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[lectures/latex.git] / posic / publications / emrs2012.tex

diff --git a/posic/publications/emrs2012.tex b/posic/publications/emrs2012.tex
index 45c02f5..5a4433a 100644 (file)
--- a/posic/publications/emrs2012.tex
+++ b/posic/publications/emrs2012.tex
@@ -101,7 +101,7 @@ These findings are compared to empirical potential results, which, by taking int
 
 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}.
 
 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.
 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.


@@ -124,7 +124,7 @@ Structural relaxation of defect structures is treated by the same algorithms at
 
 \section{Defect configurations in silicon}
 
 
 \section{Defect configurations in silicon}
 

-Table~\ref{tab:defects} summarizes the formation energies of relevant defect structures for the EA and DFT calculations, which are shown in Figs.~\ref{fig:intrinsic_def} and \ref{fig:carbon_def}.
+Table~\ref{tab:defects} summarizes the formation energies of relevant defect structures for the EA and DFT calculations, which are shown in Fig.~\ref{fig:intrinsic_def} and \ref{fig:carbon_def}.

 \begin{table*}
 \centering
 \begin{tabular}{l c c c c c c c c c}
 \begin{table*}
 \centering
 \begin{tabular}{l c c c c c c c c c}


@@ -139,6 +139,8 @@ Erhart/Albe & 4.39 & 4.48$^*$ & 3.40 & 5.42 & 3.13 & 0.75 & 3.88 & 5.18 & 5.59$^
 \label{tab:defects}
 \end{table*}
 \begin{figure}
 \label{tab:defects}
 \end{table*}
 \begin{figure}

+\subfloat[Intrinsic Si point defects.]{%
+\begin{minipage}{0.9\columnwidth}

 \centering
 \begin{minipage}[t]{0.43\columnwidth}
 \centering
 \centering
 \begin{minipage}[t]{0.43\columnwidth}
 \centering


@@ -160,10 +162,12 @@ Erhart/Albe & 4.39 & 4.48$^*$ & 3.40 & 5.42 & 3.13 & 0.75 & 3.88 & 5.18 & 5.59$^
 \underline{Si$_{\text{i}}$ \hkl<1 0 0> DB}\\
 \includegraphics[width=0.8\columnwidth]{si100_bonds.eps}
 \end{minipage}
 \underline{Si$_{\text{i}}$ \hkl<1 0 0> DB}\\
 \includegraphics[width=0.8\columnwidth]{si100_bonds.eps}
 \end{minipage}

-\caption{Configurations of intrinsic Si point defects. Dumbbell configurations are abbreviated by DB.}
+%\caption{Configurations of intrinsic Si point defects. Dumbbell configurations are abbreviated by DB.}
+\end{minipage}

 \label{fig:intrinsic_def}
 \label{fig:intrinsic_def}

-\end{figure}
-\begin{figure}
+}\\
+\subfloat[C point defects in Si.]{%
+\begin{minipage}{0.9\columnwidth}

 \centering
 \begin{minipage}[t]{0.43\columnwidth}
 \centering
 \centering
 \begin{minipage}[t]{0.43\columnwidth}
 \centering


@@ -185,8 +189,11 @@ Erhart/Albe & 4.39 & 4.48$^*$ & 3.40 & 5.42 & 3.13 & 0.75 & 3.88 & 5.18 & 5.59$^
 \underline{C$_{\text{i}}$ bond-centered}\\
 \includegraphics[width=0.8\columnwidth]{cbc_bonds.eps}
 \end{minipage}
 \underline{C$_{\text{i}}$ bond-centered}\\
 \includegraphics[width=0.8\columnwidth]{cbc_bonds.eps}
 \end{minipage}

-\caption{Configurations of carbon point defects in silicon. Silicon and carbon atoms are illustrated by yellow and gray spheres respectively. Dumbbell configurations are abbreviated by DB.}
+%\caption{Configurations of carbon point defects in silicon. Silicon and carbon atoms are illustrated by yellow and gray spheres respectively. Dumbbell configurations are abbreviated by DB.}
+\end{minipage}

 \label{fig:carbon_def}
 \label{fig:carbon_def}

+}
+\caption{Defect configurations in Si. Si and C atoms are illustrated by yellow and gray spheres respectively. Dumbbell configurations are abbreviated by DB.}

 \end{figure}
 
 Regarding intrinsic defects in Si, classical potential and {\em ab initio} methods predict energies of formation that are within the same order of magnitude.
 \end{figure}
 
 Regarding intrinsic defects in Si, classical potential and {\em ab initio} methods predict energies of formation that are within the same order of magnitude.


@@ -201,21 +208,19 @@ It is worth to note that the bond-centered (BC) configuration constitutes a real
 \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.
 \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.

-The migration pathways are shown in Figs.\ref{fig:vasp_mig} and \ref{fig:albe_mig} respectively.
+The migration pathways are shown in Fig.~\ref{fig:mig}.

 
 \begin{figure}
 
 \begin{figure}

-\begin{center}
+\subfloat[Transition path obtained by first-principles methods.]{%

 \includegraphics[width=\columnwidth]{path2_vasp_s.ps}
 \includegraphics[width=\columnwidth]{path2_vasp_s.ps}

-\end{center}
-\caption{Migration barrier and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition as obtained by first principles methods.}
-\label{fig:vasp_mig}
-\end{figure} 
-\begin{figure}
-\begin{center}
+}\\
+%\caption{Migration barrier and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition as obtained by first principles methods.}
+\subfloat[Transition involving the {\hkl[1 1 0]} DB (center) configuration within the EA description.]{%

