\label{chapter:md}
The molecular dynamics (MD) technique is used to gain insight into the behavior of C existing in different concentrations in c-Si on the microscopic level at finite temperatures.
-The simulations are restricted to classical potential simulations utilizing the analytical EA bond order potential as described in section \ref{subsection:interact_pot}.
-Parameters are chosen according to the discussion in section \ref{section:classpotmd}.
+The simulations are restricted to classical potential simulations utilizing the analytical EA bond order potential as described in section~\ref{subsection:interact_pot}.
+Parameters are chosen according to the discussion in section~\ref{section:classpotmd}.
At the beginning, simulations are performed, which try to mimic the conditions during IBS.
Results reveal limitations of the employed potential and MD in general.
$V_2$ approximately corresponds to the volume of a minimal 3C-SiC precipitate.
$V_3$ is approximately the volume containing the amount of Si atoms necessary to form such a precipitate, which is slightly smaller than $V_2$ due to the slightly lower Si density of 3C-SiC compared to c-Si.
The two latter insertion volumes are considered since no diffusion of C atoms is expected within the simulated period of time at prevalent temperatures.
-This is due to the overestimated activation energy for the diffusion of a \ci \hkl<1 0 0> DB, as pointed out in section \ref{subsection:defects:mig_classical}.
+This is due to the overestimated activation energy for the diffusion of a \ci \hkl<1 0 0> DB, as pointed out in section~\ref{subsection:defects:mig_classical}.
For rectangularly shaped precipitates with side length $L$ the amount of C atoms in 3C-SiC and Si atoms in c-Si is given by
\begin{equation}
N_{\text{C}}^{\text{3C-SiC}} =4 \left( \frac{L}{a_{\text{SiC}}}\right)^3
N_{\text{Si}}^{\text{c-Si}} =8 \left( \frac{L}{a_{\text{Si}}}\right)^3 \text{ .}
\label{eq:md:n_prec}
\end{equation}
-Table \ref{table:md:ins_vols} summarizes the side length of each of the three different insertion volumes determined by equations \eqref{eq:md:n_prec} and the resulting C concentrations inside these volumes.
+Table~\ref{table:md:ins_vols} summarizes the side length of each of the three different insertion volumes determined by equations \eqref{eq:md:n_prec} and the resulting C concentrations inside these volumes.
Looking at the C concentrations, simulations can be distinguished in simulations occupying low ($V_1$) and high ($V_2$, $V_3$) concentrations of C.
\begin{table}[tp]
\begin{center}
Thus, the simulation is continued without adding more C atoms until the system temperature is equal to the chosen temperature again.
This is realized by the thermostat, which decouples excessive energy.
Every inserted C atom must exhibit a distance greater or equal to \unit[1.5]{\AA} to neighbored atoms to prevent the occurrence of too high forces.
-Once the total amount of C is inserted, the simulation is continued for \unit[100]{ps} followed by a cooling-down process until room temperature, i.e. \unit[20]{$^{\circ}$C}, is reached.
+Once the total amount of C is inserted, the simulation is continued for \unit[100]{ps} followed by a cooling-down process until room temperature, i.e.\ \unit[20]{$^{\circ}$C}, is reached.
Fig.~\ref{fig:md:prec_fc} displays a flow chart of the applied steps involved in the simulation sequence.
\begin{figure}[tp]
\begin{center}
\label{fig:md:prec_fc}
\end{figure}
-The radial distribution function $g(r)$ for C-C and Si-Si distances is shown in Fig. \ref{fig:md:pc_si-si_c-c}.
+The radial distribution function $g(r)$ for C-C and Si-Si distances is shown in Fig.~\ref{fig:md:pc_si-si_c-c}.
\begin{figure}[tp]
\begin{center}
\includegraphics[width=0.7\textwidth]{sic_prec_450_si-si_c-c.ps}
The bottom of Fig.~\ref{fig:md:pc_si-si_c-c} shows the radial distribution of Si-Si bonds together with a reference graph for pure c-Si.
Indeed, non-zero $g(r)$ values around \unit[0.31]{nm} are observed while the amount of Si pairs at regular c-Si distances of \unit[0.24]{nm} and \unit[0.38]{nm} decreases.
However, no clear peak is observed but the interval of enhanced $g(r)$ values corresponds to the width of the C-C $g(r)$ peak.
-In addition the abrupt increase of Si pairs at \unit[0.29]{nm} can be attributed to the Si-Si cut-off radius of \unit[0.296]{nm} as used in the present bond order potential.
