X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fdpg_2008.tex;h=d7e97e8dd4239e1e65459451199119bf71c8ab1b;hb=7324e1b27ab305d480e7c00917d371a4c6a0c63f;hp=00e9aafe8e7e867d6cc4501b7c77d6e77a86dbcb;hpb=b3f67410beb238a88261d42fc5a78d08f8ee29ed;p=lectures%2Flatex.git diff --git a/posic/talks/dpg_2008.tex b/posic/talks/dpg_2008.tex index 00e9aaf..d7e97e8 100644 --- a/posic/talks/dpg_2008.tex +++ b/posic/talks/dpg_2008.tex @@ -28,10 +28,14 @@ \articlemag{1} +\special{landscape} + \begin{document} \extraslideheight{10in} -\slideframe{plain} +\slideframe{none} + +\pagestyle{empty} % specify width and height \slidewidth 27.7cm @@ -39,13 +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} @@ -130,10 +137,10 @@ \item Integrator, potential, ensemble control \item Simulation sequence \end{itemize} - \item Results gained by simulation + \item Simulation results \begin{itemize} - \item Carbon interstitials in silicon - \item Existence of $SiC$-precipitates + \item Interstitials in silicon + \item SiC-precipitation experiments \end{itemize} \item Conclusion / Outlook \end{itemize} @@ -141,5 +148,367 @@ % 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 + Motivation / Introduction + } + + \small + \vspace{6pt} + + Supposed mechanism of the conversion of heavily carbon doped Si into SiC: + + \vspace{8pt} + + \begin{minipage}{3.8cm} + \includegraphics[width=3.7cm]{sic_prec_seq_01.eps} + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + \includegraphics[width=3.7cm]{sic_prec_seq_02.eps} + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + \includegraphics[width=3.7cm]{sic_prec_seq_03.eps} + \end{minipage} + + \vspace{8pt} + + \begin{minipage}{3.8cm} + Formation of C-Si dumbbells on regular c-Si lattice sites + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + Agglomeration into large clusters (embryos)\\ + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + Precipitation of 3C-SiC + Creation of interstitials\\ + \end{minipage} + + \vspace{12pt} + + Experimentally observed: + \begin{itemize} + \item Minimal diameter of precipitation: 4 - 5 nm + \item (hkl)-planes identical for Si and SiC + \end{itemize} + +\end{slide} + +\begin{slide} + + {\large\bf + 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-dimensional phase space + \item Observables obtained by time average + \end{itemize} + + \vspace{12pt} + + Application details: + \begin{itemize} + \item Integrator: Velocity Verlet, timestep: $1\, fs$ + \item Ensemble control: NVT, Berendsen thermostat, $\tau=100.0$ + \item Potential: Tersoff-like bond order potential\\ + \[ + E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad + \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] + \] + \begin{center} + {\scriptsize P. Erhart und K. Albe. Phys. Rev. B 71 (2005) 035211} + \end{center} + \end{itemize} + + \begin{picture}(0,0)(-240,-70) + \includegraphics[width=5cm]{tersoff_angle.eps} + \end{picture} + +\end{slide} + +\begin{slide} + + {\large\bf + 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 $(0,0,0)$ $\rightarrow$ {\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} + + {\large\bf + Simulation details + } + + \small + + SiC precipitation experiments: + \begin{itemize} + \item Initial configuration: $31\times31\times31$ unit cells Si + \item Periodic boundary conditions + \item $T=450\, ^{\circ}C$ + \item Steady state time: $600\, fs$ + \item C insertion steps: + \begin{itemize} + \item If $T=450\pm 1\, ^{\circ}C$:\\ + Insertion of 10 atoms at random positions within $V_{ins}$ + \item Otherwise: Annealing for another $100\, fs$ + \end{itemize} + \item Annealing: ($T_a: 450\rightarrow 20 \, ^{\circ}C$) + \begin{itemize} + \item If $T=T_a$: Decrease $T_a$ by $1\, ^{\circ}C$ + \item Otherwise: Annealing for another $50\, fs$ + \end{itemize} + \end{itemize} + + Szenarios: + \begin{enumerate} + \item $V_{ins}$: total simulation volume $V$ + \item $V_{ins}$: $12\times12\times12$ SiC unit cells + ($\sim$ volume of minimal SiC precipitation) + \item $V_{ins}$: $9\times9\times9$ SiC unit cells + ($\sim$ volume of necessary amount of Si) + \end{enumerate} + +\end{slide} + +\begin{slide} + + {\large\bf + 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} + + {\large\bf + 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} + + {\large\bf + Results + } + + \vspace{8pt} + + Carbon \underline{random insertion} experiments: + + \vspace{8pt} + + bar + +\end{slide} + +\begin{slide} + + {\large\bf + Results + } + + SiC-precipitation experiments: + +\end{slide} + +\begin{slide} + + {\large\bf + Conclusion / Outlook + } + +\end{slide} + \end{document}