+High resolution transmission electron microscopy (HREM) investigations of C-implanted Si at room temperature followed by rapid thermal annealing (RTA) indicate the formation of C-Si dumbbell agglomerates, which are stable up to annealing temperatures of about \unit[700--800]{$^{\circ}$C}, and a transformation into 3C-SiC precipitates at higher temperatures~\cite{werner96,werner97}.
+The precipitates with diameters between \unit[2]{nm} and \unit[5]{nm} are incorporated in the Si matrix without any remarkable strain fields, which is explained by the nearly equal atomic density of C-Si agglomerates and the SiC unit cell.
+Implantations at \unit[500]{$^{\circ}$C} likewise suggest an initial formation of C-Si dumbbells on regular Si lattice sites, which agglomerate into large clusters~\cite{lindner99_2}.
+The agglomerates of such dimers, which do not generate lattice strain but lead to a local increase of the lattice potential~\cite{werner96,werner97}, are indicated by dark contrasts and otherwise undisturbed Si lattice fringes in HREM, as can be seen in Fig.~\ref{fig:sic:hrem:c-si}.
+\begin{figure}[t]
+\begin{center}
+\subfigure[]{\label{fig:sic:hrem:c-si}\includegraphics[width=0.25\columnwidth]{tem_c-si-db.eps}}
+\subfigure[]{\label{fig:sic:hrem:sic}\includegraphics[width=0.25\columnwidth]{tem_3c-sic.eps}}
+\end{center}
+\caption[High resolution transmission electron microscopy (HREM) micrographs of agglomerates of C-Si dimers showing dark contrasts and otherwise undisturbed Si lattice fringes and equally sized Moir\'e patterns indicating 3C-SiC precipitates.]{High resolution transmission electron microscopy (HREM) micrographs~\cite{lindner99_2} of agglomerates of C-Si dimers showing dark contrasts and otherwise undisturbed Si lattice fringes (a) and equally sized Moir\'e patterns indicating 3C-SiC precipitates (b).}
+\label{fig:sic:hrem}
+\end{figure}
+A topotactic transformation into a 3C-SiC precipitate occurs once a critical radius of \unit[2]{nm} to \unit[4]{nm} is reached.
+The precipitation is manifested by the disappearance of the dark contrasts in favor of Moir\'e patterns (Fig.~\ref{fig:sic:hrem:sic}) due to the lattice mismatch of \unit[20]{\%} of the 3C-SiC precipitate and the Si host.
+The insignificantly lower Si density of SiC of approximately \unit[3]{\%} compared to c-Si results in the emission of only a few excess Si atoms.
+The same mechanism was identified by high resolution x-ray diffraction~\cite{eichhorn99}.
+For implantation temperatures of \unit[500]{$^{\circ}$C}, C-Si dumbbells agglomerate in an initial stage followed by the additional appearance of aligned SiC precipitates in a slightly expanded Si region with increasing dose.
+The precipitation mechanism based on a preceding dumbbell agglomeration as indicated by the above-mentioned experiments is schematically displayed in Fig.~\ref{fig:sic:db_agglom}.
+\begin{figure}[t]
+\begin{center}
+\subfigure[]{\label{fig:sic:db_agglom:seq01}\includegraphics[width=0.30\columnwidth]{sic_prec_seq_01.eps}}
+%C-Si dumbbell formation
+\hspace*{0.2cm}
+\subfigure[]{\label{fig:sic:db_agglom:seq02}\includegraphics[width=0.30\columnwidth]{sic_prec_seq_02.eps}}
+%Dumbbell agglomeration
+\hspace*{0.2cm}
+\subfigure[]{\label{fig:sic:db_agglom:seq03}\includegraphics[width=0.30\columnwidth]{sic_prec_seq_03.eps}}
+%SiC formation and release of excess Si atoms
+\end{center}
+\caption[Two dimensional schematic of the assumed SiC precipitation mechanism based on an initial C-Si dumbbell agglomeration.]{Two dimensional schematic of the assumed SiC precipitation mechanism based on an initial C-Si dumbbell agglomeration. C atoms (red dots) incorporated into the Si (black dots) host form C-Si dumbbells (a), which agglomerate into clusters (b) followed by precipitation of SiC and the emission of a few excess Si atoms (black circles), which are located in the interstitial Si lattice (c). The dotted lines mark the atomic spacing of c-Si in \hkl[1 0 0] direction indicating the $4/5$ ratio of the lattice constants of c-Si and 3C-SiC.}
+\label{fig:sic:db_agglom}
+\end{figure}
+The incorporated C atoms form C-Si dumbbells on regular Si lattice sites.
+With increasing dose and proceeding time, the highly mobile dumbbells agglomerate into large clusters.
+Finally, when the cluster size reaches a critical radius, the high interfacial energy due to the 3C-SiC/c-Si lattice misfit is overcome and precipitation occurs.
+Due to the slightly lower silicon density of 3C-SiC, excessive silicon atoms exist, which will most probably end up as self-interstitials in the c-Si matrix since there is more space than in 3C-SiC.
+
+In contrast, IR spectroscopy and HREM investigations on the thermal stability of strained Si$_{1-y}$C$_y$/Si heterostructures formed by solid-phase epitaxy (SPE)~\cite{strane94} and MBE~\cite{guedj98}, which finally involve the incidental formation of SiC nanocrystallites, suggest a coherent initiation of precipitation by agglomeration of substitutional instead of interstitial C.
+These experiments show that the C atoms, which are initially incorporated substitutionally at regular lattice sites, form C-rich clusters maintaining coherency with the Si lattice during annealing above a critical temperature prior to the transition into incoherent 3C-SiC precipitates.
+Increased temperatures in the annealing process enable the diffusion and agglomeration of C atoms.