The plane-wave based Vienna {\em ab initio} simulation package (VASP) \cite{kresse96} is used for the first-principles calculations based on density functional theory (DFT).
Exchange and correlation is taken into account by the generalized-gradient approximation \cite{perdew86,perdew92}.
-Norm-conserving ultra-soft pseudopotentials \cite{hamann79} as implemented in VASP \cite{vanderbilt90} are used to describe the electron-ion interaction.
+Norm-con\-ser\-ving ultra-soft pseudopotentials \cite{hamann79} as implemented in VASP \cite{vanderbilt90} are used to describe the electron-ion interaction.
A kinetic energy cut-off of \unit[300]{eV} is employed.
Defect structures and migration paths were modelled in cubic supercells with a side length of \unit[1.6]{nm} containing $216$ Si atoms.
These structures are large enough to restrict sampling of the Brillouin zone to the $\Gamma$-point and formation energies and structures are reasonably converged.
\section{Mobility of the carbon defect}
-The migration barriers of the ground-state C defect are investigated by both, first-principles as well as the empirical method, their migration pathways shown in Fig.~\ref{fig:mig}.
+The migration barriers of the ground-state C defect are investigated by both, first-principles as well as the empirical method.
+The migration pathways are shown in Fig.~\ref{fig:mig}.
\begin{figure}
\subfloat[Transition path obtained by first-principles methods.]{%
In contrast, the empirical approach does not reproduce the same path.
Related to the above mentioned instability of the BC configuration, a pathway involving the C$_{\text{i}}$ \hkl<1 1 0> DB as an intermediate configuration must be considered most plausible \cite{zirkelbach11}.
Considering a two step diffusion process and assuming equal preexponential factors, a total effective migration barrier 3.5 times higher than the one obtained by first-principles methods is obtained.
-A more detailed description can be found in previous studies \cite{zirkelbach10,zirkelbach11}.
+A more detailed description can be found in previous studies \cite{zirkelbach11,zirkelbach10}.
\section{Defect combinations}
The C atom moves towards the vacant site forming a stable C$_{\text{s}}$ configuration resulting in the release of a huge amount of energy.
The second most favorable configuration is accomplished for a V located right next to the Si atom of the DB structure.
This is due to the reduction of compressive strain of the Si DB atom and its two upper Si neighbors present in the isolated C$_{\text{i}}$ DB configuration.
-This configuration is followed by the structure, in which the V is created at one of the neighbored lattice site below one of the Si atoms that are bound to the C atom of the initial DB.
+This configuration is followed by the structure, in which the V is created at one of the neighbored lattice sites below one of the Si atoms that are bound to the C atom of the initial DB.
Relaxed structures of the latter two defect combinations are shown in the bottom left of Fig.~\ref{fig:314-539} and \ref{fig:059-539} respectively together with their energetics during transition into the ground state.
\begin{figure}
\subfloat[V created right next to the Si atom of the initial DB. Activation energy: {\unit[0.1]{eV}}.]{%
Considering the small activation energies, a high probability for the formation of stable C$_{\text{s}}$ must be concluded.
In addition, it is instructive to investigate combinations of C$_{\text{s}}$ and Si$_{\text{i}}$, which can be created in IBS by highly energetic C atoms that kick out a Si atom from its lattice site, resulting in a Si self-interstitial accompanied by a vacant site, which might get occupied by another C atom that lost almost all of its kinetic energy.
-Provided that the first C atom has enough kinetic energy to escape the affected region, the remaining C$_{\text{s}}$-Si$_{\text{i}}$ pair can be described as a separated defect complex.
-Considering the energetically most favorable Si$_{\text{i}}$ defect, i.e. the Si$_{\text{i}}$ \hkl<1 1 0> DB, the most favorable combination is found for C$_{\text{s}}$ located right next to that DB enabling the largest possible reduction of strain.
-The configuration and the transition into the ground-state configuration, i.e. the C$_{\text{i}}$ hkl<1 0 0> DB is displayed in Fig.~\ref{fig:162-097}
+The most favorable configuration, which is C$_{\text{s}}$ located right next to the ground-state Si$_{\text{i}}$ defect, i.e.\ the Si$_{\text{i}}$ \hkl<1 1 0> DB, and the transition of this structure into the ground-state configuration, i.e. the C$_{\text{i}}$ \hkl<1 0 0> DB is displayed in Fig.~\ref{fig:162-097}
\begin{figure}
\includegraphics[width=\columnwidth]{162-097.ps}
\caption{Transition of a \hkl[1 1 0] Si$_{\text{i}}$ DB next to C$_{\text{s}}$ (right) into the C$_{\text{i}}$ \hkl[0 0 -1] DB configuration (left).}
\label{fig:162-097}
\end{figure}
Due to the low barrier of \unit[0.12]{eV}, the C$_{\text{i}}$ \hkl<1 0 0> DB configuration is very likely to occur.
-However, the barrier of only \unit[0.77]{eV} for the reverse process indicates a high probability for the the formation of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB out of the ground state, which must be considered to be activated without much effort either thermally or by introduced energy of the implantation process.
