\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
+ Saddle point configuration check
+ }
+
+ Simulations:
+ \begin{itemize}
+ \item Displacing the C atom in the BC configuration
+ \begin{itemize}
+ \item in \hkl<1 -1 0> direction\\
+ $(0.1240, 0.1240, 0.0409) \rightarrow
+ (0.1340, 0.1140, 0.0409)$
+ \item in \hkl<1 0 0> direction\\
+ $(0.1240, 0.1240, 0.0409) \rightarrow
+ (0.1440, 0.1240, 0.0409)$
+ \end{itemize}
+ \item Full relaxation of the configuration
+ \end{itemize}
+
+ Results:
+ \begin{itemize}
+ \item Both displacement simulations relax to
+ the BC configuration
+ \item Obviously the second derivative with respect to the
+ migration direction is also positive
+ \end{itemize}
+
+ \begin{center}
+ $\Downarrow$\\
+ Bond centered configuration is a
+ {\color{blue}real local minimum}
+ and {\color{red}not} a saddle point configuration
+ \end{center}
+
+\end{slide}
+
\begin{slide}
{\large\bf\boldmath
\begin{slide}
{\large\bf\boldmath
- \hkl<0 0 -1> to \hkl<0 0 1> migration
+ BC to \hkl<0 0 -1> migration
in the $3\times 3\times 3$ Type 2 supercell
}
+ \begin{minipage}{6cm}
+ Method:
+ \begin{itemize}
+ \item Starting configuration:\\
+ C bond centered
+ \item CRT towards \hkl<0 0 -1> configuration
+ \item Spin polarized calculations
+ \end{itemize}
+ Results:\\
+ Video \href{../video/c_im_00-1_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_im_00-1_vasp.avi}{$\rhd_{\text{remote url}}$}
+ \begin{itemize}
+ \item Still abrupt changes in configuration and energy
+ \item Migration barrier $>$ 1 eV
+ \end{itemize}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \includegraphics[width=6cm]{c_im_001_mig_vasp.ps}
+ \includegraphics[width=6cm]{c_im_001_mig_rc_vasp.ps}
+ \end{minipage}
+
\end{slide}
\begin{slide}
in the $3\times 3\times 3$ Type 2 supercell
}
+ \includegraphics[width=6cm]{c_00-1_0-10_mig_vasp.ps}
+ \includegraphics[width=6cm]{c_00-1_0-10_mig_dis_vasp.ps}
+
+ Calculations without spin:\\
+ Video \href{../video/c_00-1_0-10_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_00-1_0-10_vasp.avi}{$\rhd_{\text{remote url}}$} ... WAAAAH!!!
+ \begin{itemize}
+ \item Refined starting from 70\% due to
+ abrubt jumps in energy and configuration
+ \item Displacement from 80 to 85\% disastrous
+ \item Subsequent displacements too large
+ \end{itemize}
+
+ Waiting for spin polarized calculations before deciding what to do ...
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ C \hkl<1 0 0> migration - yet another method!
+ }
+
+ {\color{red}Problem:}
+
+ Abrubt changes in atomic configurations (and energy)
+ in consecutive steps.
+ In addition - sometimes - the final configuration is not obtained!
+
+ {\color{blue}New method:}
+
+ Displace {\color{red}all} atoms towards the final configuration
+ and apply corresponding constraints for each atom.
+
+ Usage:
+ (\href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/sd_rot_all-atoms.patch}{Patch})
+
+\footnotesize
+
+\begin{verbatim}
+cubic diamond
+ 5.48000000000000
+ 2.9909698580839312 0.0039546630279804 -0.0039658085666586
+ 0.0039548953566878 2.9909698596656376 -0.0039660323646892
+ -0.0039680658132861 -0.0039674231313905 2.9909994291263242
+ 216 1
+Transformed selective dynamics
+Direct
+ 0.994174 0.994174 -0.000408732 T F T 45 36.5145
+ 0.182792 0.182792 0.981597 T F T -135 -5.95043
+ ...
+ 0.119896 0.119896 0.0385525 T F T -135 21.8036
+\end{verbatim}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ BC to \hkl<0 0 -1> migration (all atoms CRT)
+ }
+
+ \includegraphics[width=6cm]{im_00-1_nosym_sp_fullct.ps}
+ \includegraphics[width=6cm]{im_00-1_nosym_sp_fullct_rc.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ \hkl<0 0 -1> to \hkl<0 -1 0> migration (all atoms CRT)
+ }
+
+ \includegraphics[width=6cm]{00-1_0-10_nosym_sp_fullct.ps}
+ \includegraphics[width=6cm]{00-1_0-10_nosym_sp_fullct_rc.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ \hkl<0 0 -1> to \hkl<0 -1 0> migration in place (all atoms CRT)
+ }
+
+ \includegraphics[width=6cm]{00-1_ip0-10_nosym_sp_fullct.ps}
+ \includegraphics[width=6cm]{00-1_ip0-10_nosym_sp_fullct_rc.ps}
+
+ in progress ...
+
\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
+ Silicon point defects
+ }
+
+ \begin{minipage}{3.1cm}
+ \underline{\hkl<1 0 0> interstitial}
+ \begin{itemize}
+ \item $E_{\text{f}}=4.41\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/100_2333.eps}\\
+ \end{minipage}
+ \begin{minipage}{3.7cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/100_2333_ksl.ps}\\
+ {\scriptsize \hkl<1 0 0> interstitial}
+ \end{center}
+ \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
+ Carbon point defects in silicon
+ }
+
+ \begin{minipage}{3.2cm}
+ \underline{C bond centered}
+ \begin{itemize}
+ \item $E_{\text{f}}=4.10\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{c_pd_vasp/bc_2333.eps}
+ \underline{\hkl<1 1 0> interstitial}
+ \begin{itemize}
+ \item $E_{\text{f}}=3.60\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{c_pd_vasp/110_2333.eps}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{c_pd_vasp/110_2333_ksl.ps}
+ {\scriptsize \hkl<1 1 0> interstitial}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{c_pd_vasp/bc_2333_ksl.ps}
+ {\scriptsize C bond centered}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Carbon point defects in silicon
+ }
+
+ The hexagonal and tetrahedral C configurations both relax into the
+ \hkl<0 0 1> interstitial configuration!
