more c_i c_i interaction

diff --git a/posic/publications/defect_combos.tex b/posic/publications/defect_combos.tex
index 0cfc29f..fc55378 100644 (file)
--- a/posic/publications/defect_combos.tex
+++ b/posic/publications/defect_combos.tex
@@ -50,7 +50,7 @@ However, in another IBS study Nejim et al. propose a topotactic transformation r
 Solving this controversy and understanding the effective underlying processes will enable significant technological progress in 3C-SiC thin film formation driving the superior polytype for potential applications in high-performance electronic device production\cite{wesch96}.\r
 \r
 Atomistic simulations offer a powerful tool of investigation providing detailed insight not accessible by experiment.\r
 Solving this controversy and understanding the effective underlying processes will enable significant technological progress in 3C-SiC thin film formation driving the superior polytype for potential applications in high-performance electronic device production\cite{wesch96}.\r
 \r
 Atomistic simulations offer a powerful tool of investigation providing detailed insight not accessible by experiment.\r

-A lot of theoretical work has been done on intrinsic point defects in Si\cite{bar-yam84,bar-yam84_2,car84,batra87,bloechl93,tang97,leung99,colombo02,goedecker02,al-mushadani03,posselt08,ma10}, threshold displacement energies in Si\cite{mazzarolo01,holmstroem08} important in ion implantation, C defects and defect reactions in Si\cite{tersoff90,dal_pino93,capaz94,burnard93,leary97,capaz98,zhu98,mattoni2002,park02,jones04}, the SiC/Si interface\cite{chirita97,kitabatake93,cicero02,pizzagalli03} and defects in SiC\cite{bockstedte03,rauls03a,gao04,posselt06,gao07}.\r
+A lot of theoretical work has been done on intrinsic point defects in Si\cite{bar-yam84,bar-yam84_2,car84,batra87,bloechl93,tang97,leung99,colombo02,goedecker02,al-mushadani03,hobler05,posselt08,ma10}, threshold displacement energies in Si\cite{mazzarolo01,holmstroem08} important in ion implantation, C defects and defect reactions in Si\cite{tersoff90,dal_pino93,capaz94,burnard93,leary97,capaz98,zhu98,mattoni2002,park02,jones04}, the SiC/Si interface\cite{chirita97,kitabatake93,cicero02,pizzagalli03} and defects in SiC\cite{bockstedte03,rauls03a,gao04,posselt06,gao07}.\r

 However, none of the mentioned studies consistently investigates entirely the relevant defect structures and reactions concentrated on the specific problem of 3C-SiC formation in C implanted Si.\r
 % but mattoni2002 actually did a lot. maybe this should be mentioned!\r
 In fact, in a combined analytical potential molecular dynamics and ab initio study\cite{mattoni2002} the interaction of substitutional C with Si self-interstitials and C interstitials is evaluated.\r
 However, none of the mentioned studies consistently investigates entirely the relevant defect structures and reactions concentrated on the specific problem of 3C-SiC formation in C implanted Si.\r
 % but mattoni2002 actually did a lot. maybe this should be mentioned!\r
 In fact, in a combined analytical potential molecular dynamics and ab initio study\cite{mattoni2002} the interaction of substitutional C with Si self-interstitials and C interstitials is evaluated.\r


