From: hackbard Date: Fri, 29 Aug 2008 11:37:02 +0000 (+0200) Subject: Merge branch 'master' of hackdaworld.org:/chroot/git/lectures/latex X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=commitdiff_plain;h=b6098683403f972737e7399d20ea97ca596aef55;hp=c2a58bcaff43c65b589fdbf4a6f51e269369cd9d Merge branch 'master' of hackdaworld.org:/chroot/git/lectures/latex --- diff --git a/posic/talks/helsinki_2008.tex b/posic/talks/helsinki_2008.tex index 5a5ceda..35aeade 100644 --- a/posic/talks/helsinki_2008.tex +++ b/posic/talks/helsinki_2008.tex @@ -170,6 +170,8 @@ Crystalline silicon and cubic silicon carbide } + \vspace{8pt} + {\bf Lattice types and unit cells:} \begin{itemize} \item Crystalline silicon (c-Si) has diamond structure\\ @@ -179,6 +181,7 @@ $\Rightarrow {\color{si-yellow}\bullet}$ are Si atoms, ${\color{gray}\bullet}$ are C atoms \end{itemize} + \vspace{8pt} \begin{minipage}{8cm} {\bf Lattice constants:} \[ @@ -199,7 +202,7 @@ \begin{slide} {\large\bf - Motivation / Introduction + Supposed Si to 3C-SiC conversion } \small @@ -237,11 +240,18 @@ \vspace{12pt} - Experimentally observed: + \begin{minipage}{7cm} + Experimentally observed [3]: \begin{itemize} \item Minimal diameter of precipitation: 4 - 5 nm \item Equal orientation of Si and SiC (hkl)-planes \end{itemize} + \end{minipage} + \begin{minipage}{6cm} + \vspace{32pt} + \hspace{16pt} + {\tiny [3] J. K. N. Lindner, Appl. Phys. A 77 (2003) 27.} + \end{minipage} \end{slide} @@ -251,32 +261,37 @@ Simulation details } - \vspace{12pt} + \small - MD basics: + {\bf MD basics:} \begin{itemize} \item Microscopic description of N particle system \item Analytical interaction potential \item Hamilton's equations of motion as propagation rule\\ in 6N-dimensional phase space - \item Observables obtained by time average + \item Observables obtained by time or ensemble averages \end{itemize} - - \vspace{12pt} - - Application details: + {\bf Application details:} \begin{itemize} - \item Integrator: Velocity Verlet, timestep: $1\, fs$ - \item Ensemble: NVT, Berendsen thermostat, $\tau=100.0$ - \item Potential: Tersoff-like bond order potential\\ + \item Integrator: Velocity Verlet, timestep: $1\text{ fs}$ + \item Ensemble: isothermal-isobaric NPT [4] + \begin{itemize} + \item Berendsen thermostat: + $\tau_{\text{T}}=100\text{ fs}$ + \item Brendsen barostat:\\ + $\tau_{\text{P}}=100\text{ fs}$, + $\beta^{-1}=100\text{ GPa}$ + \end{itemize} + \item Potential: Tersoff-like bond order potential [5] \[ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] \] - \begin{center} - {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211} - \end{center} \end{itemize} + {\tiny + [4] L. Verlet, Phys. Rev. 159 (1967) 98.}\\ + {\tiny + [5] P. Erhart and K. Albe, Phys. Rev. B 71 (2005) 35211.} \begin{picture}(0,0)(-240,-70) \includegraphics[width=5cm]{tersoff_angle.eps} @@ -287,22 +302,22 @@ \begin{slide} {\large\bf - Simulation details + Simulation sequence } \vspace{8pt} - Interstitial simulations: + Interstitial configurations: \vspace{8pt} \begin{pspicture}(0,0)(7,8) - \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{ + \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ \parbox{7cm}{ \begin{itemize} \item Initial configuration: $9\times9\times9$ unit cells Si \item Periodic boundary conditions - \item $T=0 \, K$ + \item $T=0\text{ K}$, $p=0\text{ bar}$ \end{itemize} }}}} \rput(3.5,3.5){\rnode{insert}{\psframebox{ @@ -310,13 +325,16 @@ Insertion of C / Si atom: \begin{itemize} \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral} + (${\color{red}\triangleleft}$) \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal} + (${\color{green}\triangleright}$) \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\ $\rightarrow$ {\color{magenta}110 dumbbell} + (${\color{magenta}\Box}$,$\circ$) \item random positions (critical distance check) \end{itemize} }}}} - \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{ + \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{ \parbox{3.5cm}{ Relaxation time: $2\, ps$ }}}} @@ -325,7 +343,7 @@ \end{pspicture} \begin{picture}(0,0)(-210,-45) - \includegraphics[width=6cm]{unit_cell.eps} + \includegraphics[width=6cm]{unit_cell_s.eps} \end{picture} \end{slide} @@ -340,33 +358,33 @@ \begin{minipage}[t]{4.3cm} \underline{Tetrahedral}\\ - $E_f=3.41\, eV$\\ + $E_f=3.41$ eV\\ \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps} \end{minipage} \begin{minipage}[t]{4.3cm} \underline{110 dumbbell}\\ - $E_f=4.39\, eV$\\ + $E_f=4.39$ eV\\ \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps} \end{minipage} \begin{minipage}[t]{4.3cm} \underline{Hexagonal} \hspace{4pt} \href{../video/si_self_int_hexa.avi}{$\rhd$}\\ - $E_f^{\star}\approx4.48\, eV$ (unstable!)\\ + $E_f^{\star}\approx4.48$ eV (unstable!)\\ \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps} \end{minipage} \underline{Random insertion} \begin{minipage}{4.3cm} - $E_f=3.97\, eV$\\ + $E_f=3.97$ eV\\ \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps} \end{minipage} \begin{minipage}{4.3cm} - $E_f=3.75\, eV$\\ + $E_f=3.75$ eV\\ \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps} \end{minipage} \begin{minipage}{4.3cm} - $E_f=3.56\, eV$\\ + $E_f=3.56$ eV\\ \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps} \end{minipage} @@ -382,18 +400,18 @@ \begin{minipage}[t]{4.3cm} \underline{Tetrahedral}\\ - $E_f=2.67\, eV$\\ + $E_f=2.67$ eV\\ \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps} \end{minipage} \begin{minipage}[t]{4.3cm} \underline{110 dumbbell}\\ - $E_f=1.76\, eV$\\ + $E_f=1.76$ eV\\ \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps} \end{minipage} \begin{minipage}[t]{4.3cm} \underline{Hexagonal} \hspace{4pt} \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\ - $E_f^{\star}\approx5.6\, eV$ (unstable!)\\ + $E_f^{\star}\approx5.6$ eV (unstable!)\\ \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps} \end{minipage} @@ -402,22 +420,22 @@ \footnotesize \begin{minipage}[t]{3.3cm} - $E_f=0.47\, eV$\\ + $E_f=0.47$ eV\\ \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps} \begin{picture}(0,0)(-15,-3) - 001 dumbbell + 100 dumbbell \end{picture} \end{minipage} \begin{minipage}[t]{3.3cm} - $E_f=1.62\, eV$\\ + $E_f=1.62$ eV\\ \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps} \end{minipage} \begin{minipage}[t]{3.3cm} - $E_f=2.39\, eV$\\ + $E_f=2.39$ eV\\ \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps} \end{minipage} \begin{minipage}[t]{3.0cm} - $E_f=3.41\, eV$\\ + $E_f=3.41$ eV\\ \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps} \end{minipage} @@ -426,7 +444,38 @@ \begin{slide} {\large\bf - Simulation details + Results + } - <100> dumbbell configuration + + \vspace{8pt} + + \small + + \begin{minipage}{4cm} + \begin{itemize} + \item $E_f=0.47$ eV + \item Very often observed + \item Most energetically\\ + favorable configuration + \item Experimental\\ + evidence [6] + \end{itemize} + \vspace{24pt} + {\tiny + [6] G. D. Watkins and K. L. Brower,\\ + Phys. Rev. Lett. 36 (1976) 