On the other hand, if elevated temperatures enable migrations with huge activation energies, comparably small differences in configurational energy can be neglected resulting in an almost equal occupation of such configurations.\r
In both cases the configuration yielding a binding energy of \unit[-2.25]{eV} is promising.\r
First of all, it constitutes the second most energetically favorable structure.\r
-Secondly, a migration path with a barrier as low as \unit[?.?]{eV} exists starting from a configuration of largely separated defects exhibiting a low binding energy (\unit[-1.88]{eV}).\r
+Secondly, a migration path with a barrier as low as \unit[0.47]{eV} exists starting from a configuration of largely separated defects exhibiting a low binding energy (\unit[-1.88]{eV}).\r
The migration barrier and correpsonding structures are shown in Fig.~\ref{fig:188-225}.\r
% 188 - 225 transition in progress\r
\begin{figure}\r
\includegraphics[width=\columnwidth]{188-225.ps}\r
-\caption{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 5 (left) into a C$_{\text{i}}$ \hkl[1 0 0] DB at position 1 (right). An activation energy of \unit[?.?]{eV} is observed.}\r
+\caption{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 5 (left) into a C$_{\text{i}}$ \hkl[1 0 0] DB at position 1 (right). An activation energy of \unit[0.47]{eV} is observed.}\r
\label{fig:188-225}\r
\end{figure}\r
Finally, this type of defect pair is represented four times (two times more often than the ground state configuration) within the systematically investigated configuration space.\r
%./visualize_contcar -w 640 -h 480 -d results/c_00-1_c3_csub_B -nll -0.20 -0.4 -0.1 -fur 0.9 0.6 0.9 -c 0.5 -1.5 0.375 -L 0.5 0 0.3 -r 0.6 -A -1 2.465\r
\begin{figure}\r
\includegraphics[width=\columnwidth]{093-095.ps}\r
-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 3 (left) into a configuration of a twofold coordinated Si$_{\text{i}}$ located inbetween two C$_{\text{s}}$ atoms occupying the lattice sites of the initial DB and position 3 (right). An activation energy of \unit[0.?]{eV} is observed.}\r
+\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 3 (left) into a configuration of a twofold coordinated Si$_{\text{i}}$ located inbetween two C$_{\text{s}}$ atoms occupying the lattice sites of the initial DB and position 3 (right). An activation energy of \unit[0.44]{eV} is observed.}\r
\label{fig:093-095}\r
\end{figure}\r
Configuration A consists of a C$_{\text{i}}$ \hkl[0 0 -1] DB with threefold coordinated Si and C DB atoms slightly disturbed by the C$_{\text{s}}$ at position 3, facing the Si DB atom as a next neighbor.\r
% mattoni: A favored by 0.4 eV - NO, it is indeed B (reinforce Song and Capaz)!\r
%\r
% AB transition\r
-% ...\r
+The migration barrier was identified to be \unit[0.44]{eV}, almost three times higher than the experimental value of \unit[0.16]{eV}\cite{song90_2} estimated for the neutral charge state transition in p- and n-type Si.\r
+Keeping in mind the formidable agreement of the energy difference with experiment, the overestimated activation energy is quite unexpected and disappointing.\r
+Obviously, either the CRT algorithm fails to seize the actual saddle point structure or the influence of dopants has exceptional effect in the experimentally covered diffusion process being responsible for the low migration barrier.\r
+% not satisfactory!\r
\r
% a b\r
\begin{figure}\r
Configurations a, A and B are not affected by spin polarization and show zero magnetization.\r
Mattoni et~al.\cite{mattoni2002}, in contrast, find configuration b less favorable than configuration A by \unit[0.2]{eV}.\r
Next to differences in the XC-functional and plane-wave energy cut-off this discrepancy might be attributed to the missing accounting for spin polarization in their calculations, which -- as has been shown for the C$_{\text{i}}$ BC configuration -- results in an increase of configurational energy.\r
-\r
+Indeed, investigating the migration path from configurations a to b and, in doing so, reusing the wave functions of the previous migration step the final structure, i.e. configuration b, was obtained with zero magnetization and an increase in configurational energy by \unit[0.2]{eV}.\r
+Obviously a different energy minimum of the electronic system is obatined indicating hysteresis behavior.\r
+However, since the total energy is lower for the magnetic result it is believed to constitute the real, i.e. global, minimum with respect to electronic minimization.\r
+%\r
+% a b transition\r
A low activation energy of \unit[0.1]{eV} is observed for the a$\rightarrow$b transition.\r
Thus, configuration a is very unlikely to occur in favor of configuration b.\r
-However, migration barriers yielding\r
-...\r
\r
-% mig a-b\r
+% repulsive along 110\r
+A repulsive interaction is observed for C$_{\text{s}}$ at lattice sites along \hkl[1 1 0], i.e. positions 1 (configuration a) and 5.\r
+This is due to tensile strain originating from both, the C$_{\text{i}}$ DB and the C$_{\text{s}}$ atom residing within the \hkl[1 1 0] bond chain.\r
+This finding agrees well with results by Mattoni et~al.\cite{mattoni2002}.\r
+% all other investigated results: attractive interaction. stress compensation.\r
+In contrast, all other investigated configurations show attractive interactions.\r
+Explain all three remaining confs, from most fav to less fav conf ...\r
+\r
+% c agglomeration vs c clustering ... migs to b conf\r
% 2 more migs: 051 -> 128 and 026! forgot why ... probably it's about probability of C clustering\r
+Whether C agglomeration or clustering is expected has, again, been answered by investigating migration barriers.\r
+Therefor, several migration paths were investigated, which result in configuration b.\r
+\r
\r
\subsection{C$_{\text{i}}$ next to V}\r
\r
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