Since thermally activated C clustering is, thus, only possible by traversing energetically unfavored configurations, mass C clustering is not expected.\r
Furthermore, the migration barrier of \unit[1.2]{eV} is still higher than the activation energy of \unit[0.9]{eV} observed for a single C$_{\text{i}}$ \hkl<1 0 0> DB in c-Si.\r
The migration barrier of a C$_{\text{i}}$ DB in a complex system is assumed to approximate the barrier of a DB in a separated system with increasing defect separation.\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
+Accordingly, lower migration barriers are expected for pathways resulting in larger separations of the C$_{\text{i}}$ DBs.\r
+% acknowledged by 188-225 (reverse order) 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 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
First of all, it constitutes the second most energetically favorable structure.\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[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
-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 defect agglomeration indeed is expected but only a low probability is assumed for C-C clustering by thermally activated processes with regard to the considered period of time.\r
+The latter is considered very important at high temperatures, accompanied by an increase in the entropic contribution to structure formation.\r
+As a result, C defect agglomeration indeed is expected, but only a low probability is assumed for C-C clustering by thermally activated processes with regard to the considered process time in IBS.\r
+% alternatively: ... considered period of time (of the IBS process).\r
+%\r
% ?!?\r
% look for precapture mechnism (local minimum in energy curve)\r
% also: plot energy all confs with respect to C-C distance\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$_{\text{s}}$ 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
+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
-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
+Again a single bond switch, i.e. the breaking of the bond of the 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
\r
\subsection{C$_{\text{i}}$ next to V}\r
\r
-In the last subsection configurations of a C$_{\text{i}}$ DB with C$_{\text{s}}$ occupying a vacant site created by the implantation process have been investigated.\r
-Additionally, configurations might arise in IBS, in which the impinging C atom creates a vacant site near a C$_{\text{i}}$ DB but does not occupy it.\r
-Resulting binding energies of a C$_{\text{i}}$ DB with a nearby vacancy are listed in the second row of Table~\ref{table:dc_c-sv}.\r
+In the last subsection configurations of a C$_{\text{i}}$ DB with C$_{\text{s}}$ occupying a vacant site have been investigated.\r
+Additionally, configurations might arise in IBS, in which the impinging C atom creates a vacant site near a C$_{\text{i}}$ DB, but does not occupy it.\r
+Resulting binding energies of a C$_{\text{i}}$ DB and a nearby vacancy are listed in the second row of Table~\ref{table:dc_c-sv}.\r
All investigated structures are prefered compared to isolated largely separated defects.\r
In contrast to C$_{\text{s}}$ this is also valid for positions along \hkl[1 1 0] resulting in an entirely attractive interaction between defects of these types.\r
Even for the largest possible distance (R) achieved in the calculations of the periodic supercell a binding energy as low as \unit[-0.31]{eV} is observed.\r
\end{figure}\r
Activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} are observed.\r
In the first case the Si and C atom of the DB move towards the vacant and initial DB lattice site respectively.\r
-In total three Si-Si and one more Si-C bond is formed during the transition.\r
+In total three Si-Si and one more Si-C bond is formed during transition.\r
In the second case the lowest barrier is found for the migration of Si number 1 , which is substituted by the C$_{\text{i}}$ atom, towards the vacant site.\r
-A net amount of five Si-Si and one Si-C bond are additionally formed during the transition.\r
+A net amount of five Si-Si and one Si-C bond are additionally formed during transition.\r
The direct migration of the C$_{\text{i}}$ atom onto the vacant lattice site results in a somewhat higher barrier of \unit[1.0]{eV}.\r
In both cases, the formation of additional bonds is responsible for the vast gain in energy rendering almost impossible the reverse processes.\r
\r
\r
\subsection{C$_{\text{s}}$ next to Si$_{\text{i}}$}\r
\r
-As shown in section~\ref{subsection:sep_def} C$_{\text{s}}$ exhibits the lowest energy of formation.\r
+As shown in section~\ref{subsection:sep_def}, C$_{\text{s}}$ exhibits the lowest energy of formation.\r
Considering a perfect Si crystal and conservation of particles, however, the occupation of a Si lattice site by a slowed down implanted C atom is necessarily accompanied by the formation of a Si self-interstitial.\r
There are good reasons for the existence of regions exhibiting such configurations with regard to the IBS process.\r
-Highly energetic C atoms are able to kick out a Si atom from its lattice site, resulting in a Si self-interstitial accompanied by a vacant site, which might get occupied by another C atom, which lost almost all of its kinetic energy.\r
-Thus, configurations of C$_{\text{s}}$ and Si self-interstitials are investigated in the following.\r
+Highly energetic C atoms are able to kick out a Si atom from its lattice site, resulting in a Si self-interstitial accompanied by a vacant site, which might get occupied by another C atom that lost almost all of its kinetic energy.\r
+%Thus, configurations of C$_{\text{s}}$ and Si self-interstitials are investigated in the following.\r
+Provided that the first C atom, which created the V and Si$_{\text{i}}$ pair had enough kinetic energy to escape the affected region, we are left ... WEITER\r
The Si$_{\text{i}}$ \hkl<1 1 0> DB, which was found to exhibit the lowest energy of formation within the investigated self-interstitial configurations, is assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$.\r
\r
\begin{table}\r
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