From d3f8210e257ca02ed836e1cbd3c7eac867e2c82c Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 16 Jun 2010 16:48:47 +0200 Subject: [PATCH] finisched limtation part --- posic/talks/seminar_2010.tex | 425 +++++++++++++++++++++++++++++++++-- 1 file changed, 407 insertions(+), 18 deletions(-) diff --git a/posic/talks/seminar_2010.tex b/posic/talks/seminar_2010.tex index 19a8578..ce2956b 100644 --- a/posic/talks/seminar_2010.tex +++ b/posic/talks/seminar_2010.tex @@ -1,5 +1,6 @@ \pdfoutput=0 \documentclass[landscape,semhelv,draft]{seminar} +%\documentclass[landscape,semhelv]{seminar} \usepackage{verbatim} \usepackage[greek,german]{babel} @@ -74,6 +75,9 @@ % 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} @@ -1384,6 +1388,8 @@ $ Energetically most favorable combinations along \hkl<1 1 0> +\vspace*{0.1cm} + {\scriptsize \begin{tabular}{l c c c c c c} \hline @@ -1396,16 +1402,79 @@ Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \h \end{tabular} } -\vspace*{0.1cm} +\vspace*{0.3cm} \begin{minipage}{7.0cm} -\includegraphics[width=7cm,draft=false]{db_along_110_cc.ps} +\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 Interaction proportional to reciprocal cube of C-C distance - \item - \item + \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} @@ -1413,25 +1482,138 @@ Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \h \begin{slide} - {\large\bf - Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials + {\large\bf\boldmath + Migration in C-Si \hkl<1 0 0> and vacancy combinations } - \small + \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 - Migration of combined defects + Conclusion of defect / migration / combined defect simulations } \small - present (describe) two starting confs, i.e. vac in c-Si +\vspace*{0.1cm} - present migration results $\rightarrow$ SiC +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} @@ -1442,21 +1624,228 @@ Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \h } \small - - restricted to classical MD - explain procedure +{\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} +} - then there is: +\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} - 1. temperature as in exps +\begin{slide} + + {\large\bf\boldmath + Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS + } - 2. exkurs: limitations of conv... + \small - 3. increased temp ... high and low +\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)(-262,-10) +\frame{ +\begin{minipage}{4.3cm} +\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,-152) +\frame{ +\begin{minipage}{2.6cm} +\tiny +\begin{center} +retain proper\\ +thermodynmic sampling +\end{center} +\end{minipage} +} +\end{picture} + +\end{slide} + +\begin{slide} + + {\large\bf + Increased temperature simulations + } + +\small + +Low concentration simulation + + + + +\end{slide} + +\begin{slide} + + {\large\bf + Increased temperature simulations + } + +\small + +High concentration simulation + + + + +\end{slide} + +\begin{slide} + + {\large\bf + Silicon carbide precipitation simulations + } + + \small + 4. temperature limit + +\end{slide} + +\begin{slide} + + {\large\bf + Silicon carbide precipitation simulations + } + + \small + 5. final TODO \end{slide} -- 2.20.1