+Concerning the mobility of the ground state Si$_{\text{i}}$, an activation energy shortly below \unit[0.7]{eV} was found for the migration of a Si$_{\text{i}}$ $\langle 0 1 -1\rangle$ into a $\langle 1 1 0\rangle$ DB configuration located at the next neighboured Si lattice site in $[1 1 -1]$ direction.\r
+% look for values in literature for neutraly charged Si_i diffusion\r
+\r
+\subsection{Pairs of C$_{\text{i}}$}\r
+\r
+C$_{\text{i}}$ pairs of the $\langle 1 0 0\rangle$-type have been considered in the first part.\r
+Table~\ref{table:dc_c-c} summarizes the binding energies obtained for configurations, in which an initial C$_{\text{i}}$ $\langle 0 0 -1\rangle$ DB located at position Si$_{\text{i}}$/C$_{\text{i}}$ is combined with a defect of the same type occupying various orientations at positions 1 to 5 (see Fig.~\ref{fig:combos}).\r
+\begin{table}\r
+\begin{ruledtabular}\r
+\begin{tabular}{l c c c c c c }\r
+ & 1 & 2 & 3 & 4 & 5 & R \\\r
+\hline\r
+ $\langle 0 0 -1\rangle$ & -0.08 & -1.15 & -0.08 & 0.04 & -1.66 & -0.19\\\r
+ $\langle 0 0 1\rangle$ & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\\r
+ $\langle 0 -1 0\rangle$ & -2.39 & -0.17 & -0.10 & -0.27 & -1.88 & -0.05\\\r
+ $\langle 0 1 0\rangle$ & -2.25 & -1.90 & -2.25 & -0.12 & -1.38 & -0.06\\\r
+ $\langle -1 0 0\rangle$ & -2.39 & -0.36 & -2.25 & -0.12 & -1.88 & -0.05\\\r
+ $\langle 1 0 0\rangle$ & -2.25 & -2.16 & -0.10 & -0.27 & -1.38 & -0.06\\\r
+\end{tabular}\r
+\end{ruledtabular}\r
+\caption{Binding energies of C$_{\text{i}}$ $\langle 1 0 0\rangle$-type defect pairs in eV. Equivalent configurations exhibit equal energies. The first column lists the orientation of the defect, which is combined with the initial C$_{\text{i}}$ $\langle 0 0 -1\rangle$ dumbbell. The position index of the second defect is given in the first row according to Fig.~\ref{fig:combos}. R corresponds to the position located at $\frac{a_{\text{Si}}}{2} \langle3 2 3 \rangle$ relative to the initial defect position, which is the maximum realizable distance due to periodic boundary conditions.}\r
+\label{table:dc_c-c}\r
+\end{table}\r
+Most of the obtained configurations result in binding energies well below zero indicating a preferable agglomeration of these type of defects.\r
+For increasing distances of the defect pair the binding energy approaches to zero (R in Table~\ref{table:dc_c-c}) as it is expected for non-interacting isolated defects.\r
+Energetically favorable and unfavorable configurations can be explained by stress compensation and increase respectively, which is due to the resulting net strain of the respective configuration of the defect combination.\r
+Antiparallel orientations of the second defect ($\langle 0 0 1\rangle$) at positions located below the (001) plane with respect to the initial one (positions 1, 2 and 4) show the energetically most unfavorable configurations.\r
+In contrast, the parallel and particularly the twisted orientations constitute energetically favorable configurations, in which a vast reduction of strain is enabled by combination of these defects.\r
+\r
+Mattoni et al.\cite{mattoni2002} predict the ground state configuration for a $\langle 1 0 0\rangle$ or equivalently a $\langle 0 1 0\rangle$ defect created at position 1 with both defects basically maintaining the DB structure, resulting in a binding energy of \unit[-2.1]{eV}.\r
+% in mattoni db structures are basically amintained. there is further relaxation in our case and a lower binding energy\r
+In this work we found a further relaxation of this defect structure.\r
+The C atom of the second and the Si atom of the initial DB move towards each other forming a bond, which results in a somewhat lower binding energy of \unit[-2.25]{eV}.\r
+Furthermore a more favorable configuration was found for the combination with a $\langle 0 -1 0\rangle$ and $\langle -1 0 0\rangle$ DB respectively, which is assumed to constitute the actual ground state configuration of two C$_{\text{i}}$ DBs in Si.\r
+The two C atoms form a strong C-C bond, which is responsible for the large gain in energy resulting in a binding energy of \unit[-2.39]{eV}.\r
