\usepackage{upgreek}
+\usepackage{miller}
+
\begin{document}
\extraslideheight{10in}
\includegraphics[width=7.0cm]{si_self_int.ps}
\end{minipage}
\begin{minipage}{5cm}
- $E_{\textrm{f}}^{\textrm{110},\,32\textrm{pc}}=3.38\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\hkl<1 1 0>,\,32\textrm{pc}}=3.38\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{tet},\,32\textrm{pc}}=3.41\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{hex},\,32\textrm{pc}}=3.42\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{vac},\,32\textrm{pc}}=3.51\textrm{ eV}$\\\\
$E_{\textrm{f}}^{\textrm{hex},\,54\textrm{pc}}=3.42\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{tet},\,54\textrm{pc}}=3.45\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{vac},\,54\textrm{pc}}=3.47\textrm{ eV}$\\
- $E_{\textrm{f}}^{\textrm{110},\,54\textrm{pc}}=3.48\textrm{ eV}$
+ $E_{\textrm{f}}^{\hkl<1 1 0>,\,54\textrm{pc}}=3.48\textrm{ eV}$
\end{minipage}
Comparison with literature (PRL 88 235501 (2002)):\\[0.2cm]
\end{itemize}
\end{minipage}
\begin{minipage}{5cm}
- $E_{\textrm{f}}^{\textrm{110}}=3.31 / 2.88\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\hkl<1 1 0>}=3.31 / 2.88\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{hex}}=3.31 / 2.87\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{vac}}=3.17 / 3.56\textrm{ eV}$
\end{minipage}
\begin{center}
Error in lattice constant of plain Si ($1\times 1\times 1$ Type 2):
$0.025\,\%$\\
- Error in position of the 110 interstitital in Si ($1\times 1\times 1$ Type 2):
+ Error in position of the \hkl<1 1 0> interstitital in Si
+ ($1\times 1\times 1$ Type 2):
$0.026\,\%$\\
$\Downarrow$\\
{\bf\color{blue}
\begin{slide}
- {\large\bf
+ {\large\bf\boldmath
Energy cut-off for $\Gamma$-point only caclulations
}
\begin{slide}
- {\large\bf
- C 100 interstitial migration along 110 in c-Si (Albe potential)
+ {\large\bf\boldmath
+ C \hkl<1 0 0> interstitial migration along \hkl<1 1 0>
+ in c-Si (Albe)
}
\small
\item Fix border atoms of the simulation cell
\item Constraints and displacement of the C atom:
\begin{itemize}
- \item along {\color{green}110 direction}\\
+ \item along {\color{green}\hkl<1 1 0> direction}\\
displaced by {\color{green} $\frac{1}{10}(\Delta x,\Delta y)$}
\item C atom {\color{red}entirely fixed in position}\\
displaced by
\begin{slide}
- {\large\bf
- C 100 interstitial migration along 110 in c-Si (Albe potential)
+ {\large\bf\boldmath
+ C \hkl<1 0 0> interstitial migration along \hkl<1 1 0>
+ in c-Si (Albe)
}
\footnotesize
\begin{slide}
- {\large\bf
- C 100 interstitial migration along 110 in c-Si (Albe potential)\\
+ {\large\bf\boldmath
+ C \hkl<1 0 0> interstitial migration along \hkl<1 1 0>
+ in c-Si (Albe)\\
}
Displacement step size decreased to
\begin{slide}
- {\large\bf
- C 100 interstitial migration along 110 in c-Si (Albe potential)
+ {\large\bf\boldmath
+ C \hkl<1 0 0> interstitial migration along \hkl<1 1 0>
+ in c-Si (Albe)
}
{\color{blue}New approach:}\\
\begin{slide}
- {\large\bf
- C 100 interstitial migration along 110 in c-Si (VASP)
+ {\large\bf\boldmath
+ C \hkl<1 0 0> interstitial migration along \hkl<1 1 0> in c-Si (VASP)
}
\small
\begin{itemize}
\item Place interstitial carbon atom at the respective coordinates
into perfect c-Si
- \item 110 direction fixed for the C atom
+ \item \hkl<1 1 0> direction fixed for the C atom
\item $4\times 4\times 3$ Type 1, $198+1$ atoms
\item Atoms with $x=0$ or $y=0$ or $z=0$ fixed
\end{itemize}
\begin{slide}
