This finding is in agreement with several theoretical \cite{dal_pino93,capaz94,burnard93,leary97,jones04} and experimental \cite{watkins76,song90} investigations, which all predict this configuration to be the ground state.
It is worth to note that the bond-centered (BC) configuration constitutes a real local minimum in spin polarized calculations in contrast to results \cite{capaz94} without spin predicting a saddle point configuration as well as to the empirical description, which shows a relaxation into the C$_{\text{i}}$ \hkl<1 0 0> DB ground-state configuration.
-\section{Defect mobility}
+\section{Mobility of the carbon defect}
-HIER MEHR ...
-Indeed Capaz et al. propose another path and find it to be the lowest in energy\cite{capaz94}, in which a C$_{\text{i}}$ \hkl[0 0 -1] DB migrates to a C$_{\text{i}}$ \hkl[0 -1 0] DB located at the neighbored Si lattice site in \hkl[1 1 -1] direction.
-Calculations in this work reinforce this path by an additional improvement of the quantitative conformance of the barrier height (\unit[0.90]{eV}) to experimental values.
-A more detailed description can be found in a previous study \cite{zirkelbach10}.
+In the following, the migration barriers of the ground-state C defect are investigated by both, first-principles as well as the empircal method.
+The migration pathways are shown in Figs.\ref{fig:vasp_mig} and \ref{fig:albe_mig} respectively.
-Concerning the mobility of the ground state Si$_{\text{i}}$, we found an activation energy of \unit[0.67]{eV} for the transition of the Si$_{\text{i}}$ \hkl[0 1 -1] to \hkl[1 1 0] DB located at the neighbored Si lattice site in \hkl[1 1 -1] direction.
-Further investigations revealed a barrier of \unit[0.94]{eV} for the Si$_{\text{i}}$ \hkl[1 1 0] DB to Si$_{\text{i}}$ H, \unit[0.53]{eV} for the Si$_{\text{i}}$ \hkl[1 1 0] DB to Si$_{\text{i}}$ T and \unit[0.35]{eV} for the Si$_{\text{i}}$ H to Si$_{\text{i}}$ T transition.
-These are of the same order of magnitude as values of other {\em ab initio} studies \cite{bloechl93,sahli05}.
-
-\section{Defect combinations}
-
-C$_{\text{i}}$ pairs of the \hkl<1 0 0> type have been investigated in the first part.
-Fig.~\ref{fig:combos_ci} schematically displays the initial C$_{\text{i}}$ \hkl[0 0 -1] DB structure and various positions for the second defect (1-5) that have been used for investigating defect pairs.
-Table~\ref{table:dc_c-c} summarizes resulting binding energies for the combination with a second C-Si \hkl<1 0 0> DB obtained for different orientations at positions 1 to 5.
-\begin{figure}
-\subfloat[]{\label{fig:combos_ci}\includegraphics[width=0.45\columnwidth]{combos_ci.eps}}
-\hspace{0.1cm}
-\subfloat[]{\label{fig:combos_si}\includegraphics[width=0.45\columnwidth]{combos.eps}}
-\caption{Position of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB (I) (Fig.~\ref{fig:combos_ci}) and of the lattice site chosen for the initial Si$_{\text{i}}$ \hkl<1 1 0> DB (Si$_{\text{i}}$) (Fig.~\ref{fig:combos_si}). Lattice sites for the second defect used for investigating defect pairs are numbered from 1 to 5.}
-\label{fig:combos}
-\end{figure}
-\begin{table}
-\begin{tabular}{l c c c c c c }
- & 1 & 2 & 3 & 4 & 5 & R \\
-\hline
- \hkl[0 0 -1] & -0.08 & -1.15 & -0.08 & 0.04 & -1.66 & -0.19\\
- \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
- \hkl[0 -1 0] & -2.39 & -0.17 & -0.10 & -0.27 & -1.88 & -0.05\\
- \hkl[0 1 0] & -2.25 & -1.90 & -2.25 & -0.12 & -1.38 & -0.06\\
- \hkl[-1 0 0] & -2.39 & -0.36 & -2.25 & -0.12 & -1.88 & -0.05\\
- \hkl[1 0 0] & -2.25 & -2.16 & -0.10 & -0.27 & -1.38 & -0.06\\
-\end{tabular}
-\caption{Binding energies in eV of C$_{\text{i}}$ \hkl<1 0 0>-type defect pairs. Equivalent configurations exhibit equal energies. Column 1 lists the orientation of the second defect, which is combined with the initial C$_{\text{i}}$ \hkl[0 0 -1] DB. 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 $\frac{a_{\text{Si}}}{2}\hkl[3 2 3]$ relative to the initial defect position, which is the maximum realizable defect separation distance ($\approx \unit[1.3]{nm}$) due to periodic boundary conditions.}
-\label{table:dc_c-c}
-\end{table}
-Most of the obtained configurations result in binding energies well below zero indicating a preferable agglomeration of this type of defects.
-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.
