Tersoff indeed predicts a metastable BC configuration.
However, it is not in the correct order and lower in energy than the \ci{} \hkl<1 1 0> DB.
Quantum-mechanical results of this configuration are discussed in more detail in section \ref{subsection:bc}.
-In another {\em ab inito} study, Capaz~et~al. \cite{capaz94} in turn found BC configuration to be an intermediate saddle point structure of a possible migration path, which is \unit[2.1]{eV} higher than the \ci{} \hkl<1 0 0> DB structure.
+In another {\em ab inito} study, Capaz~et~al.~\cite{capaz94} in turn found the BC configuration to be an intermediate saddle point structure of a possible migration path, which is \unit[2.1]{eV} higher than the \ci{} \hkl<1 0 0> DB structure.
This is assumed to be due to the neglection of the electron spin in these calculations.
Another {\textsc vasp} calculation without fully accounting for the electron spin results in the smearing of a single electron over two non-degenerate states for the BC configuration.
This problem is resolved by spin polarized calculations resulting in a net spin of one accompanied by a reduction of the total energy by \unit[0.3]{eV} and the transformation into a metastable local minimum configuration.
As will be shown in subsequent migration simulations the same would happen to structures where the C atom is displaced along the migration direction, which approximately is the \hkl[1 1 0] direction.
These relaxations indicate that the BC configuration is a real local minimum instead of an assumed saddle point configuration.
Fig. \ref{img:defects:bc_conf} shows the structure, charge density isosurface and Kohn-Sham levels of the BC configuration.
+In fact, the net magnetization of two electrons is already suggested by simple molecular orbital theory considerations with respect to the bonding of the C atom.
The linear bonds of the C atom to the two Si atoms indicate the $sp$ hybridization of the C atom.
Two electrons participate to the linear $\sigma$ bonds with the Si neighbors.
The other two electrons constitute the $2p^2$ orbitals resulting in a net magnetization.
Although classical potential simulations reproduce the same order in energy of the \ci{} \hkl<1 0 0> and \hkl<1 1 0> DB interstitial configurations as obtained by more accurate quantum-mechanical calculations, the obtained migration pathways and resulting activation energies differ to a great extent.
On the one hand, the most favorable pathways differ.
-On the other hand, the activation energies obtained by classical potential simulations are tremendously overestimated by a factor of 2.4 to 3.5.
+However, the pathway, which is considered most probable in the classical potential treatment, exhibits the same starting and final configuration of the DB structure as well as the change in orientation during migration as obtained by quantum-mechanical calculations.
+On the other hand, the activation energy obtained by classical potential simulations is tremendously overestimated by a factor of 2.4 to 3.5.
+The overestimated barrier is due to the short range character of the potential, which drops the interaction to zero within the first and next neighbor distance.
+Since the total binding energy is accommodated within a short distance, which according to the universal energy relation would usually correspond to a much larger distance, unphysical high forces between two neighbored atoms arise.
+This is explained in more detail in a previous study \cite{mattoni2007}.
Thus, atomic diffusion is wrongly described in the classical potential approach.
The probability of already rare diffusion events is further decreased for this reason.
However, agglomeration of C and diffusion of Si self-interstitials are an important part of the proposed SiC precipitation mechanism.
Thus, a serious limitation that has to be taken into account for appropriately modeling the C/Si system using the otherwise quite promising EA potential is revealed.
Possible workarounds are discussed in more detail in section \ref{section:md:limit}.
-\section{Combination of point defects}
+\section{Combination of point defects and related diffusion processes}
The study proceeds with a structural and energetic investigation of pairs of the ground-state and, thus, most probable defect configurations that are believed to be fundamental in the Si to SiC conversion.
Investigations are restricted to quantum-mechanical calculations.
The interpolated graph suggests the disappearance of attractive interaction forces, which are proportional to the slope of the graph, in between the two lowest separation distances of the defects.
This finding, in turn, supports the previously established assumption of C agglomeration and absence of C clustering.
-\subsection{Diffusion processes among configurations of \ci{} pairs}
+%\subsection{Diffusion processes among configurations of \ci{} pairs}
+To draw further conclusions on the probability of C clustering, transitions into the ground-state configuration are investigated.
Based on the lowest energy migration path of a single \ci{} \hkl<1 0 0> DB, the configuration, in which the second \ci{} DB is oriented along \hkl[0 1 0] at position 2 is assumed to constitute an ideal starting point for a transition into the ground state.
In addition, the starting configuration exhibits a low binding energy (\unit[-1.90]{eV}) and is, thus, very likely to occur.
However, a smooth transition path is not found.
\label{chapter:summary}
In a short review of the C/Si compound and the fabrication of the technologically promising semiconductor SiC by IBS, two controversial assumptions of the precipitation mechanism of 3C-SiC in c-Si are elaborated.
+These propose the precipitation of SiC by agglomeration of \ci{} DBs followed by a sudden formation of SiC and otherwise a formation by successive accumulation of \cs{} via intermediate stretched SiC structures, which are coherent to the Si lattice.
To solve this controversy and contribute to the understanding of SiC precipitation in c-Si, a series of atomistic simulations is carried out.