- {\large\bf
- C 100 interstitial migration along 110 in c-Si (VASP)
+ {\large\bf\boldmath
+ C \hkl<1 0 0> interstitial migration along \hkl<1 1 0> in c-Si (VASP)
}
\small
{\color{blue}Method:}
\begin{itemize}
\item Continue with atomic positions of the last run
- \item Displace the C atom in 110 direction
- \item 110 direction fixed for the C atom
+ \item Displace the C atom in \hkl<1 1 0> direction
+ \item \hkl<1 1 0> direction fixed for the C atom
\item $4\times 4\times 3$ Type 1, $198+1$ atoms
\item Atoms with $x=0$ or $y=0$ or $z=0$ fixed
\end{itemize}
\begin{slide}
- {\large\bf
- Again: C 100 interstitial migration
+ {\large\bf\boldmath
+ Again: C \hkl<1 0 0> interstitial migration
}
\small
\begin{enumerate}
\item Method
\begin{itemize}
- \item Start in relaxed 100 interstitial configuration
- \item Displace C atom along 110 direction
+ \item Start in relaxed \hkl<1 0 0> interstitial configuration
+ \item Displace C atom along \hkl<1 1 0> direction
\item Relaxation (Berendsen thermostat)
\item Continue with configuration of the last run
\end{itemize}
{\color{blue}In both methods:}
\begin{itemize}
\item Fixed border atoms
- \item Applied 110 constraint for the C atom
+ \item Applied \hkl<1 1 0> constraint for the C atom
\end{itemize}
{\color{red}Pitfalls} and {\color{green}refinements}:
\begin{itemize}
Relaxation of stress not possible\\
$\Rightarrow$
{\color{green}Fix only one Si atom} (the one furthermost to the defect)
- \item {\color{red}110 constraint not sufficient}\\
+ \item {\color{red}\hkl<1 1 0> constraint not sufficient}\\
$\Rightarrow$ {\color{green}Apply 11x constraint}
(connecting line of initial and final C positions)
\end{itemize}
\begin{slide}
- {\large\bf
- Again: C 100 interstitial migration (Albe)
+ {\large\bf\boldmath
+ Again: C \hkl<1 0 0> interstitial migration (Albe)
}
- Constraint applied by modyfing the Velocity Verlet algorithm
+ Constraint applied by modifying the Velocity Verlet algorithm
{\color{blue}Results:}
(Video \href{../video/c_in_si_fmig_albe.avi}{$\rhd_{\text{local}}$ } $|$
\begin{slide}
- {\large\bf
- Again: C 100 interstitial migration (VASP)
+ {\large\bf\boldmath
+ Again: C \hkl<1 0 0> interstitial migration (VASP)
}
Transformation for the Type 2 supercell
\begin{slide}
- {\large\bf
- Again: C 100 interstitial migration\\
+ {\large\bf\boldmath
+ Again: C \hkl<1 0 0> interstitial migration\\
}
{\color{blue}Reminder:}\\
\begin{slide}
- {\large\bf
- The C 100 defect configuration
+ {\large\bf\boldmath
+ The C \hkl<1 0 0> defect configuration
}
Needed so often for input configurations ...\\[0.8cm]
- \begin{minipage}{7.7cm}
- \includegraphics[width=7cm]{100-c-si-db_light.eps}
- \hfill
+ \begin{minipage}{7.0cm}
+ \includegraphics[width=6.5cm]{100-c-si-db_light.eps}\\
+ Qualitative {\color{red}and} quantitative {\color{red}difference}!
\end{minipage}
- \begin{minipage}{4.5cm}
+ \begin{minipage}{5.5cm}
+ \scriptsize
+ \begin{center}
\begin{tabular}{|l|l|l|}
\hline
& a & b \\
in \AA & 0.84 & 0.91 \\
\hline
\end{tabular}
+ \includegraphics[width=6.1cm]{c_100_pc_vasp.ps}
+ \end{center}
\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Again: C \hkl<1 0 0> interstitial migration (VASP)
+ }
+
+ $\hkl<0 0 -1> \rightarrow \hkl<0 0 1>$ migration:
+
+ \small
+
+ \begin{minipage}[t]{4.1cm}
+ \underline{Starting configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/start.eps}
\begin{center}
- Qualitative {\color{red}and} quantitative {\color{red}difference}!
