This is particularly important since the energy of formation of C$_{\text{s}}$ is drastically underestimated by the EA potential.
A possible occurrence of C$_{\text{s}}$ could then be attributed to a lower energy of formation of the C$_{\text{s}}$-Si$_{\text{i}}$ combination due to the low formation energy of C$_{\text{s}}$, which is obviously wrong.
-Since quantum-mechanical calculations reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB as the ground-state configuration of Si$_{\text{i}}$ in Si, it was assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$ in the calculations carried out in section \ref{subsection:cs-si}.
+Since quantum-mechanical calculations reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB as the ground-state configuration of Si$_{\text{i}}$ in Si, it was assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$ in the calculations carried out in section \ref{subsection:si-cs}.
Empirical potentials, however, predict Si$_{\text{i}}$ T to be the energetically most favorable configuration.
Thus, investigations of the relative energies of formation of defect pairs need to include combinations of C$_{\text{s}}$ with Si$_{\text{i}}$ T.
Results of {\em ab initio} and classical potential calculations are summarized in Table~\ref{tab:defect_combos}.
\section{Conclusions concerning the SiC conversion mechanism}
-The ground state configuration of a carbon interstitial in crystalline siliocn is found to be the C-Si \hkl<1 0 0> dumbbell interstitial configuration, in which the threefold coordinated carbon and silicon atom share a usual silicon lattice site.
-This supports the assumption of C-Si \hkl<1 0 0>-type dumbbel interstitial formation in the first steps of the IBS process as proposed by the precipitation model introduced in section \ref{section:assumed_prec}.
-
-Migration simulations reveal this carbon interstitial to be mobile at prevailing implantation temperatures requireing an activation energy of approximately 0.9 eV for migration as well as reorientation processes.
-This enables possible migration of the defects to form defect agglomerates as demanded by the model.
-Unfortunately classical potential simulations show tremendously overestimated migration barriers indicating a possible failure of the necessary agglomeration of such defects.
-
-Investigations of two carbon interstitials of the \hkl<1 0 0>-type and varying separations and orientations state an attractive interaction between these interstitials.
-Depending on orientation, energetically favorable configurations are found in which these two interstitials are located close together instead of the occurernce of largely separated and isolated defects.
+Obtained results for separated point defects in Si are in good agreement to previous theoretical work on this subject, both for intrinsic defects \cite{leung99,al-mushadani03} as well as for C point defects \cite{dal_pino93,capaz94}.
+The ground-state configurations of these defects, i.e. the Si$_{\text{i}}$ \hkl<1 1 0> and C$_{\text{i}}$ \hkl<1 0 0> DB, are reproduced and compare well to previous findings of theoretical investigations on Si$_{\text{i}}$ \cite{leung99,al-mushadani03} as well as theoretical \cite{dal_pino93,capaz94,burnard93,leary97,jones04} and experimental \cite{watkins76,song90} studies on C$_{\text{i}}$.
+A quantitatively improved activation energy of \unit[0.9]{eV} for a qualitatively equal migration path based on studies by Capaz et.~al.~\cite{capaz94} to experimental values \cite{song90,lindner06,tipping87} ranging from \unit[0.70-0.87]{eV} reinforce their derived mechanism of diffusion for C$_{\text{i}}$ in Si
+However, it turns out that the BC configuration is not a saddle point configuration as proposed by Capaz et~al.~\cite{capaz94} but constitutes a real local minimum if the electron spin is properly accounted for.
+A net magnetization of two electrons, which is already clear by simple molecular orbital theory considerations on the bonding of the $sp$ hybridized C atom, is settled.
+By investigating the charge density isosurface it turns out that the two resulting spin up electrons are localized in a torus around the C atom.
+With an activation energy of \unit[0.9]{eV} the C$_{\text{i}}$ carbon interstitial can be expected to be highly mobile at prevailing temperatures in the process under investigation, i.e. IBS.
+Since the \ci{} \hkl<1 0 0> DB is the ground-state configuration and highly mobile, possible migration of these DBs to form defect agglomerates, as demanded by the model introduced in section \ref{section:assumed_prec}, is considered possible.
