\usepackage{pstricks}
\usepackage{pst-node}
+\usepackage{slashbox}
+
%\usepackage{epic}
%\usepackage{eepic}
}
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 \\
fractional & 0.1547 & 0.1676 \\
in \AA & 0.84 & 0.91 \\
\hline
- \end{tabular}
- \end{minipage}
-
- \begin{center}
- Qualitative {\color{red}and} quantitative {\color{red}difference}!
+ \end{tabular}\\[0.2cm]
+ {\scriptsize\underline{PC (Vasp)}}
+ \includegraphics[width=6.1cm]{c_100_pc_vasp.ps}
\end{center}
+ \end{minipage}
\end{slide}
Again: C \hkl<1 0 0> interstitial migration (VASP)
}
- $\hkl<0 0 -1> \rightarrow \hkl<0 0 1>$ migration:
+ $\hkl<0 0 -1> \rightarrow \hkl<0 0 1>$ migration
+ ($3\times 3\times 3$ Type 2):
\small
Again: C \hkl<1 0 0> interstitial migration (VASP)
}
- $\hkl<0 0 -1> \rightarrow \hkl<0 -1 0>$ migration:
+ $\hkl<0 0 -1> \rightarrow \hkl<0 -1 0>$ migration
+ ($3\times 3\times 3$ Type 2):
\small
\Rightarrow \Delta E_{\text{f}} = E_{\text{mig}} = ?.?? \text{ eV}
\]
- Unexpected \& ({\color{red}more} or {\color{orange}less}) fatal:
+ \vspace*{0.5cm}
+ {\large\bf
+ Intermediate configuration {\color{red}not found} by now!
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ C in Si interstitial configurations (VASP)
+ }
+
+ Check of Kohn-Sham eigenvalues\\
+
+ \small
+
+ \begin{minipage}{6cm}
+ \hkl<1 0 0> interstitial\\
+ \end{minipage}
+ \begin{minipage}{6cm}
+ Saddle point configuration\\
+ \end{minipage}
+ \underline{$4\times 4\times 3$ Type 1 - fixed border atoms}\\
+ \begin{minipage}{6cm}
+385: 4.8567 - 2.00000\\
+386: 4.9510 - 2.00000\\
+387: 5.3437 - 0.00000\\
+388: 5.4930 - 0.00000
+ \end{minipage}
+ \begin{minipage}{6cm}
+385: 4.8694 - 2.00000\\
+386: {\color{red}4.9917} - 1.92603\\
+387: {\color{red}5.1181} - 0.07397\\
+388: 5.4541 - 0.00000
+ \end{minipage}\\[0.2cm]
+ \underline{$4\times 4\times 3$ Type 1 - no constraints}\\
+ \begin{minipage}{6cm}
+385: 4.8586 - 2.00000\\
+386: 4.9458 - 2.00000\\
+387: 5.3358 - 0.00000\\
+388: 5.4915 - 0.00000
+ \end{minipage}
+ \begin{minipage}{6cm}
+385: 4.8693 - 2.00000\\
+386: {\color{red}4.9879} - 1.92065\\
+387: {\color{red}5.1120} - 0.07935\\
+388: 5.4544 - 0.00000
+ \end{minipage}\\[0.2cm]
+ \underline{$3\times 3\times 3$ Type 2 - no constraints}\\
+ \begin{minipage}{6cm}
+433: 4.8054 - 2.00000\\
+434: 4.9027 - 2.00000\\
+435: 5.2543 - 0.00000\\
+436: 5.5718 - 0.00000
+ \end{minipage}
+ \begin{minipage}{6cm}
+433: 4.8160 - 2.00000\\
+434: {\color{green}5.0109} - 1.00264\\
+435: {\color{green}5.0111} - 0.99736\\
+436: 5.5364 - 0.00000
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Once again: C \hkl<1 0 0> interstitial migration (VASP)