-Energetically favorable and unfavorable configurations can be explained by stress compensation and increase respectively based on the resulting net strain of the respective configuration of the defect combination.
-Antiparallel orientations of the second defect, i.e. \hkl[0 0 1] for positions located below the \hkl(0 0 1) plane with respect to the initial one (positions 1, 2 and 4) form the energetically most unfavorable configurations.
-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.
-
-Mattoni et al.\cite{mattoni2002} predict the ground state configuration for a \hkl[1 0 0] or equivalently a \hkl[0 1 0] defect created at position 1 with both defects basically maintaining the as-isolated DB structure, resulting in a binding energy of \unit[-2.1]{eV}.
-In this work we observed a further relaxation of this defect structure.
-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}.
-Apart from that, we found a more favorable configuration for the combination with a \hkl[0 -1 0] and \hkl[-1 0 0] DB respectively, which is assumed to constitute the actual ground state configuration of two C$_{\text{i}}$ DBs in Si.
-The atomic arrangement is shown in the bottom right of Fig.~\ref{fig:036-239}.
-The two C$_{\text{i}}$ 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}.
-
-Investigating migration barriers allows to predict the probability of formation of defect complexes by thermally activated diffusion processes.
-% ground state configuration, C cluster
-Based on the lowest energy migration path of a single C$_{\text{i}}$ DB the configuration, in which the second C$_{\text{i}}$ DB is oriented along \hkl[0 1 0] at position 2 is assumed to constitute an ideal starting point for a transition into the ground state.
-In addition, the starting configuration exhibits a low binding energy (\unit[-1.90]{eV}) and is, thus, very likely to occur.
-However, a barrier height of more than \unit[4]{eV} was detected resulting in a low probability for the transition.
-The high activation energy is attributed to the stability of such a low energy configuration, in which the C atom of the second DB is located close to the initial DB.
-Low barriers have only been identified for transitions starting from energetically less favorable configurations, e.g. the configuration of a \hkl[-1 0 0] DB located at position 2 (\unit[-0.36]{eV}).
-Starting from this configuration, an activation energy of only \unit[1.2]{eV} is necessary for the transition into the ground state configuration.
-The corresponding migration energies and atomic configurations are displayed in Fig.~\ref{fig:036-239}.
\begin{figure}
-\includegraphics[width=\columnwidth]{036-239.ps}
-\caption{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[-1 0 0] DB at position 2 (left) into a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 1 (right). An activation energy of \unit[1.2]{eV} is observed.}
-\label{fig:036-239}
-\end{figure}
-% strange mig from -190 -> -2.39 (barrier > 4 eV)
-% C-C migration -> idea:
-% mig from low energy confs has extremely high barrier!
-% low barrier only from energetically less/unfavorable confs (?)! <- prove!
-% => low probability of C-C clustering ?!?
-%
-% should possibly be transfered to discussion section
-Since thermally activated C clustering is, thus, only possible by traversing energetically unfavored configurations, extensive C clustering is not expected.
-Furthermore, the migration barrier of \unit[1.2]{eV} is still higher than the activation energy of \unit[0.9]{eV} observed for a single C$_{\text{i}}$ \hkl<1 0 0> DB in c-Si.
-The migration barrier of a C$_{\text{i}}$ DB in a complex system is assumed to approximate the barrier of a DB in a separated system with increasing defect separation.
-Accordingly, lower migration barriers are expected for pathways resulting in larger separations of the C$_{\text{i}}$ DBs.
-% acknowledged by 188-225 (reverse order) calc
-However, if the increase of separation is accompanied by an increase in binding energy, this difference is needed in addition to the activation energy for the respective migration process.
-Configurations, which exhibit both, a low binding energy as well as afferent transitions with low activation energies are, thus, most probable C$_{\text{i}}$ complex structures.
-On the other hand, if elevated temperatures enable migrations with huge activation energies, comparably small differences in configurational energy can be neglected resulting in an almost equal occupation of such configurations.
-In both cases the configuration yielding a binding energy of \unit[-2.25]{eV} is promising.
-First of all, it constitutes the second most energetically favorable structure.
-Secondly, a migration path with a barrier as low as \unit[0.47]{eV} exists starting from a configuration of largely separated defects exhibiting a low binding energy (\unit[-1.88]{eV}).
-The migration barrier and corresponding structures are shown in Fig.~\ref{fig:188-225}.
