% fabrication
-\ifnum1=0
-\begin{slide}
-
-\headphd
- {\large\bf
- Fabrication of silicon carbide
- }
-
- \small
-
- \vspace{2pt}
-
-\begin{center}
- {\color{gray}
- \emph{Silicon carbide --- Born from the stars, perfected on earth.}
- }
-\end{center}
-
-\vspace{2pt}
-
-SiC thin films by MBE \& CVD
-\begin{itemize}
- \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
- \item \underline{Commercially available} semiconductor power devices based on
- \underline{\foreignlanguage{greek}{a}-SiC}
- \item Production of favored \underline{3C-SiC} material
- \underline{less advanced}
- \item Quality and size not yet sufficient
-\end{itemize}
-\begin{picture}(0,0)(-310,-20)
- \includegraphics[width=2.0cm]{cree.eps}
-\end{picture}
-
-\vspace{-0.5cm}
-
-%\begin{center}
-%\color{red}
-%\framebox{
-%{\footnotesize\color{black}
-% Mismatch in \underline{thermal expansion coeefficient}
-% and \underline{lattice parameter} w.r.t. substrate
-%}
-%}
-%\end{center}
-
-\vspace{0.1cm}
-
-{\bf Alternative approach}\\
-Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
-
-\vspace{0.1cm}
-
-\scriptsize
-
-\framebox{
-\begin{minipage}{3.15cm}
- \begin{center}
-\includegraphics[width=3cm]{imp.eps}\\
- {\tiny
- Carbon implantation
- }
- \end{center}
-\end{minipage}
-\begin{minipage}{3.15cm}
- \begin{center}
-\includegraphics[width=3cm]{annealing.eps}\\
- {\tiny
- Postannealing at $>$ \degc{1200}
- }
- \end{center}
-\end{minipage}
-}
-\begin{minipage}{5.5cm}
- \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
- \begin{center}
- {\tiny
- XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
- }
- \end{center}
-\end{minipage}
-
-%\begin{minipage}{5.5cm}
-%\begin{center}
-%{\footnotesize
-%No surface bending effects\\
-%High areal homogenity\\[0.1cm]
-%$\Downarrow$\\[0.1cm]
-%Synthesis of large area SiC films possible
-%}
-%\end{center}
-%\end{minipage}
-
-\end{slide}
-\fi
-
\begin{slide}
\headphd
\end{center}
\end{minipage}
\begin{minipage}{5cm}
+\begin{center}
\begin{pspicture}(0,0)(0,0)
\rnode{box}{
\psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
-\begin{minipage}{5.3cm}
+\begin{minipage}{3.3cm}
\begin{center}
{\color{blue}
3C-SiC precipitation\\
not yet fully understood
}
\end{center}
- \vspace*{0.1cm}
- \renewcommand\labelitemi{$\Rightarrow$}
- Details of the SiC precipitation
- \begin{itemize}
- \item significant technological progress\\
- in SiC thin film formation
- \item perspectives for processes relying\\
- upon prevention of SiC precipitation
- \end{itemize}
+% \vspace*{0.1cm}
+% \renewcommand\labelitemi{$\Rightarrow$}
+% Details of the SiC precipitation
+% \begin{itemize}
+% \item significant technological progress\\
+% in SiC thin film formation
+% \item perspectives for processes relying\\
+% upon prevention of SiC precipitation
+% \end{itemize}
\end{minipage}
}}
-\rput(-6.8,5.5){\pnode{h0}}
-\rput(-3.0,5.5){\pnode{h1}}
+\rput(-5.3,5.5){\pnode{h0}}
+\rput(-1.95,5.5){\pnode{h1}}
\ncline[linecolor=blue]{-}{h0}{h1}
\ncline[linecolor=blue]{->}{h1}{box}
\end{pspicture}
+\end{center}
\end{minipage}
\end{slide}
\end{itemize}
$\Rightarrow$ mobile {\color{red}\ci} opposed to
stable {\color{blue}\cs{}} configurations
-\item Strained silicon \& Si$_{1-y}$C$_y$ heterostructures
+\item Strained Si$_{1-y}$C$_y$/Si heterostructures
{\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
\begin{itemize}
- \item Initial {\color{blue}coherent} SiC precipitates (tensile strain)
- \item Incoherent SiC (strain relaxation)
+ \item Initial {\color{blue}coherent} SiC structures (tensile strain)
+ \item Incoherent SiC nanocrystals (strain relaxation)
\end{itemize}
\end{itemize}
\vspace{0.1cm}
\end{minipage}
\end{minipage}
-\vspace{0.2cm}
+\vspace{0.3cm}
-\begin{minipage}[b]{6cm}
+\begin{minipage}[t]{6cm}
{\bf Defect formation energy}\\
\framebox{
-$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
-Particle reservoir: Si \& SiC\\[0.2cm]
+$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.5cm]
+%Particle reservoir: Si \& SiC\\[0.2cm]
{\bf Binding energy}\\
\framebox{
$
$E_{\text{b}}<0$: energetically favorable configuration\\