+
+\end{slide}
+
\begin{slide}
{\large\bf\boldmath
\begin{itemize}
\item Supercell: $3\times 3\times 3$ Type 2
\item Starting configuration: \hkl<0 0 -1> C-Si interstitial
+ ($E_{\text{f}}=3.15\text{ eV}$)
\item Energies: $E_{\text{f}}$ of the interstitial combinations in eV
\end{itemize}
\underline{Along \hkl<1 1 0>:}
- \begin{tabular}{|l|p{1.8cm}|p{1.8cm}|p{1.8cm}|p{1.8cm}|}
+ \begin{tabular}{|l|p{2.0cm}|p{1.8cm}|p{1.8cm}|p{1.8cm}|}
\hline
{\scriptsize
\backslashbox{2nd interstitial}{Distance $[\frac{a}{4}]$}
}
& \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 & 1.39 ($\rightarrow\text{ C}_{\text{S}}$)& 5.81 & 5.47 & 6.50 \\
\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
+ }
+
+ \small
+
+ Initial C \hkl<0 0 -1> insterstital at: $\frac{1}{4}\hkl<1 1 1>$
+
+ {\footnotesize
+ \begin{tabular}{|l|l|l|l|l|l|}
+ \hline
+ & 2 & 3 & 4 & 5 & 6 \\
+ \hline
+C \hkl<0 0 -1> & 6.23/-0.08 & 5.16/-1.15 & 6.23/-0.08 & 6.35/0.04 & 4.65/-1.66\\
+ \hline
+C \hkl<0 0 1> & 6.64/0.34 & 6.31/0.01 & 4.26/-2.05 & 6.57/0.26 & 4.78/-1.53 \\
+ \hline
+C \hkl<1 0 0> & 4.06/-2.25 & 6.13/-0.17 & 6.21/-0.10 & 6.03/-0.27 & 4.93/-1.38 \\
+ \hline
+C \hkl<-1 0 0> & \hkl<0 -1 0> & 4.41/-1.90 & 4.06/-2.25 & 6.19/-0.12 & 4.43/-1.88 \\
+ \hline
+C \hkl<0 1 0> & \hkl<1 0 0> & 5.95/-0.36 & \hkl<-1 0 0> & \hkl<-1 0 0> & \hkl<1 0 0> \\
+ \hline
+C \hkl<0 -1 0> & 3.92/-2.39 & 4.15/-2.16 & \hkl<1 0 0> & \hkl<1 0 0> & \hkl <-1 0 0> \\
+ \hline
+Vacancy & 1.39/-5.39 ($\rightarrow\text{ C}_{\text{S}}$) & 6.19/-0.59 & 3.65/-3.14 & 6.24/-0.54 & 6.50/-0.50 \\
+ \hline
+C$_{\text{sub}}$ & 4.80/0.26 & 4.03/-0.51 & 3.62/-0.93 & 4.39/-0.15 & 5.03/0.49 \\
+\hline
+ \end{tabular}\\[0.2cm]
+ }
+
+ \begin{minipage}{8cm}
+ Energies: $x/y$\\
+ $x$: Defect formation energy of the complex\\
+ $y$:
+ $E_{\text{f}}^{\text{defect combination}}-
+ E_{\text{f}}^{\text{isolated C \hkl<0 0 -1>}}-
+ E_{\text{f}}^{\text{isolated 2nd defect}}
+ $\\[0.3cm]
+ {\color{blue}
+ If $y<0$ $\rightarrow$ favored compared to far-off isolated defects
+ }
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \includegraphics[width=5.0cm]{00-1dc/energy.ps}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: \hkl<0 0 -1>
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/00-1_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/00-1_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/00-1_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/00-1_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/00-1_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_00x.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: \hkl<0 0 1>
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/001_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/001_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/001_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/001_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/001_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_001.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: \hkl<1 0 0> or equivalent one
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_100.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+
+ Type of second defect: \hkl<-1 0 0> or equivalent one
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/0-10_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/-100_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/-100_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/-100_5.eps}
\end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/0-10_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_x00.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: \hkl<0 1 0> or equivalent one
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/010_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/-100_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/-100_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_010.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+
+ Type of second defect: \hkl<0 -1 0> or equivalent one
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/0-10_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/0-10_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/0-10_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_0x0.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: Vacancy
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/vac_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/vac_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/vac_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/vac_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/vac_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_vac.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: C$_{\text{sub}}$
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/csub_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/csub_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/csub_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/csub_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/csub_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_csub.ps}
+
+\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 ...)
+ }
+
+ \small
+
+ \underline{Volume of the MD cell}
+ \begin{itemize}
+ \item $T=450, 900, 1400\text{ K}$ - (no melting, N\underline{V}T!)
+ \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 first 900 K simulations: 5.4705 \AA\\
+ BUT: Better use plain Si lattice constant! (only local distortions)\\
+ $\Rightarrow a(1400\text{ K})=5.4728\text{ \AA}$
+
+ \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, no volume relaxation, scaled volume)
+ \item Use this configuration as the MD initial configuration
+ \end{itemize}
\end{slide}
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}
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