end{minipage}
+
+\begin{picture}(0,0)(-150,0)
+ \includegraphics[width=7cm]{polytypes.eps}
+\end{picture}
+
+\vspace{0.6cm}
+
+\footnotesize
+
+\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}
+
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=green](5.7,2.05)(0.4,0.50)
+\end{pspicture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
+\end{pspicture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=red](10.45,0.42)(0.4,0.20)
+\end{pspicture}
+
+\end{slide}
+
+\begin{slide}
+
+\footnotesize
+
+\headphd
+{\large\bf
+ Si self-interstitial point defects in silicon\\[0.1cm]
+}
+
+\begin{center}
+\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
+ \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}\\[0.4cm]
+\end{center}
+
+\begin{minipage}{3cm}
+\begin{center}
+\underline{Vacancy}\\
+\includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{3cm}
+\begin{center}
+\underline{\hkl<1 1 0> DB}\\
+\includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{3cm}
+\begin{center}
+\underline{\hkl<1 0 0> DB}\\
+\includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{3cm}
+\begin{center}
+\underline{Tetrahedral}\\
+\includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
+\end{center}
+\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_bonds.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_bonds.eps}
+\end{minipage}
+}
+\begin{minipage}{5.5cm}
+\begin{center}
+{\tiny nearly T $\rightarrow$ T}\\
+\end{center}
+\includegraphics[width=6.0cm]{nhex_tet.ps}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+\headphd
+{\large\bf\boldmath
+ C-Si dimer \& bond-centered interstitial configuration
+}
+
+\footnotesize
+
+\vspace{0.1cm}
+
+\begin{minipage}[t]{4.1cm}
+{\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
+\begin{minipage}{2.0cm}
+\begin{center}
+\underline{Erhart/Albe}
+\includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{2.0cm}
+\begin{center}
+\underline{\textsc{vasp}}
+\includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
+\end{center}
+\end{minipage}\\[0.2cm]
+Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
+$\Rightarrow$ $sp$ hybridization\\[0.1cm]
+Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
+$\Rightarrow$ $sp^2$ hybridization
+\begin{center}
+\includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
+{\tiny Charge density isosurface}
+\end{center}
+\end{minipage}
+\begin{minipage}{0.2cm}
+\hfill
+\end{minipage}
+\begin{minipage}[t]{8.1cm}
+\begin{flushright}
+{\bf Bond-centered interstitial}\\[0.1cm]
+\begin{minipage}{4.4cm}
+%\scriptsize
+\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}
+\begin{minipage}{2.7cm}
+%\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
+\vspace{0.2cm}
+\includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
+\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}
+}\\[0.4cm]
+
+%\framebox{
+\begin{minipage}{3.0cm}
+%\scriptsize
+\underline{Charge density}\\
+{\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}
+\begin{minipage}{3.6cm}
+\includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
+\end{minipage}
+%}
+
+\end{flushright}
+
+\end{minipage}
+\begin{pspicture}(0,0)(0,0)
+\psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
+\end{pspicture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Increased temperature simulations at high C concentration
+ }
+
+\footnotesize
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=6.4cm]{12_pc_thesis.ps}
+\end{minipage}
+\begin{minipage}{6.0cm}
+\includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
+\end{minipage}
+
+\vspace{0.1cm}
+
+\scriptsize
+
+\framebox{
+\begin{minipage}[t]{5.5cm}
+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}{0.1cm}
+\hfill
+\end{minipage}
+\framebox{
+\begin{minipage}[t]{5.9cm}
+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}
+}
+
+\begin{itemize}
+\item Decreasing cut-off artifact
+\item {\color{red}Amorphous} SiC-like phase remains
+\item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
+\item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
+\end{itemize}
+
+\begin{center}
+{\color{blue}
+\framebox{
+{\color{black}
+High C \& small $V$ \& short $t$
+$\Rightarrow$
+}
+\begin{minipage}{4cm}
+\begin{center}
+Slow structural evolution due to strong C-C bonds
+\end{center}
+\end{minipage}
+{\color{black}
+$\Leftarrow$
+High C \& low T implants
+}
+}
+}
+\end{center}
+
+\end{slide}
+
+
+
+\begin{slide}
+
+ {\large\bf
+ Valuation of a practicable temperature limit
+ }
+
+ \small
+
+\vspace{0.1cm}
+
+\begin{center}
+\framebox{
+{\color{blue}
+Recrystallization is a hard task!
+$\Rightarrow$ Avoid melting!
