The consequential superposition of these defects and the high amounts of damage generate new displacement arrangements for the C-C as well as for the 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 only hardly visible is the long range order.
This indicates the formation of an amorphous SiC-like phase.
-In fact the 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 fact the 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.
Thus, the average time of a transition from one potential basin to another corresponds to a great deal of vibrational periods, which in turn determine the integration time step.
Hence, time scales covering the necessary amount of infrequent events to observe long-term evolution are not accessible by traditional MD simulations, which are limited to the order of nanoseconds.
New methods have been developed to bypass the time scale problem.
-The most famous approaches are hyperdynamics (HMD) \cite{voter97,voter97_2}, parallel replica dynamics \cite{voter98}, temperature accelerated dynamics (TAD) \cite{sorensen2000} and self-guided dynamics (SGMD) \cite{wu99}, which accelerate phase space propagation while retaining proper thermodynamic sampling.
+The most famous approaches are hyperdynamics (HMD)~\cite{voter97,voter97_2}, parallel replica dynamics~\cite{voter98}, temperature accelerated dynamics (TAD)~\cite{sorensen2000} and self-guided dynamics (SGMD)~\cite{wu99}, which accelerate phase space propagation while retaining proper thermodynamic sampling.
In addition to the time scale limitation, problems attributed to the short range potential exist.
-The sharp cut-off function, which limits the interacting ions to the next neighbored atoms by gradually pushing the interaction force and energy to zero between the first and second next neighbor distance, is responsible for overestimated and unphysical high forces of next neighbored atoms \cite{tang95,mattoni2007}.
+The sharp cut-off function, which limits the interacting ions to the next neighbored atoms by gradually pushing the interaction force and energy to zero between the first and second next neighbor distance, is responsible for overestimated and unphysical high forces of next neighbored atoms~\cite{tang95,mattoni2007}.
This is supported by the overestimated activation energies necessary for C diffusion as investigated in section \ref{subsection:defects:mig_classical}.
Indeed, it is not only the strong C-C bond, which is hard to break, inhibiting C diffusion and further rearrangements.
This is also true for the low concentration simulations dominated by the occurrence of C-Si DBs spread over the whole simulation volume.
These unphysical effects inherent to this type of model potentials are solely attributed to their short range character.
While cohesive and formational energies are often well described, these effects increase for non-equilibrium structures and dynamics.
However, since valuable insights into various physical properties can be gained using this potentials, modifications mainly affecting the cut-off were designed.
-One possibility is to simply skip the force contributions containing the derivatives of the cut-off function, which was successfully applied to reproduce the brittle propagation of fracture in SiC at zero temperature \cite{mattoni2007}.
-Another one is to use variable cut-off values scaled by the system volume, which properly describes thermomechanical properties of 3C-SiC \cite{tang95} but might be rather ineffective for the challenge inherent to this study.
+One possibility is to simply skip the force contributions containing the derivatives of the cut-off function, which was successfully applied to reproduce the brittle propagation of fracture in SiC at zero temperature~\cite{mattoni2007}.
+Another one is to use variable cut-off values scaled by the system volume, which properly describes thermomechanical properties of 3C-SiC~\cite{tang95} but might be rather ineffective for the challenge inherent to this study.
To conclude the obstacle needed to get passed is twofold.
The sharp cut-off of the employed bond order model potential introduces overestimated high forces between next neighbored atoms enhancing the problem of slow phase space propagation immanent to MD simulations.
Due to this, pushing the time scale to the limits of computational resources or applying one of the above mentioned accelerated dynamics methods exclusively will not be sufficient enough.
Instead, the approach followed in this study, is the use of higher temperatures as exploited in TAD to find transition pathways of one local energy minimum to another one more quickly.
-Since merely increasing the temperature leads to different equilibrium kinetics than valid at low temperatures, TAD introduces basin-constrained MD allowing only those transitions that should occur at the original temperature and a properly advancing system clock \cite{sorensen2000}.
+Since merely increasing the temperature leads to different equilibrium kinetics than valid at low temperatures, TAD introduces basin-constrained MD allowing only those transitions that should occur at the original temperature and a properly advancing system clock~\cite{sorensen2000}.
The TAD corrections are not applied in coming up simulations.
This is justified by two reasons.
First of all, a compensation of the overestimated bond strengths due to the short range potential is expected.
-Secondly, there is no conflict applying higher temperatures without the TAD corrections, since crystalline 3C-SiC is also observed for higher temperatures than \unit[450]{$^{\circ}$C} in IBS \cite{nejim95,lindner01}.
+Secondly, there is no conflict applying higher temperatures without the TAD corrections, since crystalline 3C-SiC is also observed for higher temperatures than \unit[450]{$^{\circ}$C} in IBS~\cite{nejim95,lindner01}.
It is therefore expected that the kinetics affecting the 3C-SiC precipitation are not much different at higher temperatures aside from the fact that it is occurring much more faster.
Moreover, the interest of this study is focused on structural evolution of a system far from equilibrium instead of equilibrium properties which rely upon proper phase space sampling.
On the other hand, during implantation, the actual temperature inside the implantation volume is definitely higher than the experimentally determined temperature tapped from the surface of the sample.
