\caption[Structure, charge density isosurface and Kohn-Sham level diagram of the bond-centered interstitial configuration.]{Structure, charge density isosurface and Kohn-Sham level diagram of the bond-centered interstitial configuration. Gray, green and blue surfaces mark the charge density of spin up, spin down and the resulting spin up electrons in the charge density isosurface, in which the carbon atom is represented by a red sphere. In the energy level diagram red and green lines mark occupied and unoccupied states.}
\label{img:defects:bc_conf}
\end{figure}
-In the BC insterstitial configuration the interstitial atom is located inbetween two next neighbored Si atoms forming linear bonds.
+In the BC insterstitial configuration the interstitial atom is located in between two next neighbored Si atoms forming linear bonds.
In a previous study this configuration was found to constitute an intermediate saddle point configuration determining the migration barrier of one possibe migration path of a \ci{} \hkl<1 0 0> DB configuration into an equivalent one \cite{capaz94}.
This is in agreement with results of the EA potential simulations, which reveal this configuration to be unstable relaxing into the \ci{} \hkl<1 1 0> configuration.
However, this fact could not be reproduced by spin polarized {\textsc vasp} calculations performed in this work.
Figures \ref{fig:defects:cp_00-1_0-10_mig} and \ref{fig:defects:cp_00-1_ip0-10_mig} show the migration barriers of the \ci{} \hkl<0 0 -1> to \hkl<0 -1 0> DB transition.
In the first case, the transition involves a change in the lattice site of the C atom whereas in the second case, a reorientation at the same lattice site takes place.
In the first case, the pathways for the two different time cosntants look similar.
-A local minimum exists inbetween two peaks of the graph.
+A local minimum exists in between two peaks of the graph.
The corresponding configuration, which is illustrated for the results obtained for a time constant of \unit[1]{fs}, looks similar to the \ci{} \hkl<1 1 0> configuration.
Indeed, this configuration is obtained by relaxation simulations without constraints of configurations near the minimum.
Activation energies of roughly \unit[2.8]{eV} and \unit[2.7]{eV} are needed for migration.
Fig.~\ref{fig:defects:050} shows the relaxed structure of a vacancy created at position 5.
The Si DB atom is largely displaced along \hkl[1 1 0] and somewhat less along \hkl[0 0 -1], which corresponds to the direction towards the vacancy.
The \si DB atom approaches Si atom number 1.
-Indeed, a non-zero charge density is observed inbetween these two atoms exhibiting a cylinder-like shape superposed with the charge density known from the DB itself.
+Indeed, a non-zero charge density is observed in between these two atoms exhibiting a cylinder-like shape superposed with the charge density known from the DB itself.
Strain reduced by this huge displacement is partially absorbed by tensile strain on Si atom number 1 originating from attractive forces of the C atom and the vacancy.
A binding energy of \unit[-0.50]{eV} is observed.
The vast amount of strongly bonded C-C bonds in the high concentration simulations make these configurations energetically more favorable compared to the low concentration configuration.
However, in the same way, a lot of energy is needed to break these bonds to get out of the local energy minimum advancing towards the global minimum configuration.
Thus, such conformational changes are very unlikely to happen.
-This is in accordance with the constant total energy observed in the continuation step of \unit[100]{ps} inbetween the end of C insertion and the cooling process.
+This is in accordance with the constant total energy observed in the continuation step of \unit[100]{ps} in between the end of C insertion and the cooling process.
Obviously, no energetically favorable relaxation is taking place at a system temperature of \unit[450]{$^{\circ}$C}.
The C-C peak at about \unit[0.31]{nm} perfectly matches the nearest neighbor distance of two C atoms in the 3C-SiC lattice.
However, since the quality value does not account for bond lengthes, bond angles, crystallinity or the stacking sequence, high values of $Q$ not necessarily correspond to structures close to 3C-SiC.
Structures that look promising due to high quality values need to be further investigated by other means.
-\subsection{Low C concetration simulations}
+\subsection{Low C concentration simulations}
\begin{figure}[tp]
\begin{center}
%
Obviously, the shift of the peak is caused by the advancing transformation of the C$_{\text{i}}$ DB into the C$_{\text{s}}$ defect.
Next to combinations of two \cs{} atoms or \ci{} \hkl<1 0 0> DBs, combinations of \ci{} \hkl<1 0 0> DBs with a \cs{} atom arise.
-In addition, structures form that result in distances residing inbetween the ones obtained from combinations of mixed defect types and the ones obtained by \cs{} configurations, as can be seen by quite high $g(r)$ values in between the continuous dashed line and the first arrow with a solid line.
