\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 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}.
Thus, higher annealing temperatures and longer annealing times were considered necessary for the formation of homogeneous SiC layers.
Indeed, for the first time, buried homogeneous and stoichiometric epitaxial 3C-SiC layers embedded in single crystalline Si were obtained by the same group consequently applying annealing temperatures of \unit[1405]{$^{\circ}$C} for \unit[90]{min} and implantation temperatures of approximately \unit[550]{$^{\circ}$C} \cite{reeson87}.
The necessity of the applied extreme temperature and time scale is attributed to the stability of substitutional C within the Si matrix being responsible for high activation energies necessary to dissolve such precipitates and, thus, allow for redistribution of the implanted C atoms.
-In order to avoid extreme annealing temperatures close to the melting temperature of Si, triple-energy implantations in the range from \unit[180-190]{keV} with stoichiometric doses at a constant target temperature of \unit[860]{$^{\circ}$C} achieved by external substrate heating were performed \cite{martin90}.
+In order to avoid extreme annealing temperatures close to the melting temperature of Si, triple-energy implantations in the range from \unit[180--190]{keV} with stoichiometric doses at a constant target temperature of \unit[860]{$^{\circ}$C} achieved by external substrate heating were performed \cite{martin90}.
It was shown that a thick buried layer of SiC is directly formed during implantation, which consists of small, only slightly misorientated but severely twinned 3C-SiC crystallites.
The authors assumed that due to the auxiliary heating rather than ion beam heating as employed in all the preceding studies, the complexity of the remaining defects in the synthesized structure is fairly reduced.
Even better qualities by direct synthesis were obtained for implantations at \unit[950]{$^{\circ}$C} \cite{nejim95}.
Since no amorphous or polycrystalline regions have been identified, twinning is considered to constitute the main limiting factor in the IBS of SiC.
Further studies revealed the possibility to form buried layers of SiC by IBS at moderate substrate and anneal temperatures \cite{lindner95,lindner96}.
-Different doses of C ions with an energy of \unit[180]{keV} were implanted at \unit[330-440]{$^{\circ}$C} and annealed at \unit[1200]{$^{\circ}$C} or \unit[1250]{$^{\circ}$C} for \unit[5-10]{h}.
+Different doses of C ions with an energy of \unit[180]{keV} were implanted at \unit[330--440]{$^{\circ}$C} and annealed at \unit[1200]{$^{\circ}$C} or \unit[1250]{$^{\circ}$C} for \unit[5--10]{h}.
For a critical dose, which was found to depend on the Si substrate orientation, the formation of a stoichiometric buried layer of SiC exhibiting a well-defined interface to the Si host matrix was observed.
In case of overstoichiometric C concentrations the excess C is not redistributed.
These investigations demonstrate the presence of an upper dose limit, which corresponds to a \unit[53]{at.\%} C concentration at the implantation peak, for the thermally induced redistribution of the C atoms from a Gaussian to a box-shaped depth profile upon annealing.
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}.
+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.
Implantations at \unit[400]{$^{\circ}$C} resulted in buried layers of SiC subdivided into a polycrystalline upper and an epitaxial lower part.
This corresponds to the region of randomly oriented SiC crystallites and epitaxially aligned precipitates surrounded by thin amorphous layers without crystalline SiC inclusions in the as-implanted state.
To form a narrow, box-like density profile of oriented SiC nanocrystals, \unit[93]{\%} of the total dose of \unit[$8.5\cdot 10^{17}$]{cm$^{-2}$} is implanted at \unit[500]{$^{\circ}$C}.
The remaining dose is implanted at \unit[250]{$^{\circ}$C}, which leads to the formation of amorphous zones above and below the SiC precipitate layer and the destruction of SiC nanocrystals within these zones.
After annealing for \unit[10]{h} at \unit[1250]{$^{\circ}$C} a homogeneous, stoichiometric SiC layer with sharp interfaces is formed.
-Fig. \ref{fig:sic:hrem_sharp} shows the respective high resolution transmission electron microscopy micrographs.