+\begin{center}
+\includegraphics[width=\columnwidth]{path2_vasp_s.ps}
+\end{center}
+\caption{Migration barrier and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition as obtained by first principles methods.}
+\label{fig:vasp_mig}
+\end{figure}
\begin{figure}
-\includegraphics[width=\columnwidth]{188-225.ps}
-\caption{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 5 (left) into a C$_{\text{i}}$ \hkl[1 0 0] DB at position 1 (right). An activation energy of \unit[0.47]{eV} is observed.}
-\label{fig:188-225}
+\begin{center}
+\includegraphics[width=\columnwidth]{110mig.ps}
+\end{center}
+\caption{Migration barrier and structures of the C$_{\text{i}}$ \hkl[0 0 -1] DB (left) to the hkl[0 -1 0] DB (right) transition involving the \hkl[1 1 0] DB (center) configuration within EA description. Migration simulations were performed utilizing time constants of \unit[1]{fs} (solid line) and \unit[100]{fs} (dashed line) for the Berendsen thermostat.}
+\label{fig:albe_mig}
\end{figure}
-Finally, this type of defect pair is represented four times (two times more often than the ground state configuration) within the systematically investigated configuration space.
-The latter is considered very important at high temperatures, accompanied by an increase in the entropic contribution to structure formation.
-As a result, C defect agglomeration indeed is expected, but only a low probability is assumed for C-C clustering by thermally activated processes with regard to the considered process time in IBS.
-% alternatively: ... considered period of time (of the IBS process).
-%
-% ?!?
-% look for precapture mechanism (local minimum in energy curve)
-% also: plot energy all confs with respect to C-C distance
-% maybe a pathway exists traversing low energy confs ?!?
-
-% point out that configurations along 110 were extended up to the 6th NN in that direction
-The binding energies of the energetically most favorable configurations with the second DB located along the \hkl[1 1 0] direction and resulting C-C distances of the relaxed structures are summarized in Table~\ref{table:dc_110}.
-\begin{table}
-\begin{tabular}{l c c c c c c }
- & 1 & 2 & 3 & 4 & 5 & 6 \\
-\hline
- $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
-C-C distance [nm] & 0.14 & 0.46 & 0.65 & 0.86 & 1.05 & 1.08
-\end{tabular}
-\caption{Binding energies $E_{\text{b}}$ and C-C distance of energetically most favorable C$_{\text{i}}$ \hkl<1 0 0>-type defect pairs separated along the \hkl[1 1 0] bond chain.}
-\label{table:dc_110}
-\end{table}
-The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:dc_110}.
+
+In qualitative agreement with the results of Capaz~et~al.\ \cite{capaz94}, the lowest migration barrier of the ground-state C$_{\text{i}}$ defect within the quantum-mechanical treatment is found for the path, in which a C$_{\text{i}}$ \hkl[0 0 -1] DB migrates to a C$_{\text{i}}$ \hkl[0 -1 0] DB located at the neighbored Si lattice site in \hkl[1 1 -1] direction.
+Calculations in this work reinforce this path by an additional improvement of the quantitative conformance of the barrier height of \unit[0.90]{eV} to experimental values (\unit[0.70-0.87]{eV}) \cite{lindner06,tipping87,song90}.
+
+In contrast, the empirical approach does not reproduce the same path.
+Related to the instability of the BC configuration \cite{zirkelbach11}, a pathway involving the C$_{\text{i}}$ \hkl<1 1 0> DB as an intermediate configuration must be considered most plausible.
+Considering a two step diffusion process and assuming equal preexponential factors, an total effective migration barrier 3.5 times higher than the one obtained by first-principles methods is obtained.
+A more detailed description can be found in previous studies \cite{zirkelbach10,zirkelbach11}.
+
+\section{Defect combinations}
+
+The implantation of highly energetic C atoms results in a multiplicity of possible point defects and respective combinations.
+Thus, defect combinations of an initial C$_{\text{i}}$ DB and further types of defects created at certain neighbor positions have been investigated \cite{zirkelbach11} exclusively by DFT calculations.
+Some of the most important results are presented in the following.
+
\begin{figure}
\includegraphics[width=\columnwidth]{db_along_110_cc_n.ps}
\caption{Minimum binding energy of dumbbell combinations separated along \hkl[1 1 0] 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.}
\label{fig:dc_110}
\end{figure}
-The interaction is found to be proportional to the reciprocal cube of the C-C distance for extended separations of the C$_{\text{i}}$ and saturates for the smallest possible separation, i.e. the ground state configuration.
-Not considering the previously mentioned elevated barriers for migration an attractive interaction between the C$_{\text{i}}$ defects indeed is detected with a capture radius that clearly exceeds \unit[1]{nm}.
-The interpolated graph suggests the disappearance of attractive interaction forces, which are proportional to the slope of the graph, in between the two lowest separation distances of the defects.
-This finding, in turn, supports the previously established assumption of C agglomeration and absence of C clustering.
-
-\begin{table}
-\begin{tabular}{l c c c c c c }
- & 1 & 2 & 3 & 4 & 5 & R \\
-\hline
-C$_{\text{s}}$ & 0.26$^a$/-1.28$^b$ & -0.51 & -0.93$^A$/-0.95$^B$ & -0.15 & 0.49 & -0.05\\
-V & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31
-\end{tabular}
-\caption{Binding energies of combinations of the C$_{\text{i}}$ \hkl[0 0 -1] defect with a substitutional C or vacancy located at positions 1 to 5 according to Fig.~\ref{fig:combos_ci}. R corresponds to the position located at $\frac{a_{\text{Si}}}{2}\hkl[3 2 3]$ relative to the initial defect position, which is the maximum realizable distance due to periodic boundary conditions.}
-\label{table:dc_c-sv}
-\end{table}
-\subsection{C$_{\text{i}}$ next to C$_{\text{s}}$}
-
-The first row of Table~\ref{table:dc_c-sv} lists the binding energies of C$_{\text{s}}$ next to the C$_{\text{i}}$ \hkl[0 0 -1] DB.