+
+Unfortunately the description of the same processes fails if classical potential methods are used.
+Already the geometry of the most stable DB configuration differs considerably from that obtained by first-principles calculations.
+The classical approach is unable to reproduce the correct character of bonding due to the deficiency of quantum-mechanical effects in the potential.
+Nevertheless, both methods predict the same type of interstitial as the ground-state configuration and also the order in energy of the remaining defects is reproduced fairly well.
+From this, a description of defect structures by classical potentials looks promising.
+%
+However, focussing on the description of diffusion processes the situation changes completely.
+Qualitative and quantitative differences exist.
+First of all, a different pathway is suggested as the lowest energy path, which again might be attributed to the absence of quantum-mechanical effects in the classical interaction model.
+Secondly, the activation energy is overestimated by a factor of 2.4 to 3.5 compared to the more accurate quantum-mechanical methods and experimental findings.
+This is attributed to the sharp cut-off of the short range potential.
+As already pointed out in a previous study \cite{mattoni2007}, the short cut-off is responsible for overestimated and unphysical high forces of next neighbor atoms.
+The overestimated migration barrier, however, affects the diffusion behavior of the C interstitials.
+By this artifact, the mobility of the C atoms is tremendously decreased resulting in an inaccurate description or even absence of the DB agglomeration as proposed by one of the precipitation models.
+
+Quantum-mechanical investigations of two \ci{} of the \hkl<1 0 0>-type and varying separations and orientations state an attractive interaction between these interstitials.
+Obtained results for the most part compare well with results gained in previous studies \cite{leary97,capaz98,mattoni2002,liu02} and show an astonishingly good agreement with experiment \cite{song90}.
+%
+Depending on orientation, energetically favorable configurations are found, in which these two interstitials are located close together instead of the occurernce of largely separated and isolated defects.
This is due to strain compensation enabled by the combination of such defects in certain orientations.
-For dumbbells oriented along the \hkl<1 1 0> direction and the assumption that there is the possibility of free orientation, an interaction energy proportional to the reciprocal cube of the distance in the far field regime is found.
-These findings support the assumption of the C-Si dumbbell agglomeration proposed by the precipitation model.
-
-Next to the C-Si \hkl<1 0 0> dumbbell interstitial configuration, in which the C atom is sharing a Si lattice site with the corresponding Si atom the C atom could occupy the site of the Si atom, which in turn forms a Si self-interstitial.
-Combinations of substitutional C and a \hkl<1 1 0> Si self-interstitial, which is the ground state configuration for a Si self-interstitial and, thus, assumed to be the energetically most favorable configuration for combined structures, show formation energies 0.5 eV to 1.5 eV greater than that of the C-Si \hkl<1 0 0> interstitial configuration, which remains the energetically most favorable configuration.
-However, the binding energy of substitutional C and the Si self-interstitial quickly drops to zero already for short separations indicating a low interaction capture radius.
-Thus, due to missing attractive interaction forces driving the system to form C-Si \hkl<1 0 0> dumbbell interstitial complexes substitutional C, while thermodynamically not stable, constitutes a most likely configuration occuring in IBS, a process far from equlibrium.
-
-Due to the low interaction capture radius substitutional C can be treated independently of the existence of separated Si self-interstitials.
-This should be also true for combinations of C-Si interstitials next to a vacancy and a further separated Si self-interstitial excluded from treatment, which again is a conveivable configuration in IBS.
-By combination of a \hkl<1 0 0> dumbbell with a vacancy in the absence of the Si self-interstitial it is found that the configuration of substitutional carbon occupying the vacant site is the energetically most favorable configuration.
-Low migration barriers are necessary to obtain this configuration and in contrast comparatively high activation energies necessary for the reverse process.
-Thus, carbon interstitials and vacancies located close together are assumed to end up in such a configuration in which the carbon atom is tetrahedrally coordinated and bound to four silicon atoms as expected in silicon carbide.
