From: hackbard Date: Thu, 10 Nov 2011 00:54:53 +0000 (+0100) Subject: inc temps low c conc ... X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=3461fcb9d5e496f1deea8c5ad3d61e7a8fbcea3a;p=lectures%2Flatex.git inc temps low c conc ... --- diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex index 358698d..af83477 100644 --- a/posic/talks/mpi_app.tex +++ b/posic/talks/mpi_app.tex @@ -2044,9 +2044,6 @@ $\rightarrow$ Consider $V_2$ and $V_3$ \end{slide} -% continue here -\fi - \begin{slide} \headphd @@ -2056,198 +2053,227 @@ $\rightarrow$ Consider $V_2$ and $V_3$ \small -\begin{minipage}{6.2cm} -\hspace{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps} +\begin{minipage}{6.3cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\ +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps} \hfill \end{minipage} -\begin{minipage}{6.2cm} -\includegraphics[width=6.5cm]{sic_prec_450_energy.ps} -\end{minipage} - -\begin{minipage}{6.2cm} -\hspace{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps} -\hfill -\end{minipage} -\begin{minipage}{6.2cm} +\begin{minipage}{6.1cm} \scriptsize -\underline{Low C concentration ($V_1$)}\\ +\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm] \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 + \item Si-C bumbs around \unit[0.19]{nm} + \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\ + concatenated differently oriented \ci{} DBs + \item Si-Si NN distance stretched to \unit[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} +\begin{pspicture}(0,0)(6.0,1.0) +\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{6cm} +\centering +Formation of \ci{} dumbbells\\ +C atoms in proper 3C-SiC distance first +\end{minipage} +}} +\end{pspicture}\\[0.1cm] +\underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}} +\begin{itemize} +\item High amount of strongly bound C-C bonds +\item Increased defect \& damage density\\ + $\rightarrow$ Arrangements hard to categorize and trace +\item Only short range order observable +\end{itemize} +\begin{pspicture}(0,0)(6.0,0.8) +\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{6cm} +\centering +Amorphous SiC-like phase +\end{minipage} +}} +\end{pspicture}\\[0.3cm] +\begin{pspicture}(0,0)(6.0,2.0) +\rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{ +\begin{minipage}{6cm} +\hfill +\vspace{2.5cm} +\end{minipage} +}} +\end{pspicture} \end{minipage} \end{slide} -\end{document} -\ifnum1=0 - \begin{slide} - {\large\bf\boldmath - Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS - } - - \small +\headphd +{\large\bf\boldmath + Silicon carbide precipitation simulations at \degc{450} as in IBS +} -\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} +\small -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{sic_prec_450_si-c.ps} +\begin{minipage}{6.3cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\ +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps} +\hfill \end{minipage} -\begin{minipage}{6.5cm} +\begin{minipage}{6.1cm} \scriptsize -\underline{Low C concentration ($V_1$)}\\ +\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm] \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 + \item Si-C bumbs around \unit[0.19]{nm} + \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\ + concatenated differently oriented \ci{} DBs + \item Si-Si NN distance stretched to \unit[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} - -\begin{pspicture}(0,0)(0,0) -\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{ -\begin{minipage}{10cm} -\small -{\color{red}\bf 3C-SiC formation fails to appear} +\begin{pspicture}(0,0)(6.0,1.0) +\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{6cm} +\centering +Formation of \ci{} dumbbells\\ +C atoms in proper 3C-SiC distance first +\end{minipage} +}} +\end{pspicture}\\[0.1cm] +\underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}} \begin{itemize} -\item Low C concentration simulations - \begin{itemize} - \item Formation of \ci{} indeed occurs - \item Agllomeration not observed - \end{itemize} -\item High C concentration simulations - \begin{itemize} - \item Amorphous SiC-like structure\\ - (not expected at prevailing temperatures) - \item Rearrangement and transition into 3C-SiC structure missing - \end{itemize} +\item High amount of strongly bound C-C bonds +\item Increased defect \& damage density\\ + $\rightarrow$ Arrangements hard to categorize and trace +\item Only short range order observable \end{itemize} +\begin{pspicture}(0,0)(6.0,0.8) +\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{6cm} +\centering +Amorphous SiC-like phase \end{minipage} - }}} +}} +\end{pspicture}\\[0.3cm] +\begin{pspicture}(0,0)(6.0,2.0) +\rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{ +\begin{minipage}{6cm} +\vspace{0.1cm} +\centering +{\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm] +\begin{minipage}{0.8cm} +{\bf\boldmath $V_1$:} +\end{minipage} +\begin{minipage}{5.1cm} +Formation of \ci{} indeed occurs\\ +Agllomeration not observed +\end{minipage}\\[0.3cm] +\begin{minipage}{0.8cm} +{\bf\boldmath $V_{2,3}$:} +\end{minipage} +\begin{minipage}{5.1cm} +Amorphous