-For C$_{\text{s}}$ located at position 1 and 3 the configurations a and A correspond to the naive relaxation of the structure by substituting the Si atom by a C atom in the initial C$_{\text{i}}$ \hkl[0 0 -1] DB structure at positions 1 and 3 respectively.
-However, small displacements of the involved atoms near the defect result in different stable structures labeled b and B respectively.
-Fig.~\ref{fig:093-095} and \ref{fig:026-128} show structures A, B and a, b together with the barrier of migration for the A to B and a to b transition respectively.
-
-% A B
-%./visualize_contcar -w 640 -h 480 -d results/c_00-1_c3_csub_B -nll -0.20 -0.4 -0.1 -fur 0.9 0.6 0.9 -c 0.5 -1.5 0.375 -L 0.5 0 0.3 -r 0.6 -A -1 2.465
-\begin{figure}
-\includegraphics[width=\columnwidth]{093-095.ps}
-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 3 (left) into a configuration of a twofold coordinated Si$_{\text{i}}$ located in between two C$_{\text{s}}$ atoms occupying the lattice sites of the initial DB and position 3 (right). An activation energy of \unit[0.44]{eV} is observed.}
-\label{fig:093-095}
-\end{figure}
-Configuration A consists of a C$_{\text{i}}$ \hkl[0 0 -1] DB with threefold coordinated Si and C DB atoms slightly disturbed by the C$_{\text{s}}$ at position 3, facing the Si DB atom as a neighbor.
-By a single bond switch, i.e. the breaking of a Si-Si in favor of a Si-C bond, configuration B is obtained, which shows a twofold coordinated Si atom located in between two substitutional C atoms residing on regular Si lattice sites.
-This configuration has been identified and described by spectroscopic experimental techniques\cite{song90_2} as well as theoretical studies\cite{leary97,capaz98}.
-Configuration B is found to constitute the energetically slightly more favorable configuration.
-However, the gain in energy due to the significantly lower energy of a Si-C compared to a Si-Si bond turns out to be smaller than expected due to a large compensation by introduced strain as a result of the Si interstitial structure.
-Present results show a difference in energy of states A and B, which exactly matches the experimental value of \unit[0.02]{eV}\cite{song90_2} reinforcing qualitatively correct results of previous theoretical studies on these structures.
-% mattoni: A favored by 0.4 eV - NO, it is indeed B (reinforce Song and Capaz)!
-%
-% AB transition
-The migration barrier was identified to be \unit[0.44]{eV}, almost three times higher than the experimental value of \unit[0.16]{eV}\cite{song90_2} estimated for the neutral charge state transition in p- and n-type Si.
-Keeping in mind the formidable agreement of the energy difference with experiment, the overestimated activation energy is quite unexpected.
-Obviously, either the CRT algorithm fails to seize the actual saddle point structure or the influence of dopants has exceptional effect in the experimentally covered diffusion process being responsible for the low migration barrier.
-% not satisfactory!
-
-% a b
-\begin{figure}
-\includegraphics[width=\columnwidth]{026-128.ps}
-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 1 (left) into a C-C \hkl[1 0 0] DB occupying the lattice site at position 1 (right). An activation energy of \unit[0.1]{eV} is observed.}
-\label{fig:026-128}
-\end{figure}
-Configuration a is similar to configuration A, except that the C$_{\text{s}}$ atom at position 1 is facing the C DB atom as a neighbor resulting in the formation of a strong C-C bond and a much more noticeable perturbation of the DB structure.
-Nevertheless, the C and Si DB atoms remain threefold coordinated.
-Although the C-C bond exhibiting a distance of \unit[0.15]{nm} close to the distance expected in diamond or graphite should lead to a huge gain in energy, a repulsive interaction with a binding energy of \unit[0.26]{eV} is observed due to compressive strain of the Si DB atom and its top neighbors (\unit[0.230]{nm}/\unit[0.236]{nm}) along with additional tensile strain of the C$_{\text{s}}$ and its three neighboring Si atoms (\unit[0.198-0.209]{nm}/\unit[0.189]{nm}).
-Again a single bond switch, i.e. the breaking of the bond of the Si atom bound to the fourfold coordinated C$_{\text{s}}$ atom and the formation of a double bond between the two C atoms, results in configuration b.
-The two C atoms form a \hkl[1 0 0] DB sharing the initial C$_{\text{s}}$ lattice site while the initial Si DB atom occupies its previously regular lattice site.