+In addition, the abrupt increase of Si pairs at \unit[0.29]{nm} can be attributed to the Si-Si cut-off radius of \unit[0.296]{nm} as used in the present bond order potential.
The cut-off function causes artificial forces pushing the Si atoms out of the cut-off region.
Without the abrupt increase, a maximum around \unit[0.31]{nm} gets even more conceivable.
-Analyses of randomly chosen configurations, in which distances around \unit[0.3]{nm} appear, identify \ci{} \hkl<1 0 0> DBs to be responsible for stretching the Si-Si next neighbor distance for low C concentrations, i.e. for the $V_1$ and early stages of $V_2$ and $V_3$ simulation runs.
+Analyses of randomly chosen configurations, in which distances around \unit[0.3]{nm} appear, identify \ci{} \hkl<1 0 0> DBs to be responsible for stretching the Si-Si next neighbor distance for low C concentrations, i.e.\ for the $V_1$ and early stages of $V_2$ and $V_3$ simulation runs.
This excellently agrees with the calculated value $r(13)$ in Table~\ref{tab:defects:100db_cmp} for a resulting Si-Si distance in the \ci \hkl<1 0 0> DB configuration.
\begin{figure}[tp]
Not only the peak locations but also the peak widths and heights become comprehensible.
The distinct peak at \unit[0.26]{nm}, which exactly matches the cut-off radius of the Si-C interaction, is again a potential artifact.
-For high C concentrations, i.e. the $V_2$ and $V_3$ simulation corresponding to a C density of about 8 atoms per c-Si unit cell, the defect concentration is likewise increased and a considerable amount of damage is introduced in the insertion volume.
+For high C concentrations, i.e.\ the $V_2$ and $V_3$ simulation corresponding to a C density of about 8 atoms per c-Si unit cell, the defect concentration is likewise increased and a considerable amount of damage is introduced in the insertion volume.
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.
+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.
+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.
Vibrations of the covalent bond take place on the order of \unit[10$^{-14}$]{s}, of which the thermodynamic and kinetic properties are well described by MD simulations.
To avoid discretization errors, the integration time step needs to be chosen smaller than the fastest vibrational frequency in the system.
On the other hand, infrequent processes, such as conformational changes, reorganization processes during film growth, defect diffusion and phase transitions are processes undergoing long-term evolution in the range of microseconds.
-This is due to the existence of several local minima in the free energy surface separated by large energy barriers compared to the kinetic energy of the particles, i.e. the system temperature.
+This is due to the existence of several local minima in the free energy surface separated by large energy barriers compared to the kinetic energy of the particles, i.e.\ the system temperature.
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}.
-This is supported by the overestimated activation energies necessary for C diffusion as investigated in section \ref{subsection:defects:mig_classical}.
+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.
The bonds of these C-Si pairs are also affected by the cut-off artifact preventing C diffusion and agglomeration of the DBs.
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.
+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.
This obstacle could be referred to as {\em potential enhanced slow phase space propagation}.
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.
Due to the limitations of short range potentials and conventional MD as discussed above, elevated temperatures are used in the following.
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.
-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.
+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.
+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.
A simple quality value $Q$ is introduced, which helps to estimate the progress of structural evolution.
In bulk 3C-SiC every C atom has four next neighbored Si atoms and every Si atom four next neighbored C atoms.
\includegraphics[width=0.7\textwidth]{tot_pc_thesis.ps}\\
\includegraphics[width=0.7\textwidth]{tot_ba.ps}
\end{center}
-\caption[Si-C radial distribution and evolution of quality $Q$ for the low concentration simulations at different elevated temperatures.]{Si-C radial distribution and evolution of quality $Q$ according to equation \ref{eq:md:qdef} for the low concentration simulations at different elevated temperatures. All structures are cooled down to \degc{20}. The gray line shows resulting Si-C bonds in a configuration of \cs{} in c-Si (C$_\text{sub}$) at zero temperature. Arrows in the quality plot mark the end of C insertion and the start of the cooling down step. A fit function according to equation \eqref{eq:md:fit} shows the estimated evolution of quality in the absence of the cooling down sequence.}
+\caption[Si-C radial distribution and evolution of quality $Q$ for the low concentration simulations at different elevated temperatures.]{Si-C radial distribution and evolution of quality $Q$ according to equation~\ref{eq:md:qdef} for the low concentration simulations at different elevated temperatures. All structures are cooled down to \degc{20}. The gray line shows resulting Si-C bonds in a configuration of \cs{} in c-Si (C$_\text{sub}$) at zero temperature. Arrows in the quality plot mark the end of C insertion and the start of the cooling down step. A fit function according to equation \eqref{eq:md:fit} shows the estimated evolution of quality in the absence of the cooling down sequence.}
\label{fig:md:tot_si-c_q}
\end{figure}
Fig.~\ref{fig:md:tot_si-c_q} shows the radial distribution of Si-C bonds for different temperatures and the corresponding evolution of quality $Q$ as defined above for the low concentration simulation.
