From a7be94ca23f82bdac34105879c39592f2e65892c Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 1 May 2012 23:19:30 +0200 Subject: [PATCH] some on mobility ... --- posic/publications/emrs2012.tex | 23 ++++++----------------- 1 file changed, 6 insertions(+), 17 deletions(-) diff --git a/posic/publications/emrs2012.tex b/posic/publications/emrs2012.tex index e946701..552cff7 100644 --- a/posic/publications/emrs2012.tex +++ b/posic/publications/emrs2012.tex @@ -184,29 +184,18 @@ Next to the substitutional C (C$_{\text{s}}$) configuration, which is not an int This finding is in agreement with several theoretical \cite{dal_pino93,capaz94,burnard93,leary97,jones04} and experimental \cite{watkins76,song90} investigations, which all predict this configuration to be the ground state. It is worth to note that the bond-centered (BC) configuration constitutes a real local minimum in spin polarized calculations in contrast to results \cite{capaz94} without spin predicting a saddle point configuration as well as to the empirical description, which shows a relaxation into the C$_{\text{i}}$ \hkl<1 0 0> DB ground-state configuration. -\section{Mobility of the carbon defect} - -Instead, Capaz et al.\cite{capaz94}, investigating migration pathways of the C$_{\text{i}}$ \hkl<1 0 0> DB, find this defect to be \unit[2.1]{eV} lower in energy than the bond-centered (BC) configuration. -The BC configuration is claimed to constitute the saddle point within the C$_{\text{i}}$ \hkl[0 0 -1] DB migration path residing in the \hkl(1 1 0) plane and, thus, interpreted as the barrier of migration for the respective path. -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 of \unit[0.3]{eV} due to the spin, the difference we found is much smaller (\unit[0.94]{eV}), which would nicely compare to experimentally observed migration barriers of \unit[0.70-0.87]{eV}\cite{lindner06,tipping87,song90}. -However, since the BC configuration constitutes a real local minimum another barrier exists which is about \unit[1.2]{eV} in height. +\section{Defect mobility} + +HIER MEHR ... 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 to a C$_{\text{i}}$ \hkl[0 -1 0] DB located at the 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[0.90]{eV}) to experimental values. -A more detailed description can be found in a previous study\cite{zirkelbach10a}. - -Next to the C$_{\text{i}}$ BC configuration the vacancy and Si$_{\text{i}}$ \hkl<1 0 0> DB have to be treated by taking into account the spin of the electrons. -For the vacancy the net spin up electron density is localized in caps at the four surrounding Si atoms directed towards the vacant site. -In the Si$_{\text{i}}$ \hkl<1 0 0> DB configuration the net spin up density is localized in two caps at each of the two DB atoms perpendicularly aligned to the bonds to the other two Si atoms respectively. -No other configuration, within the ones that are mentioned, is affected. +A more detailed description can be found in a previous study \cite{zirkelbach10}. Concerning the mobility of the ground state Si$_{\text{i}}$, we found an activation energy of \unit[0.67]{eV} for the transition of the Si$_{\text{i}}$ \hkl[0 1 -1] to \hkl[1 1 0] DB located at the neighbored Si lattice site in \hkl[1 1 -1] direction. Further investigations revealed a barrier of \unit[0.94]{eV} for the Si$_{\text{i}}$ \hkl[1 1 0] DB to Si$_{\text{i}}$ H, \unit[0.53]{eV} for the Si$_{\text{i}}$ \hkl[1 1 0] DB to Si$_{\text{i}}$ T and \unit[0.35]{eV} for the Si$_{\text{i}}$ H to Si$_{\text{i}}$ T transition. -%Obtained values are of the same order of magnitude than values derived from other ab initio studies\cite{bloechl93,sahli05}. -These are of the same order of magnitude than values derived from other ab initio studies\cite{bloechl93,sahli05}. +These are of the same order of magnitude as values of other {\em ab initio} studies \cite{bloechl93,sahli05}. -\subsection{Pairs of C$_{\text{i}}$} +\section{Defect combinations} C$_{\text{i}}$ pairs of the \hkl<1 0 0> type have been investigated in the first part. Fig.~\ref{fig:combos_ci} schematically displays the initial C$_{\text{i}}$ \hkl[0 0 -1] DB structure and various positions for the second defect (1-5) that have been used for investigating defect pairs. -- 2.20.1