X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fseminar_2010.tex;h=75ceb623d387c9fb9f95b9e3a3c2025e25f8ea88;hp=5fe206d7d781e026aaae74b576584bda1ecaa399;hb=e08a97849ebaf34c088eef126bf83fa8a4267119;hpb=3e0cf069d29304120c01c063368bfa4d04365e57 diff --git a/posic/talks/seminar_2010.tex b/posic/talks/seminar_2010.tex index 5fe206d..75ceb62 100644 --- a/posic/talks/seminar_2010.tex +++ b/posic/talks/seminar_2010.tex @@ -1,4 +1,5 @@ \pdfoutput=0 +%\documentclass[landscape,semhelv,draft]{seminar} \documentclass[landscape,semhelv]{seminar} \usepackage{verbatim} @@ -71,6 +72,12 @@ % itemize level ii \renewcommand\labelitemii{{\color{gray}$\bullet$}} +% nice phi +\renewcommand{\phi}{\varphi} + +% roman letters +\newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}} + % colors \newrgbcolor{si-yellow}{.6 .6 0} \newrgbcolor{hb}{0.75 0.77 0.89} @@ -147,14 +154,14 @@ \end{pspicture} -\begin{picture}(0,0)(-10,68) +\begin{picture}(0,0)(-3,68) \includegraphics[width=2.6cm]{wide_band_gap.eps} \end{picture} -\begin{picture}(0,0)(-295,-165) -\includegraphics[width=3cm]{sic_led.eps} +\begin{picture}(0,0)(-285,-162) +\includegraphics[width=3.38cm]{sic_led.eps} \end{picture} -\begin{picture}(0,0)(-215,-165) -\includegraphics[width=2.5cm]{6h-sic_3c-sic.eps} +\begin{picture}(0,0)(-195,-162) +\includegraphics[width=2.8cm]{6h-sic_3c-sic.eps} \end{picture} \begin{picture}(0,0)(-313,65) \includegraphics[width=2.2cm]{infineon_schottky.eps} @@ -162,6 +169,12 @@ \begin{picture}(0,0)(-220,65) \includegraphics[width=2.9cm]{sic_wechselrichter_ise.eps} \end{picture} +\begin{picture}(0,0)(0,-160) +\includegraphics[width=3.0cm]{sic_proton.eps} +\end{picture} +\begin{picture}(0,0)(-60,65) +\includegraphics[width=3.4cm]{sic_switch.eps} +\end{picture} \end{slide} @@ -174,7 +187,7 @@ } \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} @@ -307,6 +320,19 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ } \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} @@ -342,6 +368,7 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ XTEM micrograph of single crystalline 3C-SiC in Si\hkl(1 0 0) } \end{minipage} +\framebox{ \begin{minipage}{6.3cm} \begin{center} {\color{blue} @@ -356,6 +383,7 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \end{itemize} \end{center} \end{minipage} +} \end{slide} @@ -432,8 +460,14 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5) \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)} \psline[linewidth=4pt]{->}(4.0,2)(4.5,2) +\rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ + $4a_{\text{Si}}=5a_{\text{SiC}}$ + }}} +\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\hkl(h k l) planes match + }}} \end{pspicture} - + \end{slide} \begin{slide} @@ -520,7 +554,7 @@ 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 $n(r)$ @@ -552,8 +586,10 @@ which in turn depends on $n(r)$ \[ \rightarrow \text{Fourier series: } \Phi_i=\sum_{|G+k| dumbbell interstitial } - \small +\scriptsize + + {\small Investigated pathways} + +\begin{minipage}{8.5cm} +\begin{minipage}{8.3cm} +\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\ +\begin{minipage}{2.4cm} +\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps} +\end{minipage} +\begin{minipage}{0.4cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{2.4cm} +\includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps} +\end{minipage} +\begin{minipage}{0.4cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{2.4cm} +\includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps} +\end{minipage} +\end{minipage}\\ +\begin{minipage}{8.3cm} +\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\ +\begin{minipage}{2.4cm} +\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps} +\end{minipage} +\begin{minipage}{0.4cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{2.4cm} +\includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps} +\end{minipage} +\begin{minipage}{0.4cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{2.4cm} +\includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps} +\end{minipage} +\end{minipage}\\ +\begin{minipage}{8.3cm} +\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\ +\begin{minipage}{2.4cm} +\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps} +\end{minipage} +\begin{minipage}{0.4cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{2.4cm} +\includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps} +\end{minipage} +\begin{minipage}{0.4cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{2.4cm} +\includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps} +\end{minipage} +\end{minipage} +\end{minipage} +\framebox{ +\begin{minipage}{4.2cm} + {\small Constrained relaxation\\ + technique (CRT) method}\\ +\includegraphics[width=4cm]{crt_orig.eps} +\begin{itemize} + \item Constrain diffusing atom + \item Static constraints +\end{itemize} +\vspace*{0.3cm} + {\small Modifications}\\ +\includegraphics[width=4cm]{crt_mod.eps} +\begin{itemize} + \item Constrain all atoms + \item Update individual\\ + constraints +\end{itemize} +\end{minipage} +} \end{slide} \begin{slide} - {\large\bf - Investigation of a silicon carbide precipitate in silicon + {\large\bf\boldmath + Migration of the C \hkl<1 0 0> dumbbell interstitial } - \small +\scriptsize + +\framebox{ +\begin{minipage}{5.9cm} +\begin{flushleft} +\includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm] +\end{flushleft} +\begin{center} +\begin{picture}(0,0)(60,0) +\includegraphics[width=1cm]{vasp_mig/00-1.eps} +\end{picture} +\begin{picture}(0,0)(-5,0) +\includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps} +\end{picture} +\begin{picture}(0,0)(-55,0) +\includegraphics[width=1cm]{vasp_mig/bc.eps} +\end{picture} +\begin{picture}(0,0)(12.5,10) +\includegraphics[width=1cm]{110_arrow.eps} +\end{picture} +\begin{picture}(0,0)(90,0) +\includegraphics[height=0.9cm]{001_arrow.eps} +\end{picture} +\end{center} +\vspace*{0.35cm} +\end{minipage} +} +\begin{minipage}{0.3cm} +\hfill +\end{minipage} +\framebox{ +\begin{minipage}{5.9cm} +\begin{flushright} +\includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm] +\end{flushright} +\begin{center} +\begin{picture}(0,0)(60,0) +\includegraphics[width=1cm]{vasp_mig/00-1_a.eps} +\end{picture} +\begin{picture}(0,0)(5,0) +\includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps} +\end{picture} +\begin{picture}(0,0)(-55,0) +\includegraphics[width=1cm]{vasp_mig/0-10.eps} +\end{picture} +\begin{picture}(0,0)(12.5,10) +\includegraphics[width=1cm]{100_arrow.eps} +\end{picture} +\begin{picture}(0,0)(90,0) +\includegraphics[height=0.9cm]{001_arrow.eps} +\end{picture} +\end{center} +\vspace*{0.3cm} +\end{minipage}\\ +} + +\vspace*{0.05cm} + +\framebox{ +\begin{minipage}{5.9cm} +\begin{flushleft} +\includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm] +\end{flushleft} +\begin{center} +\begin{picture}(0,0)(60,0) +\includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps} +\end{picture} +\begin{picture}(0,0)(10,0) +\includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps} +\end{picture} +\begin{picture}(0,0)(-60,0) +\includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps} +\end{picture} +\begin{picture}(0,0)(12.5,10) +\includegraphics[width=1cm]{100_arrow.eps} +\end{picture} +\begin{picture}(0,0)(90,0) +\includegraphics[height=0.9cm]{001_arrow.eps} +\end{picture} +\end{center} +\vspace*{0.3cm} +\end{minipage} +} +\begin{minipage}{0.3cm} +\hfill +\end{minipage} +\begin{minipage}{6.5cm} +VASP results +\begin{itemize} + \item Energetically most favorable path + \begin{itemize} + \item Path 2 + \item Activation energy: $\approx$ 0.9 eV + \item Experimental values: 0.73 ... 