+Just as for the Si self-interstitial a carbon \hkl<1 1 0> dumbbell configuration exists.
+For the Erhard/Albe potential the formation energy is situated in the same order as found by quantum-mechanical results.
+Similar structures arise in both types of simulations with the silicon and carbon atom sharing a silicon lattice site aligned along \hkl[1 1 0] where the carbon atom is localized slightly closer to the next nearest silicon atom located in the opposite direction to the site-sharing silicon atom even forming a bond to the next but one silicon atom in this direction.
+
+The bond-centered configuration is unstable for the Erhard/Albe potential.
+The system moves into the \hkl<1 1 0> interstitial configuration.
+This, like in the hexagonal case, is also true for the unmodified Tersoff potential and the given relaxation conditions.
+Quantum-mechanical results of this configuration are discussed in more detail in section \ref{subsection:bc}.
+In another ab inito study Capaz et al. \cite{capaz94} determined this configuration as an intermediate saddle point structure of a possible migration path, which is 2.1 eV higher than the \hkl<1 0 0> dumbbell configuration.
+In calculations performed in this work the bond-centered configuration in fact is a real local minimum and an energy barrier is needed to reach this configuration starting from the \hkl<1 0 0> dumbbell configuration, which is discussed in section \ref{subsection:100mig}.
+
+\subsection[\hkl<1 0 0> dumbbell interstitial configuration]{\boldmath\hkl<1 0 0> dumbbell interstitial configuration}
+\label{subsection:100db}
+
+As the \hkl<1 0 0> dumbbell interstitial is the lowest configuration in energy it is the most probable hence important interstitial configuration of carbon in silicon.
+It was first identified by infra-red (IR) spectroscopy \cite{bean70} and later on by electron paramagnetic resonance (EPR) spectroscopy \cite{watkins76}.
+
+Figure \ref{fig:defects:100db_cmp} schematically shows the \hkl<1 0 0> dumbbell structure and table \ref{tab:defects:100db_cmp} lists the details of the atomic displacements, distances and bond angles obtained by analytical potential and quantum-mechanical calculations.
+For comparison, the obtained structures for both methods visualized out of the atomic position data are presented in figure \ref{fig:defects:100db_vis_cmp}.
+\begin{figure}[h]
+\begin{center}
+\includegraphics[width=12cm]{100-c-si-db_cmp.eps}
+\end{center}
+\caption[Sketch of the \hkl<1 0 0> dumbbell structure.]{Sketch of the \hkl<1 0 0> dumbbell structure. Atomic displacements, distances and bond angles are listed in table \ref{tab:defects:100db_cmp}.}
+\label{fig:defects:100db_cmp}
+\end{figure}
+%
+\begin{table}[h]
+\begin{center}
+Displacements\\
+\begin{tabular}{l c c c c c c c c c}
+\hline
+\hline
+ & & & & \multicolumn{3}{c}{Atom 2} & \multicolumn{3}{c}{Atom 3} \\
+ & $a$ & $b$ & $|a|+|b|$ & $\Delta x$ & $\Delta y$ & $\Delta z$ & $\Delta x$ & $\Delta y$ & $\Delta z$ \\
+\hline
+Erhard/Albe & 0.084 & -0.091 & 0.175 & -0.015 & -0.015 & -0.031 & -0.014 & 0.014 & 0.020 \\
+VASP & 0.109 & -0.065 & 0.174 & -0.011 & -0.011 & -0.024 & -0.014 & 0.014 & 0.025 \\
+\hline
+\hline
+\end{tabular}\\[0.5cm]
+\end{center}
+\begin{center}
+Distances\\
+\begin{tabular}{l c c c c c c c c r}
+\hline
+\hline
+ & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ & $a_{\text{Si}}^{\text{equi}}$\\
+\hline
+Erhard/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 & 0.543 \\
+VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 & 0.548 \\
+\hline
+\hline
+\end{tabular}\\[0.5cm]
+\end{center}
+\begin{center}
+Angles\\
+\begin{tabular}{l c c c c }
+\hline
+\hline
+ & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
+\hline
+Erhard/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
+VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
+\hline
+\hline
+\end{tabular}\\[0.5cm]
+\end{center}
+\caption[Atomic displacements, distances and bond angles of the \hkl<1 0 0> dumbbell structure obtained by the Erhard/Albe potential and VASP calculations.]{Atomic displacements, distances and bond angles of the \hkl<1 0 0> dumbbell structure obtained by the Erhard/Albe potential and 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 figure \ref{fig:defects:100db_cmp}. In addition, the equilibrium lattice constant for crystalline silicon is listed.}
+\label{tab:defects:100db_cmp}
+\end{table}
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}{6cm}
+\begin{center}
+\underline{Erhard/Albe}
+\includegraphics[width=5cm]{c_pd_albe/100_cmp.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{6cm}
+\begin{center}
+\underline{VASP}
+\includegraphics[width=5cm]{c_pd_vasp/100_cmp.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Comparison of the visualized \hkl<1 0 0> dumbbel structures obtained by Erhard/Albe potential and VASP calculations.}
+\label{fig:defects:100db_vis_cmp}
+\end{figure}
+\begin{figure}[h]
+\begin{center}
+\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 C \hkl<1 0 0> dumbbell structure obtained by VASP calculations.]{Charge density isosurface and Kohn-Sham levels of the C \hkl<1 0 0> dumbbell structure obtained by VASP calculations. Yellow and grey spheres correspond to silicon and carbon 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 silicon atom numbered '1' and the C atom compose the dumbbell structure.
+They share the lattice site which is indicated by the dashed red circle and which they are displaced from by length $a$ and $b$ respectively.
+The atoms no longer have four tetrahedral bonds to the silicon atoms located on the alternating opposite edges of the cube.
+Instead, each of the dumbbell atoms forms threefold coordinated bonds, which are located in a plane.
+One bond is formed to the other dumbbell atom.
+The other two bonds are bonds to the two silicon edge atoms located in the opposite direction of the dumbbell atom.
+The distance of the two dumbbell atoms is almost the same for both types of calculations.
+However, in the case of the VASP calculation, the dumbbell structure is pushed upwards compared to the Erhard/Albe results.
+This is easily identified by comparing the values for $a$ and $b$ and the two structures in figure \ref{fig:defects:100db_vis_cmp}.
+Thus, the angles of bonds of the silicon dumbbell atom ($\theta_1$ and $\theta_2$) are closer to $120^{\circ}$ signifying the predominance of $sp^2$ hybridization.
+On the other hand, the carbon atom forms an almost collinear bond ($\theta_3$) with the two silicon edge atoms implying the predominance of $p$ and $sp$ bonding.
+This is supported by the image of the charge density isosurface in figure \ref{img:defects:charge_den_and_ksl}.
+In the same figure the Kohn-Sham levels are shown.
+There is no magnetization density.
+An acceptor level arises resulting in a band gap of 0.35 eV compared to 0.75 eV as obtained for plain silicon.
+
+\subsection{Bond-centered interstitial configuration}
+\label{subsection:bc}
+
+In the bond-centerd insterstitial configuration the interstitial atom is located inbetween two next neighboured silicon atoms.
+In former studies this configuration is found to be an intermediate saddle point configuration determining the migration barrier of one possibe migration path of a \hkl<1 0 0> dumbbel configuration into another one \cite{capaz94}.
+Hier ist es aber ein echtes Minimum.
+Eine 'weitere' Barriere muss ueberschritten werden um dahin zu kommen.
+Genaueres in section \ref{subsection:100mig}.
+Die Konfiguration besitzt ein magnetisches Moment.
+Bild der spin-ladungen.