+ }
+
+ Method:
\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}$\bullet$}}
+ \item Start in fully relaxed (assumed) saddle point configuration
+ \item Move towards \hkl<1 0 0> configuration using updated values
+ for $\Delta x$, $\Delta y$ and $\Delta z$ (CRT)
+ \item \hkl<1 1 0> constraints applied, 1 Si atom fixed
+ \item $4\times 4\times 3$ Type 1 supercell
\end{itemize}
-
+
+ Results:
+
+ \begin{minipage}{6.2cm}
+ \includegraphics[width=6.0cm]{c_100_110sp-i_vasp.ps}
+ \end{minipage}
+ \begin{minipage}{6.2cm}
+ \includegraphics[width=6.0cm]{c_100_110sp-i_rc_vasp.ps}
+ \end{minipage}
+
+ Reaction coordinate:
+ $r_{i+1}=r_i+\sum_{\text{atoms j}} \left| r_{j,i+1}-r_{j,i} \right|$
+
\end{slide}
\begin{slide}
- {\large\bf
- Molecular dynamics simulations (VASP)
+ {\large\bf\boldmath
+ Investigation of the migration path along \hkl<1 1 0> (VASP)
}
\small
+ \underline{Minimum:}\\
+ \begin{minipage}{4cm}
+ \includegraphics[width=3.5cm]{c_100_mig_vasp/110_c-si_split.eps}
+ \end{minipage}
+ \begin{minipage}{8cm}
+ \begin{itemize}
+ \item Starting conf: 35 \% displacement results (1443)
+ \item \hkl<1 1 0> constraint disabled
+ \end{itemize}
+ \begin{center}
+ $\Downarrow$
+ \end{center}
+ \begin{itemize}
+ \item C-Si \hkl<1 1 0> split interstitial
+ \item Stable configuration
+ \item $E_{\text{f}}=4.13\text{ eV}$
+ \end{itemize}
+ \end{minipage}\\[0.1cm]
+
+ \underline{Maximum:}\\
+ \begin{minipage}{6cm}
+ \begin{center}
+ \includegraphics[width=2.3cm]{c_100_mig_vasp/100-110_01.eps}
+ \includegraphics[width=2.3cm]{c_100_mig_vasp/100-110_02.eps}\\
+ 20 \% $\rightarrow$ 25 \%\\
+ Breaking of Si-C bond
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \includegraphics[width=6.2cm]{c_100_110sp-i_upd_vasp.ps}
+ \end{minipage}
+
\end{slide}
\begin{slide}
- {\large\bf
- Density Functional Theory
+ {\large\bf\boldmath
+ Displacing the \hkl<1 1 0> Si-C split along \hkl<1 -1 0> (VASP)
}
- Hohenberg-Kohn theorem
+ \small
+
+ $4\times 4\times 3$ Type 1 supercell
+
+ \underline{Structures:}
+
+ \begin{minipage}[t]{4.1cm}
+ \includegraphics[height=3.0cm]{c_100_mig_vasp/start.eps}\\
+ \hkl<0 0 -1> dumbbell\\
+ $E_{\text{f}}={\color{orange}3.2254}\text{ eV}$
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \includegraphics[height=3.0cm]{c_100_mig_vasp/110_c-si_split.eps}\\
+ Assumed \hkl<1 1 0> C-Si split\\
+ $E_{\text{f}}=4.1314\text{ eV}$
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \includegraphics[height=3.0cm]{c_100_mig_vasp/110_dis_0-10.eps}\\
+ First guess: \hkl<0 -1 0> dumbbell\\
+ {\color{red}but:} $E_{\text{f}}={\color{orange}2.8924}\text{ eV}$\\
+ Third bond missing!
