\author{%
F. Zirkelbach\textsuperscript{\Ast,\textsf{\bfseries 1}},
- B. Stritzker\textsuperscript{\Ast,\textsf{\bfseries 1}},
- K. Nordlund\textsuperscript{\Ast,\textsf{\bfseries 2}},
- W. G. Schmidt\textsuperscript{\Ast,\textsf{\bfseries 3}},
- E. Rauls\textsuperscript{\Ast,\textsf{\bfseries 3}},
- J. K. N. Lindner\textsuperscript{\Ast,\textsf{\bfseries 3}}
+ B. Stritzker\textsuperscript{\textsf{\bfseries 1}},
+ K. Nordlund\textsuperscript{\textsf{\bfseries 2}},
+ W. G. Schmidt\textsuperscript{\textsf{\bfseries 3}},
+ E. Rauls\textsuperscript{\textsf{\bfseries 3}},
+ J. K. N. Lindner\textsuperscript{\textsf{\bfseries 3}}
}
\authorrunning{F. Zirkelbach et al.}
To solve this controversy and in order to understand the effective underlying processes on a microscopic level atomistic simulations are performed.
% ????
-A lot of theoretical work has been done on intrinsic point defects in Si \cite{bar-yam84,bar-yam84_2,car84,batra87,bloechl93,tang97,leung99,colombo02,goedecker02,al-mushadani03,hobler05,sahli05,posselt08,ma10}, threshold displacement energies in Si \cite{mazzarolo01,holmstroem08} important in ion implantation, C defects and defect reactions in Si \cite{tersoff90,dal_pino93,capaz94,burnard93,leary97,capaz98,zhu98,mattoni2002,park02,jones04}, the SiC/Si interface \cite{chirita97,kitabatake93,cicero02,pizzagalli03} and defects in SiC \cite{bockstedte03,rauls03a,gao04,posselt06,gao07}.
+A lot of theoretical work has been done on intrinsic point defects in Si \cite{bar-yam84,bar-yam84_2,car84,batra87,bloechl93,tang97,leung99,colombo02,goedecker02,al-mushadani03,hobler05,sahli05,posselt08,ma10} and C defects and defect reactions in Si \cite{tersoff90,dal_pino93,capaz94,burnard93,leary97,capaz98,zhu98,mattoni2002,park02,jones04}.
However, none of the mentioned studies consistently investigates entirely the relevant defect structures and reactions concentrated on the specific problem of 3C-SiC formation in C implanted Si.
% ????
Accordingly, energetically favorable configurations result in binding energies below zero while unfavorable configurations show positive values for the binding energy.
The interaction strength, i.e. the absolute value of the binding energy, approaches zero for increasingly non-interacting isolated defects.
-In the classical potential calculations defect structures are modeled in a supercell of nine Si lattice constants in each direction consisting of 5832 Si atoms.
-Reproducing SiC precipitation is attempted by successive insertion of 6000 C atoms to form a minimal 3C-SiC precipitate with a radius of about \unit[3.1]{nm} into the Si host, which has a size of 31 Si unit cells in each direction consisting of 238328 Si atoms.
+Within the empirical approach, defect structures are modeled in a supercell of nine Si lattice constants in each direction consisting of 5832 Si atoms.
+Reproducing SiC precipitation is attempted by successive insertion of 6000 C atoms to form a minimal 3C-SiC precipitate with a radius of about \unit[3.1]{nm} within the Si host consisting of 31 unit cells (238328 atoms) in each direction.
At constant temperature 10 atoms are inserted at a time.
-Three different regions within the total simulation volume are considered for a statistically distributed insertion of the C atoms: $V_1$ corresponding to the total simulation volume, $V_2$ corresponding to the size of the precipitate and $V_3$, which holds the necessary amount of Si atoms of the precipitate.
-After C insertion, the simulation has been continued for \unit[100]{ps} and is cooled down to \unit[20]{$^{\circ}$C} afterwards.
-A Tersoff-like bond order potential by Erhart and Albe (EA)\cite{albe_sic_pot} has been utilized, which accounts for nearest neighbor interactions realized by a cut-off function dropping the interaction to zero in between the first and second nearest neighbor distance.
-The potential was used as is, i.e. without any repulsive potential extension at short interatomic distances.
-Constant pressure simulations are realized by the Berendsen barostat\cite{berendsen84} using a time constant of \unit[100]{fs} and a bulk modulus of \unit[100]{GPa} for Si.
-The temperature was kept constant by the Berendsen thermostat\cite{berendsen84} with a time constant of \unit[100]{fs}.
-Integration of the equations of motion was realized by the velocity Verlet algorithm\cite{verlet67} and a fixed time step of \unit[1]{fs}.
-For structural relaxation of defect structures, the same algorithm was used with the temperature set to 0 K.
+Three different regions inside the total simulation volume are considered for a statistically distributed insertion of C atoms.
+$V_1$ corresponds to the total simulation volume, $V_2$ to the size of the precipitate and $V_3$ holds the necessary amount of Si atoms of the precipitate.
+After C insertion, the simulation is continued for \unit[100]{ps} and cooled down to \unit[20]{$^{\circ}$C} afterwards.