-The transition is accompanied by a large gain in energy as can be seen in Fig.~\ref{fig:026-128}, making it the ground state configuration of a C$_{\text{s}}$ and C$_{\text{i}}$ DB in Si yet \unit[0.33]{eV} lower in energy than configuration B.
-This finding is in good agreement with a combined ab initio and experimental study of Liu et~al.\cite{liu02}, who first proposed this structure as the ground state identifying an energy difference compared to configuration B of \unit[0.2]{eV}.
-% mattoni: A favored by 0.2 eV - NO! (again, missing spin polarization?)
-A net magnetization of two spin up electrons, which are equally localized as in the Si$_{\text{i}}$ \hkl<1 0 0> DB structure is observed.
-In fact, these two configurations are very similar and are qualitatively different from the C$_{\text{i}}$ \hkl<1 0 0> DB that does not show magnetization but a nearly collinear bond of the C DB atom to its two neighbored Si atoms while the Si DB atom approximates \unit[120]{$^{\circ}$} angles in between its bonds.
-Configurations a, A and B are not affected by spin polarization and show zero magnetization.
-Mattoni et~al.\cite{mattoni2002}, in contrast, find configuration b less favorable than configuration A by \unit[0.2]{eV}.
-Next to differences in the XC functional and plane-wave energy cut-off this discrepancy might be attributed to the neglect of spin polarization in their calculations, which -- as has been shown for the C$_{\text{i}}$ BC configuration -- results in an increase of configurational energy.
-Indeed, investigating the migration path from configurations a to b and, in doing so, reusing the wave functions of the previous migration step the final structure, i.e. configuration b, was obtained with zero magnetization and an increase in configurational energy by \unit[0.2]{eV}.
-Obviously a different energy minimum of the electronic system is obtained indicating hysteresis behavior.
-However, since the total energy is lower for the magnetic result it is believed to constitute the real, i.e. global, minimum with respect to electronic minimization.
-%
-% a b transition
-A low activation energy of \unit[0.1]{eV} is observed for the a$\rightarrow$b transition.
-Thus, configuration a is very unlikely to occur in favor of configuration b.
-
-% repulsive along 110
-A repulsive interaction is observed for C$_{\text{s}}$ at lattice sites along \hkl[1 1 0], i.e. positions 1 (configuration a) and 5.
-This is due to tensile strain originating from both, the C$_{\text{i}}$ DB and the C$_{\text{s}}$ atom residing within the \hkl[1 1 0] bond chain.
-This finding agrees well with results by Mattoni et~al.\cite{mattoni2002}.
-% all other investigated results: attractive interaction. stress compensation.
-In contrast, all other investigated configurations show attractive interactions.
-The most favorable configuration is found for C$_{\text{s}}$ at position 3, which corresponds to the lattice site of one of the upper neighbored Si atoms of the DB structure that is compressively strained along \hkl[1 -1 0] and \hkl[0 0 1] by the C-Si DB.
-The substitution with C allows for most effective compensation of strain.
-This structure is followed by C$_{\text{s}}$ located at position 2, the lattice site of one of the neighbor atoms below the two Si atoms that are bound to the C$_{\text{i}}$ DB atom.
-As mentioned earlier these two lower Si atoms indeed experience tensile strain along the \hkl[1 1 0] bond chain, however, additional compressive strain along \hkl[0 0 1] exists.
-The latter is partially compensated by the C$_{\text{s}}$ atom.
-Yet less of compensation is realized if C$_{\text{s}}$ is located at position 4 due to a larger separation although both bottom Si atoms of the DB structure are indirectly affected, i.e. each of them is connected by another Si atom to the C atom enabling the reduction of strain along \hkl[0 0 1].
-
-% c agglomeration vs c clustering ... migs to b conf
-% 2 more migs: 051 -> 128 and 026! forgot why ... probably it's about probability of C clustering
-Obviously agglomeration of C$_{\text{i}}$ and C$_{\text{s}}$ is energetically favorable except for separations along one of the \hkl<1 1 0> directions.
-The energetically most favorable configuration (configuration b) forms a strong but compressively strained C-C bond with a separation distance of \unit[0.142]{nm} sharing a Si lattice site.
-Again, conclusions concerning the probability of formation are drawn by investigating migration paths.
-Since C$_{\text{s}}$ is unlikely to exhibit a low activation energy for migration the focus is on C$_{\text{i}}$.
-Pathways starting from the two next most favored configurations were investigated, which show activation energies above \unit[2.2]{eV} and \unit[3.5]{eV} respectively.
-Although lower than the barriers for obtaining the ground state of two C$_{\text{i}}$ defects the activation energies are yet considered too high.
-For the same reasons as in the last subsection, structures other than the ground state configuration are, thus, assumed to arise more likely due to much lower activation energies necessary for their formation and still comparatively low binding energies.
-
-\subsection{C$_{\text{i}}$ next to V}
-
-In the last subsection configurations of a C$_{\text{i}}$ DB with C$_{\text{s}}$ occupying a vacant site have been investigated.
