From: hackbard Date: Wed, 8 Jul 2009 13:44:00 +0000 (+0200) Subject: ome silicon point defects calculated X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=fee777e5d2af71751eddd51826ede4945aea40e7;p=lectures%2Flatex.git ome silicon point defects calculated --- diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex index cb717df..e95c0fb 100644 --- a/posic/talks/upb-ua-xc.tex +++ b/posic/talks/upb-ua-xc.tex @@ -330,64 +330,83 @@ POTIM = 0.1 \begin{slide} {\large\bf - Silicon point defects + Cohesive energies } + {\bf\color{red} From now on ...} + + {\small Energies used: free energy without entropy ($\sigma \rightarrow 0$)} + \small - {\color{red}\bf\LARGE - HIER NOCH NICHT LESEN! :)\\ - } - \begin{minipage}{6.5cm} - <110> Si interstitial - \begin{itemize} - \item 2 pc's: - $E_{\textrm{f}}=-5.47342\,\textrm{eV}$ - \item 4 pc's: - $E_{\textrm{f}}=-5.65098\,\textrm{eV}$ - \item 32 pc's: running ... - $E_{\textrm{f}}=\,\textrm{eV}$ - \end{itemize} - \end{minipage} - \begin{minipage}{6.5cm} - plain Si \begin{itemize} - \item 2 pc's: - $E_{\textrm{coh}}=-6.00846\,\textrm{eV}$ - \item 4 pc's: - $E_{\textrm{coh}}=-5.97464\,\textrm{eV}$ - \item 32 pc's: - $E_{\textrm{coh}}=-5.97633\,\textrm{eV}$ - \end{itemize} - \end{minipage}\\[0.2cm] - \begin{minipage}{6.5cm} - hexagonal Si interstitial - \begin{itemize} - \item 2 pc's: - $E_{\textrm{f}}=-5.60654\,\textrm{eV}$ - \item 4 pc's: - $E_{\textrm{f}}=-5.60174\,\textrm{eV}$ - \item 32 pc's: running ... - $E_{\textrm{f}}=\,\textrm{eV}$ - \end{itemize} - tetrahedral Si interstitial - \begin{itemize} - \item 2 pc's: $E_{\textrm{f}}=-5.53623\,\textrm{eV}$ - \item 4 pc's: $E_{\textrm{f}}=-5.64704\,\textrm{eV}$ - \item 32 pc's: $E_{\textrm{f}}=-5.92383\,\textrm{eV}$ + \item $E_{\textrm{free,sp}}$: + energy of spin polarized free atom + \begin{itemize} + \item $k$-points: Monkhorst $1\times 1\times 1$ + \item Symmetry switched off + \item Spin polarized calculation + \item Interpolation formula according to Vosko Wilk and Nusair + for the correlation part of the exchange correlation functional + \item Gaussian smearing for the partial occupancies $f_{nk}$ + ($\sigma=0.05$) + \item Magnetic mixing: AMIX = 0.2, BMIX = 0.0001 + \item Supercell: one atom in cubic + $10\times 10\times 10$ \AA$^3$ box + \end{itemize} + {\color{blue} + $E_{\textrm{free,sp}}(\textrm{Si},250\, \textrm{eV})= + -0.70036911\,\textrm{eV}$ + }, + {\color{gray} + $E_{\textrm{free,sp}}(\textrm{C},xxx\, \textrm{eV})= + yyy\,\textrm{eV}$ + } + \item $E$: + energy (non-polarized) of system of interest composed of\\ + n atoms of type N, m atoms of type M, \ldots \end{itemize} - Si vacancy + \vspace*{0.3cm} + {\color{red} + \[ + \Rightarrow + E_{\textrm{coh}}=\frac{ + -\Big(E(N_nM_m\ldots)-nE_{\textrm{free,sp}}(N)-mE_{\textrm{free,sp}}(M) + -\ldots\Big)} + {n+m+\ldots} + \] + } + +\end{slide} + +\begin{slide} + + {\large\bf + Silicon point defects\\ + } + + \small + + Calculation of formation energy $E_{\textrm{f}}$ \begin{itemize} - \item 2 pc's: $E_{\textrm{f}}=-5.65965\,\textrm{eV}$ - \item 4 pc's: $E_{\textrm{f}}=-5.56361\,\textrm{eV}$ - \item 32 pc's:$E_{\textrm{f}}=-5.92053\,\textrm{eV}$ + \item $E_{\textrm{coh}}^{\textrm{initial conf}}$: + cohesive energy per atom of the initial system + \item $E_{\textrm{coh}}^{\textrm{interstitial conf}}$: + cohesive energy per atom of the interstitial system + \item N: amount of atoms in the interstitial system \end{itemize} - \end{minipage} - \begin{minipage}{6.5cm} + \vspace*{0.2cm} + {\color{blue} + \[ + \Rightarrow + E_{\textrm{f}}=\Big(E_{\textrm{coh}}^{\textrm{interstitial conf}} + -E_{\textrm{coh}}^{\textrm{initial conf}}\Big) N + \] + } + \begin{center} - \includegraphics[width=6.5cm]{si_self_int.ps} + \includegraphics[width=7.0cm]{si_self_int.ps} \end{center} - \end{minipage} \end{slide}