SiC-like structure\\ +(not expected at \degc{450})\\[0.05cm] +No rearrangement/transition into 3C-SiC +\end{minipage}\\[0.1cm] +\end{minipage} +}} \end{pspicture} +\end{minipage} \end{slide} \begin{slide} - {\large\bf - Limitations of molecular dynamics and short range potentials - } +\headphd +{\large\bf + Limitations of MD and short range potentials +} -\footnotesize +\small \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 +{\bf Time scale problem of MD}\\[0.2cm] +Precise integration \& thermodynamic sampling\\ +$\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$, + $\omega$: vibrational mode\\ +$\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm] +Several local minima 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] +$\Rightarrow$ Phase transition consists of {\color{red}\underline{many}} + infrequent transition events\\[0.2cm] {\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} +\vspace{0.2cm} -\framebox{ -\color{red} -Potential enhanced problem of slow phase space propagation -} +{\bf Limitations related to the short range potential}\\[0.2cm] +Cut-off function limits interaction to next neighbours\\ +$\Rightarrow$ Overestimated unphysical high forces of next neighbours -\vspace{0.3cm} +\vspace{1.4cm} -\underline{Approach to the (twofold) problem}\\[0.2cm] +{\bf Approach to the (twofold) problem}\\[0.2cm] Increased temperature simulations without TAD corrections\\ -(accelerated methods or higher time scales exclusively not sufficient) +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} +\begin{pspicture}(0,0)(0,0) +\rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{ +\begin{minipage}{7.5cm} +\centering +\vspace{0.05cm} +Potential enhanced slow phase space propagation \end{minipage} -} -\end{picture} - -\begin{picture}(0,0)(-305,-155) -\framebox{ -\begin{minipage}{2.5cm} +}} +\rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{2.7cm} \tiny -\begin{center} +\centering retain proper\\ -thermodynmic sampling -\end{center} +thermodynamic sampling \end{minipage} -} -\end{picture} +}} +\psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7) +\rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{ +\begin{minipage}{3.6cm} +\tiny +\centering +\underline{IBS}\\[0.1cm] +3C-SiC also observed for higher T\\[0.1cm] +Higher T inside sample\\[0.1cm] +Structural evolution vs.\\ +equilibrium properties +\end{minipage} +}} +\psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0) +\end{pspicture} \end{slide} +% continue here +\fi + \begin{slide} - {\large\bf - Increased temperature simulations at low C concentration - } +\headphd +{\large\bf\boldmath + Increased temperature simulations --- $V_1$ +} \small -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{tot_pc_thesis.ps} +\begin{minipage}{6.2cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps} +\hfill \end{minipage} -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{tot_pc3_thesis.ps} +\begin{minipage}{6.2cm} +\includegraphics[width=6.5cm]{tot_pc3_thesis.ps} \end{minipage} -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{tot_pc2_thesis.ps} +\begin{minipage}{6.2cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps} +\hfill \end{minipage} -\begin{minipage}{6.5cm} +\begin{minipage}{6.3cm} \scriptsize \underline{Si-C bonds:} \begin{itemize} @@ -2274,40 +2300,30 @@ thermodynmic sampling \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 low C concentration - } +\headphd +{\large\bf\boldmath + Increased temperature simulations --- $V_1$ +} \small -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{tot_pc_thesis.ps} +\begin{minipage}{6.2cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps} +\hfill \end{minipage} -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{tot_pc3_thesis.ps} +\begin{minipage}{6.2cm} +\includegraphics[width=6.5cm]{tot_pc3_thesis.ps} \end{minipage} -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{tot_pc2_thesis.ps} +\begin{minipage}{6.2cm} +\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps} +\hfill \end{minipage} -\begin{minipage}{6.5cm} +\begin{minipage}{6.3cm} \scriptsize \underline{Si-C bonds:} \begin{itemize} @@ -2334,24 +2350,19 @@ in c-Si \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} - +% md support \begin{pspicture}(0,0)(0,0) -\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{ -\begin{minipage}{10cm} +\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{ +\begin{minipage}{14cm} +\hfill +\vspace{14cm} +\end{minipage} +}} +\rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{ +\begin{minipage}{9cm} +\vspace{0.2cm} \small -{\color{blue}\bf Stretched SiC in c-Si} +{\color{blue}\bf Stretched structures of SiC in c-Si} \begin{itemize} \item Consistent to precipitation model involving \cs{} \item Explains annealing behavior of high/low T C implants @@ -2362,8 +2373,9 @@ in c-Si \end{itemize} $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\ $\Rightarrow$ Precipitation mechanism involving \cs{} + \end{minipage} - }}} +}} \end{pspicture} \end{slide} @@ -2434,6 +2446,9 @@ High C \& low T implants \end{slide} +\end{document} +\ifnum1=0 + \begin{slide} {\large\bf