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}.
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 synthsized structure is fairly reduced.
+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 \ac{IBS} of SiC.
-... maybe nejim?!?
-... lindner limit in dose -> 1250
-... two temp implantation ... sharp interface
-By understanding some basic processes (32-36), \ac{IBS} nowadays has become a promising method to form thin SiC layers of high quality exclusively of the 3C polytype embedded in and epitactically aligned to the Si host featuring a sharp interface \cite{lindner99,lindner01,lindner02}.
+
+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}.
+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.
+This is explained by the formation of strong graphitic C-C bonds for higher C concentrations \cite{calcagno96}.
+Increased temperatures exceeding the Si melting point are expected to be necessary for the dissociation of these C clusters.
+Furthermore, higher implantation energies were found to result in layers of variable composition exhibiting randomly distributed SiC precipitates.
+In another study \cite{serre95} high dose C implantations were performed at room temperature and \unit[500]{$^{\circ}$C} respectively.
+Implantations at room temperature lead to the formation of a buried amorphous carbide layer in addition to a thin C-rich film at the surface, which is attributed to the migration of C atoms towards the surface.
+In contrast, implantations at elevated temperatures result in the exclusive formation of a buried layer consisting of 3C-SiC precipitates epitaxially aligned to the Si host, which obviously is more favorable than the C migration towards the surface.
+Annealing at temperatures up to \unit[1150]{$^{\circ}$C} does not alter the C profile.
+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.
+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.
+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.
+However, an abrupt interface to the Si host is observed after annealing.
+As expected, single-crystalline layers were achieved for an increased temperature of \unit[600]{$^{\circ}$C}.
+However, these layers show an extremely poor interface to the Si top layer governed by a high density of SiC precipitates, which are not affected in the C redistribution during annealing and, thus, responsible for the rough interface.
+Hence, to obtain sharp interfaces and single-crystalline SiC layers temperatures between \unit[400]{$^{\circ}$C} and \unit[600]{$^{\circ}$C} have to be used.
+Indeed, reasonable results were obtained at \unit[500]{$^{\circ}$C} \cite{lindner98} and even better interfaces were observed for \unit[450]{$^{\circ}$C} \cite{lindner99_2}.
+To further improve the interface quality and crystallinity a two-temperature implantation technique was developed \cite{lindner99}.
+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 desctruction 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.
+
+To summarize, by understanding some basic processes, \ac{IBS} nowadays has become a promising method to form thin SiC layers of high quality exclusively of the 3C polytype embedded in and epitaxially aligned to the Si host featuring a sharp interface.
+Due to the high areal homogeneity achieved in \ac{IBS}, the size of the layers is only limited by the width of the beam-scanning equipment used in the implantation system as opposed to deposition techniques, which have to deal with severe wafer bending.
+This enables the synthesis of large area SiC films.
\section{Substoichiometric concentrations of carbon in crystalline silicon}
+In the following some basic properties of C in crystalline Si are reviewed.
+A lot of work has been done contributing to the understanding of C in Si either as an isovalent impurity as well as at concentrations exceeding the solid solubility limit.
+A comprehensive survey on C-mediated effects in Si has been published by Skorupa and Yankov \cite{skorupa96}.
+
+\subsection{Carbon as an impurity in silicon}
+
+Below the solid solubility, C impurities mainly occupy substitutionally Si lattice sites in Si \cite{newman65}.
+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!}}
+\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.
+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.
+This structure, the so called C-Si \hkl<1 0 0> dumbbell structure, was initially suspected by local vibrational mode absorption \cite{bean70} and finally verified by electron paramegnetic resonance \cite{watkins76} studies on irradiated Si substrates at low temperatures.
+Measuring the annealing rate of the defect as a function of temperature reveals barriers for migration ranging from \unit[0.73]{eV} \cite{song90} to \unit[0.87]{eV} \cite{tipping87}, which is highly mobile compared to substitutional C.
+% diffusion pathway?
+% expansion of the lattice (positive strain)
+
+%\subsection{Agglomeration phenomena}
+% c-si agglomerattion as an alternative to sic precipitation (due to strain)
+% -> maybe this fits better in prec model in next chapter
+
+\subsection{Suppression of transient enhanced diffusion of dopant species}
+
+The predominant diffusion mechanism of most dopants in Si based on native self-interstitials \cite{fahey89} has a large impact on the diffusion behavior of dopants that have been implanted in Si.
+The excess population of Si self-interstitials created by low-energy implantations of dopants for shallow junction formation in submicron technologies may enhance the diffusion of the respective dopant during annealing by more than one order of magnitude compared to normal diffusion.
+This kind of diffusion, labeled transient enhanced diffusion (TED), which is driven by the presence of non-equilibrium concentrations of point defects, was first discovered for implantations of boron in Si \cite{hofker74} and is well understood today \cite{michel87,cowern90,stolk95,stolk97}.
+The TED of B was found to be inhibited in the presence of a sufficient amount of incorporated C \cite{cowern96}.
+This is due to the reduction of the excess Si self-interstitials with substitutional C atoms forming the C-Si interstitial complex \cite{stolk97,zhu98}.
+Therefore, incorporation of C provides a promising method for suppressing TED enabling an improved shallow junction formation in future Si devices.
+
+% in general: high c diffusion in areas of high damage, low diffusion for substitutional or even sic prec
+
+\subsection{Strained silicon and silicon heterostructures}
+
+% 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 to be found as an interstitial.
+Depending on the way C is incorporated and whether precipitation occurs or not the volume is either reduced in the case of substitutionally incorporated C or expanded in the case of C interstitial formation \cite{goesele85}.
+
+There are, however, ...
+In implanted Si the location of C is to a great deal incorporated as an interstitial atom due to a reduced topological contraint.
+Other methods exist to realize only substitutional C.
+
+% -> my own links: strane etc ...
+% -> skorupa 3.5: heterostructures
+
\section{Assumed cubic silicon carbide conversion mechanisms}
\label{section:assumed_prec}
+Although much progress has been made in 3C-SiC thin film growth in the above-mentioned growth methods during the last decades, there is still potential
+.. compatible to the established and highly developed technology based on silicon.
+
+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 statisfactory.
+
+... \cite{lindner99_2} ...
+
+% -> skorupa 3.2: c sub vs sic prec
+
on surface ... md contraction along 110 ... kitabatake ... and ref in lindner ... rheed from si to sic ...
in ibs ... lindner and skorupa ...
nejim however ...
+ high temps -> good alignment with substrate
+ C occupies predominantly substitutional lattice sites
+ also indictaed by other direct synthesis experiments like martin90 and conclusions of reeson8X ...
+
+eichhornXX, koegler, lindner ...
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