+In addition, structures form that result in distances residing in between the ones obtained from combinations of mixed defect types and the ones obtained by \cs{} configurations, as can be seen by quite high $g(r)$ values in between the continuous dashed line and the first arrow with a solid line.
For the most part, these structures can be identified as configurations of \cs{} with either another C atom that basically occupies a Si lattice site but is displaced by a \si{} atom residing in the very next surrounding or a C atom that nearly occupies a Si lattice site forming a defect other than the \hkl<1 0 0>-type with the Si atom.
Again, this is a quite promising result since the C atoms are taking the appropriate coordination as expected in 3C-SiC.
%However, this is contrary to the initial precipitation model proposed in section \ref{section:assumed_prec}, which assumes that the transformation into 3C-SiC takes place in a very last step once enough C-Si DBs agglomerated.
Isolated structures of stretched SiC, which are adjusted to the c-Si host with respect to the lattice constant and alignement, are formed.
It would be conceivable that by agglomeration of further \cs{} atoms the interfacial energy could be overcome and a transition from a coherent and stretched SiC structure into an incoherent and partially strain-compensated SiC precipitate could occur.
-\subsection{High C concetration simulations}
+\subsection{High C concentration simulations}
\begin{figure}[tp]
\begin{center}
Thus, elevated temperatures are considered to constitute a necessary condition to deviate the system from equilibrium, as it is the case in IBS.
It is concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.~\cite{nejim95}.
-This agrees well with a previous results of the {\em ab initio} study on defects in C implanted Si, which show C$_{\text{s}}$ to occur in all probability.
+This agrees well with previous results of the {\em ab initio} study on defects in C implanted Si, which show C$_{\text{s}}$ to occur in all probability.
However, agglomeration and rearrangement is enabled by mobile C$_{\text{i}}$, which has to be present at the same time and is formed by recombination of C$_{\text{s}}$ and Si$_{\text{i}}$.
In contrast to assumptions of an abrupt precipitation of an agglomerate of C$_{\text{i}}$ \cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}, however, structural evolution is believed to occur by a successive occupation of usual Si lattice sites with substitutional C.
This mechanism satisfies the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate, whereas 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.
However, EA predicts the tetrahedral configuration to be most stable.
The particular problem is due to the cut-off and the fact that the second neighbors are only slightly more distant than the first neighbors within the tetrahedral configuration.
Furthermore, the hexagonal defect structure is not stable opposed to results of the authors of the potential \cite{albe_sic_pot}.
-The obtained structure after relaxation, which is similar to the tetrahedral configuration, has a formation energy equal to the one given by the authors for the hexagonal one.
-Obviously, the authors did not check the structure after relaxation still assuming a hexagonal configuration.
-The actual structure equals the tetrahedral configuration, which is slightly displaced along the three coordinate axes.
+The obtained structure after relaxation, which is similar to the tetrahedral configuration, exhibits a formation energy equal to the one given by the authors for the hexagonal one.
+Obviously, the authors did not check the relaxed structure still assuming a hexagonal configuration.
+The actual structure is equal to the tetrahedral configuration, which is slightly displaced along the three coordinate axes.
Variations exist with displacements along two or a single \hkl<1 0 0> direction indicating a potential artifact.
However, finite temperature simulations are not affected by this artifact due to a low activation energy necessary for a transition into the energetically more favorable tetrahedral configuration.
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}.
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.
+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.
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.
+Subsequent investigations focus on defect combinations exclusively by the first-principles description.
+These configurations are constructed in such a way as to allow for a quantum-mechanical treatment.
+
+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.
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.
+Results of combinations of \ci{} and \cs{} revealed two additional metastable structures different to these obtained by a naive relaxation.
+Small displacements result in a structure of a \hkl<1 1 0> C-C DB and in a structure of a twofold coordinated Si atom located in between two substitutional C atoms residing on regular Si lattice sites.
+Both structures are lower in energy compared to the respetive counterparts.
+These results, for the most part, compare well with results gained in previous studies \cite{leary97,capaz98,liu02} and show an astonishingly good agreement with experiment \cite{song90_2}.
+Again, spin polarized calculations are revealed necessary.
+A net magnetization of two electrons is observed for the \hkl<1 1 0> C-C DB configuration, which constitutes the ground state.
+A repulsive interaction is observed for C$_{\text{s}}$ at lattice sites along \hkl[1 1 0] due to tensile strain originating from both, the C$_{\text{i}}$ DB and the C$_{\text{s}}$ atom.
+All other investigated configurations show attractive interactions, which suggest an energetically favorable agglomeration of C$_{\text{i}}$ and C$_{\text{s}}$ except for separations along one of the \hkl<1 1 0> directions.