-Additionally, configurations might arise in IBS, in which the impinging C atom creates a vacant site near a C$_{\text{i}}$ DB, but does not occupy it.
-Resulting binding energies of a C$_{\text{i}}$ DB and a nearby vacancy are listed in the second row of Table~\ref{table:dc_c-sv}.
-All investigated structures are preferred compared to isolated largely separated defects.
-In contrast to C$_{\text{s}}$ this is also valid for positions along \hkl[1 1 0] resulting in an entirely attractive interaction between defects of these types.
-Even for the largest possible distance (R) achieved in the calculations of the periodic supercell a binding energy as low as \unit[-0.31]{eV} is observed.
-The ground state configuration is obtained for a V at position 1.
-The C atom of the DB moves towards the vacant site forming a stable C$_{\text{s}}$ configuration resulting in the release of a huge amount of energy.
-The second most favorable configuration is accomplished for a V located at position 3 due to the reduction of compressive strain of the Si DB atom and its two upper Si neighbors present in the C$_{\text{i}}$ DB configuration.
-This configuration is followed by the structure, in which a vacant site is created at position 2.
-Similar to the observations for C$_{\text{s}}$ in the last subsection a reduction of strain along \hkl[0 0 1] is enabled by this configuration.
-Relaxed structures of the latter two defect combinations are shown in the bottom left of Fig.~\ref{fig:314-539} and \ref{fig:059-539} respectively together with their energetics during transition into the ground state.
+The agglomeration of interstitial C is found to be energetically favorable.
+As can be seen in Fig.~\ref{fig:dc_110}, which shows the binding energies of DB combinations separated along the \hkl[1 1 0] chain, a capture radius clearly exceeding \unit[1]{nm} is observed.
+The interaction is proportional to the reciprocal cube of the C-C distance for extended separations of the defects.
+However, the interpolated graph shows the disappearance of attractive forces corresponding to the slope of the graph in between the two lowest separation distances, which clearly indicates a preferable C agglomeration but the absence of C clustering.
+
+In IBS, configurations may arise, in which the impinging C atom creates a vacant site (V) near a C$_{\text{i}}$ DB, but does not occupy it.
+All these structures were found to be energetically preferred compared to isolated largely separated defects \cite{zirkelbach11} showing an entirely attractive interaction between defects of these types.
+The ground-state configuration is obtained for a V located right next to the C atom of the DB.
+The C atom moves towards the vacant site forming a stable C$_{\text{s}}$ configuration resulting in the release of a huge amount of energy.
+The second most favorable configuration is accomplished for a V located right next to the Si atom of the DB structure.
+This is due to the reduction of compressive strain of the Si DB atom and its two upper Si neighbors present in the isolated C$_{\text{i}}$ DB configuration.
+This configuration is followed by the structure, in which the V is created at one of the neighbored lattice site below one of the Si atoms that are bound to the C atom of the initial DB.
+Relaxed structures of the latter two defect combinations are shown in the bottom left of Figs.~\ref{fig:314-539} and \ref{fig:059-539} respectively together with their energetics during transition into the ground state.
\begin{figure}
\includegraphics[width=\columnwidth]{314-539.ps}
-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created at position 3 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.1]{eV} is observed.}
+\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created right next to the Si atom of the initial DB (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.1]{eV} is observed.}
\label{fig:314-539}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{059-539.ps}
-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created at position 2 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.6]{eV} is observed.}
+\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created next to one of the Si atoms that is bound to the C atom of the initial DB (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.6]{eV} is observed.}
\label{fig:059-539}
\end{figure}
-Activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} are observed.
+These transitions exhibit activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV}.
In the first case the Si and C atom of the DB move towards the vacant and initial DB lattice site respectively.
-In total three Si-Si and one more Si-C bond is formed during transition.
-In the second case the lowest barrier is found for the migration of Si number 1, which is substituted by the C$_{\text{i}}$ atom, towards the vacant site.
-A net amount of five Si-Si and one Si-C bond are additionally formed during transition.
-The direct migration of the C$_{\text{i}}$ atom onto the vacant lattice site results in a somewhat higher barrier of \unit[1.0]{eV}.
+In the second case Si number 1, which is substituted by the C$_{\text{i}}$ atom, migrates towards the vacant site.
In both cases, the formation of additional bonds is responsible for the vast gain in energy rendering almost impossible the reverse processes.
+Considering the small activation energies, a high probability for the formation of stable C$_{\text{s}}$ must be concluded.
-In summary, pairs of C$_{\text{i}}$ DBs and Vs, like no other before, show highly attractive interactions for all investigated combinations independent of orientation and separation direction of the defects.
-Furthermore, small activation energies, even for transitions into the ground state exist.
-Based on these results, a high probability for the formation of C$_{\text{s}}$ must be concluded.