+A Tersoff-like bond order potential by Erhart and Albe (EA) \cite{albe_sic_pot} has been utilized, which accounts for nearest neighbor interactions realized by a cut-off function dropping the interaction to zero in between the first and second nearest neighbor distance.
+The Berendsen barostat and thermostat \cite{berendsen84} with a time constant of \unit[100]{fs} enables the isothermal-isobaric ensemble.
+The velocity Verlet algorithm \cite{verlet67} and a fixed time step of \unit[1]{fs} is used to integrate the equations motion.
+Structural relaxation of defect structures is treated by the same algorithms at zero temperature.
\section{Results}
-The implantation of highly energetic C atoms results in a multiplicity of possible defect configurations.
-Next to individual Si$_{\text{i}}$, C$_{\text{i}}$, V and C$_{\text{s}}$ defects, combinations of these defects and their interaction are considered important for the problem under study.
-First of all, structure and energetics of separated defects are presented.
-The investigations proceed with pairs of the ground state and, thus, most probable defect configurations that are believed to be fundamental in the Si to SiC conversion.
-
-\subsection{Separated defects in silicon}
-\label{subsection:sep_def}
-% we need both: Si self-int & C int ground state configuration (for combos)
+\subsection{Carbon and silicon defect configurations}
Several geometries have been calculated to be stable for individual intrinsic and C related defects in Si.
Fig.~\ref{fig:sep_def} shows the obtained structures while the corresponding energies of formation are summarized and compared to values from literature in Table~\ref{table:sep_eof}.
\begin{figure}
-\begin{minipage}[t]{0.32\columnwidth}
+\begin{minipage}[t]{0.48\columnwidth}
\underline{Si$_{\text{i}}$ \hkl<1 1 0> DB}\\
-\includegraphics[width=\columnwidth]{si110.eps}
+\includegraphics[width=\columnwidth]{si110_bonds.eps}
\end{minipage}
-\begin{minipage}[t]{0.32\columnwidth}
+\begin{minipage}[t]{0.48\columnwidth}
\underline{Si$_{\text{i}}$ hexagonal}\\
-\includegraphics[width=\columnwidth]{sihex.eps}
-\end{minipage}
-\begin{minipage}[t]{0.32\columnwidth}
-\underline{Si$_{\text{i}}$ tetrahedral}\\
-\includegraphics[width=\columnwidth]{sitet.eps}
+\includegraphics[width=\columnwidth]{sihex_bonds.eps}
\end{minipage}\\
-\begin{minipage}[t]{0.32\columnwidth}
+\begin{minipage}[t]{0.48\columnwidth}
+\underline{Si$_{\text{i}}$ tetrahedral}\\
+\includegraphics[width=\columnwidth]{sitet_bonds.eps}
+\end{minipage}
+\begin{minipage}[t]{0.48\columnwidth}
\underline{Si$_{\text{i}}$ \hkl<1 0 0> DB}\\
-\includegraphics[width=\columnwidth]{si100.eps}
+\includegraphics[width=\columnwidth]{si100_bonds.eps}
\end{minipage}
-\begin{minipage}[t]{0.32\columnwidth}
-\underline{Vacancy}\\
-\includegraphics[width=\columnwidth]{sivac.eps}
+\caption{Configurations of intrinsic silicon point defects. Dumbbell configurations are abbreviated by DB.}
+\label{fig:intrinsic_def}
+\end{figure}
+\begin{figure}
+\begin{minipage}[t]{0.48\columnwidth}
+\underline{C$_{\text{s}}$}
+\includegraphics[width=\columnwidth]{csub_bonds.eps}
\end{minipage}
-\begin{minipage}[t]{0.32\columnwidth}
-\underline{C$_{\text{s}}$}\\
-\includegraphics[width=\columnwidth]{csub.eps}
-\end{minipage}\\
-\begin{minipage}[t]{0.32\columnwidth}
+\begin{minipage}[t]{0.48\columnwidth}
\underline{C$_{\text{i}}$ \hkl<1 0 0> DB}\\
-\includegraphics[width=\columnwidth]{c100.eps}
-\end{minipage}
-\begin{minipage}[t]{0.32\columnwidth}
+\includegraphics[width=\columnwidth]{c100_bonds.eps}
+\end{minipage}\\
+\begin{minipage}[t]{0.48\columnwidth}
\underline{C$_{\text{i}}$ \hkl<1 1 0> DB}\\
-\includegraphics[width=\columnwidth]{c110.eps}
+\includegraphics[width=\columnwidth]{c110_bonds.eps}
\end{minipage}
-\begin{minipage}[t]{0.32\columnwidth}
+\begin{minipage}[t]{0.48\columnwidth}
\underline{C$_{\text{i}}$ bond-centered}\\
-\includegraphics[width=\columnwidth]{cbc.eps}
+\includegraphics[width=\columnwidth]{cbc_bonds.eps}
\end{minipage}
-\caption{Configurations of silicon and carbon point defects in silicon. Silicon and carbon atoms are illustrated by yellow and gray spheres respectively. Bonds are drawn whenever considered appropriate to ease identifying defect structures for the reader. Dumbbell configurations are abbreviated by DB.}
-\label{fig:sep_def}
+\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.}
+\label{fig:carbon_def}
\end{figure}
\begin{table*}
\begin{tabular}{l c c c c c c c c c}
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