+Although the most favorable configuration exhibits a C-C bond, migration paths show large barriers exceeding \unit[2.2]{eV} for transitions into the ground state.
+As before, structures other than the ground-state configuration are assumed to arise more likely.
+Thus, agglomeration of C defects in contrast to C clustering is again reinforced by these findings.
+
+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 a configuration of \cs{}.
+
+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.
+Low diffusion barriers of \si{} enable further separation of the defect pair.
+Thus, elevated temperatures might lead to configurations of C$_{\text{s}}$ and a remaining Si atom in the near interstitial lattice, which is likewise supported by the result of the MD run.
+
+% maybe preliminary conclusions here ...
+
+Classical potential MD calculations targeting the direct simulation of SiC precipitation in Si are adopted.
+Therefore, the necessary amount of C is gradually incorporated into a large c-Si host.
+Simulations at temperatures used in IBS result in structures dominated by the C$_{\text{i}}$ \hkl<1 0 0> DB and its combinations if C is inserted into the total volume.
+Incorporation into volumes $V_2$ and $V_3$, which correspond to the volume of the expected precipitate and the volume containing the necessary amount of Si, lead to an amorphous SiC-like structure within the respective volume.
+Both results are not expected with respect to the outcome of the IBS experiments.
+In the first case, i.e. the low C concentration simulations, \ci{} \hkl<1 0 0> DBs are indeed formed.
+However, sufficient defect agglomeration is not observed.
+In the second case, i.e. the high C concentration simulations, crystallization of the amorphous structure, which is not expected at prevailing temperatures, is likewise not observed.
+
+Limitations of the MD technique in addition to overestimated bond strengths due to the short range potential are identified to be responsible.
+The approach of using increased temperatures during C insertion is followed to work around this problem termed {\em potential enhanced slow phase space propagation}.
+Higher temperatures are justified for severeal reasons.
+Elevated temperatures are expected to compensate the overestimated diffusion barriers and accelerate strcutural evolution.
+In addition, formation of SiC is also observed at higher implantation temperatures \cite{nejim95,lindner01} and temperatures in the implantation region is definetly higher than the temperature determined experimentally at the surface of the sample.
+Furthermore, the present study focuses on structural transitions in a system far from equilibrium.
+
+No significant change is observed for high C concentrations at increased temperatures.
+The amorphous phase is maintained.
+The huge amount of damage hampers identification of investigated structures, which in many cases lost the alignment to the c-Si host.
+Obviously, inccorporation of a high quantity of C into a small volume within a short period of time creates damage, which decelerates structural evolution.
+For the low C concentrations, time scales are still too low to observe C agglomeration.
+However, a phase transition of the C$_{\text{i}}$-dominated into a clearly C$_{\text{s}}$-dominated structure is observed.
+The amount of \cs{} increases with increasing temperature.
+Diamond and graphite like bonds as well as the artificial bonds due to the cut-off are reduced.
+Loose structures of stretched SiC, which are adjusted to the Si lattice with respect to the lattice constant and alignment, are identified.
+\si{} is often found in the direct surrounding.
+Entropic contributions are assumed to be responsible for these structures at elevated temperatures that deviate from the ground state at 0 K.
+
+% conclusions 2nd part
+
-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}.
+HIER WEITER ...
Experimental studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates \cite{kimura82,eichhorn02}.
In particular, restructuring of strong C-C bonds is affected \cite{deguchi92}, which preferentially arise if additional kinetic energy provided by an increase of the implantation temperature is missing to accelerate or even enable atomic rearrangements.
Si$_{\text{i}}$ serves either as a supply of Si atoms needed in the surrounding of the contracted precipitates or as an interstitial defect minimizing the emerging strain energy of a coherent precipitate.
The latter has been directly identified in the present simulation study, i.e. structures of two C$_{\text{s}}$ atoms and Si$_{\text{i}}$ located in the vicinity.
-It is, thus, concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.\cite{nejim95}.
+It is, thus, concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.~\cite{nejim95}.
This agrees well with a previous ab initio study on defects in C implanted Si\cite{zirkelbach11a}, which showed C$_{\text{s}}$ to occur in all probability.
However, agglomeration and rearrangement is enabled by mobile C$_{\text{i}}$, which has to be present at the same time and is formed by recombination of C$_{\text{s}}$ and Si$_{\text{i}}$.
In contrast to assumptions of an abrupt precipitation of an agglomerate of C$_{\text{i}}$\cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}, however, structural evolution is believed to occur by a successive occupation of usual Si lattice sites with substitutional C.
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