From 97846012cd10a7bc34d70e4a514920bd73f8f59c Mon Sep 17 00:00:00 2001 From: hackbard Date: Fri, 27 Aug 2010 17:43:50 +0200 Subject: [PATCH] nearly finihsed si_i c_s ... restructure possibly necessary --- posic/publications/defect_combos.tex | 27 ++++++++++++++++++++++++--- 1 file changed, 24 insertions(+), 3 deletions(-) diff --git a/posic/publications/defect_combos.tex b/posic/publications/defect_combos.tex index 0092208..3440103 100644 --- 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. 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. 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. -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. +However, since the BC configuration constitutes a real local minimum another barrier exists which is about \unit[1.2]{eV} in height. 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. 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. A more detailed description can be found in a previous study\cite{zirkelbach10a}. @@ -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 \\ $r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\ \end{tabular} -\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.} +\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.} \label{table:dc_si-s_e} \end{ruledtabular} \end{table*} 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}. -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}. +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}. +In total ten different configurations exist within the investigated range. +Configuration \RM{1} constitutes the energetically most favorable structure exhibiting a formation energy of \unit[4.37]{eV}. +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. +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]. +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. +The transition involving the latter two configurations is shown in Fig.~\ref{fig:dc_si-s}. +\begin{figure} +\includegraphics[width=\columnwidth]{162-097.ps} +\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.} +\label{fig:162-097} +\end{figure} +An activation energy as low as \unit[0.12]{eV} is necessary for the migration into the ground state configuration. +Thus, the C$_{\text{i}}$ \hkl<1 0 0> DB configuration is assumed to occur more likely. +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. +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. +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. \begin{figure} \includegraphics[width=\columnwidth]{c_sub_si110.ps} \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.} \label{fig:dc_si-s} \end{figure} +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. +The interaction of the defects is well approximated by a Lennard-Jones 6-12 potential, which was used for curve fitting. +The binding energy quickly drops to zero with the fit estimating almost zero interaction at \unit[0.6]{nm}. +This indicates a low interaction capture radius of the defect pair. +In IBS highly energetic collisions are considered to produce configurations of these defects with separation distances exceeding the capture radius. Non-zero temperature, entropy, spatial separation of these defects possible, indeed observed in ab initio MD run. -- 2.20.1