+}
+}
+\end{center}
+
+\vspace{0.1cm}
+
+\footnotesize
+
+\begin{minipage}{6.4cm}
+\includegraphics[width=6.4cm]{fe_and_t.ps}
+\end{minipage}
+\begin{minipage}{5.7cm}
+\underline{Melting does not occur instantly after}\\
+\underline{exceeding the melting point $T_{\text{m}}=2450\text{ K}$}
+\begin{itemize}
+\item required transition enthalpy
+\item hysterisis behaviour
+\end{itemize}
+\underline{Heating up c-Si by 1 K/ps}
+\begin{itemize}
+\item transition occurs at $\approx$ 3125 K
+\item $\Delta E=0.58\text{ eV/atom}=55.7\text{ kJ/mole}$\\
+ (literature: 50.2 kJ/mole)
+\end{itemize}
+\end{minipage}
+
+\vspace{0.1cm}
+
+\framebox{
+\begin{minipage}{4cm}
+Initially chosen temperatures:\\
+$1.0 - 1.2 \cdot T_{\text{m}}$
+\end{minipage}
+}
+\begin{minipage}{2cm}
+\begin{center}
+$\Longrightarrow$
+\end{center}
+\end{minipage}
+\framebox{
+\begin{minipage}{5cm}
+Introduced C (defects)\\
+$\rightarrow$ reduction of transition point\\
+$\rightarrow$ melting already at $T_{\text{m}}$
+\end{minipage}
+}
+
+\vspace{0.4cm}
+
+\begin{center}
+\framebox{
+{\color{blue}
+Maximum temperature used: $0.95\cdot T_{\text{m}}$
+}
+}
+\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]{4.3cm}
+\begin{center}
+\underline{Low C concentration, Si-C}
+\includegraphics[width=4.3cm]{c_in_si_95_v1_si-c.ps}\\
+Sharper peaks!
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{4.3cm}
+\begin{center}
+\underline{Low C concentration, C-C}
+\includegraphics[width=4.3cm]{c_in_si_95_v1_c-c.ps}\\
+Sharper peaks!\\
+No C agglomeration!
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{3.4cm}
+\begin{center}
+\underline{High C concentration}
+\includegraphics[width=4.3cm]{c_in_si_95_v2.ps}\\
+No significant changes\\
+iC-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
+ Investigation of a silicon carbide precipitate in silicon
+ }
+
+ \scriptsize
+
+\vspace{0.2cm}
+
+\framebox{
+\scriptsize
+\begin{minipage}{5.3cm}
+\[
+\frac{8}{a_{\text{Si}}^3}(
+\underbrace{21^3 a_{\text{Si}}^3}_{=V}
+-\frac{4}{3}\pi x^3)+
+\underbrace{\frac{4}{y^3}\frac{4}{3}\pi x^3}_{\stackrel{!}{=}5500}
+=21^3\cdot 8
+\]
+\[
+\Downarrow
+\]
+\[
+\frac{8}{a_{\text{Si}}^3}\frac{4}{3}\pi x^3=5500
+\Rightarrow x = \left(\frac{5500 \cdot 3}{32 \pi} \right)^{1/3}a_{\text{Si}}
+\]
+\[
+y=\left(\frac{1}{2} \right)^{1/3}a_{\text{Si}}
+\]
+\end{minipage}
+}
+\begin{minipage}{0.1cm}
+\hfill
+\end{minipage}
+\begin{minipage}{6.3cm}
+\underline{Construction}
+\begin{itemize}
+ \item Simulation volume: 21$^3$ unit cells of c-Si
+ \item Spherical topotactically aligned precipitate\\
+ $r=3.0\text{ nm}$ $\Leftrightarrow$ $\approx$ 5500 C atoms
+ \item Create c-Si but skipped inside sphere\\
+ of radius $x$
+ \item Create 3C-SiC inside sphere of radius $x$\\
+ and lattice constant $y$
+ \item Strong coupling to heat bath ($T=20\,^{\circ}\mathrm{C}$)
+\end{itemize}
+\end{minipage}
+
+\vspace{0.3cm}
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=6cm]{pc_0.ps}
+\end{minipage}
+\begin{minipage}{6.1cm}
+\underline{Results}
+\begin{itemize}
+ \item Slight increase of c-Si lattice constant!
