-Calculations based on the EA potential yield a different picture.
-Fig.~\ref{fig:albe_mig} shows the evolution of structure and energy along the lowest energy migration path (path~1) based on the EA potential.
-Due to symmetry it is sufficient to merely consider the migration from the BC to the C$_{\text{i}}$ configuration.
-Two different pathways are obtained for different time constants of the Berendsen thermostat.
-With a time constant of \unit[1]{fs} the C atom resides in the \hkl(1 1 0) plane resulting in a migration barrier of \unit[2.4]{eV}.
-However, weaker coupling to the heat bath realized by an increase of the time constant to \unit[100]{fs} enables the C atom to move out of the \hkl(1 1 0) plane already at the beginning, which is accompanied by a reduction in energy, approaching the final configuration on a curved path.
-The energy barrier of this path is \unit[0.2]{eV} lower in energy than the direct migration within the \hkl(1 1 0) plane.
-It should be noted that the BC configuration is actually not a local minimum configuration in EA based calculations since a relaxation into the \hkl<1 1 0> dumbbell configuration occurs.
-However, investigating further migration pathways involving the \hkl<1 1 0> interstitial did not yield lower migration barriers.
-Thus, the activation energy should at least amount to \unit[2.2]{eV}.
-
-\section{Discussion}
-
-The first-principles results are in good agreement to previous work on this subject\cite{burnard93,leary97,dal_pino93,capaz94}.
-The C-Si \hkl<1 0 0> dumbbell interstitial is found to be the ground state configuration of a C defect in Si.
-The lowest migration path already proposed by Capaz et~al.\cite{capaz94} is reinforced by an additional improvement of the quantitative conformance of the barrier height calculated in this work (\unit[0.9]{eV}) with experimentally observed values (\unit[0.70]{eV} -- \unit[0.87]{eV})\cite{lindner06,song90,tipping87}.
-However, it turns out that the bond-centered 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.
-
-We found that the description of the same processes fails if classical potential methods are used.
-Already the geometry of the most stable dumbbell 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.
-%ref mod: language - energy / order
-%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.
-Nevertheless, both methods predict the same type of interstitial as the ground state configuration.
-Furthermore, the relative energies of the other defects are reproduced fairly well.
-From this, a description of defect structures by classical potentials looks promising.
-% ref mod: language - changed
-%However, focussing on the description of diffusion processes the situation is changing completely.
-However, focussing on the description of diffusion processes the situation has changed 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 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 dumbbell agglomeration as proposed by the precipitation model.
-
-\section{Summary}
-
-To conclude, we have shown that ab initio calculations on interstitial carbon in silicon are very close to the results expected from experimental data.
-The calculations presented in this work agree well with other theoretical results.
-So far, the best quantitative agreement with experimental findings has been achieved concerning the interstitial carbon mobility.
-For the first time, we have shown that the bond-centered configuration indeed constitutes a real local minimum configuration resulting in a net magnetization if spin polarized calculations are performed.
-Classical potentials, however, fail to describe the selected processes.
-This has been shown to have two reasons, i.e. the overestimated barrier of migration due to the artificial interaction cut-off on the one hand, and on the other hand the lack of quantum-mechanical effects which are crucial in the problem under study.
-% ref mod: language - being investigated
-%In order to get more insight on the SiC precipitation mechanism, further ab initio calculations are currently investigated.
-In order to get more insight on the SiC precipitation mechanism, further ab initio calculations are currently being performed.
+There is no significant difference between C insertion into $V_2$ and $V_3$.
+Thus, in the following, the focus is on low ($V_1$) and high ($V_2$, $V_3$) C concentration simulations only.
+
+In the low C concentration simulation the number of C-C bonds is small, as can be seen in the upper part of Fig.~\ref{fig:450:a}.
+On average, there are only 0.2 C atoms per Si unit cell.
+By comparing the Si-C peaks of the low concentration simulation with the resulting Si-C distances of a C$_{\text{i}}$ \hkl<1 0 0> DB in Fig.~\ref{fig:450:b} it becomes evident that the structure is clearly dominated by this kind of defect.
+One exceptional peak at \unit[0.26]{nm} (marked with an arrow in Fig.~\ref{fig:450:b}) exists, which is due to the Si-C cut-off, at which the interaction is pushed to zero.