In the first part, intrinsic and C related point defects in c-Si as well as some selected diffusion processes of the C defect are investigated by means of first-principles quatum-mechanical calculations based on DFT and classical potential calculations employing a Tersoff-like analytical bond order potential.
Shortcomings of the computationally efficient though less accurate classical potential approach compared to the quantum-mechanical treatment are revealed.
Next to the known problem of the underestimated formation energy of the tetrahedral configuration \cite{tersoff90}, the energetic sequence of the defect structures is well reproduced by the EA calculations.
Migration barriers of \si{} investigated by quantum-mechanical calculations are found to be of the same order of magnitude than values derived in other ab initio studies \cite{bloechl93,sahli05}.
-HIER WEITER
-
-Defects of C in c-Si are well described by both methods.
-
-
-
-
+Defects of C in Si are well described by both methods.
+The \ci{} \hkl<1 0 0> DB is found to constitute the most favorable interstitial configuration in agreement with several theoretical\cite{burnard93,leary97,dal_pino93,capaz94,jones04} and experimental\cite{watkins76,song90} investigations.
+Almost equal formation energies are predicted by the EA and DFT calculations for this defect.
+A small discrepancy in the resulting equilibrium structure with respect to the DFT method exists due to missing quantum-mechanical effects within the calssical treatment.
+The high formation energies of the tetrahedral and hexagonal configuration obtained by classical potentials act in concert with the fact that these configurations are found unstable by the first-principles description.
+The BC configuration turns out to be unstable relaxing into the \ci{} \hkl<1 1 0> DB configuration within the EA approach.
+This is supported by another {\em ab inito} study \cite{capaz94}, which in turn finds the BC configuration to be an intermediate saddle point structure of a possible migration path, which is \unit[2.1]{eV} higher than the \ci{} \hkl<1 0 0> DB structure.
+By quantum-mechanical calculations performed in this work, however, it turns out that the BC configuration constitutes a real local minimum if the electron spin is fully accounted for.
+Indeed, spin polarization is absolutely necessary for the BC configuration resulting in a net magnetization of two electrons accompanied by a reduction of the total energy by \unit[0.3]{eV}.
+The resulting spin up density is localized in a torus around the C perpendicular to the linear Si-C-Si bond.
+No other configuration is affected by spin polarization.
+The underestimated formation energy of \cs{} is a definite drawback of the classical potential.
+However, the creation of \cs{} is necessarily accompanied by a \si{} in a perfect Si crystal, in which a C atom is incorporated.
+Fortunately, the energetics of combinations of \cs{} and \si{} are quite well described by the EA potential.
+Thus, the underestimated formation energy does not pose a serious limitation.
+Based on the above findings, it is concluded that modeling of the SiC precipitation by the EA potential might lead to trustable results.
+
+Quantum-mechanical investigations of the mobility of the \ci{} \hkl<1 0 0> DB yield a migration barrier of \unit[0.9]{eV}, which excellently agrees to experimental values ranging from \unit[0.70]{eV} to \unit[0.87]{eV} \cite{lindner06,song90,tipping87}.
+The respective path correpsonds to a \ci{} \hkl[0 0 -1] DB migrating towards the next neighbored Si atom located in \hkl[1 1 -1] direction forming a \ci{} \hkl[0 -1 0] DB.
+The identified migration path involves a change in orientation of the DB.
+Thus, the same path explains the experimentally determined activation energies for reorientation of the DB ranging from \unit[0.77]{eV} \cite{watkins76} upto \unit[0.88]{eV} \cite{song90}.
+Investigations based on the EA bond order potential suggest a migration involving an intermediate \ci{} \hkl<1 1 0> DB configuration.
+Although different, starting and final configuration as well as the change in orientation of the \hkl<1 0 0> DB are equal to the identified pathway by the {\em ab initio} calculations.
+However, barrier heights, which are overestimated by a factor of 2.4 to 3.5 depending on the character of migration, i.e. a single step or two step process, compared to the DFT results, are obtained.
+Obviously, the EA potential fails to describe \ci{} diffusion yielding a drastically overestimated activation energy, which has to be taken into account in subsequent investigations.
+
+Quantum-mechanical investigations of two \ci{} defects of the \hkl<1 0 0>-type for varying separations and orientations state a rather attractive interaction between these interstitials.
+Primiraly, energetically favorable configurations of two interstitials are found.
+This is due to strain compensation enabled by the combination of such defects in certain orientations.
+An interaction energy proportional to the reciprocal cube of the distance in the far field regime is found supporting the assumption of \ci{} DB agglomeration.
+The energetically most favorable configuration consists of a C-C bond.
+However, due to high activation energies of respective pathways or alternative pathways featuring less high activation energies, which, however, involve intermediate unfavorable configurations, this structure is less likely to arise than structures of C atoms that are interconnected by another Si atom.
+Thus, agglomeration of C$_{\text{i}}$ is expected whereas the formation of C-C bonds is assumed to fail to appear by thermally activated diffusion processes.
+HIER WEITER
+% for c_s c_i combos ...
+%Obtaind 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}.
Experimental studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates \cite{kimura82,eichhorn02}.
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