$E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
\end{minipage}
-\begin{minipage}[b]{6cm}
+\begin{minipage}[t]{6cm}
+\vspace{1.4cm}
{\bf Migration barrier}
\footnotesize
\begin{itemize}
\begin{itemize}
\item Bond-centered configuration unstable\\
$\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
- \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
+ \item Minimum of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
$\rightarrow$ \ci{} \hkl<1 1 0> DB
\end{itemize}
\vspace{0.1cm}
{\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
\begin{minipage}[t]{3.2cm}
\underline{\hkl[1 0 0] at position 1}\\[0.1cm]
+{\color{cyan}
+\framebox{
\includegraphics[width=2.8cm]{00-1dc/2-25.eps}
+}}
\end{minipage}
\begin{minipage}[t]{3.0cm}
\underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
-\includegraphics[width=2.8cm]{00-1dc/2-39.eps}
+{\color{orange}
+\framebox{
+\includegraphics[width=2.5cm]{00-1dc/2-39.eps}
+}}
\end{minipage}
\begin{minipage}[t]{6.1cm}
\vspace{0.7cm}
\begin{itemize}
\item \ci{} agglomeration energetically favorable
- \item Most favorable: C clustering\\
+ \item Most favorable: strong C-C bond\\
{\color{red}However \ldots}\\
\ldots high migration barrier ($>4\,\text{eV}$)\\
\ldots entropy:
\headphd
{\large\bf\boldmath
- Defect combinations
+ Defect combinations --- ab inito
}
\footnotesize
{\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
\begin{minipage}[t]{3.2cm}
\underline{\hkl[1 0 0] at position 1}\\[0.1cm]
+{\color{cyan}
+\framebox{
\includegraphics[width=2.8cm]{00-1dc/2-25.eps}
+}}
\end{minipage}
\begin{minipage}[t]{3.0cm}
\underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
-\includegraphics[width=2.8cm]{00-1dc/2-39.eps}
+{\color{orange}
+\framebox{
+\includegraphics[width=2.5cm]{00-1dc/2-39.eps}
+}}
\end{minipage}
\begin{minipage}[t]{6.1cm}
\vspace{0.7cm}
\begin{itemize}
\item total simulation volume {\pnode{in1}}
\item volume of minimal SiC precipitate size {\pnode{in2}}
- \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
+ %\item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
+ \item volume containing Si atoms to form a minimal {\pnode{in3}}\\
precipitate
\end{itemize}
}}}}
\begin{minipage}{6.1cm}
\scriptsize
\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
-\hkl<1 0 0> C-Si dumbbell dominated structure
+\ci{} \hkl<1 0 0> dumbbell dominated structure
\begin{itemize}
\item Si-C bumbs around \unit[0.19]{nm}
\item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
\begin{minipage}{6cm}
\centering
Formation of \ci{} dumbbells\\
-C atoms in proper 3C-SiC distance first
+C atoms separated as expected in 3C-SiC
\end{minipage}
}}
\end{pspicture}\\[0.1cm]
\begin{minipage}{6.1cm}
\scriptsize
\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
-\hkl<1 0 0> C-Si dumbbell dominated structure
+\ci{} \hkl<1 0 0> dumbbell dominated structure
\begin{itemize}
\item Si-C bumbs around \unit[0.19]{nm}
\item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
\begin{minipage}{6cm}
\centering
Formation of \ci{} dumbbells\\
-C atoms in proper 3C-SiC distance first
+C atoms separated as expected in 3C-SiC
\end{minipage}
}}
\end{pspicture}\\[0.1cm]
\begin{minipage}{6cm}
\vspace{0.1cm}
\centering
-{\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
+{\bf\color{red}Formation of 3C-SiC fails to appear}\\[0.3cm]
\begin{minipage}{0.8cm}
{\bf\boldmath $V_1$:}
\end{minipage}
\vspace{0.2cm}
{\bf Time scale problem of MD}\\[0.2cm]
-Precise integration \& thermodynamic sampling\\
+Minimize integration error \& precise thermodynamic sampling\\
$\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
$\omega$: vibrational mode\\
$\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
\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$_{\text{sub}}$
+ \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$
+ {\color{blue}\cs{}}
\end{itemize}
\underline{Si-Si bonds:}
{\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
\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}
+ \item Peak at 0.3 nm slightly shifted\\[0.05cm]
+ $\searrow$ \ci{} combinations (dashed arrows)\\
