The atomic arrangement is shown in the bottom right of Fig.~\ref{fig:036-239}.\r
The two C atoms form a strong C-C bond, which is responsible for the large gain in energy resulting in a binding energy of \unit[-2.39]{eV}.\r
\r
-Investigating migration barriers enables to predict the probability of formation of the thermodynamic ground state defect complex by thermally activated diffusion processes.\r
-High activation energies are necessary for the migration of low energy configurations, in which the C atom of the second DB is located in the vicinity of the initial DB.\r
-The transition of the configuration, in which the second DB oriented along \hkl[0 1 0] at position 2 (\unit[-1.90]{eV}) into a \hkl[0 1 0] DB at position 1 (\unit[-2.39]{eV}) for instance, revealed a barrier height of more than \unit[4]{eV}.\r
-Low barriers do only exist from energetically less favorable configurations, e.g. the configuration of the \hkl[-1 0 0] DB located at position 2 (\unit[-0.36]{eV}).\r
+Investigating migration barriers enables to predict the probability of formation of defect complexes by thermally activated diffusion processes.\r
+% ground state configuration, C cluster\r
+Based on the lowest energy migration path of a single C$_{\text{i}}$ DB the configuration, in which the second C$_{\text{i}}$ DB is oriented along \hkl[0 1 0] at position 2 is assumed to constitute an ideal starting point for a transition into the ground state.\r
+In addition, the starting configuration exhibits a low binding energy (\unit[-1.90]{eV}) and is, thus, very likely to occur.\r
+However, a barrier height of more than \unit[4]{eV} was detected resulting in a low probability for the transition.\r
+The high activation energy is attributed to the stability of such a low energy configuration, in which the C atom of the second DB is located close to the initial DB.\r
+Low barriers have only been identified for transitions starting from energetically less favorable configurations, e.g. the configuration of a \hkl[-1 0 0] DB located at position 2 (\unit[-0.36]{eV}).\r
Starting from this configuration, an activation energy of only \unit[1.2]{eV} is necessary for the transition into the ground state configuration.\r
The corresponding migration energies and atomic configurations are displayed in Fig.~\ref{fig:036-239}.\r
\begin{figure}\r
Thus, lower migration barriers are expected for pathways resulting in larger separations of the C$_{\text{i}}$ DBs.\r
% calculate?!? ... hopefully acknowledged by 188-225 calc\r
However, if the increase of separation is accompanied by an increase in binding energy, this difference is needed in addition to the activation energy for the respective migration process.\r
-Configurations, which exhibit both, a low binding energy as well as targeting transitions with low activation energies are, thus, most probable C$_{\text{i}}$ complex structures.\r
-On the other hand, if elevated temperatures enable migrations with huge activation energies, the comparably small differences in configurational energy can be neglected resulting in an almost equal occupation of these configurations.\r
+Configurations, which exhibit both, a low binding energy as well as afferent transitions with low activation energies are, thus, most probable C$_{\text{i}}$ complex structures.\r
+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
+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
The migration barrier and correpsonding structures are shown in Fig.~\ref{fig:188-225}.\r
% 188 - 225 transition in progress\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
\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 investigated configuration space.\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
The latter is considered very important for high temperatures, which is accompanied by an increase in the entropic contribution to structure formation.\r
Thus, C agglomeration indeed is expected but only a low probability is assumed for C clustering by thermally activated processes with regard to the considered period of time.\r
% ?!?\r
\end{figure}\r
The interaction is found to be proportional to the reciprocal cube of the C-C distance for extended separations of the C$_{\text{i}}$ and saturates for the smallest possible separation, i.e. the ground state configuration.\r
Not considering the previously mentioned elevated barriers for migration an attractive interaction between the C$_{\text{i}}$ defects indeed is detected with a capture radius that clearly exceeds the \unit[1]{nm} mark.\r
+The interpolated graph suggests the disappearance of attractive interaction forces, which are proportional to the slope of the graph, inbetween the two lowest separation distances of the defects.\r
+This finding, in turn, supports the previously established assumption of C agglomeration and absence of C clsutering.\r
\r
\begin{table}\r
\begin{ruledtabular}\r
\subsection{C$_{\text{i}}$ next to C$_{\text{s}}$}\r
\r
The first row of Table~\ref{table:dc_c-sv} lists the binding energies of C$_{\text{s}}$ next to the C$_{\text{i}}$ \hkl[0 0 -1] DB.\r
-For C$_{\text{s}}$ located at position 1 and 3 the configurations a and A correspond to the naive relaxation of the structure by substituting a Si atom with C in the initial C$_{\text{i}}$ \hkl[0 0 -1] DB structure at positions 1 and 3 respectively.\r
+For C$_{\text{s}}$ located at position 1 and 3 the configurations a and A correspond to the naive relaxation of the structure by substituting the Si atom by a C atom in the initial C$_{\text{i}}$ \hkl[0 0 -1] DB structure at positions 1 and 3 respectively.\r
