}
\begin{itemize}
- \item Polyteps and fabrication of silicon carbide
+ \item Polytyps and fabrication of silicon carbide
\item Supposed precipitation mechanism of SiC in Si
\item Utilized simulation techniques
\begin{itemize}
}
\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}
n(r)=\sum_i^N|\Phi_i(r)|^2
\]
\item \underline{Self-consistent solution}\\
-$n(r)$ depends on $\Phi_i$, which depends on $V_{\text{eff}}$,
+$n(r)$ 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 $n(r)$
Increased temperature simulations without TAD corrections\\
(accelerated methods or higher time scales exclusively not sufficient)
-\begin{picture}(0,0)(-262,-10)
-\frame{
-\begin{minipage}{4.3cm}
+\begin{picture}(0,0)(-260,-30)
+\framebox{
+\begin{minipage}{4.2cm}
\tiny
\begin{center}
\vspace{0.03cm}
}
\end{picture}
-\begin{picture}(0,0)(-305,-152)
-\frame{
-\begin{minipage}{2.6cm}
+\begin{picture}(0,0)(-305,-155)
+\framebox{
+\begin{minipage}{2.5cm}
\tiny
\begin{center}
retain proper\\
\begin{slide}
{\large\bf
- Increased temperature simulations
+ Increased temperature simulations at low C concentration
}
\small
-Low concentration simulation
-
+\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
+ Increased temperature simulations at high C concentration
}
-\small
+\footnotesize
-High concentration simulation
+\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
- Silicon carbide precipitation simulations
+ 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}
- 4. temperature limit
+\vspace{0.1cm}
+
+\footnotesize
+
+\begin{minipage}{7.5cm}
+\includegraphics[width=7cm]{fe_and_t.ps}
+\end{minipage}
+\begin{minipage}{5.5cm}
+\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}{3cm}
+\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
- Silicon carbide precipitation simulations
+ Long time scale simulations at maximum temperature
}
\small
- 5. final TODO
+\vspace{1cm}
+
+\underline{Differences}
+\begin{itemize}
+ \item Cubic volume $\Rightarrow$ spherical volume
+ \item Amount of C atoms: 6000 $\rightarrow$ 5500
+ \item Temperature set to $0.95 \cdot T_{\text{m}}$
+ \item Simulation volume: 21 unit cells of c-Si in each direction
+\end{itemize}
+
+\vspace{1cm}
+
+\begin{center}
+ {\bf
+Simulations in progress! :)\\
+ }
+... show evolution of radial distribution in ns timesteps ...
+\end{center}
+
+\vspace{4cm}
\end{slide}
\begin{slide}
{\large\bf
- Silicon carbide precipitation simulations
+ Investigation of a silicon carbide precipitate in silicon
}
- \small
+ \footnotesize
+
+\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}{0.3cm}
+\hfill
+\end{minipage}
+\begin{minipage}{7.0cm}
+\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}{6.2cm}
+\includegraphics[width=6cm,draft=false]{pc_0.ps}
+\end{minipage}
+\begin{minipage}{6.8cm}
+\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}
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}{6cm}
+\includegraphics[width=6.7cm]{fe_and_t_sic.ps}
+\end{minipage}
+
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{sic_prec/melt_01.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{sic_prec/melt_02.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{sic_prec/melt_03.eps}
+\end{minipage}
+
+\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 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]{6.2cm}
+ \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}
+}
+\framebox{
+\begin{minipage}[t]{6.2cm}
+ \underline{Constructed 3C-SiC precipitate}
+ \begin{itemize}
+ \item Summary \& conclusion
+ \begin{itemize}
+ \item Small / stable / compressed 3C-SiC\\
+ precipitate in slightly stretched\\
+ c-Si matrix
+ \item Interface tension matches experiemnts
+ \end{itemize}
+ \item Todo
+ \begin{itemize}
+ \item Try to improve interface
+ \item Precipitates of different size
+ \end{itemize}
+ \end{itemize}
+\end{minipage}
+}
+
+ \small
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Acknowledgements
+ }
+
\small
projects / lectures / latex.git / blobdiff