In the following the simulation methods used within the scope of this study are introduced.
Enabling the investigation of the evolution of structure on the atomic scale, molecular dynamics (MD) simulations are chosen for modeling the behavior and precipitation of C introduced into an initially crystalline Si environment.
To be able to model systems with a large amount of atoms computational efficient classical potentials to describe the interaction of the atoms are most often used in MD studies.
-For reasons of flexibility in executing this non-standard task and in order to be able to use a novel interaction potential \cite{albe_sic_pot} an appropriate MD code called \textsc{posic}\footnote{{\textsc posic} is an abbreviation for {\bf p}recipitation {\bf o}f {\bf SiC}} including a library collecting respective MD subroutines was developed from scratch\footnote{Source code: http://www.physik.uni-augsburg.de/\~{}zirkelfr/posic}.
+For reasons of flexibility in executing this non-standard task and in order to be able to use a novel interaction potential \cite{albe_sic_pot} an appropriate MD code called \textsc{posic}\footnote{\textsc{posic} is an abbreviation for {\bf p}recipitation {\bf o}f {\bf SiC}} including a library collecting respective MD subroutines was developed from scratch\footnote{Source code: http://www.physik.uni-augsburg.de/\~{}zirkelfr/posic}.
The basic ideas of MD in general and the adopted techniques as implemented in \textsc{posic} in particular are outlined in section \ref{section:md}, while the functional form and derivative of the employed classical potential is presented in appendix \ref{app:d_tersoff}.
An overview of the most important tools within the MD package is given in appendix \ref{app:code}.
Although classical potentials are often most successful and at the same time computationally efficient in calculating some physical properties of a particular system, not all of its properties might be described correctly due to the lack of quantum-mechanical effects.
V_{\text{nl}}(\vec{r}) = \sum_{lm} | lm \rangle V_l(\vec{r}) \langle lm |
\text{ .}
\end{equation}
-Applying of the operator $V_{\text{nl}}(\vec{r})$ decomposes the electronic wave functions into spherical harmonics $| lm \rangle$, i.e.\ the orbitals with azimuthal angular momentum $l$ and magnetic number $m$, which are then multiplied by the respective pseudopotential $V_l(\vec{r})$ for angular momentum $l$.
+Applying the operator $V_{\text{nl}}(\vec{r})$ decomposes the electronic wave functions into spherical harmonics $| lm \rangle$, i.e.\ the orbitals with azimuthal angular momentum $l$ and magnetic number $m$, which are then multiplied by the respective pseudopotential $V_l(\vec{r})$ for angular momentum $l$.
The standard generation procedure of pseudopotentials proceeds by varying its parameters until the pseudo eigenvalues are equal to the all-electron valence eigenvalues and the pseudo wave functions match the all-electron valence wave functions beyond a certain cut-off radius determining the core region.
Modified methods to generate ultra-soft pseudopotentials were proposed, which address the rapid convergence with respect to the size of the plane wave basis set \cite{vanderbilt90,troullier91}.
Except for Tersoff's results for the tetrahedral configuration, the \ci{} \hkl<1 0 0> DB is the energetically most favorable interstitial configuration.
As mentioned above, the low energy of formation for the tetrahedral interstitial in the case of the Tersoff potential is believed to be an artifact of the abrupt cut-off set to \unit[2.5]{\AA} (see Ref. 11 and 13 in \cite{tersoff90}) and the real formation energy is, thus, supposed to be located between \unit[3--10]{eV}.
Keeping these considerations in mind, the \ci{} \hkl<1 0 0> DB is the most favorable interstitial configuration for all interaction models.
-This finding is in agreement with several theoretical\cite{burnard93,leary97,dal_pino93,capaz94,jones04} and experimental\cite{watkins76,song90} investigations, which all predict this configuration to be the ground state.
+This finding is in agreement with several theoretical~\cite{burnard93,leary97,dal_pino93,capaz94,jones04} and experimental~\cite{watkins76,song90} investigations, which all predict this configuration to be the ground state.
However, no energy of formation for this type of defect based on first-principles calculations has yet been explicitly stated in literature.
The defect is frequently generated in the classical potential simulation runs, in which C is inserted at random positions in the c-Si matrix.
In quantum-mechanical simulations the unstable tetrahedral and hexagonal configurations undergo a relaxation into the \ci{} \hkl<1 0 0> DB configuration.
-Thus, this configuration is of great importance and discussed in more detail in section \ref{subsection:100db}.
+Thus, this configuration is of great importance and discussed in more detail in section~\ref{subsection:100db}.
It should be noted that EA and DFT predict almost equal formation energies.
The highest energy is observed for the hexagonal interstitial configuration using classical potentials.
\hline
\end{tabular}\\[0.5cm]
\end{center}
-\caption[Atomic displacements, distances and bond angles of the \ci{} \hkl<1 0 0> DB structure obtained by \textsc{posic} and {\textsc vasp} calculations.]{Atomic displacements, distances and bond angles of the \ci{} \hkl<1 0 0> DB structure obtained by {\textsc posic} and {\textsc vasp} calculations. The displacements and distances are given in nm and the angles are given in degrees. Displacements, distances and angles are schematically displayed in Fig.~\ref{fig:defects:100db_cmp}. In addition, the equilibrium lattice constant for crystalline Si is listed.}
+\caption[Atomic displacements, distances and bond angles of the \ci{} \hkl<1 0 0> DB structure obtained by \textsc{posic} and \textsc{vasp} calculations.]{Atomic displacements, distances and bond angles of the \ci{} \hkl<1 0 0> DB structure obtained by \textsc{posic} and \textsc{vasp} calculations. The displacements and distances are given in nm and the angles are given in degrees. Displacements, distances and angles are schematically displayed in Fig.~\ref{fig:defects:100db_cmp}. In addition, the equilibrium lattice constant for crystalline Si is listed.}
\label{tab:defects:100db_cmp}
\end{table}%
\begin{figure}[tp]
\end{center}
\end{minipage}
\end{center}
-\caption{Comparison of the \ci{} \hkl<1 0 0> DB structures obtained by \textsc{posic} and {\textsc vasp} calculations.}
+\caption{Comparison of the \ci{} \hkl<1 0 0> DB structures obtained by \textsc{posic} and \textsc{vasp} calculations.}
\label{fig:defects:100db_vis_cmp}
\end{figure}%
\begin{figure}[tp]
\includegraphics[height=10cm]{c_pd_vasp/eden.eps}
\includegraphics[height=12cm]{c_pd_vasp/100_2333_ksl.ps}
\end{center}
-\caption[Charge density isosurface and Kohn-Sham levels of the \ci{} \hkl<1 0 0> DB structure obtained by \textsc{vasp} calculations.]{Charge density isosurface and Kohn-Sham levels of the \ci{} \hkl<1 0 0> DB structure obtained by {\textsc vasp} calculations. Yellow and gray spheres correspond to Si and C atoms. The blue surface is the charge density isosurface. In the energy level diagram red and green lines and dots mark occupied and unoccupied states.}
+\caption[Charge density isosurface and Kohn-Sham levels of the \ci{} \hkl<1 0 0> DB structure obtained by \textsc{vasp} calculations.]{Charge density isosurface and Kohn-Sham levels of the \ci{} \hkl<1 0 0> DB structure obtained by \textsc{vasp} calculations. Yellow and gray spheres correspond to Si and C atoms. The blue surface is the charge density isosurface. In the energy level diagram red and green lines and dots mark occupied and unoccupied states.}
\label{img:defects:charge_den_and_ksl}
\end{figure}%
The Si atom labeled `1' and the C atom compose the DB structure.
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