-
-\subsection{C$_{\text{s}}$ next to Si$_{\text{i}}$}
-
-As shown in section~\ref{subsection:sep_def}, C$_{\text{s}}$ exhibits the lowest energy of formation.
-Considering a perfect Si crystal and conservation of particles, however, the occupation of a Si lattice site by a slowed down implanted C atom is necessarily accompanied by the formation of a Si self-interstitial.
-There are good reasons for the existence of regions exhibiting such configurations with regard to the IBS process.
-Highly energetic C atoms are able to kick out a Si atom from its lattice site, resulting in a Si self-interstitial accompanied by a vacant site, which might get occupied by another C atom that lost almost all of its kinetic energy.
-%Thus, configurations of C$_{\text{s}}$ and Si self-interstitials are investigated in the following.
-Provided that the first C atom, which created the V and Si$_{\text{i}}$ pair has enough kinetic energy to escape the affected region, the C$_{\text{s}}$-Si$_{\text{i}}$ pair can be described as a separated defect complex.
-The Si$_{\text{i}}$ \hkl<1 1 0> DB, which was found to exhibit the lowest energy of formation within the investigated self-interstitial configurations, is assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$.
-
-\begin{table}
-\begin{tabular}{l c c c c c c}
- & \hkl[1 1 0] & \hkl[-1 1 0] & \hkl[0 1 1] & \hkl[0 -1 1] &
- \hkl[1 0 1] & \hkl[-1 0 1] \\
-\hline
-1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
-2 & \RM{2} & \RM{6} & \RM{6} & \RM{2} & \RM{8} & \RM{5} \\
-3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
-4 & \RM{4} & \RM{7} & \RM{9} & \RM{10} & \RM{10} & \RM{9} \\
-5 & \RM{5} & \RM{8} & \RM{6} & \RM{2} & \RM{6} & \RM{2} \\
-\end{tabular}
-\caption{Equivalent configurations labeled \RM{1}-\RM{10} of \hkl<1 1 0>-type Si$_{\text{i}}$ DBs created at position I and C$_{\text{s}}$ created at positions 1 to 5 according to Fig.~\ref{fig:combos_si}. The respective orientation of the Si$_{\text{i}}$ DB is given in the first row.}
-\label{table:dc_si-s}
-\end{table}
-\begin{table*}
-\begin{tabular}{l c c c c c c c c c c}
- & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & \RM{6} & \RM{7} & \RM{8} & \RM{9} & \RM{10} \\
-\hline
-$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
-$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
-$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
-\end{tabular}
-\caption{Formation energies $E_{\text{f}}$, binding energies $E_{\text{b}}$ and C$_{\text{s}}$-Si$_{\text{i}}$ separation distances of configurations combining C$_{\text{s}}$ and Si$_{\text{i}}$ as defined in Table~\ref{table:dc_si-s}.}
-\label{table:dc_si-s_e}
-\end{table*}
-Table~\ref{table:dc_si-s} classifies equivalent configurations of \hkl<1 1 0>-type Si$_{\text{i}}$ DBs created at position I and C$_{\text{s}}$ created at positions 1 to 5 according to Fig.~\ref{fig:combos_si}.
-Corresponding formation as well as binding energies and the separation distances of the C$_{\text{s}}$ atom and the Si$_{\text{i}}$ DB lattice site are listed in Table~\ref{table:dc_si-s_e}.
-In total ten different configurations exist within the investigated range.
-Configuration \RM{1} constitutes the energetically most favorable structure exhibiting a formation energy of \unit[4.37]{eV}.
-Obviously the configuration of a Si$_{\text{i}}$ \hkl[1 1 0] DB and a neighbored C$_{\text{s}}$ atom along the bond chain, which has the same direction as the alignment of the DB, enables the largest possible reduction of strain.
-The relaxed structure is displayed in the bottom right of Fig.~\ref{fig:162-097}.
-Compressive strain originating from the Si$_{\text{i}}$ is compensated by tensile strain inherent to the C$_{\text{s}}$ configuration.
-The Si$_{\text{i}}$ DB atoms are displaced towards the lattice site occupied by the C$_{\text{s}}$ atom in such a way that the Si$_{\text{i}}$ DB atom closest to the C atom does no longer form bonds to its top Si neighbors, but to the next neighbored Si atom along \hkl[1 1 0].
-
-However, the configuration is energetically less favorable than the \hkl<1 0 0> C$_{\text{i}}$ DB, which, thus, remains the ground state of a C atom introduced into otherwise perfect c-Si.
-The transition involving the latter two configurations is shown in Fig.~\ref{fig:162-097}.
+In addition, it is instructive to investigate combinations of C$_{\text{s}}$ and Si$_{\text{i}}$, which can be created in IBS by highly energetic C atoms that kick out a Si atom from its lattice site, resulting in a Si self-interstitial accompanied by a vacant site, which might get occupied by another C atom that lost almost all of its kinetic energy.
+Provided that the first C atom has enough kinetic energy to escape the affected region, the remaining C$_{\text{s}}$-Si$_{\text{i}}$ pair can be described as a separated defect complex.
