\end{slide}
+\begin{slide}
+
+ {\large\bf\boldmath
+ Kohn-Sham levels visualized
+ }
+
+ \begin{minipage}{6cm}
+ \underline{\hkl<0 0 -1> configuration}
+ \begin{center}
+ \includegraphics[height=8cm]{c_100_mig_vasp/100_ksl.ps}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \underline{Saddle point configuration}
+ \begin{center}
+ \includegraphics[height=8cm]{c_100_mig_vasp/im_ksl.ps}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
\begin{slide}
{\large\bf\boldmath
in the $3\times 3\times 3$ Type 2 supercell
}
+ \includegraphics[width=6cm]{c_00-1_0-10_mig_vasp.ps}
+
\end{slide}
\begin{slide}
\end{slide}
+\begin{slide}
+
+ {\large\bf\boldmath
+ Silicon point defects
+ }
+
+ \begin{minipage}{3.2cm}
+ \underline{Vacancy}
+ \begin{itemize}
+ \item $E_{\text{f}}=3.63\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/vac_2333.eps}\\
+ \underline{\hkl<1 1 0> interstitial}
+ \begin{itemize}
+ \item $E_{\text{f}}=3.39\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/110_2333.eps}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/vac_2333_ksl.ps}\\
+ {\scriptsize Vacancy}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/110_2333_ksl.ps}
+ {\scriptsize \hkl<1 1 0> interstitial}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Silicon point defects
+ }
+
+ \begin{minipage}{3.1cm}
+ \underline{Hexagonal}
+ \begin{itemize}
+ \item $E_{\text{f}}=3.42\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/hex_2333.eps}\\
+ \underline{Tetrahedral}
+ \begin{itemize}
+ \item $E_{\text{f}}=3.77\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/tet_2333.eps}
+ \end{minipage}
+ \begin{minipage}{3.7cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/hex_2333_ksl.ps}\\
+ {\scriptsize Hexagonal}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{3.7cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/tet_2333_ksl.ps}
+ {\scriptsize Tetrahedral}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[c]{0.1cm}
+ \hfill
+ \end{minipage}
+ \begin{minipage}[c]{1.9cm}
+{\tiny
+\underline{Energy - Occup.}\\
+5.5063 - 0.32840\\
+5.5064 - 0.32793\\
+5.5064 - 0.32764\\
+5.5777 - 0.00691\\
+5.5777 - 0.00691\\
+5.6031 - 0.00074\\
+5.6031 - 0.00074\\
+5.6035 - 0.00071\\
+5.6357 - 0.00002\\
+5.6453 - 0.00001\\
+5.6453 - 0.00001
+}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Carbon point defects in silicon
+ }
+
+ \begin{minipage}{3.2cm}
+ \underline{C substitutional}
+ \begin{itemize}
+ \item $E_{\text{f}}=1.39\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{c_pd_vasp/sub_2333.eps}\\
+ \underline{\hkl<1 0 0> interstitial}
+ \begin{itemize}
+ \item $E_{\text{f}}=3.15\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{c_pd_vasp/100_2333.eps}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{c_pd_vasp/sub_2333_ksl.ps}\\
+ {\scriptsize C substitutional}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{c_pd_vasp/100_2333_ksl.ps}
+ {\scriptsize \hkl<1 0 0> interstitial}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
\begin{slide}
{\large\bf\boldmath
}
& \hkl<1 1 -1> & \hkl<2 2 0> & \hkl<3 3 -1> & \hkl<4 4 0>\\
\hline
- \hkl<0 0 -1> & 6.23514\newline {\color{blue}6.23514}
- & 4.65214\newline {\color{blue}4.65014}
- & 5.97314\newline {\color{blue}5.97314}
- & 6.45514\newline {\color{blue}6.45714} \\
+ \hkl<0 0 -1> & 6.23\newline {\color{blue}6.23514}
+ & 4.65\newline {\color{blue}4.65014}