0.87 eV + \end{itemize} + $\Rightarrow$ {\color{blue}Diffusion} path identified! + \item Reorientation (path 3) + \begin{itemize} + \item More likely composed of two consecutive steps of type 2 + \item Experimental values: 0.77 ... 0.88 eV + \end{itemize} + $\Rightarrow$ {\color{blue}Reorientation} transition identified! +\end{itemize} +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Migration of the C \hkl<1 0 0> dumbbell interstitial + } + +\scriptsize + +\begin{minipage}{6.5cm} + +\framebox{ +\begin{minipage}{5.9cm} +\begin{flushleft} +\includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm] +\end{flushleft} +\begin{center} +\begin{pspicture}(0,0)(0,0) +\psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7) +\end{pspicture} +\begin{picture}(0,0)(60,-50) +\includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps} +\end{picture} +\begin{picture}(0,0)(5,-50) +\includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps} +\end{picture} +\begin{picture}(0,0)(-55,-50) +\includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps} +\end{picture} +\begin{picture}(0,0)(12.5,-40) +\includegraphics[width=1cm]{110_arrow.eps} +\end{picture} +\begin{picture}(0,0)(90,-45) +\includegraphics[height=0.9cm]{001_arrow.eps} +\end{picture}\\ +\begin{pspicture}(0,0)(0,0) +\psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6) +\end{pspicture} +\begin{picture}(0,0)(60,-15) +\includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps} +\end{picture} +\begin{picture}(0,0)(35,-15) +\includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps} +\end{picture} +\begin{picture}(0,0)(-5,-15) +\includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps} +\end{picture} +\begin{picture}(0,0)(-55,-15) +\includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps} +\end{picture} +\begin{picture}(0,0)(12.5,-5) +\includegraphics[width=1cm]{100_arrow.eps} +\end{picture} +\begin{picture}(0,0)(90,-15) +\includegraphics[height=0.9cm]{010_arrow.eps} +\end{picture} +\end{center} +\end{minipage} +}\\[0.1cm] + +\begin{minipage}{5.9cm} +Erhart/Albe results +\begin{itemize} + \item Lowest activation energy: $\approx$ 2.2 eV + \item 2.4 times higher than VASP + \item Different pathway + \item Transition minima ($\rightarrow$ \hkl<1 1 0> dumbbell) +\end{itemize} +\end{minipage} + +\end{minipage} +\begin{minipage}{6.5cm} + +\framebox{ +\begin{minipage}{5.9cm} +\begin{flushright} +\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm] +\end{flushright} +\begin{center} +\begin{pspicture}(0,0)(0,0) +\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1) +\end{pspicture} +\begin{picture}(0,0)(60,-5) +\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps} +\end{picture} +\begin{picture}(0,0)(0,-5) +\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps} +\end{picture} +\begin{picture}(0,0)(-55,-5) +\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps} +\end{picture} +\begin{picture}(0,0)(12.5,5) +\includegraphics[width=1cm]{100_arrow.eps} +\end{picture} +\begin{picture}(0,0)(90,0) +\includegraphics[height=0.9cm]{001_arrow.eps} +\end{picture} +\end{center} +\vspace{0.2cm} +\end{minipage} +}\\[0.2cm] + +\framebox{ +\begin{minipage}{5.9cm} +\includegraphics[width=5.9cm]{00-1_ip0-10.ps} +\end{minipage} +} + +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Migrations involving the C \hkl<1 1 0> dumbbell interstitial + } + +\small + +\vspace*{0.1cm} + +VASP + +\begin{minipage}{6.0cm} +\includegraphics[width=6cm]{vasp_mig/110_mig_vasp.ps} +\end{minipage} +\begin{minipage}{7cm} +\underline{Alternative pathway and energies [eV]}\\[0.1cm] +\hkl<0 -1 0> $\stackrel{0.7}{{\color{red}\longrightarrow}}$ +\hkl<1 1 0> $\stackrel{0.95}{{\color{blue}\longrightarrow}}$ +BC $\stackrel{0.25}{\longrightarrow}$ \hkl<0 0 -1>\\[0.3cm] +Composed of three single