\end{slide}
+\begin{slide}
+
+ {\large\bf\boldmath
+ C \hkl<1 0 0> interstitial migration (VASP)
+ }
+
+ \small
+
+ \begin{minipage}{6.2cm}
+ \begin{itemize}
+ \item $3\times 3\times 3$ Type 2 supercell
+ \item \hkl<1 1 0> constraints applied
+ (\href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/sd_rot.patch}{Patch})
+ \item Move from \hkl<1 0 0> towards\\
+ bond centered configuration
+ \end{itemize}
+ \underline{Sd Rot usage (POSCAR):}
+\begin{verbatim}
+cubic diamond
+5.480
+ 3.0 0.0 0.0
+ 0.0 3.0 0.0
+ 0.0 0.0 3.0
+216 1
+Transformed selective dynamics
+45.0 0.0
+Direct
+ ...
+\end{verbatim}
+Only works in direct mode!\\
+$z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
+ \end{minipage}
+ \begin{minipage}{6.2cm}
+ \includegraphics[width=5cm]{c_100_110sp-i_2333_vasp.ps}
+ \includegraphics[width=5cm]{c_100_110sp-i_2333_rc_vasp.ps}\\
+ {\color{red}One fixed Si atom not enough!}\\
+ Video: \href{../video/c_in_si_233_110mig_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_233_110mig_vasp.avi}{$\rhd_{\text{remote url}}$}\\
+ \end{minipage}
+
+ {\color{blue}
+ Next: Migration calculation in 2333 using CRT
+ (\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1> and \hkl<0 -1 0>)
+ }
+
+\end{slide}
+
\begin{slide}
{\large\bf\boldmath
\begin{slide}
{\large\bf\boldmath
- C \hkl<1 0 0> interstitial migration (VASP)
- }
-
- \small
-
- \begin{minipage}{6.2cm}
- \begin{itemize}
- \item $3\times 3\times 3$ Type 2 supercell
- \item \hkl<1 1 0> constraints applied
- (\href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/sd_rot.patch}{Patch})
- \item Move from \hkl<1 0 0> towards\\
- bond centered configuration
- \end{itemize}
- \underline{Sd Rot usage (POSCAR):}
-\begin{verbatim}
-cubic diamond
-5.480
- 3.0 0.0 0.0
- 0.0 3.0 0.0
- 0.0 0.0 3.0
-216 1
-Transformed selective dynamics
-45.0 0.0
-Direct
- ...
-\end{verbatim}
-Only works in direct mode!\\
-$z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
- \end{minipage}
- \begin{minipage}{6.2cm}
- \includegraphics[width=6cm]{c_100_110sp-i_2333_vasp.ps}
- \includegraphics[width=6cm]{c_100_110sp-i_2333_rc_vasp.ps}
- \end{minipage}
-
- {\color{blue}
- Next: Migration calculation in 2333 using CRT
- (\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1> and \hkl<0 -1 0>)
- }
-
-\end{slide}
-
-\begin{slide}
-
- {\large\bf\boldmath
- \hkl<0 0 -1> to \hkl <0 0 1> migration
- in the $3\times 3\times 3$ Type 2 supercell
- }
-
-\end{slide}
-
-\begin{slide}
-
- {\large\bf\boldmath
- \hkl<0 0 -1> to \hkl <0 -1 0> migration
- in the $3\times 3\times 3$ Type 2 supercell
- }
-
-\end{slide}
-
-\begin{slide}
-
- {\large\bf\boldmath
- Defect configurations in $3\times 3\times 3$ Type 2 supercells revisited
+ Defect configurations in $3\times 3\times 3$ Type 2 supercells revisited\\
}
\footnotesize
434: 5.0113 - 1.00140\newline
435: 5.0114 - 0.99860} \\
\hline
- $+$ spin polarized & $E_{\text{f}}=??\text{ eV}$\newline
+ $+$ spin polarized & $E_{\text{f}}=3.16107\text{ eV}$\newline
{\tiny
{\color{blue}
- ??\newline
- ??\newline%
+ 434: 4.9033 - 1.00000\newline
+ 435: 5.2544 - 0.00000\newline%
}%
{\color{green}%
- ??\newline
- ??}}
- & $E_{\text{f}}={\color{red}??}\text{ eV}$\newline
+ 434: 4.9035 - 1.00000\newline
+ 435: 5.2550 - 0.00000}}
+ & $E_{\text{f}}=??\text{ eV}$\newline
{\tiny
{\color{blue}
??\newline
\hline
\end{tabular}
+ \normalsize
+
+ \vspace*{0.3cm}
+
+ {\color{blue}Tracer:}\\
+ Smearing of electrons over two or more (degenerated) energy levels\\
+ $\Rightarrow$ use spin polarized calculations!