+Fig.~\ref{fig:sic:hrem_sharp} shows the respective high resolution transmission electron microscopy micrographs.
\begin{figure}[t]
\begin{center}
\includegraphics[width=0.6\columnwidth]{ibs_3c-sic.eps}
\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.
% increase of C at substitutional sites
Epitaxial layers with \unit[1.4]{at.\%} of substitutional C have been successfully synthesized in preamorphized Si$_{0.86}$Ge$_{0.14}$ layers, which were grown by CVD on Si substrates, using multiple-energy C implantation followed by solid-phase epitaxial regrowth at \unit[700]{$^{\circ}$C} \cite{strane93}.
The tensile strain induced by the C atoms is found to compensate the compressive strain present due to the Ge atoms.
-Studies on the thermal stability of Si$_{1-y}$C$_y$/Si heterostructures formed in the same way and equal C concentrations showed a loss of substitutional C accompanied by strain relaxation for temperatures ranging from \unit[810-925]{$^{\circ}$C} and the formation of spherical 3C-SiC precipitates with diameters of \unit[2-4]{nm}, which are incoherent but aligned to the Si host \cite{strane94}.
+Studies on the thermal stability of Si$_{1-y}$C$_y$/Si heterostructures formed in the same way and equal C concentrations showed a loss of substitutional C accompanied by strain relaxation for temperatures ranging from \unit[810--925]{$^{\circ}$C} and the formation of spherical 3C-SiC precipitates with diameters of \unit[2--4]{nm}, which are incoherent but aligned to the Si host \cite{strane94}.
During the initial stages of precipitation C-rich clusters are assumed, which maintain coherency with the Si matrix and the associated biaxial strain.
Using this technique a metastable solubility limit was achieved, which corresponds to a C concentration exceeding the solid solubility limit at the Si melting point by nearly three orders of magnitude and, furthermore, a reduction of the defect density near the metastable solubility limit is assumed if the regrowth temperature is increased by rapid thermal annealing \cite{strane96}.
Since high temperatures used in the solid-phase epitaxial regrowth method promotes SiC precipitation, other groups realized substitutional C incorporation for strained Si$_{1-y}$C$_y$/Si heterostructures \cite{iyer92,fischer95,powell93,osten96,osten99,laveant2002} or partially to fully strain-compensated (even inversely distorted \cite{osten94_2}) Si$_{1-x-y}$Ge$_x$C${_y}$ layers on Si \cite{eberl92,powell93_2,osten94,dietrich94} by MBE.
Although high-quality films of single-crystalline 3C-SiC can be produced by means of IBS the precipitation mechanism in bulk Si is not yet fully understood.
Indeed, closely investigating the large amount of literature pulled up in the last two sections and a cautious combination of some of the findings reveals controversial ideas of SiC formation, which are reviewed in more detail in the following.
-High resolution transmission electron microscopy (HREM) investigations of C-implanted Si at room temperature followed by rapid thermal annealing (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}.
+High resolution transmission electron microscopy (HREM) investigations of C-implanted Si at room temperature followed by rapid thermal annealing (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 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}.
Estimates of the SiC/Si interfacial energy \cite{taylor93} and the consequent critical size correspond well with the experimentally observed precipitate radii within these studies.
This different mechanism of precipitation might be attributed to the respective method of fabrication.
-While in CVD and MBE surface effects need to be taken into account, SiC formation during IBS takes place in the bulk of the Si crystal.
+While in CVD and MBE, surface effects need to be taken into account, SiC formation during IBS takes place in the bulk of the Si crystal.
However, in another IBS study Nejim et~al. \cite{nejim95} propose a topotactic transformation that is likewise based on substitutional C, which replaces four of the eight Si atoms in the Si unit cell accompanied by the generation of four Si interstitials.
Since the emerging strain due to the expected volume reduction of \unit[48]{\%} would result in the formation of dislocations, which, however, are not observed, the interstitial Si is assumed to react with further implanted C atoms in the released volume.
The resulting strain due to the slightly lower Si density of SiC compared to Si of about \unit[3]{\%} is sufficiently small to legitimate the absence of dislocations.
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