\label{fig:sic:unit_cell}
\end{figure}
Its unit cell is shown in Fig.~\ref{fig:sic:unit_cell}.
-3C-SiC grows in zincblende structure, i.e. it is composed of two face-centered cubic (fcc) lattices, which are displaced by one quarter of the volume diagonal as in Si.
+3C-SiC grows in zincblende structure, i.e.\ it is composed of two face-centered cubic (fcc) lattices, which are displaced by one quarter of the volume diagonal as in Si.
However, in 3C-SiC, one of the fcc lattices is occupied by Si atoms while the other one is occupied by C atoms.
-Its lattice constant of \unit[0.436]{nm} compared to \unit[0.543]{nm} from that of Si results in a lattice mismatch of almost \unit[20]{\%}, i.e. four lattice constants of Si approximately match five SiC lattice constants.
-Thus, the Si density of SiC is only slightly lower, i.e. \unit[97]{\%} of plain Si.
+Its lattice constant of \unit[0.436]{nm} compared to \unit[0.543]{nm} from that of Si results in a lattice mismatch of almost \unit[20]{\%}, i.e.\ four lattice constants of Si approximately match five SiC lattice constants.
+Thus, the Si density of SiC is only slightly lower, i.e.\ \unit[97]{\%} of plain Si.
\section{Fabrication of silicon carbide}
%In the so called step-controlled epitaxy, lateral growth proceeds from atomic steps without the necessity of preceding nucleation events.
Investigations indicate that in the so-called step-controlled epitaxy, crystal growth proceeds through the adsorption of Si species at atomic steps and their carbonization by hydrocarbon molecules.
This growth mechanism does not require two-dimensional nucleation.
-Instead, crystal growth is governed by mass transport, i.e. the diffusion of reactants in a stagnant layer.
+Instead, crystal growth is governed by mass transport, i.e.\ the diffusion of reactants in a stagnant layer.
In contrast, layers of the 3C polytype are formed on exactly oriented \hkl(0 0 0 1) 6H-SiC substrates by two-dimensional nucleation on terraces.
These films show a high density of double positioning boundary (DPB) defects, which is a special type of twin boundary arising at the interface of regions that occupy one of the two possible orientations of the hexagonal stacking sequence, which are rotated by \unit[60]{$^{\circ}$} relative to each other, respectively.
However, lateral 3C-SiC growth was also observed on low tilt angle off-axis substrates originating from intentionally induced dislocations \cite{powell91}.
Additionally, 6H-SiC was observed on clean substrates even for a tilt angle as low as \unit[0.1]{$^{\circ}$} due to low surface mobilities that facilitate arriving molecules to reach surface steps.
Thus, 3C nucleation is assumed as a result of migrating Si and C containing molecules interacting with surface disturbances by a yet unknown mechanism, in contrast to a model \cite{ueda90}, in which the competing 6H versus 3C growth depends on the density of surface steps.
-Combining the fact of a well defined 3C lateral growth direction, i.e. the tilt direction, and an intentionally induced dislocation enables the controlled growth of a 3C-SiC film mostly free of DPBs \cite{powell91}.
+Combining the fact of a well defined 3C lateral growth direction, i.e.\ the tilt direction, and an intentionally induced dislocation enables the controlled growth of a 3C-SiC film mostly free of DPBs \cite{powell91}.
Lower growth temperatures, a clean growth ambient, in situ control of the growth process, layer-by-layer deposition and the possibility to achieve dopant profiles within atomic dimensions due to the reduced diffusion at low growth temperatures reveal MBE as a promising technique to produce SiC epitaxial layers.
Using alternating supply of the gas beams Si$_2$H$_6$ and C$_2$H$_2$ in GSMBE, 3C-SiC epilayers were obtained on 6H-SiC substrates at temperatures between \unit[850]{$^{\circ}$C} and \unit[1000]{$^{\circ}$C} \cite{yoshinobu92}.
Although tremendous progress has been achieved in the above-mentioned growth methods during the last decades, available wafer dimensions and crystal qualities are not yet satisfactory.