+ \item C-C peaks\\
+ (imply same distanced Si-Si peaks)
+ \begin{itemize}
+ \item New peak at 0.307 nm: 2$^{\text{nd}}$ NN in 3C-SiC
+ \item Bumps ({\color{green}$\downarrow$}):
+ 4$^{\text{th}}$ and 6$^{\text{th}}$ NN
+ \end{itemize}
+ \item 3C-SiC lattice constant: 4.34 \AA (bulk: 4.36 \AA)\\
+ $\rightarrow$ compressed precipitate
+ \item Interface tension:\\
+ 20.15 eV/nm$^2$ or $3.23 \times 10^{-4}$ J/cm$^2$\\
+ (literature: $2 - 8 \times 10^{-4}$ J/cm$^2$)
+\end{itemize}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Investigation of a silicon carbide precipitate in silicon
+ }
+
+ \footnotesize
+
+\begin{minipage}{7cm}
+\underline{Appended annealing steps}
+\begin{itemize}
+ \item artificially constructed interface\\
+ $\rightarrow$ allow for rearrangement of interface atoms
+ \item check SiC stability
+\end{itemize}
+\underline{Temperature schedule}
+\begin{itemize}
+ \item rapidly heat up structure up to $2050\,^{\circ}\mathrm{C}$\\
+ (75 K/ps)
+ \item slow heating up to $1.2\cdot T_{\text{m}}=2940\text{ K}$
+ by 1 K/ps\\
+ $\rightarrow$ melting at around 2840 K
+ (\href{../video/sic_prec_120.avi}{$\rhd$})
+ \item cooling down structure at 100 \% $T_{\text{m}}$ (1 K/ps)\\
+ $\rightarrow$ no energetically more favorable struture
+\end{itemize}
+\end{minipage}
+\begin{minipage}{5cm}
+\includegraphics[width=5.5cm]{fe_and_t_sic.ps}
+\end{minipage}
+
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{sic_prec/melt_01.eps}
+\end{minipage}
+\begin{minipage}{0.2cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{sic_prec/melt_02.eps}
+\end{minipage}
+\begin{minipage}{0.2cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{3.7cm}
+\includegraphics[width=4cm]{sic_prec/melt_03.eps}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ DFT parameters
+ }
+
+\scriptsize
+
+\vspace{0.1cm}
+
+Equilibrium lattice constants and cohesive energies
+
+\begin{tabular}{l r c c c c c}
+\hline
+\hline
+ & & USPP, LDA & USPP, GGA & PAW, LDA & PAW, GGA & Exp. \\
+\hline
+Si (dia) & $a$ [\AA] & 5.389 & 5.455 & - & - & 5.429 \\
+ & $\Delta_a$ [\%] & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - & - & - \\
+ & $E_{\text{coh}}$ [eV] & -5.277 & -4.591 & - & - & -4.63 \\
+ & $\Delta_E$ [\%] & \unit[{\color{red}14.0}]{\%} & \unit[{\color{green}0.8}]{\%} & - & - & - \\
+\hline
+C (dia) & $a$ [\AA] & 3.527 & 3.567 & - & - & 3.567 \\
+ & $\Delta_a$ [\%] & \unit[{\color{green}1.1}]{\%} & \unit[{\color{green}0.01}]{\%} & - & - & - \\
+ & $E_{\text{coh}}$ [eV] & -8.812 & -7.703 & - & - & -7.374 \\
+ & $\Delta_E$ [\%] & \unit[{\color{red}19.5}]{\%} & \unit[{\color{orange}4.5}]{\%} & - & - & - \\
+\hline
+3C-SiC & $a$ [\AA] & 4.319 & 4.370 & 4.330 & 4.379 & 4.359 \\
+ & $\Delta_a$ [\%] & \unit[{\color{green}0.9}]{\%} & \unit[{\color{green}0.3}]{\%} & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - \\
+ & $E_{\text{coh}}$ [eV] & -7.318 & -6.426 & -7.371 & -6.491 & -6.340 \\
+ & $\Delta_E$ [\%] & \unit[{\color{red}15.4}]{\%} & \unit[{\color{green}1.4}]{\%} & \unit[{\color{red}16.3}]{\%} & \unit[{\color{orange}2.4}]{\%} & - \\
+\hline
+\hline
+\end{tabular}
+
+\vspace{0.3cm}
+
+\begin{minipage}{7cm}
+\begin{center}
+\begin{tabular}{l c c c}
+\hline
+\hline
+ & Si (dia) & C (dia) & 3C-SiC \\
+\hline
+$a$ [\AA] & 5.458 & 3.562 & 4.365 \\
+$\Delta_a$ [\%] & 0.5 & 0.1 & 0.1 \\
+\hline
+$E_{\text{coh}}$ [eV] & -4.577 & -7.695 & -6.419 \\
+$\Delta_E$ [\%] & 1.1 & 4.4 & 1.2 \\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\end{minipage}
+\begin{minipage}{5cm}
+$\leftarrow$ entire parameter set
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ DFT parameters\\
+ }
+
+\footnotesize
+
+\begin{minipage}{6cm}
+\begin{center}
+\includegraphics[width=6cm]{sic_32pc_gamma_cutoff_lc.ps}
+\end{center}
+\end{minipage}
+\begin{minipage}{6cm}
+\begin{center}
+Lattice constants with respect to the PW cut-off energy
+\end{center}
+\end{minipage}
+
+\begin{minipage}{6cm}
+\begin{center}
+\includegraphics[width=6cm]{si_self_int_thesis.ps}
+\end{center}
+\end{minipage}
+\begin{minipage}{6cm}
+\begin{center}
+Defect formation energy with respect to the size of the supercell\\[0.1cm]
+\end{center}
+
+\end{minipage}
+
+\end{slide}
+
+\end{document}
+