+Investigating the C-C peak at \unit[0.31]{nm}, which is also available for low C concentrations as can be seen in the upper inset of Fig.~\ref{fig:450:a}, reveals a structure of two concatenated, differently oriented C$_{\text{i}}$ \hkl<1 0 0> DBs to be responsible for this distance.
+Additionally, in the inset of the bottom part of Fig.\ref{fig:450:a} the Si-Si radial distribution shows non-zero values at distances around \unit[0.3]{nm}, which, again, is due to the DB structure stretching two neighbored Si atoms.
+This is accompanied by a reduction of the number of bonds at regular Si distances of c-Si.
+A more detailed description of the resulting C-Si distances in the C$_{\text{i}}$ \hkl<1 0 0> DB configuration and the influence of the defect on the structure is available in a previous study\cite{zirkelbach09}.
+
+For high C concentrations, the defect concentration is likewise increased and a considerable amount of damage is introduced in the insertion volume.
+A subsequent superposition of defects generates new displacement arrangements for the C-C as well as Si-C pair distances, which become hard to categorize and trace and obviously lead to a broader distribution.
+Short range order indeed is observed, i.e. the large amount of strong neighbored C-C bonds at \unit[0.15]{nm} as expected in graphite or diamond and Si-C bonds at \unit[0.19]{nm} as expected in SiC, but hardly visible is the long range order.
+This indicates the formation of an amorphous SiC-like phase.
+In fact, resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modified Tersoff potential\cite{gao02}.
+
+In both cases, i.e. low and high C concentrations, the formation of 3C-SiC fails to appear.
+With respect to the precipitation model, the formation of C$_{\text{i}}$ \hkl<1 0 0> DBs indeed occurs for low C concentrations.
+However, sufficient defect agglomeration is not observed.
+For high C concentrations, a rearrangement of the amorphous SiC structure, which is not expected at prevailing temperatures, and a transition into 3C-SiC is not observed either.
+On closer inspection two reasons for describing this obstacle become evident.
+
+First of all, there is the time scale problem inherent to MD in general.
+To minimize the integration error the discretized time step must be chosen smaller than the reciprocal of the fastest vibrational mode resulting in a time step of \unit[1]{fs} for the investigated materials system.
+Limitations in computer power result in a slow propagation in phase space.
+Several local minima exist, which are separated by large energy barriers.
+Due to the low probability of escaping such a local minimum, a single transition event corresponds to a multiple of vibrational periods.
+Long-term evolution, such as a phase transformation and defect diffusion, in turn, are made up of a multiple of these infrequent transition events.
+Thus, time scales to observe long-term evolution are not accessible by traditional MD.
+New accelerated methods have been developed to bypass the time scale problem retaining proper thermodynamic sampling\cite{voter97,voter97_2,voter98,sorensen2000,wu99}.
+
+However, the applied potential comes up with an additional limitation, as previously mentioned in the introduction.
+%The cut-off function of the short range potential limits the interaction to nearest neighbors, which results in overestimated and unphysical high forces between neighbored atoms.
+The cut-off function of the short range potential limits the interaction to nearest neighbors.
+Since the total binding energy is, thus, accommodated within this 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.
+While cohesive and formational energies are often well described, these effects increase for non-equilibrium structures and dynamics.
+This behavior, as observed and discussed for the Tersoff potential\cite{tang95,mattoni2007}, is supported by the overestimated activation energies necessary for C diffusion as investigated in section \ref{subsection:cmob}.
+Indeed, it is not only the strong, hard to break C-C bond inhibiting C diffusion and further rearrangements in the case of the high C concentration simulations.
+This is also true for the low concentration simulations dominated by the occurrence of C$_{\text{i}}$ \hkl<1 0 0> DBs spread over the whole simulation volume, which are unable to agglomerate due to the high migration barrier.
+
+\subsection{Increased temperature simulations}
+
+Due to the problem of slow phase space propagation, which is enhanced by the employed potential, pushing the time scale to the limits of computational resources or applying one of the above mentioned accelerated dynamics methods exclusively might not be sufficient.
+Instead, higher temperatures are utilized to compensate overestimated diffusion barriers.
+These are overestimated by a factor of 2.4 to 3.5.