 \includegraphics[width=\columnwidth]{110mig.ps}
 \includegraphics[width=\columnwidth]{110mig.ps}

-\end{center}
-\caption{Migration barrier and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the hkl[0 -1 0] DB (right) transition involving the \hkl[1 1 0] DB (center) configuration within EA description. Migration simulations were performed utilizing time constants of \unit[1]{fs} (solid line) and \unit[100]{fs} (dashed line) for the Berendsen thermostat.}
-\label{fig:albe_mig}
+}
+\caption{Migration barriers and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the hkl[0 -1 0] DB (right) transition.}
+%\caption{Migration barrier and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the hkl[0 -1 0] DB (right) transition involving the \hkl[1 1 0] DB (center) configuration within EA description. Migration simulations were performed utilizing time constants of \unit[1]{fs} (solid line) and \unit[100]{fs} (dashed line) for the Berendsen thermostat.}
+\label{fig:mig}

 \end{figure}
 
 In qualitative agreement with the results of Capaz~et~al.\  \cite{capaz94}, the lowest migration barrier of the ground-state C$_{\text{i}}$ defect within the quantum-mechanical treatment is found for the path, in which a C$_{\text{i}}$ \hkl[0 0 -1] DB migrates to a C$_{\text{i}}$ \hkl[0 -1 0] DB located at the neighbored Si lattice site in \hkl[1 1 -1] direction.
 \end{figure}
 
 In qualitative agreement with the results of Capaz~et~al.\  \cite{capaz94}, the lowest migration barrier of the ground-state C$_{\text{i}}$ defect within the quantum-mechanical treatment is found for the path, in which a C$_{\text{i}}$ \hkl[0 0 -1] DB migrates to a C$_{\text{i}}$ \hkl[0 -1 0] DB located at the neighbored Si lattice site in \hkl[1 1 -1] direction.


@@ -224,7 +229,7 @@ Calculations in this work reinforce this path by an additional improvement of th
 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.
 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}
 
 
 \section{Defect combinations}
 


@@ -249,17 +254,20 @@ The ground-state configuration is obtained for a V located right next to the C a
 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.
 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.
-Relaxed structures of the latter two defect combinations are shown in the bottom left of Figs.~\ref{fig:314-539} and \ref{fig:059-539} respectively together with their energetics during transition into the ground state.
+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}
 \begin{figure}

+\subfloat[V created right next to the Si atom of the initial DB. Activation energy: {\unit[0.1]{eV}}.]{%

 \includegraphics[width=\columnwidth]{314-539.ps}
 \includegraphics[width=\columnwidth]{314-539.ps}

-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created right next to the Si atom of the initial DB (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.1]{eV} is observed.}

 \label{fig:314-539}
 \label{fig:314-539}

-\end{figure}
-\begin{figure}
+}\\
+%\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created right next to the Si atom of the initial DB (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.1]{eV} is observed.}
+\subfloat[V created next to one of the Si atoms that is bound to the C atom of the initial DB. Activation energy: {\unit[0.6]{eV}}.]{%

 \includegraphics[width=\columnwidth]{059-539.ps}
 \includegraphics[width=\columnwidth]{059-539.ps}

-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created next to one of the Si atoms that is bound to the C atom of the initial DB (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.6]{eV} is observed.}

 \label{fig:059-539}
 \label{fig:059-539}

+}
+%\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created next to one of the Si atoms that is bound to the C atom of the initial DB (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.6]{eV} is observed.}
+\caption{Migration barrier and structures of transitions of an initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V (left) into a C$_{\text{s}}$ configuration (right).}

 \end{figure}
 These transitions exhibit activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV}.
 In the first case the Si and C atom of the DB move towards the vacant and initial DB lattice site respectively.
 \end{figure}
 These transitions exhibit activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV}.
 In the first case the Si and C atom of the DB move towards the vacant and initial DB lattice site respectively.


@@ -268,16 +276,14 @@ In both cases, the formation of additional bonds is responsible for the vast gai
 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.
 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.
 \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}
 \begin{figure}
 \includegraphics[width=\columnwidth]{c_sub_si110.ps}
 %\includegraphics[width=\columnwidth]{c_sub_si110_data.ps}


@@ -285,9 +291,9 @@ However, the barrier of only \unit[0.77]{eV} for the reverse process indicates a
 \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}
 \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.
 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.


@@ -299,27 +305,29 @@ To summarize, these obtained  results suggest an increased participation of C$_{
 
 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.
 
 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}
 \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{nejim95,strane94,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}
 
 
 \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 an 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.
+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 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, the conversion into SiC takes place by an initial agglomeration of C$_{\text{s}}$ into coherent, tensily strained structures of SiC followed by precipitation into incoherent SiC structures once a critical radius is reached.
+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.
 
 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.
 

-It is worth to point out that the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate is satisfied by the mechanism of successive positioning of C$_{\text{s}}$.
-In contrast, 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.
+%It is worth to point out that the experimentally observed alignment of the \hkl(h k l) planes of precipitate and substrate is satisfied by this mechanism.
+%In contrast, the topotactic orientation of the SiC precipitate originating from an agglomerate consisting exclusively of C-Si dimers would necessarily involve a much more profound change in structure.

 
 \begin{acknowledgement}
 We gratefully acknowledge financial support by the Bayerische Forschungsstiftung (Grant No. DPA-61/05) and the Deutsche Forschungsgemeinschaft (Grant No. DFG SCHM 1361/11).
 
 \begin{acknowledgement}
 We gratefully acknowledge financial support by the Bayerische Forschungsstiftung (Grant No. DPA-61/05) and the Deutsche Forschungsgemeinschaft (Grant No. DFG SCHM 1361/11).