SiC is a covalent material in which both, Si and C atoms are sp$^3$ hybridized.
Each of the four sp$^3$ hybridized orbitals of a Si atom overlaps with one of the four sp$^3$ hybridized orbitals of the four surrounding C atoms and vice versa.
-This results in fourfold coordinated covalent $\sigma$ bonds of equal length and strength for each atom with its neighbours.
-Although the local order of Si and C next neighbour atoms characterized by the tetrahedral bonding is the same, more than 250 different types of structures called polytypes of SiC exist \cite{fischer90}.
+This results in fourfold coordinated covalent $\sigma$ bonds of equal length and strength for each atom with its neighbors.
+Although the local order of Si and C next neighbor atoms characterized by the tetrahedral bonding is the same, more than 250 different types of structures called polytypes of SiC exist \cite{fischer90}.
The polytypes differ in the one-dimensional stacking sequence of identical, close-packed SiC bilayers.
Each SiC bilayer can be situated in one of three possible positions (abbreviated a, b or c) with respect to the lattice while maintaining the tetrahedral bonding scheme of the crystal.
\begin{figure}[t]
\begin{center}
\includegraphics[width=0.6\columnwidth]{ibs_3c-sic.eps}
\end{center}
-\caption{Bright field (a) and \hkl(1 1 1) SiC dark field (b) cross-sectional TEM micrographs of the buried SiC layer in Si created by the two-temperature implantation technique and subsequent annealing as explained in the text \cite{lindner99_2}. The inset shows a selected area diffraction pattern of the buried layer.}
+\caption[Bright field (a) and \hkl(1 1 1) SiC dark field (b) cross-sectional TEM micrographs of the buried SiC layer in Si created by the two-temperature implantation technique and subsequent annealing.]{Bright field (a) and \hkl(1 1 1) SiC dark field (b) cross-sectional TEM micrographs of the buried SiC layer in Si created by the two-temperature implantation technique and subsequent annealing as explained in the text \cite{lindner99_2}. The inset shows a selected area diffraction pattern of the buried layer.}
\label{fig:sic:hrem_sharp}
\end{figure}
Due to the much smaller covalent radius of C compared to Si every incorporated C atom leads to a decrease in the lattice constant corresponding to a lattice contraction of about one atomic volume \cite{baker68}.
The induced strain is assumed to be responsible for the low solid solubility of C in Si, which was determined \cite{bean71} to be
\begin{equation}
-c_{\text{s}}=\unit[4\times10^{24}]{cm^{-3}}
-\cdot\exp(\unit[-2.3]{eV/k_{\text{B}}T})
-\text{ .} \text{{\color{red}k recursive!}}
+c_{\text{s}}=4\times10^{24}\,\text{cm$^{-3}$}
+\cdot\exp(-2.3\,\text{eV/$k_{\text{B}}T$})
+\text{ .}
\end{equation}
The barrier of diffusion of substitutional C has been determined to be around \unit[3]{eV} \cite{newman61}.
\label{section:assumed_prec}
Although high-quality films of single-crystalline 3C-SiC can be produced by means of \ac{IBS} the precipitation mechanism in bulk Si is not yet fully understood.
-Indeed, closely investigating the large amount of literature reveals controversial ideas of SiC formation, which are reviewed in more detail in the following.
+Indeed, closely investigating the large amount of literature pulled up in the last two sections and a cautios combination of some of the findings reveals controversial ideas of SiC formation, which are reviewed in more detail in the following.
\ac{HREM} investigations of C-implanted Si at room temperature followed by \ac{RTA} show 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 diamateres 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.
\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\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).}
+\caption[High resolution transmission electron microscopy (HREM) micrographs 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).]{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.
Next to the pure scientific interest, solving this controversy and gaining new insight in the SiC conversion mechanism might enable significant progress in the heteroepitaxial growth of thin films featuring non-coherent interfaces in the C/Si system.
On the other hand, processes relying upon prevention of precipitation in order to produce strained heterostructures will likewise benefit.
-% remember!
-
+% remember
% werner96/7: rt implants followed by rta < 800: C-Si db aggloms | > 800: 3C-SiC
% taylor93: si_i reduces interfacial energy (explains metastability) of sic/si
% eichhorn02: high imp temp more efficient than postimp treatment
% eichhorn99: same as 02 + c-si agglomerates at low concentrations
-
% strane94/guedj98: my model - c redist by si int (spe) and surface diff (mbe)
% todo
-% add sharp iface image!
+% own polytype stacking sequence image
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