+Scaling the absolute temperatures accordingly results in maximum temperatures of \unit[1460-2260]{$^{\circ}$C}.
+Since melting already occurs shortly below the melting point of the potential (2450 K)\cite{albe_sic_pot} due to the presence of defects, a maximum temperature of \unit[2050]{$^{\circ}$C} is used.
+
+Fig.~\ref{fig:tot} shows the resulting radial distribution functions for various temperatures.
+\begin{figure}
+\begin{center}
+\subfigure[]{\label{fig:tot:si-c}
+\includegraphics[width=\columnwidth]{tot_pc_thesis.ps}
+}
+\subfigure[]{\label{fig:tot:si-si}
+\includegraphics[width=\columnwidth]{tot_pc3_thesis.ps}
+}
+\subfigure[]{\label{fig:tot:c-c}
+\includegraphics[width=\columnwidth]{tot_pc2_thesis.ps}
+}
+\end{center}
+\caption{Radial distribution function for Si-C (Fig.~\ref{fig:tot:si-c}), Si-Si (Fig.~\ref{fig:tot:si-si}) and C-C (Fig.~\ref{fig:tot:c-c}) pairs for the C insertion into $V_1$ at elevated temperatures. For the Si-C distribution resulting Si-C distances of a C$_{\text{s}}$ configuration are plotted. In the C-C distribution dashed arrows mark C-C distances occurring from C$_{\text{i}}$ \hkl<1 0 0> DB combinations, solid arrows mark C-C distances of pure C$_{\text{s}}$ combinations and the dashed line marks C-C distances of a C$_{\text{i}}$ and C$_{\text{s}}$ combination.}
+\label{fig:tot}
+\end{figure}
+In Fig.~\ref{fig:tot:si-c}, the first noticeable and promising change observed for the Si-C bonds is the successive decline of the artificial peak at the cut-off distance with increasing temperature.
+Obviously, sufficient kinetic energy is provided to affected atoms that are enabled to escape the cut-off region.
+Additionally, a more important structural change was observed, which is illustrated in the two shaded areas in Fig.~\ref{fig:tot:si-c}.
+Obviously, the structure obtained at \unit[450]{$^{\circ}$C}, which was found to be dominated by C$_{\text{i}}$, transforms into a C$_{\text{s}}$ dominated structure with increasing temperature.
+Comparing the radial distribution at \unit[2050]{$^{\circ}$C} to the resulting bonds of C$_{\text{s}}$ in c-Si excludes all possibility of doubt.
+
+The phase transformation is accompanied by an arising Si-Si peak at \unit[0.325]{nm} in Fig.~\ref{fig:tot:si-si}, which corresponds to the distance of next neighbored Si atoms along the \hkl<1 1 0> bond chain with C$_{\text{s}}$ in between.
+Since the expected distance of these Si pairs in 3C-SiC is \unit[0.308]{nm} the existing SiC structures embedded in the c-Si host are stretched.
+
+According to the C-C radial distribution displayed in Fig.~\ref{fig:tot:c-c}, agglomeration of C fails to appear even for elevated temperatures, as can be seen on the total amount of C pairs within the investigated separation range, which does not change significantly.
+However, a small decrease in the amount of neighbored C pairs can be observed with increasing temperature.
+This high temperature behavior is promising since breaking of these diamond- and graphite-like bonds is mandatory for the formation of 3C-SiC.
+Obviously, acceleration of the dynamics occurred by supplying additional kinetic energy.
+A slight shift towards higher distances can be observed for the maximum located shortly above \unit[0.3]{nm}.
+Arrows with dashed lines mark C-C distances resulting from C$_{\text{i}}$ \hkl<1 0 0> DB combinations while arrows with solid lines mark distances arising from combinations of C$_{\text{s}}$.
+The continuous dashed line corresponds to the distance of C$_{\text{s}}$ and a neighbored C$_{\text{i}}$ DB.
+Obviously, the shift of the peak is caused by the advancing transformation of the C$_{\text{i}}$ DB into the C$_{\text{s}}$ defect.
+Quite high g(r) values are obtained for distances 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 C$_{\text{s}}$ with either another C atom that basically occupies a Si lattice site but is displaced by a Si interstitial 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.