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.
+%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.
To summarize, results of low concentration simulations show a phase transition in conjunction with an increase in temperature.
The \ci{} \hkl<1 0 0> DB dominated structure turns into a structure characterized by the occurrence of an increasing amount of \cs{} with respect to temperature.
As for low temperatures, order in the short range exists decreasing with increasing separation.
The increase of the amount of Si-C pairs at \distn{0.186} could be positively interpreted since this type of bond also exists in 3C-SiC.
On the other hand, the amount of next neighbored C atoms with a distance of approximately \distn{0.15}, which is the distance of C in graphite or diamond, is likewise increased.
-Thus, higher temperatures seem to additionally enhance a conflictive process, i.e. the formation of C agglomerates, obviously inconsistent with the desired process of 3C-SiC formation.
+Thus, higher temperatures seem to additionally enhance a conflictive process, i.e.\ the formation of C agglomerates, obviously inconsistent with the desired process of 3C-SiC formation.
This is supported by the C-C peak at \distn{0.252}, which corresponds to the second next neighbor distance in the diamond structure of elemental C.
Investigating the atomic data indeed reveals two C atoms, which are bound to and interconnected by a third C atom, to be responsible for this distance.
The C-C peak at about \distn{0.31}, which is slightly shifted to higher distances (\distn{0.317}) with increasing temperature still corresponds quite well to the next neighbor distance of C in 3C-SiC as well as a-SiC and indeed results from C-Si-C bonds.
\section{Long time scale simulations at maximum temperature}
-As discussed in section~\ref{section:md:limit} and~\ref{section:md:inct} a further increase of the system temperature might help to overcome limitations of the short range potential and accelerate the dynamics involved in structural evolution.
+As discussed in section~\ref{section:md:limit} and~\ref{section:md:inct}, a further increase of the system temperature might help to overcome limitations of the short range potential and accelerate the dynamics involved in structural evolution.
Furthermore, these results indicate that increased temperatures are necessary to drive the system out of equilibrium enabling conditions needed for the formation of a metastable cubic polytype of SiC.
-A maximum temperature to avoid melting is determined in section \ref{section:md:tval} to be 120 \% of the Si melting point but due to defects lowering the transition point a maximum temperature of 95 \% of the Si melting temperature is considered useful.
+A maximum temperature to avoid melting is determined in section~\ref{section:md:tval} to be 120 \% of the Si melting point but due to defects lowering the transition point a maximum temperature of 95 \% of the Si melting temperature is considered useful.
This value is almost equal to the temperature of $2050\,^{\circ}\mathrm{C}$ already used in former simulations.
-Since the maximum temperature is reached the approach is reduced to the application of longer time scales.
+Since the maximum temperature is reached, the approach is reduced to the application of longer time scales.
This is considered useful since the estimated evolution of quality in the absence of the cooling down sequence in figure~\ref{fig:md:tot_si-c_q} predicts an increase in quality and, thus, structural evolution is likely to occur if the simulation is proceeded at maximum temperature.
-Next to the employment of longer time scales and a maximum temperature a few more changes are applied.
-In the following simulations the system volume, the amount of C atoms inserted and the shape of the insertion volume are modified from the values used in first MD simulations.
-To speed up the simulation the initial simulation volume is reduced to 21 Si unit cells in each direction and 5500 inserted C atoms in either the whole volume or in a sphere with a radius of 3 nm corresponding to the size of a precipitate consisting of 5500 C atoms.
+Next to the employment of longer time scales and a maximum temperature, a few more changes are applied.
+In the following simulations, the system volume, the amount of C atoms inserted and the shape of the insertion volume are modified from the values used in first MD simulations.
+To speed up the simulation, the initial simulation volume is reduced to 21 Si unit cells in each direction and 5500 inserted C atoms in either the whole volume or in a sphere with a radius of 3 nm corresponding to the size of a precipitate consisting of 5500 C atoms.
The \unit[100]{ps} sequence after C insertion intended for structural evolution is exchanged by a \unit[10]{ns} sequence, which is hoped to result in the occurrence of infrequent processes and a subsequent phase transition.
The return to lower temperatures is considered separately.
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.
%
% 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}.
%
-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}.
%
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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