Increased temperatures are expected to compensate the 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 (\unit[2450]{K}) \cite{albe_sic_pot} due to the presence of defects, temperatures ranging from \unit[450--2050]{$^{\circ}$C} are used.
+Since melting already occurs shortly below the melting point of the potential (\unit[2450]{K})~\cite{albe_sic_pot} due to the presence of defects, temperatures ranging from \unit[450--2050]{$^{\circ}$C} are used.
The simulation sequence and other parameters except for the system temperature remain unchanged as in section \ref{section:initial_sims}.
Since there is no significant difference among the $V_2$ and $V_3$ simulations only the $V_1$ and $V_2$ simulations are carried on and referred to as low C and high C concentration simulations.
Entropic contributions are assumed to be responsible for these structures at elevated temperatures that deviate from the ground state at 0 K.
Results of the MD simulations at different temperatures and C concentrations can be correlated to experimental findings.
-IBS studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates \cite{kimura82,eichhorn02}.
-In particular, the restructuring of strong C-C bonds is affected \cite{deguchi92}.
+IBS studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates~\cite{kimura82,eichhorn02}.
+In particular, the restructuring of strong C-C bonds is affected~\cite{deguchi92}.
These bonds preferentially arise if additional kinetic energy provided by an increase of the implantation temperature is missing to accelerate or even enable atomic rearrangements.
This is assumed to be related to the problem of slow structural evolution encountered in the high C concentration simulations.
The insertion of high amounts of C into a small volume within a short period of time results in essentially no time for the system to rearrange.
% rt implantation + annealing
-Furthermore, C implanted at room temperature was found to be able to migrate towards the surface and form C-rich clusters in contrast to implantations at elevated temperatures, which form stable epitaxially aligned 3C-SiC precipitates \cite{serre95}.
+Furthermore, C implanted at room temperature was found to be able to migrate towards the surface and form C-rich clusters in contrast to implantations at elevated temperatures, which form stable epitaxially aligned 3C-SiC precipitates~\cite{serre95}.
In simulation, low temperatures result in configurations of highly mobile \ci{} \hkl<1 0 0> DBs whereas elevated temperatures show configurations of \cs{}, which constitute an extremely stable configuration that is unlikely to migrate.
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% added
-This likewise agrees to results of IBS experiments utilizing implantation temperatures of \degc{550}, which require annealing temperatures as high as \degc{1405} for C segregation due to the stability of \cs{} \cite{reeson87}.
+This likewise agrees to results of IBS experiments utilizing implantation temperatures of \degc{550}, which require annealing temperatures as high as \degc{1405} for C segregation due to the stability of \cs{}~\cite{reeson87}.
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-Indeed, in the optimized recipe to form 3C-SiC by IBS \cite{lindner99}, elevated temperatures are used to improve the epitaxial orientation together with a low temperature implant to destroy stable SiC nanocrystals at the interface, which are unable to migrate during thermal annealing resulting in a rough surface.
+Indeed, in the optimized recipe to form 3C-SiC by IBS~\cite{lindner99}, elevated temperatures are used to improve the epitaxial orientation together with a low temperature implant to destroy stable SiC nanocrystals at the interface, which are unable to migrate during thermal annealing resulting in a rough surface.
Furthermore, the improvement of the epitaxial orientation of the precipitate with increasing temperature in experiment perfectly conforms to the increasing occurrence of \cs{} in simulation.
%
% todo add sync here starting from strane93, werner96 ...
-Moreover, implantations of an understoichiometric dose into preamorphized Si followed by an annealing step at \degc{700} result in Si$_{1-x}$C$_x$ layers with C residing on substitutional Si lattice sites \cite{strane93}.
-For implantations of an understoichiometric dose into c-Si at room temperature followed by thermal annealing below and above \degc{700}, the formation of small C$_{\text{i}}$ agglomerates and SiC precipitates was observed respectively \cite{werner96}.
-However, increased implantation temperatures were found to be more efficient than postannealing methods resulting in the formation of SiC precipitates for implantations at \unit[450]{$^{\circ}$C} \cite{lindner99,lindner01}.
+Moreover, implantations of an understoichiometric dose into preamorphized Si followed by an annealing step at \degc{700} result in Si$_{1-x}$C$_x$ layers with C residing on substitutional Si lattice sites~\cite{strane93}.
+For implantations of an understoichiometric dose into c-Si at room temperature followed by thermal annealing below and above \degc{700}, the formation of small C$_{\text{i}}$ agglomerates and SiC precipitates was observed respectively~\cite{werner96}.
+However, increased implantation temperatures were found to be more efficient than postannealing methods resulting in the formation of SiC precipitates for implantations at \unit[450]{$^{\circ}$C}~\cite{lindner99,lindner01}.
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Thus, at elevated temperatures, implanted C is expected to occupy substitutionally usual Si lattice sites right from the start.
These findings, which are outlined in more detail within the comprehensive description in chapter~\ref{chapter:summary}, are in perfect agreement with previous results of the quantum-mechanical investigations.
Indeed, \si{} is observed in the direct surrounding of the stretched SiC structures.
Next to the rearrangement, \si{} is required as a supply for additional C atoms to form further SiC and to compensate strain, either within the coherent and stretched SiC structure as well as at the interface of the incoherent SiC precipitate and the Si host.
%
-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.
+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.
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