nearly finihsed si_i c_s ... restructure possibly necessary

diff --git a/posic/publications/defect_combos.tex b/posic/publications/defect_combos.tex
index 009220897d9e78c1dc576f604a9d65d0c864f66f..3440103188de2b01a807f39af818a0b57548844e 100644 (file)
--- a/posic/publications/defect_combos.tex
+++ b/posic/publications/defect_combos.tex
@@ -161,7 +161,7 @@ Instead, Capaz et al.\cite{capaz94}, investigating migration pathways of the C$_
 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 $(\unit[0.70-0.87]{eV})$\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
+However, since the BC configuration constitutes a real local minimum another barrier exists which is about \unit[1.2]{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$_{\text{i}}$ \hkl[0 0 -1] DB migrates into a C$_{\text{i}}$ \hkl[0 -1 0] DB located at the next neighbored Si lattice site in \hkl[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
 A more detailed description can be found in a previous study\cite{zirkelbach10a}.\r
@@ -447,18 +447,39 @@ $E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.3
 $E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\\r
 $r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\\r
 \end{tabular}\r
-\caption{Formation energies $E_{\text{f}}$, binding energies $E_{\text{b}}$ and C$_{\text{s}}$-Si$_{\text{i}}$ separation distances of the combinational C$_{\text{s}}$ and Si$_{\text{i}}$ configurations as defined in table \ref{table:dc_si-s}. Energies are given in eV while the separation is given in nm.}\r
+\caption{Formation energies $E_{\text{f}}$, binding energies $E_{\text{b}}$ and C$_{\text{s}}$-Si$_{\text{i}}$ separation distances of the combinational C$_{\text{s}}$ and Si$_{\text{i}}$ configurations as defined in Table~\ref{table:dc_si-s}. Energies are given in eV while the separation is given in nm.}\r
 \label{table:dc_si-s_e}\r
 \end{ruledtabular}\r
 \end{table*}\r
 Table~\ref{table:dc_si-s} classifies equivalent configurations of \hkl<1 1 0>-type Si$_{\text{i}}$ DBs created at position I and C$_{\text{s}}$ created at positions 1 to 5 according to Fig.~\ref{fig:combos_si}.\r
-Corresponding formation as well as binding energies and the C$_{\text{s}}$-Si$_{\text{i}}$ distances are listed in Table~\ref{table:dc_si-s_e}.\r
+Corresponding formation as well as binding energies and the separation distances of the C$_{\text{s}}$ atom and the Si$_{\text{i}}$ DB lattice site are listed in Table~\ref{table:dc_si-s_e}.\r
+In total ten different configurations exist within the investigated range.\r
+Configuration \RM{1} constitutes the energetically most favorable structure exhibiting a formation energy of \unit[4.37]{eV}.\r
+Obviously the configuration of a \hkl[1 1 0] Si$_{\text{i}}$ DB and a next neighbored C$_{\text{s}}$ in the same direction as the alignment of the DB, as displayed in the bottom right of Fig.~\ref{fig:162-097}, enables the largest possible reduction of strain.\r
+The Si$_{\text{i}}$ DB atoms are displaced towards the lattice site occupied by the C$_{\text{s}}$ atom in such a way that the Si DB atom closest to the C atom does no longer form bonds to its top Si neighbors but to the second next neighbored Si atom along \hkl[1 1 0].\r
+However, this configuration is energetically less favorable than the \hkl<1 0 0> C$_{\text{i}}$ DB, which, thus, remains the ground state of a C atom introduced into otherwise perfect c-Si.\r
+The transition involving the latter two configurations is shown in Fig.~\ref{fig:dc_si-s}.\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{162-097.ps}\r
+\caption{Migration barrier and structures of the transition of a \hkl[1 1 0] Si$_{\text{i}}$ DB next to C$_{\text{s}}$ (right) into the C$_{\text{i}}$ \hkl[0 0 -1] DB configuration (left). An activation energy of \unit[0.12]{eV} is observed.}\r
+\label{fig:162-097}\r
+\end{figure}\r
+An activation energy as low as \unit[0.12]{eV} is necessary for the migration into the ground state configuration.\r
+Thus, the C$_{\text{i}}$ \hkl<1 0 0> DB configuration is assumed to occur more likely.\r
+However, only \unit[0.77]{eV} are needed for the reverse process, i.e. the formation of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB out of the ground state.\r
+Due to the low activation energy this process must be considered to be activated without much effort either thermally or by introduced energy of the implantation process.\r
+The configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ DBs might be especially important at higher temperatures accompanied by an increase of the entropic contribution.\r
 \r
 \begin{figure}\r
 \includegraphics[width=\columnwidth]{c_sub_si110.ps}\r
 \caption{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance. The binding energies of the defect pairs are well approximated by a Lennard-Jones 6-12 potential, which is used for curve fitting.}\r
 \label{fig:dc_si-s}\r
 \end{figure}\r
+Fig.~\ref{fig:dc_si-s} shows the binding energies of pairs of C$_{\text{s}}$ and a Si$_{\text{i}}$ \hkl<1 1 0> DB with respect to the separation distance.\r
+The interaction of the defects is well approximated by a Lennard-Jones 6-12 potential, which was used for curve fitting.\r
+The binding energy quickly drops to zero with the fit estimating almost zero interaction at \unit[0.6]{nm}.\r
+This indicates a low interaction capture radius of the defect pair.\r
+In IBS highly energetic collisions are considered to produce configurations of these defects with separation distances exceeding the capture radius.\r
 \r
 Non-zero temperature, entropy, spatial separation of these defects possible, indeed observed in ab initio MD run.\r
 \r