X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fseminar_2010.tex;h=75ceb623d387c9fb9f95b9e3a3c2025e25f8ea88;hp=ce2956bf53aaea8dcf46dcec2ca2af38de60bd26;hb=e08a97849ebaf34c088eef126bf83fa8a4267119;hpb=d3f8210e257ca02ed836e1cbd3c7eac867e2c82c diff --git a/posic/talks/seminar_2010.tex b/posic/talks/seminar_2010.tex index ce2956b..75ceb62 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} @@ -154,14 +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} @@ -169,6 +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} @@ -181,7 +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} @@ -314,6 +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} @@ -441,8 +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} @@ -529,7 +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 $n(r)$ @@ -561,8 +586,10 @@ which in turn depends on $n(r)$ \[ \rightarrow \text{Fourier series: } \Phi_i=\sum_{|G+k| $\rightarrow$ 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 + +\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} -High concentration simulation +\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 +\small + +\vspace{0.1cm} - 5. final TODO +\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 - 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]{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} @@ -1866,9 +2151,174 @@ High concentration simulation 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}