-
-While first results support the proposed precipitation model the latter suggest the formation of silicon carbide by succesive creation of substitutional carbon instead of the agglomeration of C-Si dumbbell interstitials followed by an abrupt transition.
-Prevailing conditions in the IBS process at elevated temperatures and the fact that IBS is a nonequilibrium process reinforce the possibility of formation of substitutional C instead of the thermodynamically stable C-Si dumbbell interstitials predicted by simulations at zero Kelvin.
+For dumbbells oriented along the \hkl<1 1 0> bond chain and the assumption that there is the possibility of free orientation, an interaction energy proportional to the reciprocal cube of the distance in the far field regime is found.
+These findings support the assumption of the \ci{} DB agglomeration.
+%
+The ground state configuration is found to consist of a C-C bond, which is responsible for the vast gain in energy.
+However, based on investigations of possible migration pathways, these structures are less likely to arise than structures, in which both C atoms are interconnected by another Si atom, which is due to high activation energies of the respective pathways or alternative pathways featuring less high activation energies, which, however, involve intermediate unfavorable configurations.
+Thus, agglomeration of C$_{\text{i}}$ is expected while the formation of C-C bonds is assumed to fail to appear by thermally activated diffusion processes.
+
+In contrast, C$_{\text{i}}$ and vacancies are found to efficiently react with each other exhibiting activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} resulting in stable C$_{\text{s}}$ configurations.
+In addition, a highly attractive interaction exhibiting a large capture radius, effective independent of the orientation and the direction of separation of the defects, is observed.
+Accordingly, the formation of C$_{\text{s}}$ is very likely to occur.
+Comparatively high energies necessary for the reverse process reveal this configuration to be extremely stable.
+Thus, C interstitials and vacancies located close together are assumed to end up in such a configuration, in which the C atom is tetrahedrally coordinated and bound to four Si atoms as expected in SiC.
+
+Investigating configurations of C$_{\text{s}}$ and Si$_{\text{i}}$, formation energies higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB were obtained keeping up previously derived assumptions concerning the ground state of C$_{\text{i}}$ in otherwise perfect Si.
+However, a small capture radius is identified for the respective interaction that might prevent the recombination of defects exceeding a separation of \unit[0.6]{nm} into the ground state configuration.
+In addition, a rather small activation energy of \unit[0.77]{eV} allows for the formation of a C$_{\text{s}}$-Si$_{\text{i}}$ pair originating from the C$_{\text{i}}$ \hkl<1 0 0> DB structure by thermally activated processes.
+Thus, elevated temperatures might lead to thermodynamically unstable configurations of C$_{\text{s}}$ and a remaining Si atom in the near interstitial lattice, which is supported by the result of an {\em ab initio} molecular dynamics run.
+%Thus, due to missing attractive interaction forces driving the system to form C-Si \hkl<1 0 0> dumbbell interstitial complexes substitutional C, while thermodynamically not stable, constitutes a most likely configuration occuring in IBS, a process far from equlibrium.
+
+% todo
+% maybe move above stuff to conclusion chapter, at least shorten!
+% see remember in sic chapter
+
+These findings allow to draw conclusions on the mechanisms involved in the process of SiC conversion in Si.
+Agglomeration of C$_{\text{i}}$ is energetically favored and enabled by a low activation energy for migration.
+Although ion implantation is a process far from thermodynamic equilibrium, which might result in phases not described by the Si/C phase diagram, i.e. a C phase in Si, high activation energies are believed to be responsible for a low probability of the formation of C-C clusters.
+
+In the context of the initially stated controversy present in the precipitation model, these findings suggest an increased participation of C$_{\text{s}}$ already in the initial stage due to its high probability of incidence.
+In addition, thermally activated, C$_{\text{i}}$ might turn into C$_{\text{s}}$.
+The associated emission of Si$_{\text{i}}$ serves two needs: as a vehicle for other C$_{\text{s}}$ atoms and as a supply of Si atoms needed elsewhere to form the SiC structure.