+ $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
+ $\nearrow$ \ci{} pure \cs{} combinations ($\downarrow$)\\[0.05cm]
+ Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
\end{itemize}
\end{minipage}
\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$_{\text{sub}}$
+ \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$
+ {\color{blue}\cs{}}
\end{itemize}
\underline{Si-Si bonds:}
{\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
\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}
+ \item Peak at 0.3 nm slightly shifted\\[0.05cm]
+ $\searrow$ \ci{} combinations (dashed arrows)\\
+ $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
+ $\nearrow$ \ci{} pure \cs{} combinations ($\downarrow$)\\[0.05cm]
+ Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
\end{itemize}
\end{minipage}
{\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
\end{center}
\begin{itemize}
-\item Stretched coherent SiC structures\\
-$\Rightarrow$ Precipitation process involves {\color{blue}\cs}
-\item Role of \si{}
+\item Stretched coherent SiC structures directly observed\\
+\psframebox[linecolor=blue,linewidth=0.05cm]{
+\begin{minipage}{7cm}
+\centering
+\cs{} involved in the precipitation mechanism\\
+\end{minipage}
+}
+\item Emission of \si{} serves several needs:
\begin{itemize}
\item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
\item Building block for surrounding Si host \& further SiC
\item Low T: highly mobile {\color{red}\ci}
\item High T: stable configurations of {\color{blue}\cs}
\end{itemize}
-\end{itemize}
-\vspace{0.2cm}
-\centering
\psframebox[linecolor=blue,linewidth=0.05cm]{
\begin{minipage}{7cm}
\centering
-Precipitation mechanism involving \cs\\
High T $\leftrightarrow$ IBS conditions far from equilibrium\\
\end{minipage}
}
+\end{itemize}
\end{minipage}
\vspace{0.2cm}
}}
\end{slide}
-% skip high c conc results
-\ifnum1=0
-
-\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]{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}
-}
-
-\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}
-
-\vspace{-0.1cm}
-
-\begin{center}
-{\color{blue}
-\framebox{
-{\color{black}
-High C \& small $V$ \& short $t$
-$\Rightarrow$
-}
-Slow restructuring due to strong C-C bonds
-{\color{black}
-$\Leftarrow$
-High C \& low T implants
-}
-}
-}
-\end{center}
-
-\end{slide}
-
-% skip high c conc
-\fi
-
-% for preparation
-%\fi
-
\begin{slide}
\headphd
\item Identified \ci{} migration path
\item EA drastically overestimates the diffusion barrier
\end{itemize}
- \item Combinations of defects
+ \item Combinations of defects (DFT)
\begin{itemize}
\item Agglomeration of point defects energetically favorable
\item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
\underline{Pecipitation simulations}
\begin{itemize}
\item Problem of potential enhanced slow phase space propagation
+ \item High T necessary to simulate IBS conditions (far from equilibrium)
\item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
\item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
- \item High T necessary to simulate IBS conditions (far from equilibrium)
- \item \cs{} involved in the precipitation process at elevated temperatures
+ / Structures of stretched SiC\\
+ $\Rightarrow$
+ \cs{} involved in the precipitation process at elevated temperatures
\item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
(stretched SiC, interface)
\end{itemize}
Thanks to \ldots
+\begin{minipage}[t]{6cm}
\underline{Augsburg}
\begin{itemize}
\item Prof. B. Stritzker
\item Ralf Utermann
+ \item EP \RM{4}
\end{itemize}
\underline{Helsinki}
\item Prof. G. Schmidt
\item Dr. E. Rauls
\end{itemize}
+\end{minipage}
+\begin{minipage}[t]{6cm}
+\underline{Referees}
+ \begin{itemize}
+ \item PD V. Eyert
+ \item Prof. F. Haider
+ \end{itemize}
+\end{minipage}
-\vspace{ 0.2cm}
-
+\vspace{0.5cm}
\begin{center}
\framebox{
-\normalsize\bf Thank you for your attention!
+\Large\bf Thank you for your attention!
}
\end{center}
\end{slide}
+
+
+
+
+
+
\begin{slide}
\headphd
\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}
projects / lectures / latex.git / blobdiff