+ $E_{\text{f}}=3.15 \text{ eV}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \underline{Intermediate configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/00-1_001_im.eps}
+ \begin{center}
+ $E_{\text{f}}=4.41 \text{ eV}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \underline{Final configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/final.eps}
+ \begin{center}
+ $E_{\text{f}}=3.17 \text{ eV}$
+ \end{center}
+ \end{minipage}\\[0.4cm]
+ \[
+ \Rightarrow \Delta E_{\text{f}} = E_{\text{mig}} = 1.26 \text{ eV}
+ \]
+
+ Unexpected \& ({\color{red}more} or {\color{orange}less}) fatal:
+ \begin{itemize}
+ \renewcommand\labelitemi{{\color{orange}$\bullet$}}
+ \item Difference in formation energy (0.02 eV)
+ of the initial and final configuration
+ \renewcommand\labelitemi{{\color{red}$\bullet$}}
+ \item Huge discrepancy (0.3 - 0.4 eV) to the migration barrier
+ of Type 1 (198+1 atoms) calculations
+ \renewcommand\labelitemi{{\color{black}$\bullet$}}
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Again: C \hkl<1 0 0> interstitial migration (VASP)
+ }
+
+ $\hkl<0 0 -1> \rightarrow \hkl<0 -1 0>$ migration:
+
+ \small
+
+ \begin{minipage}[t]{4.1cm}
+ \underline{Starting configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/start.eps}
+ \begin{center}
+ $E_{\text{f}}=3.154 \text{ eV}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \underline{Intermediate configuration}\\
+ in progress ...
+ \begin{center}
+ $E_{\text{f}}=?.?? \text{ eV}$
\end{center}
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \underline{Final configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/0-10.eps}
+ \begin{center}
+ $E_{\text{f}}=3.157 \text{ eV}$
+ \end{center}
+ \end{minipage}\\[0.4cm]
+ \[
+ \Rightarrow \Delta E_{\text{f}} = E_{\text{mig}} = ?.?? \text{ eV}
+ \]
+ Unexpected \& ({\color{red}more} or {\color{orange}less}) fatal:
+ \begin{itemize}
+ \renewcommand\labelitemi{{\color{orange}$\bullet$}}
+ \item Difference in formation energy (0.02 eV)
+ of the initial and final configuration
+ \renewcommand\labelitemi{{\color{red}$\bullet$}}
+ \item Huge discrepancy (0.3 - 0.4 eV) to the migration barrier
+ of Type 1 (198+1 atoms) calculations
+ \renewcommand\labelitemi{{\color{black}$\bullet$}}
+ \end{itemize}
+
\end{slide}
\begin{slide}
{\large\bf
- Again: C 100 interstitial migration
+ Molecular dynamics simulations (VASP)
}
+ 2 C atoms in $2\times 2\times 2$ Type 2 supercell
+
\small
- \underline{$00-1 \rightarrow$ bond centered $\rightarrow 001$}
+ \begin{minipage}{7.6cm}
+ Radial distribution\\
+ \includegraphics[width=7.6cm]{md_02c_2222si_pc.ps}
+ \end{minipage}
+ \begin{minipage}{5.0cm}
+ \begin{center}
+ PC average from\\
+ $t_1=50$ ps to $t_2=50.93$ ps
+ \end{center}
+ \end{minipage}
+ Diffusion:
+ \begin{itemize}
+ \item $<(x(t)-x(0))^2>$ hard to determine due to missing info of
+ boundary crossings
+ \item No jumps recognized in the
+ Video \href{../video/md_02c_2222si_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/md_02c_2222si_vasp.avi}{$\rhd_{\text{remote url}}$}
+ \end{itemize}
- $\Delta E_{\text{coh}}$\\
- $\Delta E_{\text{f}}$
-
\end{slide}
\begin{slide}
Molecular dynamics simulations (VASP)
}
-
+ 10 C atoms in $3\times 3\times 3$ Type 2 supercell
+
\small
-
+
+ \begin{minipage}{7.2cm}
+ Radial distribution (PC averaged over 1 ps)\\
+ \includegraphics[width=7.0cm]{md_10c_2333si_pc_vasp.ps}
+ \end{minipage}
+ \begin{minipage}{5.0cm}
+ \includegraphics[width=6.0cm]{md_10c_2333si_pcc_vasp.ps}
+ \end{minipage}
+ Diffusion:
+ (Video \href{../video/md_10c_2333si_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/md_10c_2333si_vasp.avi}{$\rhd_{\text{remote url}}$})
+ \begin{itemize}
+ \item $<(x(t)-x(0))^2>$ hard to determine due to missing info of
+ boundary crossings
+ \item Agglomeration of C? (Video)
+ \end{itemize}
\end{slide}
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