+As for the vehicle, Si$_{\text{i}}$ is believed to react with C$_{\text{s}}$ turning it into highly mobile C$_{\text{i}}$ again, allowing for the rearrangement of the C atom.
+The rearrangement is crucial to end up in a configuration of C atoms only occupying substitutionally the lattice sites of one of the two fcc lattices that build up the diamond lattice.
+On the other hand, the conversion of some region of Si into SiC by \cs{} is accompanied by a reduction of the volume since SiC exhibits a \unit[20]{\%} smaller lattice constant than Si.
+The reduction in volume is compensated by excess Si$_{\text{i}}$ serving as building blocks for the surrounding Si host or a further formation of SiC.
+
+To conclude, precipitation occurs by successive agglomeration of C$_{\text{s}}$.
+However, the agglomeration and rearrangement of C$_{\text{s}}$ is only possible by mobile C$_{\text{i}}$, which has to be present at the same time.
+Accordingly, the process is governed by both, C$_{\text{s}}$ accompanied by Si$_{\text{i}}$ as well as C$_{\text{i}}$.
+It is worth to mention that there is no contradiction to results of the HREM studies \cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}.
+Regions showing dark contrasts in an otherwise undisturbed Si lattice are attributed to C atoms in the interstitial lattice.
+However, there is no particular reason for the C species to reside in the interstitial lattice.
+Contrasts are also assumed for Si$_{\text{i}}$.
+Once precipitation occurs, regions of dark contrasts disappear in favor of Moir\'e patterns indicating 3C-SiC in c-Si due to the mismatch in the lattice constant.
+Until then, however, these regions are either composed of stretched coherent SiC and interstitials or of already contracted incoherent SiC surrounded by Si and interstitials, where the latter is too small to be detected in HREM.
+In both cases Si$_{\text{i}}$ might be attributed a third role, which is the partial compensation of tensile strain that is present either in the stretched SiC or at the interface of the contracted SiC and the Si host.
+
+Furthermore, the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate is satisfied by the mechanism of successive positioning of C$_{\text{s}}$.
+In contrast, there is no obvious reason for the topotactic orientation of an agglomerate consisting exclusively of C-Si dimers, which would necessarily involve a much more profound change in structure for the transition into SiC.
+
+%Prevailing conditions in the IBS process at elevated temperatures and the fact that IBS is a nonequilibrium process reinforce the possibility of formation of substitutional C instead of the thermodynamically stable C-Si dumbbell interstitials predicted by simulations at zero Kelvin.
\label{section:defects:noneq_process_02}
-{\color{blue}
+\ifnum1=0
+
+
+
In addition, there are experimental findings, which might be exploited to reinforce the non-validity of the proposed precipitation model.
High resolution TEM shows equal orientation of \hkl(h k l) planes of the c-Si host matrix and the 3C-SiC precipitate.
+
Formation of 3C-SiC realized by successive formation of substitutional C, in which the atoms belonging to one of the two fcc lattices are substituted by C atoms perfectly conserves the \hkl(h k l) planes of the initial c-Si diamond lattice.
+
Silicon self-interstitials consecutively created to the same degree are able to diffuse into the c-Si host one after another.
+
Investigated combinations of C interstitials, however, result in distorted configurations, in which C atoms, which at some point will form SiC, are no longer aligned to the host.
+
It is easily understandable that the mismatch in alignement will increase with increasing defect density.
+
In addition, the amount of Si self-interstitials equal to the amount of agglomerated C atoms would be released all of a sudden probably not being able to diffuse into the c-Si host matrix without damaging the Si surrounding or the precipitate itself.
+
In addition, IBS results in the formation of the cubic polytype of SiC only.
+
As this result conforms well with the model of precipitation by substitutional C there is no obvious reason why hexagonal polytypes should not be able to form or an equal alignement would be mandatory assuming the model of precipitation by C-Si dumbbell agglomeration.
-}
-{\color{red}Todo: C mobility higher than Si mobility? -> substitutional C is more likely to arise, since it migrates 'faster' to vacant sites?}
+\fi
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