+
\end{slide}
\begin{slide}
Bond centered configuration revisited ($3\times 3\times 3$ Type 2)
}
+ Spin polarized calculations
+
+ {\small
+ \begin{minipage}[t]{5.8cm}
+ \underline{Kohn-Sham eigenvalues}\\
+ \begin{minipage}{2.8cm}
+ Spin up:\\
+ 430: 4.2639 - 1\newline
+ 431: 4.7332 - 1\newline
+ 432: 4.7354 - 1\newline
+ 433: 4.7700 - 1\newline
+ 434: 4.8116 - 1\newline
+ 435: 4.8118 - 1\newline
+ 436: 5.5360 - 0\newline
+ 437: 5.5623 - 0
+ \end{minipage}
+ \begin{minipage}{2.8cm}
+ Spin down:\\
+ 430: 4.2682 - 1\newline
+ 431: 4.7738 - 1\newline
+ 432: 4.8150 - 1\newline
+ 433: 4.8151 - 1\newline
+ 434: 5.3475 - 0\newline
+ 435: 5.3476 - 0\newline
+ 436: 5.5455 - 0\newline
+ 437: 5.5652 - 0
+ \end{minipage}\\[0.3cm]
+ \begin{itemize}
+ \item linear Si-C-Si bond
+ \item Each Si has another 3 Si neighbours
+ \end{itemize}
+ \begin{center}
+ {\color{blue}Spin polarized calculations necessary!}\\[0.3cm]
+ \end{center}
+ {\scriptsize Charge density isosurface of
+ {\color{gray}spin up}, {\color{green}spin down} and
+ the {\color{blue}resulting spin up} electrons.\\
+ Two {\color{yellow} Si} atoms and one {\color{red}C}
+ atom are shown.
+ }
+ \end{minipage}
+ \begin{minipage}[t]{6.5cm}
+ \underline{MO diagram}\\
+ \begin{minipage}[t]{1.2cm}
+ {\color{red}Si}\\
+ {\tiny sp$^3$}\\[0.8cm]
+ \underline{${\color{red}\uparrow}$}
+ \underline{${\color{red}\uparrow}$}
+ \underline{${\color{red}\uparrow}$}
+ \underline{${\color{red}\uparrow}$}\\
+ sp$^3$
+ \end{minipage}
+ \begin{minipage}[t]{1.4cm}
+ \begin{center}
+ {\color{red}M}{\color{blue}O}\\[1.0cm]
+ \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+ $\sigma_{\text{ab}}$\\[0.5cm]
+ \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+ $\sigma_{\text{b}}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{1.0cm}
+ \begin{center}
+ {\color{blue}C}\\
+ {\tiny sp}\\[0.2cm]
+ \underline{${\color{white}\uparrow\uparrow}$}
+ \underline{${\color{white}\uparrow\uparrow}$}\\
+ 2p\\[0.4cm]
+ \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
+ \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
+ sp
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{1.4cm}
+ \begin{center}
+ {\color{blue}M}{\color{green}O}\\[1.0cm]
+ \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+ $\sigma_{\text{ab}}$\\[0.5cm]
+ \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
+ $\sigma_{\text{b}}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{1.2cm}
+ \begin{flushright}
+ {\color{green}Si}\\
+ {\tiny sp$^3$}\\[0.8cm]
+ \underline{${\color{green}\uparrow}$}
+ \underline{${\color{green}\uparrow}$}
+ \underline{${\color{green}\uparrow}$}
+ \underline{${\color{green}\uparrow}$}\\
