\pdfoutput=0
\documentclass[landscape,semhelv,draft]{seminar}
+%\documentclass[landscape,semhelv]{seminar}
\usepackage{verbatim}
\usepackage[greek,german]{babel}
% 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}
Energetically most favorable combinations along \hkl<1 1 0>
+\vspace*{0.1cm}
+
{\scriptsize
\begin{tabular}{l c c c c c c}
\hline
\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}
\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}
}
\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}
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