+
+Fig.~\ref{fig:v2} displays the radial distribution for high C concentrations.
+\begin{figure}
+\begin{center}
+\subfigure[]{\label{fig:v2:si-c}
+\includegraphics[width=\columnwidth]{12_pc_thesis.ps}
+}
+\subfigure[]{\label{fig:v2:c-c}
+\includegraphics[width=\columnwidth]{12_pc_c_thesis.ps}
+}
+\end{center}
+\caption{Radial distribution function for Si-C (Fig.~\ref{fig:v2:si-c}) and C-C (Fig.~\ref{fig:v2:c-c}) pairs for the C insertion into $V_2$ at elevated temperatures. Arrows mark the respective cut-off distances.}
+\label{fig:v2}
+\end{figure}
+\begin{figure}
+\begin{center}
+\includegraphics[width=\columnwidth]{2050.eps}
+\end{center}
+\caption{Cross section along the \hkl(1 -1 0) plane of the atomic structure of the high concentration simulation for a C insertion temperature of \unit[2050]{$^{\circ}$C}.}
+\label{fig:v2as}
+\end{figure}
+A cross-section along the \hkl(1 -1 0) plane of the atomic structure for a C insertion temperature of \unit[2050]{$^{\circ}$C} is shown in Fig.~\ref{fig:v2as}.
+The amorphous SiC-like phase remains.
+No significant change in structure is observed.
+However, the decrease of the cut-off artifact and slightly sharper peaks observed with increasing temperature, in turn, indicate a slight acceleration of the dynamics realized by the supply of kinetic energy.
+However, it is not sufficient to enable the amorphous to crystalline transition.
+In contrast, even though bonds of neighbored C atoms could be partially dissolved in the system exhibiting low C concentrations, the amount of neighbored C pairs even increased in the latter case.
+Moreover, the C-C peak at \unit[0.252]{nm} in Fig.~\ref{fig:v2:c-c}, which gets slightly more distinct, equals the second nearest neighbor distance in diamond and indeed is made up by a structure of two C atoms interconnected by a third C atom.
+Obviously, processes that appear to be non-conducive are likewise accelerated in a system, in which high amounts of C are incorporated within a short period of time, which is accompanied by a concurrent introduction of accumulating, for the reason of time non-degradable damage.
+% non-degradable, non-regenerative, non-recoverable
+Thus, for these systems even larger time scales, which are not accessible within traditional MD, must be assumed for an amorphous to crystalline transition or structural evolution in general.
+% maybe put description of bonds in here ...
+Nevertheless, some results likewise indicate the acceleration of other processes that, again, involve C$_{\text{s}}$.
+The increasingly pronounced Si-C peak at \unit[0.35]{nm} in Fig.~\ref{fig:v2:si-c} corresponds to the distance of a C and a Si atom interconnected by another Si atom.
+Additionally, the C-C peak at \unit[0.31]{nm} in Fig.~\ref{fig:v2:c-c} corresponds to the distance of two C atoms bound to a central Si atom.
+For both structures the C atom appears to reside on a substitutional rather than an interstitial lattice site.
+However, huge amounts of damage hamper identification.
+The alignment of the investigated structures to the c-Si host is lost in many cases, which suggests the necessity of much more time for structural evolution to maintain the topotactic orientation of the precipitate.
+
+\section{Discussion and Summary}
+
+Investigations are targeted at the initially stated controversy of SiC precipitation, i.e. whether precipitation occurs abruptly after enough C$_{\text{i}}$ agglomerated or after a successive agglomeration of C$_{\text{s}}$ on usual Si lattice sites (and Si$_{\text{i}}$) followed by a contraction into incoherent SiC.
+Results of a previous ab initio study on defects and defect combinations in C implanted Si\cite{zirkelbach11a} suggest C$_{\text{s}}$ to play a decisive role in the precipitation of SiC in Si.
+To support previous assumptions MD simulations, which are capable of modeling the necessary amount of atoms, i.e. the precipitate and the surrounding c-Si structure, have been employed in the current study.
+
+In a previous comparative study\cite{zirkelbach10} we have shown that the utilized empirical potential fails to describe some selected processes.
+Thus, limitations of the employed potential have been further investigated and taken into account in the present study.