However, small displacements of the involved atoms near the defect result in different stable structures labeled b and B respectively.\r
+Fig.~\ref{fig:093-095} and \ref{fig:026-128} show structures A, B and a, b together with the barrier of migration for the A to B and a to b transition respectively. \r
\r
% A B\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
+\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
-By breaking a Si-Si in favor of a Si-C bond configuration B is obtained, which shows a twofold coordinated Si atom located inbetween two substitutional C atoms residing on regular Si lattice sites.\r
+By a single bond switch, i.e. the breaking of a Si-Si in favor of a Si-C bond, configuration B is obtained, which shows a twofold coordinated Si atom located inbetween two substitutional C atoms residing on regular Si lattice sites.\r
This configuration has been identified and described by spectroscopic experimental techniques\cite{song90_2} as well as theoretical studies\cite{leary97,capaz98}.\r
-Configuration B is found to constitute the energetically more favorable configuration.\r
+Configuration B is found to constitute the energetically slightly more favorable configuration.\r
However, the gain in energy due to the significantly lower energy of a Si-C compared to a Si-Si bond turns out to be smaller than expected due to a large compensation by introduced strain as a result of the Si interstitial structure.\r
Present results show a difference in energy of states A and B, which exactly matches the experimental value of \unit[0.02]{eV}\cite{song90_2} reinforcing qualitatively correct results of previous theoretical studies on these structures.\r
% mattoni: A favored by 0.4 eV - NO, it is indeed B (reinforce Song and Capaz)!\r
%\r
% AB transition\r
-%Figure~\ref{fig:AB} displays the two configurations and migration barrier for the transition among the two states.\r
+% ...\r
\r
% a b\r
\begin{figure}\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 1 (left) into a C-C \hkl[1 0 0] DB occupying the lattice site at position 1 (right). An activation energy of \unit[0.1]{eV} is observed.}\r
\label{fig:026-128}\r
\end{figure}\r
-Configuration a is similar to configuration A except that the C$_{\text{s}}$ at position 1 is facing the C DB atom as a next neighbor resulting in the formation of a strong C-C bond and a much more noticeable perturbation of the DB structure.\r
+Configuration a is similar to configuration A except that the C$_{\text{s}}$ atom at position 1 is facing the C DB atom as a next neighbor resulting in the formation of a strong C-C bond and a much more noticeable perturbation of the DB structure.\r
Nevertheless, the C and Si DB atoms remain threefold coordinated.\r
Although the C-C bond exhibiting a distance of \unit[0.15]{nm} close to the distance expected in diamond or graphite should lead to a huge gain in energy, a repulsive interaction with a binding energy of \unit[0.26]{eV} is observed due to compressive strain of the Si DB atom and its top neighbors (\unit[0.230]{nm}/\unit[0.236]{nm}) along with additional tensile strain of the C$_{\text{s}}$ and its three neighboring Si atoms (\unit[0.198-0.209]{nm}/\unit[0.189]{nm}).\r
-\r
-...\r
-\r
-Liu et~al.\cite{liu02} propose a similar structure \unit[0.2]{eV} lower than configuration B, thus, constituting the ground state configuration.\r
-The structure labeld b indeed is the ground state configuration, in which the two C atoms form a \hkl[1 0 0] DB sharing the C$_{\text{s}}$ lattice site and the initial Si DB atom occupying the lattice site shared by the initial C$_{\text{i}}$ DB.\r
-\r
-Spin polarization for C-C Int resulting spin up electrons located as in the case of the Si 100 int.\r
+Again a single bond switch, i.e. the breaking of the bond of a Si atom bound to the fourfold coordinated C$_{\text{s}}$ atom and the formation of a double bond between the two C atoms, results in configuration b.\r
+The two C atoms form a \hkl[1 0 0] DB sharing the initial C$_{\text{s}}$ lattice site while the initial Si DB atom occupies its previously regular lattice site.\r
+The transition is accompanied by a large gain in energy as can be seen in Fig.~\ref{fig:026-128}, making it the ground state configuration of a C$_{\text{s}}$ and C$_{\text{i}}$ DB in Si yet \unit[0.33]{eV} lower in energy than configuration B.\r
+This finding is in good agreement with a combined ab initio and experimental study of Liu et~al.\cite{liu02}, who first proposed this structure as the ground state identifying an energy difference compared to configuration B of \unit[0.2]{eV}.\r
% mattoni: A favored by 0.2 eV - NO! (again, missing spin polarization?)\r
+A net magnetization of two spin up electrons, which are euqally localized as in the Si$_{\text{i}}$ \hkl<1 0 0> DB structure is observed.\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
+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
% 2 more migs: 051 -> 128 and 026! forgot why ... probably it's about probability of C clustering\r
\r
\subsection{C$_{\text{s}}$ next to Si$_{\text{i}}$}\r
\r
-Non-zeor temperature, entropy, spatial separation of these defects possible, indeed observed in ab initio MD run.\r
+Non-zero temperature, entropy, spatial separation of these defects possible, indeed observed in ab initio MD run.\r
\r
\section{Discussion}\r
+\r
Our calculations show that point defects which unavoidably are present after ion implantation significantly influence the mobility of implanted carbon \r
in the silicon crystal.\r
A large capture radius has been found for... \r
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