+However, the barrier of only \unit[0.77]{eV} for the reverse process indicates the possibility to form a C$_{\text{s}}$ and Si$_{\text{i}}$ DB out of the ground state activated without much effort either thermally or by introduced energy of the implantation process.
\begin{figure}
\includegraphics[width=\columnwidth]{c_sub_si110.ps}
%\includegraphics[width=\columnwidth]{c_sub_si110_data.ps}
\caption{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance. The interaction strength of the defect pairs are well approximated by a Lennard-Jones 6-12 potential, which is used for curve fitting.}
\label{fig:dc_si-s}
\end{figure}
-Furthermore, the interaction strength, i.e. the absolute value of the binding energy, quickly drops to zero with increasing separation distance as can be seen in Fig.~\ref{fig:dc_si-s}.
-The interaction of the defects is well approximated by a Lennard-Jones (LJ) 6-12 potential, which is used for curve fitting.
-Unable to model possible positive values of the binding energy, i.e. unfavorable configurations, located to the right of the minimum, the LJ fit should rather be thought as a guide for the eye describing the decrease of the interaction strength, i.e. the absolute value of the binding energy, with increasing separation distance.
+Furthermore, the interaction strength quickly drops to zero with increasing separation distance as can be seen in Fig.~\ref{fig:dc_si-s}.
+The interaction of the defects is well approximated by a Lennard-Jones (LJ) 6-12 potential.
+Unable to model possible positive values of the binding energy, i.e. unfavorable configurations, the LJ fit should rather be thought as a guide for the eye describing the decrease of the interaction strength, i.e. the absolute value of the binding energy, with increasing separation distance.
The LJ fit estimates almost zero interaction already at \unit[0.5-0.6]{nm}, indicating a low interaction capture radius of the defect pair.
In IBS separations exceeding this capture radius are easily produced.
For these reasons, it must be concluded that configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ instead of the thermodynamically stable C$_{\text{i}}$ \hkl<1 0 0> DB play a decisive role in IBS, a process far from equilibrium.
Results of the MD simulations at \unit[450]{$^{\circ}$C}, an operative and efficient temperature in IBS \cite{lindner01}, indicate the formation of C$_{\text{i}}$ \hkl<1 0 0> DBs if C is inserted into the total simulation volume.
However, no agglomeration is observed within the simulated time, which was increased up to several nanoseconds.
-To overcome the drastically overestimated migration barriers of the C defect, which hamper C agglomeration, the simulation temperature is successively increased up to \unit[2050]{$^{\circ}$C}.
-Fig.~\ref{fig:tot} shows the resulting radial distribution function of Si-C bonds for various elevated temperatures.
+This is attributed to the drastically overestimated migration barrier of the C defect, which hampers C agglomeration.
+To overcome this obstacle, the simulation temperature is successively increased up to \unit[2050]{$^{\circ}$C}.
+Fig.~\ref{fig:tot} shows the resulting radial distribution functions of Si-C bonds for various elevated temperatures.
\begin{figure}
\includegraphics[width=\columnwidth]{tot_pc_thesis.ps}
\caption{Radial distribution function for Si-C pairs for C insertion at various elevated temperatures. Si-C distances of a single C$_{\text{s}}$ defect configuration are plotted.}
\label{fig:tot}
\end{figure}
-A transformation from a structure dominated by C$_{\text{i}}$ into a C$_{\text{s}}$ dominated structure with increasing temperature can clearly be observed if compared with the radial distribution of C$_{\text{s}}$ in c-Si.
-Thus, the C$_{\text{s}}$ defect and, thus, stretched coherent structures of SiC, must be considered to play an important role in the IBS at elevated temperatures.
-This, in fact, is in agreement with experimental findings of annealing experiments \cite{strane94,nejim95,serre95} and also with the previous DFT results, which suggest C$_{\text{s}}$ to be involved at higher temperatures and in conditions out of thermodynamic equilibrium.
+Although not intended, a transformation from a structure dominated by C$_{\text{i}}$ into a structure consisting of C$_{\text{s}}$ with increasing temperature can clearly be observed if compared with the radial distribution of C$_{\text{s}}$ in c-Si.
+
+Thus, the C$_{\text{s}}$ defect and resulting stretched coherent structures of SiC, must be considered to play an important role in the IBS at elevated temperatures.
+This, in fact, satisfies experimental findings of annealing experiments \cite{strane94,nejim95,serre95} and as well as the previous DFT results, which suggest C$_{\text{s}}$ to be involved at higher temperatures and in conditions that deviate the system out of the thermodynamic ground state.
\section{Summary and discussion}
Although investigations of defect combinations show the agglomeration of C$_{\text{i}}$ DBs to be energetically most favorable, configurations that may arise during IBS were presented, their dynamics indicating C$_{\text{s}}$ to play an important role particularly at high temperatures.
-This is supported by the empirical MD results, which show an increased participation of C$_{\text{s}}$ at increased temperatures that allow the system to deviate from the ground state.
+This is supported by the classical MD results, which show an increased participation of C$_{\text{s}}$ at increased temperatures that allow the system to deviate from the ground state.
Based on these findings, it is concluded that in IBS at elevated temperatures, SiC conversion takes place by an initial agglomeration of C$_{\text{s}}$ into coherent, tensily strained structures of SiC followed by precipitation into incoherent SiC once a critical size is reached and the increasing strain energy of the coherent structure surpasses the interfacial energy of the incoherent precipitate.
Rearrangement of stable C$_{\text{s}}$ is enabled by excess Si$_{\text{i}}$, which not only acts as a vehicle for C but also as a supply of Si atoms needed elsewhere to form the SiC structure and to reduce possible strain at the interface of coherent SiC precipitates and the Si host.
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