+We focussed on two major shortcomings: the overestimated activation energy and the improper description of intrinsic and C point defects in Si.
+Overestimated forces between nearest neighbor atoms that are expected for short range potentials\cite{mattoni2007} have been confirmed to influence the C$_{\text{i}}$ diffusion.
+The migration barrier was estimated to be larger by a factor of 2.4 to 3.5 compared to highly accurate quantum-mechanical calculations\cite{zirkelbach10}.
+Concerning point defects, the drastically underestimated formation energy of C$_{\text{s}}$ and deficiency in the description of the Si$_{\text{i}}$ ground state necessitated further investigations on structures that are considered important for the problem under study.
+It turned out that the EA potential still favors a C$_{\text{i}}$ \hkl<1 0 0> DB over a C$_{\text{s}}$-Si$_{\text{i}}$ configuration, which, thus, does not constitute any limitation for the simulations aiming to resolve the present controversy of the proposed SiC precipitation models.
+
+MD simulations at temperatures used in IBS resulted in structures that were 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 $V_3$ led to an amorphous SiC-like structure within the respective volume.
+To compensate overestimated diffusion barriers, we performed simulations at accordingly increased temperatures.
+No significant change was observed for high C concentrations.
+The amorphous phase is maintained.
+Due to the incorporation of a huge amount of C into a small volume within a short period of time, damage is produced, which obviously decelerates structural evolution.
+For the low C concentrations, time scales are still too low to observe C agglomeration sufficient for SiC precipitation, which is attributed to the slow phase space propagation inherent to MD in general.
+However, we observed a phase transition of the C$_{\text{i}}$-dominated into a clearly C$_{\text{s}}$-dominated structure.
+The amount of substitutionally occupied C atoms increases with increasing temperature.
+Entropic contributions are assumed to be responsible for these structures at elevated temperatures that deviate from the ground state at 0 K.
+Indeed, in a previous ab initio MD simulation\cite{zirkelbach11a} performed at \unit[900]{$^{\circ}$C} we observed the departing of a Si$_{\text{i}}$ \hkl<1 1 0> DB located next to a C$_{\text{s}}$ atom instead of a recombination into the ground state configuration, i.e. a C$_{\text{i}}$ \hkl<1 0 0> DB.
+
+% postannealing less efficient than hot implantation
+Experimental studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates\cite{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.
+We assume this to be related to the problem of slow structural evolution encountered in the high C concentration simulations due to the insertion of high amounts of C into a small volume within a short period of time resulting in essentially no time for the system to rearrange.
+% rt implantation + annealing
+Implantations of an understoichiometric dose at room temperature followed by thermal annealing results in small spherical sized C$_{\text{i}}$ agglomerates at temperatures below \unit[700]{$^{\circ}$C} and SiC precipitates of the same size at temperatures above \unit[700]{$^{\circ}$C}\cite{werner96}.
+Since, however, the implantation temperature is considered more efficient than the postannealing temperature, SiC precipitates are expected -- and indeed are observed for as-implanted samples\cite{lindner99,lindner01} -- in implantations performed at \unit[450]{$^{\circ}$C}.
+Implanted C is therefore expected to occupy substitutionally usual Si lattice sites right from the start.
+
+Thus, we propose an increased participation of C$_{\text{s}}$ already in the initial stages of the implantation process at temperatures above \unit[450]{$^{\circ}$C}, the temperature most applicable for the formation of SiC layers of high crystalline quality and topotactical alignment\cite{lindner99}.
+Thermally activated, C$_{\text{i}}$ is enabled to turn into C$_{\text{s}}$ accompanied by Si$_{\text{i}}$.
+The associated emission of Si$_{\text{i}}$ is needed for several reasons.
+For the agglomeration and rearrangement of C, Si$_{\text{i}}$ is needed to turn C$_{\text{s}}$ into highly mobile C$_{\text{i}}$ again.
+Since the conversion of a coherent SiC structure, i.e. C$_{\text{s}}$ occupying the Si lattice sites of one of the two fcc lattices that build up the c-Si diamond lattice, into incoherent SiC is accompanied by a reduction in volume, large amounts of strain are assumed to reside in the coherent as well as at the surface of the incoherent structure.
+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}.
+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.
+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.