From: hackbard Date: Wed, 16 Jun 2010 20:29:12 +0000 (+0200) Subject: nearly finished precipitate X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=commitdiff_plain;h=d38736a6eb059ca733c67a1e454f7734f4d8f338 nearly finished precipitate --- diff --git a/posic/talks/seminar_2010.tex b/posic/talks/seminar_2010.tex index ce2956b..b76a6a8 100644 --- a/posic/talks/seminar_2010.tex +++ b/posic/talks/seminar_2010.tex @@ -1,6 +1,6 @@ \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} @@ -181,7 +181,7 @@ } \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} @@ -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}\\ -$n(r)$ 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 $n(r)$ @@ -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) -\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} @@ -1781,9 +1781,9 @@ Increased temperature simulations without TAD corrections\\ } \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\\ @@ -1798,72 +1798,313 @@ thermodynmic sampling \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 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 - 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 + } + + \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 + + \end{slide} \begin{slide} {\large\bf - Investigation of a silicon carbide precipitate in silicon + Acknowledgements } \small