Based on experimental studies\cite{werner96,werner97,eichhorn99,lindner99_2,koegler03} it is assumed that incorporated C atoms form C-Si dimers (dumbbells) on regular Si lattice sites.\r
The highly mobile C interstitials agglomerate into large clusters followed by the formation of incoherent 3C-SiC nanocrystallites once a critical size of the cluster is reached.\r
In contrast, investigations of the precipitation in strained Si$_{1-y}$C$_y$/Si heterostructures formed by molecular beam epitaxy (MBE)\cite{strane94,guedj98} suggest an initial coherent clustering of substitutional instead of interstitial C followed by a loss of coherency once the increasing strain energy surpasses the interfacial energy of an incoherent 3C-SiC precipitate in c-Si.\r
-These two different mechanisms of precipitation might be determined by the respective method of fabrication.\r
+These two different mechanisms of precipitation might be attributed to the respective method of fabrication.\r
However, in another IBS study Nejim et al. propose a topotactic transformation remaining structure and orientation likewise based on the formation of substitutional C and a concurrent reaction of the excess Si self-interstitials with further implanted C atoms in the initial state\cite{nejim95}.\r
Solving this controversy and understanding the effective underlying processes will enable significant technological progress in 3C-SiC thin film formation driving the superior polytype for potential applications in high-performance electronic device production\cite{wesch96}.\r
\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
-\includegraphics[width=\columnwidth]{036-239.eps}\r
+\includegraphics[width=\columnwidth]{036-239.ps}\r
\caption{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[-1 0 0] DB at position 2 (left) into a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 1 (right). An activation energy of \unit[1.2]{eV} is observed.}\r
\label{fig:036-239}\r
\end{figure}\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
-In both cases the configuration yielding a binding energy of \unit[-2.25]{eV} is promising since it constitutes the second most energetically favorable structure, exhibits a low migration barrier of transition starting from more separated defect structures and\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
+The migration barrier and correpsonding structures are shown in Fig.~\ref{fig:188-225}.\r
% 188 - 225 transition in progress\r
-is represented four times (two times more often than the ground state configuration) within the investigated configuration space.\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
+\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
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
\label{fig:dc_110}\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
\r
\begin{table}\r
\begin{ruledtabular}\r
%Figure~\ref{fig:AB} displays the two configurations and migration barrier for the transition among the two states.\r
\r
% a b\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{026-128.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 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
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
% mattoni: A favored by 0.2 eV - NO! (again, missing spin polarization?)\r
\r
% mig a-b\r
-% 2 more migs: 051 -> 128 and 026! forgot why ...\r
+% 2 more migs: 051 -> 128 and 026! forgot why ... probably it's about probability of C clustering\r
\r
\subsection{C$_{\text{i}}$ next to V}\r
\r
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