transitions\\[0.3cm] +Activation energy of second transition slightly\\ +higher than direct transition (path 2)\\[0.3cm] +$\Rightarrow$ very unlikely to happen +\end{minipage}\\[0.2cm] + +Erhart/Albe + +\begin{minipage}{6.0cm} +\includegraphics[width=6cm]{110_mig.ps} +\end{minipage} +\begin{minipage}{7cm} +\underline{Alternative pathway and energies [eV]}\\[0.1cm] +\hkl<0 0 -1> $\stackrel{2.2}{{\color{green}\longrightarrow}}$ +\hkl<1 1 0> $\stackrel{0.9}{{\color{red}\longrightarrow}}$ +\hkl<0 0 -1>\\[0.3cm] +Composed of two single transitions\\[0.3cm] +Compared to direct transition: (2.2 eV \& 0.5 eV)\\[0.3cm] +$\Rightarrow$ more readily constituting a probable transition +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Combinations with a C-Si \hkl<1 0 0>-type interstitial + } + +\small + +\vspace*{0.1cm} + +Binding energy: +$ +E_{\text{b}}= +E_{\text{f}}^{\text{defect combination}}- +E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}- +E_{\text{f}}^{\text{2nd defect}} +$ + +\vspace*{0.1cm} + +{\scriptsize +\begin{tabular}{l c c c c c c} +\hline + $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\ + \hline + \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\ + \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\ + \hkl<0 -1 0> & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\ + \hkl<0 1 0> & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\ + \hkl<-1 0 0> & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\ + \hkl<1 0 0> & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\ + \hline + C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\ + Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\ +\hline +\end{tabular} +} + +\vspace*{0.3cm} + +\footnotesize + +\begin{minipage}[t]{3.8cm} +\underline{\hkl<1 0 0> at position 1}\\[0.1cm] +\includegraphics[width=3.5cm]{00-1dc/2-25.eps} +\end{minipage} +\begin{minipage}[t]{3.5cm} +\underline{\hkl<0 -1 0> at position 1}\\[0.1cm] +\includegraphics[width=3.2cm]{00-1dc/2-39.eps} +\end{minipage} +\begin{minipage}[t]{5.5cm} +\begin{itemize} + \item Restricted to VASP simulations + \item $E_{\text{b}}=0$ for isolated non-interacting defects + \item $E_{\text{b}} \rightarrow 0$ for increasing distance (R) + \item Stress compensation / increase + \item Most favorable: C clustering + \item Unfavored: antiparallel orientations + \item Indication of energetically favored\\ + agglomeration +\end{itemize} +\end{minipage} + +\begin{picture}(0,0)(-295,-130) +\includegraphics[width=3.5cm]{comb_pos.eps} +\end{picture} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Combinations of C-Si \hkl<1 0 0>-type interstitials + } + +\small + +\vspace*{0.1cm} + +Energetically most favorable combinations along \hkl<1 1 0> + +\vspace*{0.1cm} + +{\scriptsize +\begin{tabular}{l c c c c c c} +\hline + & 1 & 2 & 3 & 4 & 5 & 6\\ +\hline +$E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\ +C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\ +Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\ +\hline +\end{tabular} +} + +\vspace*{0.3cm} + +\begin{minipage}{7.0cm} +\includegraphics[width=7cm]{db_along_110_cc.ps} +\end{minipage} +\begin{minipage}{6.0cm} +\begin{center} +{\color{blue} + Interaction proportional to reciprocal cube of C-C distance +}\\[0.2cm] + Saturation in the immediate vicinity +\end{center} +\end{minipage} + +\vspace{0.2cm} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials + } + + \scriptsize + +\begin{center} +\begin{minipage}{3.2cm} +\includegraphics[width=3cm]{sub_110_combo.eps} +\end{minipage} +\begin{minipage}{7.8cm} +\begin{tabular}{l c c c c c c} +\hline +C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> & + \hkl<1 0 1> & \hkl<-1 0 1> \\ +\hline +1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\ +2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\ +3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\ +4 & \RM{4} & B & D & E & E & D \\ +5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\ +\hline +\end{tabular} +\end{minipage} +\end{center} + +\begin{center} +\begin{tabular}{l c c c c c c c c c c} +\hline +Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\ +\hline +$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\ +$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\ +$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\ +\hline +\end{tabular} +\end{center} + +\begin{minipage}{6.0cm} +\includegraphics[width=5.8cm]{c_sub_si110.ps} +\end{minipage} +\begin{minipage}{7cm} +\small +\begin{itemize} + \item IBS: C may displace Si\\ + $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial + \item Assumption:\\ + \hkl<1 1 0>-type $\rightarrow$ favored combination + \renewcommand\labelitemi{$\Rightarrow$} + \item Less favorable than C-Si \hkl<1 0 0> dumbbell\\ + ($E_{\text{f}}=3.88\text{ eV}$) + \item Interaction drops quickly to zero\\ + (low interaction capture radius) +\end{itemize} +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Migration in C-Si \hkl<1 0 0> and vacancy combinations + } + + \footnotesize + +\vspace{0.1cm} + +\begin{minipage}[t]{3cm} +\underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\ +\includegraphics[width=2.8cm]{00-1dc/0-59.eps} +\end{minipage} +\begin{minipage}[t]{7cm} +\vspace{0.2cm} +\begin{center} + Low activation energies\\ + High activation energies for reverse processes\\ + $\Downarrow$\\ + {\color{blue}C$_{\text{sub}}$ very stable}\\ +\vspace*{0.1cm} + \hrule +\vspace*{0.1cm} + Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\ + $\Downarrow$\\ + {\color{blue}Formation of SiC by successive substitution by C} + +\end{center} +\end{minipage} +\begin{minipage}[t]{3cm} +\underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\ +\includegraphics[width=2.8cm]{00-1dc/3-14.eps} +\end{minipage} + + +\framebox{ +\begin{minipage}{5.9cm} +\includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm] +\begin{center} +\begin{picture}(0,0)(70,0) +\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps} +\end{picture} +\begin{picture}(0,0)(30,0) +\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps} +\end{picture} +\begin{picture}(0,0)(-10,0) +\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps} +\end{picture} +\begin{picture}(0,0)(-48,0) +\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps} +\end{picture} +\begin{picture}(0,0)(12.5,5) +\includegraphics[width=1cm]{100_arrow.eps} +\end{picture} +\begin{picture}(0,0)(97,-10) +\includegraphics[height=0.9cm]{001_arrow.eps} +\end{picture} +\end{center} +\vspace{0.1cm} +\end{minipage} +} +\begin{minipage}{0.3cm} +\hfill +\end{minipage} +\framebox{ +\begin{minipage}{5.9cm} +\includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm] +\begin{center} +\begin{picture}(0,0)(60,0) +\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps} +\end{picture} +\begin{picture}(0,0)(25,0) +\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps} +\end{picture} +\begin{picture}(0,0)(-20,0) +\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps} +\end{picture} +\begin{picture}(0,0)(-55,0) +\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps} +\end{picture} +\begin{picture}(0,0)(12.5,5) +\includegraphics[width=1cm]{100_arrow.eps} +\end{picture} +\begin{picture}(0,0)(95,0) +\includegraphics[height=0.9cm]{001_arrow.eps} +\end{picture} +\end{center} +\vspace{0.1cm} +\end{minipage} +} + +\end{slide} + +\begin{slide} + + {\large\bf + Conclusion of defect / migration / combined defect simulations + } + + \small + +\vspace*{0.1cm} + +Defect structures +\begin{itemize} + \item Accurately described by quantum-mechanical simulations + \item Less correct description by classical potential simulations +\end{itemize} +\vspace*{0.2cm} +\begin{itemize} + \item Consistent with solubility data of C in Si + \item \hkl<1 0 0> C-Si dumbbell interstitial ground state configuration + \item Consistent with reorientation and diffusion experiments + \item C migration pathway in Si identified +\end{itemize} + +\vspace*{0.2cm} + +Concerning the precipitation mechanism +\begin{itemize} + \item Agglomeration of C-Si dumbbells energetically favorable + \item C-Si indeed favored compared to + C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial + \item Possible low interaction capture radius of + C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial + \item In absence of nearby \hkl<1 1 0> Si self-interstitial: + C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC) +\end{itemize} + +\vspace*{0.1cm} +\begin{center} +{\color{blue}Some results point to a different precipitation mechanism!} +\end{center} + +\end{slide} + +\begin{slide} + + {\large\bf + Silicon carbide precipitation simulations + } + + \small + +{\scriptsize + \begin{pspicture}(0,0)(12,6.5) + % nodes + \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ + \parbox{7cm}{ + \begin{itemize} + \item Create c-Si volume + \item Periodc boundary conditions + \item Set requested $T$ and $p=0\text{ bar}$ + \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$ + \end{itemize} + }}}} + \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{ + \parbox{7cm}{ + Insertion of C atoms at constant T + \begin{itemize} + \item total simulation volume {\pnode{in1}} + \item volume of minimal SiC precipitate {\pnode{in2}} + \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\ + precipitate + \end{itemize} + }}}} + \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{ + \parbox{7.0cm}{ + Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$ + }}}} + \ncline[]{->}{init}{insert} + \ncline[]{->}{insert}{cool} + \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3) + \rput(7.8,6){\footnotesize $V_1$} + \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5) + \rput(9.2,4.85){\tiny $V_2$} + \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75) + \rput(9.55,4.45){\footnotesize $V_3$} + \rput(7.9,3.2){\pnode{ins1}} + \rput(9.22,2.8){\pnode{ins2}} + \rput(11.0,2.4){\pnode{ins3}} + \ncline[]{->}{in1}{ins1} + \ncline[]{->}{in2}{ins2} + \ncline[]{->}{in3}{ins3} + \end{pspicture} +} + +\begin{itemize} + \item Restricted to classical potential simulations + \item $V_2$ and $V_3$ considered due to low diffusion + \item Amount of C atoms: 6000 + ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm) + \item Simulation volume: $31\times 31\times 31$ unit cells + (238328 Si atoms) +\end{itemize} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS + } + + \small + +\begin{minipage}{6.5cm} +\includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps} +\end{minipage} +\begin{minipage}{6.5cm} +\includegraphics[width=6.4cm]{sic_prec_450_energy.ps} +\end{minipage} + +\begin{minipage}{6.5cm} +\includegraphics[width=6.4cm]{sic_prec_450_si-c.ps} +\end{minipage} +\begin{minipage}{6.5cm} +\scriptsize +\underline{Low C concentration ($V_1$)}\\ +\hkl<1 0 0> C-Si dumbbell dominated structure +\begin{itemize} + \item Si-C bumbs around 0.19 nm + \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\ + concatenated dumbbells of various orientation + \item Si-Si NN distance stretched to 0.3 nm +\end{itemize} +{\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\ +\underline{High C concentration ($V_2$, $V_3$)}\\ +High amount of strongly bound C-C bonds\\ +Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\ +Only short range order observable\\ +{\color{blue}$\Rightarrow$ amorphous SiC-like phase} +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + Limitations of molecular dynamics and short range potentials + } + +\footnotesize + +\vspace{0.2cm} + +\underline{Time scale problem of MD}\\[0.2cm] +Minimize integration error\\ +$\Rightarrow$ discretization considerably smaller than + reciprocal of fastest vibrational mode\\[0.1cm] +Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\ +$\Rightarrow$ suitable choice of time step: + $\tau=1\text{ fs}=10^{-15}\text{ s}$\\ +$\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm] +Several local minima in energy surface separated by large energy barriers\\ +$\Rightarrow$ transition event corresponds to a multiple + of vibrational periods\\ +$\Rightarrow$ phase transition made up of {\color{red}\underline{many}} + infrequent transition events\\[0.1cm] +{\color{blue}Accelerated methods:} +\underline{Temperature accelerated} MD (TAD), self-guided MD \ldots + +\vspace{0.3cm} + +\underline{Limitations related to the short range potential}\\[0.2cm] +Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$ +and 2$^{\text{nd}}$ next neighbours\\ +$\Rightarrow$ overestimated unphysical high forces of next neighbours + +\vspace{0.3cm} + +\framebox{ +\color{red} +Potential enhanced problem of slow phase space propagation +} + +\vspace{0.3cm} + +\underline{Approach to the (twofold) problem}\\[0.2cm] +Increased temperature simulations without TAD corrections\\ +(accelerated methods or higher time scales exclusively not sufficient) + +\begin{picture}(0,0)(-260,-30) +\framebox{ +\begin{minipage}{4.2cm} +\tiny +\begin{center} +\vspace{0.03cm} +\underline{IBS} +\end{center} +\begin{itemize} +\item 3C-SiC also observed for higher T +\item higher T inside sample +\item structural evolution vs.\\ + equilibrium properties +\end{itemize} +\end{minipage} +} +\end{picture} + +\begin{picture}(0,0)(-305,-155) +\framebox{ +\begin{minipage}{2.5cm} +\tiny +\begin{center} +retain proper\\ +thermodynmic sampling +\end{center} +\end{minipage} +} +\end{picture} + +\end{slide} + +\begin{slide} + + {\large\bf + Increased temperature simulations at low C concentration + } + +\small + +\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 at high C concentration + } + +\footnotesize + +\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 + 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}{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 + 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]{4.5cm} +\begin{center} +\underline{Low C concentration, Si-C} +\includegraphics[width=4.5cm]{c_in_si_95_v1_si-c.ps}\\ +Sharper peaks! +\end{center} +\end{minipage} +\begin{minipage}[t]{4.5cm} +\begin{center} +\underline{Low C concentration, C-C} +\includegraphics[width=4.5cm]{c_in_si_95_v1_c-c.ps}\\ +Sharper peaks!\\ +No C agglomeration! +\end{center} +\end{minipage} +\begin{minipage}[t]{4cm} +\begin{center} +\underline{High C concentration} +\includegraphics[width=4.5cm]{c_in_si_95_v2.ps}\\ +No significant changes +\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 + } + + \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]{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} + +\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}{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 + } + + \vspace{0.1cm} + + \small + + Thanks to \ldots + + \underline{Augsburg} + \begin{itemize} + \item Prof. B. Stritzker (accepting a simulator at EP \RM{4}) + \item Ralf Utermann (EDV) + \end{itemize} + + \underline{Helsinki} + \begin{itemize} + \item Prof. K. Nordlund (MD) + \end{itemize} + + \underline{Munich} + \begin{itemize} + \item Bayerische Forschungsstiftung (financial support) + \end{itemize} + + \underline{Paderborn} + \begin{itemize} + \item Prof. J. Lindner (SiC) + \item Prof. G. Schmidt (DFT + financial support) + \item Dr. E. Rauls (DFT + SiC) + \end{itemize} + +\vspace{0.2cm} + +\begin{center} +\framebox{ +\bf Thank you for your attention! +} +\end{center} \end{slide}