X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fupb-ua-xc.tex;h=a272ffdac1de05ff2bf47b8245a4bbbcac8d28f7;hb=880774319bbac42a2b88d07fb199c8b79d4aa781;hp=1302f66e5016d46c8cb5512169f606b8b10c81a9;hpb=888ce61b2a7c6472a2baca35e100063d55259510;p=lectures%2Flatex.git diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex index 1302f66..a272ffd 100644 --- a/posic/talks/upb-ua-xc.tex +++ b/posic/talks/upb-ua-xc.tex @@ -1914,6 +1914,27 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ \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 @@ -1934,10 +1955,31 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ \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} @@ -1948,6 +1990,19 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ } \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} @@ -1964,6 +2019,168 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ \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 + 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 @@ -1973,34 +2190,37 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ \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> & 6.65114\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<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> & 4.07014\newline alkmene - & 4.93814 - & 5.72914 - & 6.00214\\ + \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> & 3.93014 & 4.43414 & 6.02814 & 6.02414 \\ + \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} @@ -2057,6 +2277,311 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ \end{slide} +\begin{slide} + + {\large\bf\boldmath + Combination of defects + } + + \small + + Initial C \hkl<0 0 -1> insterstital at: $\frac{1}{4}\hkl<1 1 1>$ + + \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 + \end{tabular}\\[0.2cm] + 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}} + $\\ + That is: If $y<0$ $\rightarrow$ favored compared to far-off isolated defects + +\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} + + 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} + +\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} + + 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} + +\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} + + 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} + +\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} + + Type of second defect: C Substitutional + + TODO ... + +\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 @@ -2122,9 +2647,21 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ 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}