+\r
+Investigating migration barriers enables to predict the probability of formation of the thermodynamic ground state defect complex by thermally activated diffusion processes.\r
+High activation energies are necessary for the migration of low energy configurations, in which the C atom of the second DB is located in the vicinity of the initial DB.\r
+The transition of the configuration, in which the second DB is of the $\langle 0 1 0\rangle$ type at position 2 (\unit[-1.90]{eV}) into a $\langle 0 1 0\rangle$-type DB at position 1 (\unit[-2.39]{eV}) for instance, revealed a barrier height of more than \unit[4]{eV}.\r
+Low barriers do only exist from energetically less favorable configurations, e.g. the configuration of the $\langle -1 0 0\rangle$ DB located at position 2 (\unit[-0.36]{eV}).\r
+An activation energy of only \unit[?.?]{eV} is necessary for the transition into the ground state configuration.\r
+% strange mig from -190 -> -2.39 (barrier > 4 eV)\r
+% C-C migration -> idea:\r
+% mig from low energy confs has extremely high barrier!\r
+% low barrier only from energetically less/unfavorable confs (?)! <- prove!\r
+% => low probability of C-C clustering ?!?\r
+Since thermally activated C clustering is, thus, only possible by traversing energetically unfavored configurations, mass C clustering is not expected.\r
+% ?!?\r
+% look for precapture mechnism (local minimum in energy curve)\r
+% also: plot energy all confs with respect to C-C distance\r
+% maybe a pathway exists traversing low energy confs ?!?\r
+\r
+% point out that configurations along 110 were extended up to the 6th NN in that direction\r
+The binding energies of the energetically most favorable configurations with the seocnd DB located along the $\langle 1 1 0\rangle$ direction and resulting C-C distances of the relaxed structures are summarized in Table~\ref{table:dc_110}.\r
+\begin{table}\r
+\begin{ruledtabular}\r
+\begin{tabular}{l c c c c c c }\r
+ & 1 & 2 & 3 & 4 & 5 & 6 \\\r
+\hline\r
+ $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\\r
+C-C distance [nm] & 0.14 & 0.46 & 0.65 & 0.86 & 1.05 & 1.08 \r
+\end{tabular}\r
+\end{ruledtabular}\r
+\caption{Binding energies $E_{\text{b}}$ and C-C distance of energetically most favorable C$_{\text{i}}$ $\langle 1 0 0\rangle$-type defect pairs separated along bonds in $\langle 1 1 0\rangle$ direction.}\r
+\label{table:dc_110}\r
+\end{table}\r
+The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:dc_110}\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{db_along_110_cc_n.ps}\r
+\caption{Minimum binding energy of dumbbell combinations separated along $\langle 1 1 0\rangle$ with respect to the C-C distance. The blue line is a guide for the eye and the green curve corresponds to the most suitable fit function consisting of all but the first data point.}\r
+\label{fig:dc_110}\r
+\end{figure}\r
+The interaction is found to be proportional to the reciprocal cube of the C-C distance for extended separeations of the C$_{\text{i}}$ and saturates for the smallest possible separation, i.e. the ground state configuration.\r
+\r
+\subsection{C$_{\text{i}}$ next to C$_{\text{s}}$}\r
+\r
+% c_i and c_s, capaz98, mattoni2002 (restricted to 110 -110 bond chain)\r
+\begin{table}\r
+\begin{ruledtabular}\r
+\begin{tabular}{l c c c c c c }\r
+ & 1 & 2 & 3 & 4 & 5 & R \\\r
+\hline\r
+C$_{\text{s}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\\r
+Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\r
+\end{tabular}\r
+\end{ruledtabular}\r
+\caption{Binding energies of combinations of the C$_{\text{i}}$ $[0 0 -1]$ defect with a substitutional C or vacancy located at positions 1 to 5 according to Fig.~\ref{fig:combos}. R corresponds to the position located at $\frac{a_{\text{Si}}}{2} \langle3 2 3 \rangle$ relative to the initial defect position, which is the maximum realizable distance due to periodic boundary conditions.}\r
+\label{table:dc_c-sv}\r
+\end{table}\r
+Table~\ref{table:dc_c-sv} lists the binding energies of C$_{\text{s}}$ next to the C$_{\text{i}}$ $[0 0 -1]$ DB.\r