+ & 5.97\newline {\color{blue}5.97314}
+ & 6.45\newline {\color{blue}6.45714} \\
+ \hline
+ \hkl<0 0 1> & 6.64\newline {\color{blue}6.65114}
+ & 4.78\newline {\color{blue}4.78314}
+ & 6.53\newline {\color{blue}6.53614}
+ & 6.18\newline {\color{blue}6.18914} \\
\hline
- \hkl<0 0 1> & 6.65114\newline {\color{blue}6.65114}
- & 4.78514\newline {\color{blue}4.78314}
- & 6.53614\newline {\color{blue}6.53614}
- & 6.18914\newline {\color{blue}6.18914} \\
+ \hkl<1 0 0>, \hkl<0 1 0> & 4.06\newline alkmene
+ & 4.93
+ & 5.72
+ & 6.00\\
\hline
- \hkl<1 0 0>, \hkl<0 1 0> & 4.07014\newline alkmene
- & 4.93814
- & 5.72914
- & 6.00214\\
+ \hkl<-1 0 0>, \hkl<0 -1 0> & 3.92 & 4.43 & 6.02 & 6.02 \\
\hline
- \hkl<-1 0 0>, \hkl<0 -1 0> & TODO & TODO & TODO & TODO\\
+ Vacancy & ... & ... & ... & ... \\
\hline
\end{tabular}
\begin{slide}
+ \begin{minipage}{5cm}
{\large\bf\boldmath
Combination of defects
}
\scriptsize
- \begin{minipage}{6cm}
Initial insterstital at: $\frac{1}{4}\hkl<1 1 1>$
Relative silicon neighbour positions:
\begin{enumerate}
\item The dumbbell Si
- \item $\frac{1}{4}\hkl<1 1 -1>$
- \item $\frac{1}{2}\hkl<0 1 1>$,
- $\frac{1}{2}\hkl<1 0 1>$,
- $\frac{1}{2}\hkl<0 -1 -1>$
+ \item $\frac{1}{4}\hkl<1 1 -1>$, $\frac{1}{4}\hkl<-1 -1 -1>$
+ \item $\frac{1}{2}\hkl<1 0 -1>$, $\frac{1}{2}\hkl<0 1 -1>$,
+ $\frac{1}{2}\hkl<0 -1 -1>$, $\frac{1}{2}\hkl<-1 0 -1>$
\item $\frac{1}{4}\hkl<1 -1 1>$, $\frac{1}{4}\hkl<-1 1 1>$
- \item $\frac{1}{4}\hkl<-1 1 -2>$, $\frac{1}{4}\hkl<1 -1 -2>$
+ \item $\frac{1}{4}\hkl<-1 1 -3>$, $\frac{1}{4}\hkl<1 -1 -3>$
\item $\frac{1}{2}\hkl<-1 -1 0>$, $\frac{1}{2}\hkl<1 1 0>$
\item $\frac{1}{2}\hkl<1 -1 0>$, $\frac{1}{2}\hkl<-1 1 0>$
\item $\frac{1}{4}\hkl<-1 3 -1>$, $\frac{1}{4}\hkl<1 -3 -1>$,
\item $\hkl<0 0 -1>$
\item $\frac{1}{2}\hkl<1 0 1>$, $\frac{1}{2}\hkl<0 1 1>$,
$\frac{1}{2}\hkl<0 -1 1>$, $\frac{1}{2}\hkl<-1 0 1>$
- \item $\frac{1}{4}\hkl<-1 -3 1>$, $\frac{1}{4}\hkl<-3 -1 1>$
- \item $\frac{1}{4}\hkl<1 3 1>$, $\frac{1}{4}\hkl<3 1 1>$,
+ \item $\frac{1}{4}\hkl<-1 -3 1>$, $\frac{1}{4}\hkl<-3 -1 1>$,
+ $\frac{1}{4}\hkl<1 3 1>$, $\frac{1}{4}\hkl<3 1 1>$
\item $\frac{1}{4}\hkl<1 3 -3>$, $\frac{1}{4}\hkl<3 1 -3>$,
$\frac{1}{4}\hkl<-1 -3 -3>$, $\frac{1}{4}\hkl<-3 -1 -3>$
\item $\hkl<1 0 0>$, $\hkl<0 1 0>$, $\hkl<-1 0 0>$, $\hkl<0 -1 0>$
\item $\frac{1}{2}\hkl<1 1 -2>$, $\frac{1}{2}\hkl<-1 -1 -2>$,
\item $\frac{1}{2}\hkl<1 -1 -2>$, $\frac{1}{2}\hkl<-1 1 -2>$
\end{enumerate}
+ One of a kind\\
+ {\color{red}Two of a kind}\\
+ {\color{blue}Four of a kind}
\end{minipage}
\begin{minipage}{6cm}
- \includegraphics[width=7cm]{c_100_res_bonds_vasp.ps}
+ \includegraphics[width=8cm]{c_100_next_neighbours_02.eps}
+ \begin{center}
+ \includegraphics[width=5cm]{c_100_res_bonds_vasp.ps}
+ \end{center}
\end{minipage}
\end{slide}
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ \begin{tabular}{|l|l|l|l|l|l|}
+ \hline
+ & 2 & 3 & 4 & 5 & 6 \\
+ \hline
+\hkl<0 0 -1> & 6.23 & 5.16 & 6.23 & ... & 4.65\\
+ \hline
+\hkl<0 0 1> & 6.64 & 6.31 & ... & ... & 4.78 \\
+ \hline
+\hkl<1 0 0> & 4.06 & 6.13 & 6.21 & ... & 4.93 \\
+ \hline
+\hkl<-1 0 0> & \hkl<0 -1 0> & 4.41 & ... & ... & 4.43 \\
+ \hline
+\hkl<0 1 0> & \hkl<1 0 0> & 5.95 & \hkl<-1 0 0> & \hkl<-1 0 0> & \hkl<1 0 0> \\
+ \hline
+\hkl<0 -1 0> & 3.92 & ... & \hkl<1 0 0> & \hkl<1 0 0> & \hkl <-1 0 0> \\
+ \hline
+Vacancy & ... & ... & ... & ... & ... \\