+ sp$^3$
+ \end{flushright}
+ \end{minipage}\\[0.4cm]
+ \begin{flushright}
+ \includegraphics[width=6cm]{c_100_mig_vasp/im_spin_diff.eps}
+ \end{flushright}
+ \end{minipage}
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ \hkl<0 0 -1> configuration revisited ($3\times 3\times 3$ Type 2)
+ }
+
+ Spin polarized calculations
+
+ {\small
+ \begin{minipage}[t]{5.8cm}
+ \underline{Kohn-Sham eigenvalues}\\
+ \begin{minipage}{2.8cm}
+ Spin up:\\
+ 430: 4.3317 - 1\newline
+ 431: 4.7418 - 1\newline
+ 432: 4.8014 - 1\newline
+ 433: 4.8060 - 1\newline
+ 434: 4.9033 - 1\newline
+ 435: 5.2544 - 0\newline
+ 436: 5.5723 - 0\newline
+ 437: 5.5848 - 0
+ \end{minipage}
+ \begin{minipage}{2.8cm}
+ Spin down:\\
+ 430: 4.3317 - 1\newline
+ 431: 4.7420 - 1\newline
+ 432: 4.8013 - 1\newline
+ 433: 4.8059 - 1\newline
+ 434: 4.9035 - 1\newline
+ 435: 5.2550 - 0\newline
+ 436: 5.5724 - 0\newline
+ 437: 5.5846 - 0
+ \end{minipage}
+ \end{minipage}
+ \begin{minipage}[t]{6.5cm}
+ \underline{MO diagram}\\
+ \begin{minipage}[t]{1.2cm}
+ {\color{red}Si}\\
+ {\tiny sp$^2$}\\[0.1cm]
+ \underline{${\color{white}\uparrow}$}\\
+ p\\[0.4cm]
+ \underline{${\color{red}\uparrow\downarrow}$}
+ \underline{${\color{red}\uparrow}{\color{white}\downarrow}$}
+ \underline{${\color{red}\uparrow}{\color{white}\downarrow}$}\\
+ sp$^2$
+ \end{minipage}
+ \begin{minipage}[t]{1.2cm}
+ \begin{flushright}
+ {\color{red}M}\\[1.0cm]
+ \underline{${\color{white}\uparrow}{\color{white}\downarrow}$}\\
+ $\sigma_{\text{ab}}$\\[0.5cm]
+ \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+ $\sigma_{\text{b}}$
+ \end{flushright}
+ \end{minipage}
+ \begin{minipage}[t]{1.2cm}
+ \begin{flushleft}
+ {\color{blue}O}\\[0.4cm]
+ \underline{${\color{white}\uparrow}{\color{white}\downarrow}$}\\
+ $\pi_{\text{ab}}$\\[0.5cm]
+ \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+ $\pi_{\text{b}}$
+ \end{flushleft}
+ \end{minipage}
+ \begin{minipage}[t]{2.0cm}
+ \begin{center}
+ {\color{blue}C}\\
+ {\tiny sp$^2$}\\[0.5cm]
+ \underline{${\color{white}\uparrow\uparrow}$}\\
+ p\\[0.4cm]
+ \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
+ \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}
+ \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+ sp$^2$
+ \end{center}
+ \end{minipage}
+ \end{minipage}
+ }
+
+ \vspace*{0.4cm}
+
+ \begin{itemize}
+ \item Si-C double bond
+ \item Si and C atom have another 2 Si neighbours
+ \end{itemize}
+
+ \begin{center}
+ {\color{blue}Spin polarized calculations {\color{red}not} necessary!}
+ \end{center}
+
+\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}
- Besetzungen hier rein ... Netto Spin 2 ...