1329. + } + \end{minipage} + \begin{minipage}{8cm} + \includegraphics[width=9cm]{100-c-si-db_s.eps} + \end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + Simulation sequence } \small @@ -439,18 +488,18 @@ \begin{pspicture}(0,0)(12,8) % nodes - \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{ + \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ \parbox{7cm}{ \begin{itemize} \item Initial configuration: $31\times31\times31$ unit cells Si \item Periodic boundary conditions - \item $T=450\, ^{\circ}C$ - \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$ + \item $T=450\, ^{\circ}\text{C}$, $p=0\text{ bar}$ + \item Equilibration of $E_{kin}$ and $E_{pot}$ \end{itemize} }}}} - \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{ + \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{ \parbox{7cm}{ - Insertion of $6000$ carbon atoms at constant\\ + Insertion of 6000 carbon atoms at constant\\ temperature into: \begin{itemize} \item Total simulation volume {\pnode{in1}} @@ -458,7 +507,7 @@ \item Volume of necessary amount of Si {\pnode{in3}} \end{itemize} }}}} - \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{ + \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{ \parbox{3.5cm}{ Cooling down to $20\, ^{\circ}C$ }}}} @@ -480,23 +529,53 @@ \begin{slide} {\large\bf - Very first results of the SiC precipitation runs - } - - \footnotesize - - \begin{minipage}[b]{6.9cm} - \includegraphics[width=6.3cm]{../plot/sic_prec_energy.ps} - \includegraphics[width=6.3cm]{../plot/sic_prec_temp.ps} + Results + } - SiC precipitation runs + + + \includegraphics[width=6.3cm]{pc_si-c_c-c.eps} + \includegraphics[width=6.3cm]{pc_si-si.eps} + + \begin{minipage}[t]{6.3cm} + \tiny + \begin{itemize} + \item C-C peak at 0.15 nm similar to next neighbour distance of graphite + or diamond\\ + $\Rightarrow$ Formation of strong C-C bonds + (almost only for high C concentrations) + \item Si-C peak at 0.19 nm similar to next neighbour distance in 3C-SiC + \item C-C peak at 0.31 nm equals C-C distance in 3C-SiC\\ + (due to concatenated, differently oriented + <100> dumbbell interstitials) + \item Si-Si shows non-zero g(r) values around 0.31 nm like in 3C-SiC\\ + and a decrease at regular distances\\ + (no clear peak, + interval of enhanced g(r) corresponds to C-C peak width) + \end{itemize} \end{minipage} - \begin{minipage}[b]{5.5cm} - \begin{itemize} - \item {\color{red} Total simulation volume} - \item {\color{green} Volume of minimal SiC precipitation} - \item {\color{blue} Volume of necessary amount of Si} - \end{itemize} - \vspace{40pt} - \includegraphics[width=6.3cm]{../plot/foo150.ps} + \begin{minipage}[t]{6.3cm} + \tiny + \begin{itemize} + \item Low C concentration (i.e. $V_1$): + The <100> dumbbell configuration + \begin{itemize} + \item is identified to stretch the Si-Si next neighbour distance + to 0.3 nm + \item is identified to contribute to the Si-C peak at 0.19 nm + \item explains further C-Si peaks (dashed vertical lines) + \end{itemize} + $\Rightarrow$ C atoms are first elements arranged at distances + expected for 3C-SiC\\ + $\Rightarrow$ C atoms pull the Si atoms into the right + configuration at a later stage + \item High C concentration (i.e. $V_2$ and $V_3$): + \begin{itemize} + \item High amount of damage introduced into the system + \item Short range order observed but almost no long range order + \end{itemize} + $\Rightarrow$ Start of amorphous SiC-like phase formation\\ + $\Rightarrow$ Higher temperatures required for proper SiC formation + \end{itemize} \end{minipage} \end{slide}