+ \end{minipage}\\
+
+ \underline{Occupancies:}
+
+ \scriptsize
+
+ \begin{minipage}{4.1cm}
+385: 4.8586 - 2.00000\\
+386: 4.9458 - 2.00000\\
+387: 5.3358 - 0.00000\\
+388: 5.4915 - 0.00000
+\hfill
+ \end{minipage}
+ \begin{minipage}{4.1cm}
+385: 4.7790 - 2.00000\\
+386: 4.8797 - 1.99964\\
+387: 5.1321 - 0.00036\\
+388: 5.4711 - 0.00000
+\hfill
+ \end{minipage}
+ \begin{minipage}{4.1cm}
+385: 4.7670 - 2.00000\\
+386: 4.9190 - 2.00000\\
+387: 5.2886 - 0.00000\\
+388: 5.4849 - 0.00000
+\hfill
+ \end{minipage}\\
+
+\small
+
+ \begin{center}
+ {\color{red}? ! ? ! ? ! ? ! ?}
+ \end{center}
+
+\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
+ Defect configurations in $4\times 4\times 3$ Type 1 supercells revisited
+ }
+
+ \footnotesize
+
+ \begin{tabular}{l|p{2.5cm}|p{2.5cm}|p{4cm}|}
+ & \hkl<0 0 -1> interstitial
+ & local minimum\newline
+ \hkl<1 1 0> C-Si split
+ & intermediate configuration\newline
+ (bond centered conf)\\
+ \hline
+ default & $E_{\text{f}}=3.3254\text{ eV}$\newline
+ {\tiny
+ 386: 4.9458 - 2.00000\newline
+ 387: 5.3358 - 0.00000}
+ & $E_{\text{f}}=4.1314\text{ eV}$\newline
+ {\tiny
+ 386: 4.8797 - 1.99964\newline
+ 387: 5.1321 - 0.00036}
+ & $E_{\text{f}}=4.2434\text{ eV}$\newline
+ {\tiny
+ 386: 4.9879 - 1.92065\newline
+ 387: 5.1120 - 0.07935} \\
+ \hline
+ No symmetry & $E_{\text{f}}=3.3154\text{ eV}$\newline
+ {\tiny
+ 386: 4.9456 - 2.00000\newline
+ 387: 5.3366 - 0.00000}
+ & $E_{\text{f}}=4.1314\text{ eV}$\newline
+ {\tiny
+ 386: 4.8798 - 1.99961\newline
+ 387: 5.1307 - 0.00039}
+ & $E_{\text{f}}=4.2454\text{ eV}$\newline
+ {\tiny
+ 386: 4.9841 - 1.92147\newline
+ 387: 5.1085 - 0.07853} \\
+ \hline
+ $+$ spin polarized & $E_{\text{f}}=3.3154\text{ eV}$\newline
+ {\tiny
+ {\color{blue}
+ 386: 4.9449 - 1.00000\newline
+ 387: 5.3365 - 0.00000\newline%
+ }%
+ {\color{green}%
+ 386: 4.9449 - 1.00000\newline
+ 387: 5.3365 - 0.00000}}
+ & $E_{\text{f}}={\color{red}4.1314}\text{ eV}$\newline
+ {\tiny
+ {\color{blue}
+ 386: 4.8799 - 0.99980\newline
+ 387: 5.1307 - 0.00020\newline%
+ }%
+ {\color{green}%
+ 386: 4.8799 - 0.99980\newline
+ 387: 5.1306 - 0.00020}}
+ & $E_{\text{f}}=4.0254\text{ eV}$\newline
+ {\tiny
+ {\color{blue}
+ 387: 4.8581 - 1.00000\newline
+ 388: 5.4662 - 0.00000\newline%
+ }%
+ {\color{green}%
+ 385: 4.8620 - 1.00000\newline
+ 386: 5.2951 - 0.00000}} \\
+ \hline
+ $+$ spin difference 2 & $E_{\text{f}}=3.6394\text{ eV}$\newline
+ {\tiny
+ {\color{blue}
+ 387: 5.2704 - 0.99891\newline
+ 388: 5.4886 - 0.00095\newline
+ 389: 5.5094 - 0.00011\newline
+ 390: 5.5206 - 0.00003\newline%
+ }%
+ {\color{green}%
+ 385: 4.8565 - 0.98603\newline
+ 386: 5.0119 - 0.01397}}
+ & Relaxation into\newline
+ bond centered\newline
+ configuration\newline
+ $\rightarrow$
+ & $E_{\text{f}}=4.0254\text{ eV}$\newline
+ {\tiny
+ {\color{blue}
+ 387: 4.8578 - 1.00000\newline
+ 388: 5.4661 - 0.00000\newline%
+ }%
+ {\color{green}%
+ 385: 4.8618 - 1.00000\newline
+ 386: 5.2950 - 0.00000}} \\
+ \hline
+ \end{tabular}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Defect configurations in $3\times 3\times 3$ Type 2 supercells revisited\\
+ }
+
+ \footnotesize
+
+ \begin{tabular}{l|p{2.5cm}|p{2.5cm}|p{4cm}|}
+ & \hkl<0 0 -1> interstitial
+ & local minimum\newline
+ \hkl<1 1 0> C-Si split
+ & intermediate configuration\newline
+ (bond centered conf)\\
+ \hline
+ default & $E_{\text{f}}=3.15407\text{ eV}$\newline
+ {\tiny
+ 434: 4.9027 - 2.00000\newline
+ 435: 5.2543 - 0.00000}
+ & $E_{\text{f}}=??\text{ eV}$\newline
+ {\tiny
