X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fdpg_2008.tex;h=d7e97e8dd4239e1e65459451199119bf71c8ab1b;hb=7324e1b27ab305d480e7c00917d371a4c6a0c63f;hp=42a2415d535f75b2076925b21b8118339bc387b9;hpb=9e37e4e1e7789cc9ab7898066f66dd8a879f0a11;p=lectures%2Flatex.git diff --git a/posic/talks/dpg_2008.tex b/posic/talks/dpg_2008.tex index 42a2415..d7e97e8 100644 --- a/posic/talks/dpg_2008.tex +++ b/posic/talks/dpg_2008.tex @@ -33,7 +33,9 @@ \begin{document} \extraslideheight{10in} -\slideframe{plain} +\slideframe{none} + +\pagestyle{empty} % specify width and height \slidewidth 27.7cm @@ -41,13 +43,16 @@ % shift it into visual area properly \def\slideleftmargin{3.3cm} -\def\slidetopmargin{0.0cm} +\def\slidetopmargin{0.6cm} \newcommand{\ham}{\mathcal{H}} \newcommand{\pot}{\mathcal{V}} \newcommand{\foo}{\mathcal{U}} \newcommand{\vir}{\mathcal{W}} +% itemize level ii +\renewcommand\labelitemii{{\color{gray}$\bullet$}} + % topic \begin{slide} @@ -132,10 +137,10 @@ \item Integrator, potential, ensemble control \item Simulation sequence \end{itemize} - \item Results gained by simulation + \item Simulation results \begin{itemize} \item Interstitials in silicon - \item $SiC$-precipitation experiments + \item SiC-precipitation experiments \end{itemize} \item Conclusion / Outlook \end{itemize} @@ -143,6 +148,49 @@ % start of contents +\begin{slide} + + {\large\bf + Motivation / Introduction + } + + \vspace{16pt} + + Reasons for investigating C in Si: + + \begin{itemize} + \item 3C-SiC wide band gap semiconductor formation + \item Strained Si (no precipitation wanted!) + \end{itemize} + + \vspace{16pt} + + Si / 3C-SiC facts: + + \begin{minipage}{8cm} + \begin{itemize} + \item Unit cell: + \begin{itemize} + \item {\color{yellow}fcc} $+$ + \item {\color{gray}fcc shifted $1/4$ of volume diagonal} + \end{itemize} + \item Lattice constants: $4a_{Si}\approx5a_{SiC}$ + \item Silicon density: + \[ + \frac{n_{SiC}}{n_{Si}}= + \frac{4/a_{SiC}^3}{8/a_{Si}^3}= + \frac{5^3}{2\cdot4^3}={\color{cyan}97,66}\,\% + \] + \end{itemize} + \end{minipage} + \hspace{8pt} + \begin{minipage}{4cm} + \includegraphics[width=4cm]{sic_unit_cell.eps} + \end{minipage} + +\end{slide} + + \small \begin{slide} {\large\bf @@ -182,14 +230,13 @@ Precipitation of 3C-SiC + Creation of interstitials\\ \end{minipage} - \begin{center} - \[5a_{SiC}=4a_{Si} \quad \Rightarrow \quad - \frac{n_{SiC}}{n_{Si}}=\frac{\frac{4}{a_{SiC}^3}}{\frac{8}{a_{Si}^3}}= - \frac{5^3}{2\cdot4^3}=97,66\% - \] - \end{center} + \vspace{12pt} - Experimentally observed minimal diameter of precipitation: 4 - 5 nm + Experimentally observed: + \begin{itemize} + \item Minimal diameter of precipitation: 4 - 5 nm + \item (hkl)-planes identical for Si and SiC + \end{itemize} \end{slide} @@ -199,20 +246,22 @@ Simulation details } + \vspace{12pt} + 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-dimemnsional phase space + in 6N-dimensional phase space \item Observables obtained by time average \end{itemize} - \vspace{4pt} + \vspace{12pt} Application details: \begin{itemize} - \item Integrator: velocity verlet, timestep: $1\, fs$ + \item Integrator: Velocity Verlet, timestep: $1\, fs$ \item Ensemble control: NVT, Berendsen thermostat, $\tau=100.0$ \item Potential: Tersoff-like bond order potential\\ \[ @@ -224,6 +273,10 @@ \end{center} \end{itemize} + \begin{picture}(0,0)(-240,-70) + \includegraphics[width=5cm]{tersoff_angle.eps} + \end{picture} + \end{slide} \begin{slide} @@ -232,22 +285,32 @@ Simulation details } + \vspace{20pt} + Interstitial experiments: + + \vspace{12pt} + \begin{itemize} \item Initial configuration: $9\times9\times9$ unit cells Si \item Periodic boundary conditions \item $T=0 \, K$ \item Insertion of Si / C atom at \begin{itemize} - \item $(0,0,0)$ $\rightarrow$ tetrahedral - \item $(-1/8,-1/8,1/8)$ $\rightarrow$ hexagonal - \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$ - $\rightarrow$ 110 dumbbell + \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral} + \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal} + \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\ + $\rightarrow$ {\color{yellow}110 dumbbell} \item random positions (critical distance check) \end{itemize} \item Relaxation time: $2\, ps$ + \item Optional heating-up \end{itemize} + \begin{picture}(0,0)(-210,-45) + \includegraphics[width=6cm]{unit_cell.eps} + \end{picture} + \end{slide} \begin{slide} @@ -294,6 +357,73 @@ Results } + Si self-interstitial experiments: + + {\footnotesize + {\bf Note:} + \begin{itemize} + \item $r_{cutoff}^{Si-Si}=2.96>\frac{5.43}{2}$ + \item Bond length near $r_{cutoff} \Rightarrow$ small bond strength + \end{itemize} + } + + \vspace{8pt} + + \small + + \begin{minipage}[t]{4.0cm} + \underline{Tetrahedral} + \begin{itemize} + \item $E_F=3.41\, eV$ + \item essentialy tetrahedral\\ + bonds + \end{itemize} + \end{minipage} + \hspace{0.3cm} + \begin{minipage}[t]{4.0cm} + \underline{110 dumbbell} + \begin{itemize} + \item $E_F=4.39\, eV$ + \item essentially 4 bonds + \end{itemize} + \end{minipage} + \hspace{0.3cm} + \begin{minipage}[t]{4.0cm} + \underline{Hexagonal} + \begin{itemize} + \item $E_F^{\star}\approx4.48\, eV$ + \item unstable! + \end{itemize} + \end{minipage} + + \vspace{8pt} + + \begin{minipage}{4.3cm} + \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps} + \end{minipage} + \begin{minipage}{4.3cm} + \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps} + \end{minipage} + \begin{minipage}{4.3cm} + \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps} + \end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + Results + } + + \vspace{8pt} + + Si self-interstitial \underline{random insertion} experiments: + + \vspace{8pt} + + foo + \end{slide} \begin{slide} @@ -302,6 +432,48 @@ Results } + Carbon interstitial experiments: + + \vspace{8pt} + + \small + + \begin{minipage}[t]{4.0cm} + \underline{Tetrahedral} + \begin{itemize} + \item $E_F=2.67\, eV$ + \item tetrahedral bond + \end{itemize} + \end{minipage} + \hspace{0.3cm} + \begin{minipage}[t]{4.0cm} + \underline{110 dumbbell} + \begin{itemize} + \item $E_F=1.76\, eV$ + \item C forms 3 bonds + \end{itemize} + \end{minipage} + \hspace{0.3cm} + \begin{minipage}[t]{4.0cm} + \underline{Hexagonal} + \begin{itemize} + \item $E_F^{\star}\approx5.6\, eV$ + \item unstable! + \end{itemize} + \end{minipage} + + \vspace{8pt} + + \begin{minipage}{4.3cm} + \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps} + \end{minipage} + \begin{minipage}{4.3cm} + \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps} + \end{minipage} + \begin{minipage}{4.3cm} + \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps} + \end{minipage} + \end{slide} \begin{slide} @@ -310,6 +482,14 @@ Results } + \vspace{8pt} + + Carbon \underline{random insertion} experiments: + + \vspace{8pt} + + bar + \end{slide} \begin{slide} @@ -318,6 +498,8 @@ Results } + SiC-precipitation experiments: + \end{slide} \begin{slide} @@ -328,6 +510,5 @@ \end{slide} - \end{document}