+Table~\ref{tab:defects} summarizes the formation energies of defect structures for the EA and VASP calculations performed in this work as well as further results from literature.\r
+The formation energies are defined in the same way as in the articles used for comparison\cite{tersoff90,dal_pino93} chosing SiC as a reservoir for the carbon impurity.\r
+Relaxed geometries are displayed in Fig.~\ref{fig:defects}.\r
+Astonishingly there is only little literature present to compare with.\r
+\begin{table*}\r
+\begin{ruledtabular}\r
+\begin{tabular}{l c c c c c c}\r
+%\hline\r
+%\hline\r
+ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B \\\r
+\hline\r
+ Erhart/Albe & 6.09 & 9.05$^*$ & 3.88 & 5.18 & 0.75 & 5.59$^*$ \\\r
+ VASP & unstable & unstable & 3.72 & 4.16 & 1.95 & 4.66 \\\r
+ Tersoff\cite{tersoff90} & 3.8 & 6.7 & 4.6 & 5.9 & 1.6 & 5.3 \\\r
+ ab initio\cite{dal_pino93,capaz94} & - & - & x & - & 1.89 \cite{dal_pino93} & x+2.1 \cite{capaz94} \\\r
+ % there is no more ab initio data!\r
+%\hline\r
+%\hline\r
+\end{tabular}\r
+\end{ruledtabular}\r
+\caption{Formation energies of carbon point defects in crystalline silicon determined by classical potential and ab initio methods. The formation energies are given in eV. T denotes the tetrahedral, H the hexagonal, B the bond-centered and S the substitutional interstitial configuration. The dumbbell configurations are abbreviated by DB. Formation energies for unstable configurations obtained by classical potential MD are marked by an asterisk and determined by using the low kinetic energy configuration shortly before the relaxation into the more favorable configuration starts.}\r
+\label{tab:defects}\r
+\end{table*}\r
+\begin{figure}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{Tetrahedral}\\\r
+\includegraphics[width=\columnwidth]{01.eps}\r
+\end{minipage}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{Hexagonal}\\\r
+\includegraphics[width=\columnwidth]{02.eps}\r
+\end{minipage}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{\hkl<1 0 0> dumbbell}\\\r
+\includegraphics[width=\columnwidth]{03.eps}\r
+\end{minipage}\\\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{\hkl<1 1 0> dumbbell}\\\r
+\includegraphics[width=\columnwidth]{04.eps}\r
+\end{minipage}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{Substitutional}\\[0.05cm]\r
+\includegraphics[width=\columnwidth]{05.eps}\r
+\end{minipage}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{Bond-centered}\\\r
+\includegraphics[width=\columnwidth]{06.eps}\r
+\end{minipage}\r
+\caption{Configurations of carbon point defects in silicon. The silicon/carbon atoms and the bonds (only for the interstitial atom) are illustrated by yellow/grey spheres and blue lines. Bonds are drawn for atoms located within a certain distance and do not necessarily correspond to chemical bonds.}\r
+\label{fig:defects}\r
+\end{figure} \r
+\r
+Substitutional carbon (C$_{\text{sub}}$) in silicon, which is in fact not an interstitial defect, is found to be the lowest configuration with regard to energy for all potential models.\r
+VASP calculations performed in this work are in good agreement with results obtained by classical potential simulations by Tersoff\cite{tersoff90} and ab initio calculations done by Dal Pino et~al\cite{dal_pino93}.\r
+However, the EA potential dramatically underestimtes the C$_{\text{sub}}$ formation energy, which is a definite drawback of the potential.\r
+\r
+Except for the Tersoff potential the \hkl<1 0 0> dumbbell (C$_{\text{I}}$) is the energetically most favorable interstital configuration, in which the C and Si dumbbell atoms share a Si lattice site.\r
+This finding is in agreement with several theoretical\cite{burnard93,leary97,dal_pino93,capaz94} and experimental\cite{watkins76,song90} investigations.\r
+Tersoff as well, considers C$_{\text{I}}$ to be the ground state configuration and believes an artifact due to the abrupt C-Si cut-off used in the potential to be responsible for the small value of the tetrahedral formation energy\cite{tersoff90}.\r
+It should be noted that EA and VASP predict almost equal formation energies.\r
+% pick up again later, that this is why erhart/albe is more promising for the specific problem under investigation\r
+However, a qualitative difference is observed investigating the dumbbell structures.\r
+While the C-Si distance of the dumbbell atoms is almost equal for both methods, the vertical position of the dumbbell inside the tetrahedra spanned by the four next neighboured Si atoms differs significantly.\r
+The dumbbell based on the EA potential is almost centered around the regular Si lattice site as can be seen in Fig. \ref{fig:defects} whereas for VASP calculations it is translated upwards with the C atom forming an almost collinear bond to the two Si atoms of the top face of the tetrahedra and the bond angle of the Si dumbbell atom to the two bottom face Si atoms approaching \unit[120]{$^\circ$}.\r
+% maybe transfer to discussion chapter later\r
+This indicates predominant sp and sp$^2$ hybridization for the C and Si dumbbell atom respectively.\r
+Obviously the classical potential is not able to reproduce the clearly quantum-mechanically dominated character of bonding.\r
+% substitute 'dominated'\r
+\r
+Both, EA and VASP reveal the hexagonal configuration unstable relaxing into the C$_{\text{I}}$ ground state structure.\r
+Tersoff finds this configuration stable, though it is the most unfavorable.\r
+Thus, the highest formation energy observed by the EA potential is the tetrahedral configuration, which turns out to be unstable in VASP calculations.\r
+% maybe transfer to discussion chapter later\r
+The high formation energy of this defect involving a low probability to find such a defect in classical potential MD acts in concert with finding it unstable by the more accurate quantum-mechnical description.\r
+\r
+The \hkl<1 1 0> dumbbell constitutes the second most favorable configuration, reproduced by both methods.\r
+It is followed by the bond-centered (BC) configuration.\r
+However, even though EA yields the same difference in energy with repsect to the \hkl<1 1 0> defect as VASP does, the BC configuration is found to be a saddle point within the EA description relaxing into the \hkl<1 1 0> configuration.\r
+Tersoff indeed predicts a metastable BC configuration.\r
+However it is not in the correct order and lower in energy than C$_{\text{I}}$.\r
+Please note, that Capaz et~al.\cite{capaz94} in turn found this configuration to be a saddle point, which is about \unit[2.1]{eV} higher in energy than the C$_{\text{I}}$ configuration.\r
+% due to missing accounting for electron spin ...\r
+This is assumed to be due to the neglection of the electron spin in these calculations.\r
+Another VASP calculation without fully accounting for the electron spin results in the smearing of a single electron over two non-degenerated states for the BC configuration.\r
+This problem is resolved by spin polarized calculations resulting in a net spin one accompanied by a reduction of the total energy by \unit[0.3]{eV} and the transformation into a metastable local minimum configuration.\r
+All other configurations are not affected.\r
+\r
+To conclude, discrepancies are observed between the results from classical potential calculations and those obtained from first principles.\r
+Within the classical potentials EA outperforms Tersoff, which is, thus, used for further comparative studies.\r
+Nevertheless, both methods (EA and VASP) predict the \hkl<1 0 0> dumbbell interstitial configuration to be most stable.\r
+Also the remaining defects and their energetical order are described fairly well.\r
+% sth like that ... defects might still be ok but when it comes to diffusion ...\r
+It is thus concluded that -- so far -- modelling of the SiC precipitation by the EA potential might lead to trustable results.\r