+ \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
+ New default parameter set\\[1cm]
+ }
+
+ Since some defect configurations need spin polarized calculations ...\\[1cm]
+
+ from now on the default parameter set\\
+ {\bf\color{blue}
+ $+$ no symmetry\\
+ $+$ spin polarized\\
+ }
+ \ldots is used!\\[1cm]
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ \hkl<0 0 -1> to \hkl<0 0 1> migration
+ in the $3\times 3\times 3$ Type 2 supercell
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ \hkl<0 0 -1> to \hkl<0 -1 0> migration
+ 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}
{\large\bf\boldmath
\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
\underline{Along \hkl<1 1 0>:}
- \begin{tabular}{|l|l|l|l|l|}
+ \begin{tabular}{|l|p{1.8cm}|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 & 4.65014 & - & -\\
+ \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} \\
\hline
- \hkl<0 0 1> & - & - & 6.53614 & - \\
+ \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} \\
\hline
- \hkl<1 0 0>, \hkl<0 1 0> & & & &\\
+ \hkl<1 0 0>, \hkl<0 1 0> & 4.07014\newline alkmene
+ & 4.93814
+ & 5.72914
+ & 6.00214\\
\hline
- \hkl<-1 0 0>, \hkl<0 -1 0> & & & &\\
+ \hkl<-1 0 0>, \hkl<0 -1 0> & 3.93014 & 4.43414 & 6.02814 & 6.02414 \\
\hline
\end{tabular}
+
+ Spin polarized and {\color{blue}non spin polarized} results
+
+\end{slide}
+
+\begin{slide}
+
+ \begin{minipage}{5cm}
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ \scriptsize
+
+ Initial insterstital at: $\frac{1}{4}\hkl<1 1 1>$
+
+ Relative silicon neighbour positions:
+ \begin{enumerate}
+ \item The dumbbell Si
+ \item $\frac{1}{4}\hkl<1 1 -1>$, $\frac{1}{4}\hkl<-1 -1 -1>$
+ \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 $\frac{1}{4}\hkl<-1 1 -3>$, $\frac{1}{4}\hkl<1 -1 -3>$
+ \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 $\frac{1}{4}\hkl<-1 3 -1>$, $\frac{1}{4}\hkl<1 -3 -1>$,
+ $\frac{1}{4}\hkl<3 -1 -1>$. $\frac{1}{4}\hkl<-3 1 -1>$
+ \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 $\frac{1}{4}\hkl<-1 -3 1>$, $\frac{1}{4}\hkl<-3 -1 1>$,
+ $\frac{1}{4}\hkl<1 3 1>$, $\frac{1}{4}\hkl<3 1 1>$
+ \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 $\frac{1}{4}\hkl<1 1 3>$, $\frac{1}{4}\hkl<-1 -1 3>$
+ \item $\frac{1}{4}\hkl<3 3 -1>$, $\frac{1}{4}\hkl<-3 -3 -1>$
+ \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=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|}
+ \hline
+ & 2 & 3 & 4 \\
+ \hline
+\hkl<0 0 -1> & 6.23 & 5.16 & 6.23 \\
+ \hline
+\hkl<0 0 1> & 6.64 & 6.31 & ... \\
+ \hline
+\hkl<1 0 0> & 4.06 & 6.13 & ... \\
+ \hline
+\hkl<-1 0 0> & as \hkl<0 -1 0> & 4.41 & ... \\
+ \hline
+\hkl<0 1 0> & as \hkl<1 0 0> & 5.95 & as \hkl<-1 0 0> \\
+ \hline
+\hkl<0 -1 0> & 3.92 & ... & as \hkl<1 0 0>\\
+ \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}
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}
\end{slide}
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