nearly finished precipitate

diff --git a/posic/talks/seminar_2010.tex b/posic/talks/seminar_2010.tex
index ce2956b..b76a6a8 100644 (file)
--- a/posic/talks/seminar_2010.tex
+++ b/posic/talks/seminar_2010.tex
@@ -1,6 +1,6 @@
 \pdfoutput=0
 \pdfoutput=0

-\documentclass[landscape,semhelv,draft]{seminar}
-%\documentclass[landscape,semhelv]{seminar}
+%\documentclass[landscape,semhelv,draft]{seminar}
+\documentclass[landscape,semhelv]{seminar}

 
 \usepackage{verbatim}
 \usepackage[greek,german]{babel}
 
 \usepackage{verbatim}
 \usepackage[greek,german]{babel}


@@ -181,7 +181,7 @@
 }
 
  \begin{itemize}
 }
 
  \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}
   \item Supposed precipitation mechanism of SiC in Si
   \item Utilized simulation techniques
         \begin{itemize}


@@ -529,7 +529,7 @@ V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
 n(r)=\sum_i^N|\Phi_i(r)|^2
 \]
   \item \underline{Self-consistent solution}\\
 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 $n(r)$
 which in turn depends on $n(r)$
   \item \underline{Variational principle}
         - minimize total energy with respect to $n(r)$


@@ -1763,9 +1763,9 @@ Potential enhanced problem of slow phase space propagation
 Increased temperature simulations without TAD corrections\\
 (accelerated methods or higher time scales exclusively not sufficient)
 
 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}
 \tiny
 \begin{center}
 \vspace{0.03cm}


@@ -1781,9 +1781,9 @@ Increased temperature simulations without TAD corrections\\
 }
 \end{picture}
 
 }
 \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\\
 \tiny
 \begin{center}
 retain proper\\


@@ -1798,72 +1798,313 @@ thermodynmic sampling
 \begin{slide}
 
  {\large\bf
 \begin{slide}
 
  {\large\bf

-  Increased temperature simulations
+  Increased temperature simulations at low C concentration

  }
 
 \small
 
  }
 
 \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
 
 \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
 
 \end{slide}
 
 \begin{slide}
 
  {\large\bf

-  Silicon carbide precipitation simulations
+  Valuation of a practicable temperature limit

  }
 
  \small
  }
 
  \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 even 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
 
 \end{slide}
 
 \begin{slide}
 
  {\large\bf

-  Silicon carbide precipitation simulations
+  Long time scale simulations at maximum temperature

  }
 
  \small
  
  }
 
  \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
 
 \end{slide}
 
 \begin{slide}
 
  {\large\bf

-  Silicon carbide precipitation simulations
+  Investigation of a silicon carbide precipitate in silicon
+ }
+
+ \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: 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$^2$
+\end{itemize}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Summary / Conclusion / Outlook

  }
 
  \small
 
  }
 
  \small
 

+ 
+

 \end{slide}
 
 \begin{slide}
 
  {\large\bf
 \end{slide}
 
 \begin{slide}
 
  {\large\bf

-  Investigation of a silicon carbide precipitate in silicon
+  Acknowledgements

  }
 
  \small
  }
 
  \small