Thus, alternative approaches to fabricate SiC have been explored.
-The ion beam synthesis (IBS) technique, i.e. high-dose ion implantation followed by a high-temperature annealing step, turned out to constitute a promising method to directly form compound layers of high purity and accurately controllable depth and stoichiometry.
+The ion beam synthesis (IBS) technique, i.e.\ high-dose ion implantation followed by a high-temperature annealing step, turned out to constitute a promising method to directly form compound layers of high purity and accurately controllable depth and stoichiometry.
A short chronological summary of the IBS of SiC and its origins is presented in the following.
High-dose carbon implantation into crystalline silicon (c-Si) with subsequent or in situ annealing was found to result in SiC microcrystallites in Si \cite{borders71}.
Instead defect annihilation is observed and the C-rich surface layer of the room temperature implant turns into a layer consisting of SiC precipitates, which, however, are not aligned with the Si matrix indicating a mechanism different to the one of the direct formation for the high-temperature implantation.
Based on these findings, a recipe was developed to form buried layers of single-crystalline SiC featuring an improved interface and crystallinity \cite{lindner99,lindner01,lindner02}.
-Therefore, the dose must not exceed the stoichiometry dose, i.e. the dose corresponding to \unit[50]{at.\%} C concentration at the implantation peak.
+Therefore, the dose must not exceed the stoichiometry dose, i.e.\ the dose corresponding to \unit[50]{at.\%} C concentration at the implantation peak.
Otherwise clusters of C are formed, which cannot be dissolved during post-implantation annealing at moderate temperatures below the Si melting point \cite{lindner96,calcagno96}.
Annealing should be performed for \unit[5--10]{h} at \unit[1250]{$^{\circ}$C} to enable the redistribution from the as-implanted Gaussian into a box-like C depth profile \cite{lindner95}.
The implantation temperature constitutes the most critical parameter, which is responsible for the structure after implantation and, thus, the starting point for subsequent annealing steps.
\end{equation}
The barrier of diffusion of substitutional C has been determined to be around \unit[3]{eV} \cite{newman61}.
-However, as suspected due to the substitutional position, the diffusion of C requires intrinsic point defects, i.e. Si self-interstitials and vacancies.
+However, as suspected due to the substitutional position, the diffusion of C requires intrinsic point defects, i.e.\ Si self-interstitials and vacancies.
Similar to phosphorous and boron, which exclusively use self-interstitials as a diffusion vehicle, the diffusion of C atoms is expected to obey the same mechanism.
Indeed, enhanced C diffusion was observed in the presence of self-interstitial supersaturation \cite{kalejs84} indicating an appreciable diffusion component involving self-interstitials and only a negligible contribution by vacancies.
Substitutional C and interstitial Si react into a C-Si complex forming a dumbbell structure oriented along a crystallographic \hkl<1 0 0> direction on a regular Si lattice site.
% lattice location of implanted carbon
Radiation damage introduced during implantation and a high concentration of the implanted species, which results in the reduction of the topological constraint of the host lattice imposed on the implanted species, can affect the manner of impurity incorporation.
-The probability of finding C, which will be most stable at sites for which the number of neighbors equals the natural valence, i.e. substitutionally on a regular Si site of a perfect lattice, is, thus, reduced at substitutional lattice sites and likewise increased at interstitial sites.
+The probability of finding C, which will be most stable at sites for which the number of neighbors equals the natural valence, i.e.\ substitutionally on a regular Si site of a perfect lattice, is, thus, reduced at substitutional lattice sites and likewise increased at interstitial sites.
Indeed, x-ray rocking curves reveal a positive lattice strain, which is decreased but still remains with increasing annealing temperature, indicating the location of the majority of implanted C atoms at interstitial sites \cite{isomae93}.
Due to the absence of dislocations in the implanted region interstitial C is assumed to prevent clustering of implantation-induced Si self-interstitials by agglomeration of C-Si interstitials or the formation of SiC precipitates accompanied by a relaxation of the lattice strain.
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