+ \hline
+ \end{tabular}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Brainstorming: Point defects in Si (as grown and as implanted)
+ }
+
+ \small
+
+ Supercell size: $2$ - $2000 \cdot 10^{-21}\text{ cm}^3$
+
+ \underline{After crystal growth}
+ \begin{itemize}
+ \item Si point defects at $450\, ^{\circ}\text{C}$
+ \begin{itemize}
+ \item Interstitials:
+ \item Vacancies:
+ \end{itemize}
+ \item C impurities: $10^{17}\text{ cm}^{-3}$\\
+ $\Rightarrow$ $10^{-4}$ -- $10^{-1}$ per sc
+ $\rightarrow$ neglected in simulations
+ \end{itemize}
+
+ \underline{After/during implantation}
+ \begin{itemize}
+ \item Si point defects\\
+ $E_{\text{d}}^{\text{av}}=35\text{ eV}$,
+ $D_{\text{imp}}=1\text{ -- }4 \cdot 10^{17}\text{ cm }^{-2}$,
+ $d_{\text{sc}}=3\text{ -- }30\cdot 4.38\text { \AA}$,
+ $A=(3\text{ -- }30\text{ \AA})^2$,\\
+ Amount of collisions with $\Delta E > E_{\text{d}}$
+ in depth region $[h,h+d_{\text{sc}}]$: $n=$ .. (SRIM)\\
+ $\Rightarrow N_{\text{FP}}=nAD$
+ \item C point defects
+ \begin{itemize}
+ \item Substitutional C: ...
+ \item Intesrtitial C: ...
+ \end{itemize}
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Reminder (just for me to keep in mind ...)
+ }
+
+ \scriptsize
+
+ \underline{Volume of the MD cell}
+ \begin{itemize}
+ \item $T=900\text{ K}$
+ \item $\alpha=2.0 \cdot 10^{-6}\text{ K}^{-1}$
+ \item $a = a_0(1+\alpha \Delta T)$
+ \item Plain Si$(T=0)$: $a_0=5.4575\text{ \AA}$
+ $\rightarrow a(900\text{ K})=5.4674\text{ \AA}$
+ \item C \hkl<1 0 0> in Si$(T=0)$: $a_0^{\text{avg}}=
+ \frac{1}{3}(a_0^x+a_0^y+a_0^z)=5.4605\text{ \AA}$
+ $\rightarrow a(900\text{ K})=5.4704{ \AA}$
+ \end{itemize}
+ Used in the 900 K simulations: 5.4705 \AA\\
+ Consider next thoughts as well!
+
+ \underline{Zero total momentum simulations}
+ \begin{itemize}
+ \item If C is randomly inserted there is a net total momentum
+ \item No correction in the temperature control routine of VASP?
+ \item Relax a Si:C configuration first (at T=0)
+ \item Use this configuration as the MD initial configuration
+ \end{itemize}
+ Two possibilities regarding volume which came to my mind:
+ \begin{enumerate}
+ \item Calculate and use an averaged $a_0$ (in each direction)
+ from the relaxed configuration.
+ Else there might be a preferred orientation for the defect.
+ \item On the other hand this might be important
+ for the way defects agglomerate.
+ Continue using the relaxation results.
+ \end{enumerate}
+ In both methods the corrections due to the non zero temperature
+ are applied!
+
+\end{slide}
+
\begin{slide}
{\large\bf
Molecular dynamics simulations (VASP)
}
- 1 C atom in $3\times 3\times 3$ Type 2 supercell at $900\,^{\circ}\text{C}$
+ 1 C atom in $3\times 3\times 3$ Type 2 supercell at $900\,^{\circ}\text{C}$\\\\
- in progress ...
+ Video \href{../video/md_01c_2333si_900_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/md_01c_2333si_900_vasp.avi}{$\rhd_{\text{remote url}}$}\\\\
+
+ \begin{itemize}
+ \item Inserted C becomes a \hkl<0 0 1> interstitial after a few femto-seconds
+ \item {\color{red}There is a non-zero total momentum!}
+ \item Migration of the C atom not observed
+ \item C \hkl<0 0 1> configuration persists
+ \end{itemize}
+
+ Problem: Thermostat doesn't do momentum correction
+
+ TODO: Start MD using relaxed (at zero temperature) initial configuration
\end{slide}