+ ??\newline
+ ??}
+ & $E_{\text{f}}=4.40907\text{ eV}$\newline
+ {\tiny
+ 434: 5.0109 - 1.00264\newline
+ 435: 5.0111 - 0.99736}\\
+ \hline
+ No symmetry & $E_{\text{f}}=3.16107\text{ eV}$\newline
+ {\tiny
+ 434: 4.9032 - 2.00000\newline
+ 435: 5.2547 - 0.00000}
+ & $E_{\text{f}}=??\text{ eV}$\newline
+ {\tiny
+ ??\newline
+ ??}
+ & $E_{\text{f}}=4.41507\text{ eV}$\newline
+ {\tiny
+ 434: 5.0113 - 1.00140\newline
+ 435: 5.0114 - 0.99860} \\
+ \hline
+ $+$ spin polarized & $E_{\text{f}}=3.16107\text{ eV}$\newline
+ {\tiny
+ {\color{blue}
+ 434: 4.9033 - 1.00000\newline
+ 435: 5.2544 - 0.00000\newline%
+ }%
+ {\color{green}%
+ 434: 4.9035 - 1.00000\newline
+ 435: 5.2550 - 0.00000}}
+ & $E_{\text{f}}=??\text{ eV}$\newline
+ {\tiny
+ {\color{blue}
+ ??\newline
+ ??\newline%
+ }%
+ {\color{green}%
+ ??\newline
+ ??}}
+ & $E_{\text{f}}=4.10307\text{ eV}$\newline
+ {\tiny
+ {\color{blue}
+ 435: 4.8118 - 1.00000\newline
+ 436: 5.5360 - 0.00000\newline%
+ }%
+ {\color{green}%
+ 433: 4.8151 - 1.00000\newline
+ 434: 5.3475 - 0.00000}} \\
+ \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}
+
+ {\large\bf\boldmath
+ 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}
+ \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
+ 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
+ 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}
+
+ {\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}
+ \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}
+
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ TODO: introduce some Si self-interstitials and C interstitials before\\
+ BUT: Concentrate on 100 C interstitial combinations and 100 C + vacancy\\
+
+ Agglomeration of 100 defects energetically favorable?
+
+\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
+ Combination of defects
+ }
+
+ \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{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> & 6.23\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<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> & 3.92 & 4.43 & 6.02 & 6.02 \\
+ \hline
+ Vacancy & 1.39 ($\rightarrow\text{ C}_{\text{S}}$)& 5.81 & 5.47 & 6.50 \\
+ \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
+ }
+
+ \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}
+
+\begin{slide}
+
+ {\large\bf
+ Molecular dynamics simulations (VASP)
+ }
+
+ 2 C atoms in $2\times 2\times 2$ Type 2 supercell at $450\,^{\circ}\text{C}$
+
+ \small
+
+ \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}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Molecular dynamics simulations (VASP)
+ }
+
+ 10 C atoms in $3\times 3\times 3$ Type 2 supercell at $450\,^{\circ}\text{C}$
+
+ \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}
+
+\begin{slide}
+
+ {\large\bf
+ Molecular dynamics simulations (VASP)
+ }
+
+ 1 C atom in $3\times 3\times 3$ Type 2 supercell at $900\,^{\circ}\text{C}$\\\\
+
+ 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}
+
+\begin{slide}
+
+ {\large\bf
+ Molecular dynamics simulations (VASP)
+ }
+
+ 10 C atoms in $3\times 3\times 3$ Type 2 supercell at $900\,^{\circ}\text{C}$
+
+ in progress ...
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Density Functional Theory
+ }
+
+ Hohenberg-Kohn theorem
+
+ \small
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ More theory ...
+ }
+
+ Transition state theory\\
+ ART,NEB ...
+
+ Group theory
+
+ \small
+
+\end{slide}
+
+\end{document}
\end{document}
projects / lectures / latex.git / blobdiff