@@ -163,7 +163,7 @@ However, to our best knowledge, no energy of formation for this type of defect b
 Instead, Capaz et al.\cite{capaz94}, investigating migration pathways of the C$_{\text{i}}$ $\langle 1 0 0 \rangle$ DB, find this defect to be \unit[2.1]{eV} lower in energy than the bond-centered (BC) configuration, which is claimed to constitute a saddle point configuration in the migration path within the $(1 1 0)$ plane and, thus, interpreted as the barrier of migration for the respective path.\r
 However, the present study indicates a local minimum state for the BC defect if spin polarized calculations are performed resulting in a net magnetization of two electrons localized in a torus around the C atom.\r
 Another DFT calculation without fully accounting for the electron spin results in the smearing of a single electron over two non-degenerate Kohn-Sham states and an increase of the total energy by \unit[0.3]{eV} for the BC configuration.\r
 Instead, Capaz et al.\cite{capaz94}, investigating migration pathways of the C$_{\text{i}}$ $\langle 1 0 0 \rangle$ DB, find this defect to be \unit[2.1]{eV} lower in energy than the bond-centered (BC) configuration, which is claimed to constitute a saddle point configuration in the migration path within the $(1 1 0)$ plane and, thus, interpreted as the barrier of migration for the respective path.\r
 However, the present study indicates a local minimum state for the BC defect if spin polarized calculations are performed resulting in a net magnetization of two electrons localized in a torus around the C atom.\r
 Another DFT calculation without fully accounting for the electron spin results in the smearing of a single electron over two non-degenerate Kohn-Sham states and an increase of the total energy by \unit[0.3]{eV} for the BC configuration.\r

-Regardless of the rather small correction due to the spin, the difference we found is much smaller (\unit[0.9]{eV}), which would nicely compare to experimental findings $(\unit[0.73-0.87]{eV})$\cite{tipping87,song90} for the migration barrier.\r
+Regardless of the rather small correction due to the spin, the difference we found is much smaller (\unit[0.9]{eV}), which would nicely compare to experimental findings $(\unit[0.70-0.87]{eV})$\cite{lindner06,tipping87,song90} for the migration barrier.\r

 However, since the BC configuration constitutes a real local minimum another barrier exists which is about \unit[1.2]{eV} ($\unit[0.9]{eV}+\unit[0.3]{eV}$) in height.\r
 Indeed Capaz et al. propose another path and find it to be the lowest in energy\cite{capaz94}, in which a C$_{\text{i}}$ $\langle 0 0 -1\rangle$ DB migrates into a C$_{\text{i}}$ $\langle 0 -1 0\rangle$ DB located at the next neighboured Si lattice site in $[1 1 -1]$ direction.\r
 Calculations in this work reinforce this path by an additional improvement of the quantitative conformance of the barrier height (\unit[0.9]{eV}) to experimental values.\r
 However, since the BC configuration constitutes a real local minimum another barrier exists which is about \unit[1.2]{eV} ($\unit[0.9]{eV}+\unit[0.3]{eV}$) in height.\r
 Indeed Capaz et al. propose another path and find it to be the lowest in energy\cite{capaz94}, in which a C$_{\text{i}}$ $\langle 0 0 -1\rangle$ DB migrates into a C$_{\text{i}}$ $\langle 0 -1 0\rangle$ DB located at the next neighboured Si lattice site in $[1 1 -1]$ direction.\r
 Calculations in this work reinforce this path by an additional improvement of the quantitative conformance of the barrier height (\unit[0.9]{eV}) to experimental values.\r


@@ -241,10 +241,10 @@ C-C distance [nm] & 0.14 & 0.46 & 0.65 & 0.86 & 1.05 & 1.08
 The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:dc_110}\r
 \begin{figure}\r
 \includegraphics[width=\columnwidth]{db_along_110_cc_n.ps}\r
 The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:dc_110}\r
 \begin{figure}\r
 \includegraphics[width=\columnwidth]{db_along_110_cc_n.ps}\r

-\caption{Minimum binding energy of dumbbell combinations separated along $\langle 1 1 0\rangle$ with respect to the C-C distance.}\r
+\caption{Minimum binding energy of dumbbell combinations separated along $\langle 1 1 0\rangle$ with respect to the C-C distance. The blue line is a guide for the eye and the green curve corresponds to the most suitable fit function consisting of all but the first data point.}\r

 \label{fig:dc_110}\r
 \end{figure}\r
 \label{fig:dc_110}\r
 \end{figure}\r

-\r
+The interaction is found to be proportional to the reciprocal cube of the C-C distance for extended separeations of the C$_{\text{i}}$ and saturates for the smallest possible separation, i.e. the ground state configuration.\r

 \r
 \r
 \subsection{C$_I$ next to C$_{\text{s}}$}\r
 \r
 \r
 \subsection{C$_I$ next to C$_{\text{s}}$}\r