Thus, a proper description with respect to the relative energies of formation is assumed for the EA potential.
\subsection{Carbon mobility}
+\label{subsection:cmob}
To accurately model the SiC precipitation, which involves the agglomeration of C, a proper description of the migration process of the C impurity is required.
As shown in a previous study\cite{zirkelbach10a} quantum-mechanical results properly describe the C$_{\text{i}}$ \hkl<1 0 0> DB diffusion resulting in a migration barrier height of \unit[0.90]{eV} excellently matching experimental values of \unit[0.70-0.87]{eV}\cite{lindner06,tipping87,song90} and, for this reason, reinforcing the respective migration path as already proposed by Capaz et~al.\cite{capaz94}.
\includegraphics[width=\columnwidth]{../img/sic_prec_450_si-si_c-c.ps}\\
\includegraphics[width=\columnwidth]{../img/sic_prec_450_si-c.ps}
\end{center}
-\caption{Radial distribution function for C-C and Si-Si (top) as well as Si-C (bottom) pairs for a C insertion temperature of \unit[450]{$^{\circ}$C}. In the latter case the resulting C-Si distances for a C$_{\text{i}}$ \hkl<1 0 0> DB are given additionally.}
+\caption{Radial distribution function for C-C and Si-Si (top) as well as Si-C (bottom) pairs for C inserted at \unit[450]{$^{\circ}$C}. In the latter case the resulting C-Si distances for a C$_{\text{i}}$ \hkl<1 0 0> DB are given additionally.}
\label{fig:450}
\end{figure}
There is no significant difference between C insertion into $V_2$ and $V_3$.
However, sufficient defect agglomeration is not observed.
For high C concentrations a rearrangment 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.
-Inherent to MD in general ...
-Potential limitation ...
+
+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 current problem under study.
+Limitations in computer power result in a slow propgation 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 already mentioned in the introductory part.
+The cut-off function of the short range potential limits the interaction to next neighbors, which results in overestimated and unphysical high forces between next neighbor atoms.
+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 C-C bond which is hard to break inhibiting C diffusion and further rearrengements 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 1 0> DBs spread over the whole simulation volume, which are unable to agglomerate due to the high migration barrier.
\subsection{Increased temperature simulations}
-Foobar ...
+Due to the potential enhanced problem of slow phase space propagation, pushing the time scale to the limits of computational ressources 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 potetnial (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}
\includegraphics[width=\columnwidth]{../img/tot_pc_thesis.ps}\\
\includegraphics[width=\columnwidth]{../img/tot_pc3_thesis.ps}\\
\includegraphics[width=\columnwidth]{../img/tot_pc2_thesis.ps}
\end{center}
-\caption{Radial distribution function for Si-C (top), Si-Si (center) and C-C (bottom) pairs for the C insertion into $V_1$ at elevated temperatures. In the latter case dashed arrows mark C-C distances occuring 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.}
+\caption{Radial distribution function for Si-C (top), Si-Si (center) and C-C (bottom) 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 occuring 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}
-
-Barfoo ...
+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 enough 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 of the graph.
+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}, which corresponds to the distance of second next neighbored Si atoms alonga \hkl<1 1 0> boind chain with C$_{\text{s}}$ inbetween.
+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 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, wich does not change significantly.
+However, a small decrease in the amount of next neighboured C pairs can be observed with increasing temperature.
+This high temperature behavior is promising since breaking of these diomand- and graphite-like bonds is mandatory for the formation of 3C-SiC.
+Obviously acceleration of the dynamics occured 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 next neighboured 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 inbetween 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}
\includegraphics[width=\columnwidth]{../img/12_pc_thesis.ps}\\
\caption{Radial distribution function for Si-C (top) and C-C (bottom) pairs for the C insertion into $V_2$ at elevated temperatures.}
\label{fig:v2}
\end{figure}
+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 next neighbored C bonds could be partially dissolved in the system exhibiting low C concentrations the amount of next neighbored C pairs even increased in the latter case.
+Moreover the C-C peak at \unit[0.252]{nm}, which gets slightly more distinct, equals the second next 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 incoorporated 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 likewiese indicate the acceleration of other processes that, again, involve C$_{\text{s}}$.
+The increasingly pronounced Si-C peak at \unit[0.35]{nm} 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} 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 amount of damage hampers identification.
+The alignment of the investigated structures to the c-Si host is lost in many cases, which suggests the necissity of much more time for structural evolution to maintain the topotaptic orientation of the precipitate.
\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.
+Investigations are targeted on the initially stated controversy of SiC precipitation, i.e. whether precipitation occurs abrubtly after ehough C$_{\text{i}}$ agglomerated or 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{zirkelbach10b} sugeest 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{zirkelbach10a} we have schown 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 next 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{zirkelbach10a}.
+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.
+Incoorporation into volmes $V_2$ and $V_3$ led to an amorphous SiC-like structure within the respective volume.
+To ensure correct diffusion behavior simulations at elevated temperatures have been performed.
+Although ...
+
+entropic contribution.
+as in \cite{zirkelbach10b}, next neighbored Cs and Sii did not recombine, but departed from each other.
+
+Sii stress compensation ...
+Thus, we prpopose (support) the follwing model ...
+
+Concluded that C sub is very probable ...
+Alignment lost, successive substitution more probable to end up with topotactic 3C-SiC.
+
+Both, low and high, acceleration not enough to either observe C agglomeration or amorphous to crystalline transition ...
+
\section{Summary}
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