+Considering the energetically most favorable Si$_{\text{i}}$ defect, i.e. the Si$_{\text{i}}$ \hkl<1 1 0> DB, the most favorable combination is found for C$_{\text{s}}$ located right next to that DB enabling the largest possible reduction of strain.
+The configuration and the transition into the ground-state configuration, i.e. the C$_{\text{i}}$ hkl<1 0 0> DB is displayed in Fig.~\ref{fig:162-097}
\begin{figure}
\includegraphics[width=\columnwidth]{162-097.ps}
-\caption{Migration barrier and structures of the transition of a \hkl[1 1 0] Si$_{\text{i}}$ DB next to C$_{\text{s}}$ (right) into the C$_{\text{i}}$ \hkl[0 0 -1] DB configuration (left). An activation energy of \unit[0.12]{eV} and \unit[0.77]{eV} for the reverse process is observed.}
+\caption{Transition of a \hkl[1 1 0] Si$_{\text{i}}$ DB next to C$_{\text{s}}$ (right) into the C$_{\text{i}}$ \hkl[0 0 -1] DB configuration (left).}
\label{fig:162-097}
\end{figure}
-An activation energy as low as \unit[0.12]{eV} is necessary for the migration into the ground state configuration.
-Accordingly, the C$_{\text{i}}$ \hkl<1 0 0> DB configuration is assumed to occur more likely.
-However, only \unit[0.77]{eV} are needed for the reverse process, i.e. the formation of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB out of the ground state.
-Due to the low activation energy this process must be considered to be activated without much effort either thermally or by introduced energy of the implantation process.
-
+Due to the low barrier of \unit[0.12]{eV}, the C$_{\text{i}}$ \hkl<1 0 0> DB configuration is very likely to occur.
+However, the barrier of only \unit[0.77]{eV} for the reverse process indictaes a high probability for the the formation of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB out of the ground state, wich must be considered to be activated without much effort either thermally or by introduced energy of the implantation process.
\begin{figure}
-%\includegraphics[width=\columnwidth]{c_sub_si110.ps}
-\includegraphics[width=\columnwidth]{c_sub_si110_data.ps}
-\caption{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance.}
-%\caption{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance. The interaction strength of the defect pairs are well approximated by a Lennard-Jones 6-12 potential, which is used for curve fitting.}
+\includegraphics[width=\columnwidth]{c_sub_si110.ps}
+%\includegraphics[width=\columnwidth]{c_sub_si110_data.ps}
+%\caption{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance.}
+\caption{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance. The interaction strength of the defect pairs are well approximated by a Lennard-Jones 6-12 potential, which is used for curve fitting.}
\label{fig:dc_si-s}
\end{figure}
-Fig.~\ref{fig:dc_si-s} shows the binding energies of pairs of C$_{\text{s}}$ and a Si$_{\text{i}}$ \hkl<1 1 0> DB with respect to the separation distance.
-%The interaction of the defects is well approximated by a Lennard-Jones (LJ) 6-12 potential, which is used for curve fitting.
-%Unable to model possible positive values of the binding energy, i.e. unfavorable configurations, located to the right of the minimum, the LJ fit should rather be thought as a guide for the eye describing the decrease of the interaction strength, i.e. the absolute value of the binding energy, with increasing separation distance.
-%The binding energy quickly drops to zero.
-%The LJ fit estimates almost zero interaction already at \unit[0.6]{nm}, indicating a low interaction capture radius of the defect pair.
-As can be seen, the interaction strength, i.e. the absolute value of the binding energy, quickly drops to zero with increasing separation distance.
-Almost zero interaction may be assumed already at distances about \unit[0.5-0.6]{nm}, indicating a low interaction capture radius of the defect pair.
-In IBS highly energetic collisions are assumed to easily produce configurations of defects exhibiting separation distances exceeding the capture radius.
-For this reason C$_{\text{s}}$ without a Si$_{\text{i}}$ DB located within the immediate proximity, which is, thus, unable to form the thermodynamically stable C$_{\text{i}}$ \hkl<1 0 0> DB, constitutes a most likely configuration to be found in IBS.
-
-Similar to what was previously mentioned, configurations of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB might be particularly important at higher temperatures due to the low activation energy necessary for its formation.
-At higher temperatures the contribution of entropy to structural formation increases, which might result in a spatial separation even for defects located within the capture radius.
-Indeed, an ab initio molecular dynamics run at \unit[900]{$^{\circ}$C} starting from configuration \RM{1}, which -- based on the above findings -- is assumed to recombine into the ground state configuration, results in a separation of the C$_{\text{s}}$ and Si$_{\text{i}}$ DB by more than 4 neighbor distances realized in a repeated migration mechanism of annihilating and arising Si$_{\text{i}}$ DBs.
-The atomic configurations for two different points in time are shown in Fig.~\ref{fig:md}.
-Si atoms 1 and 2, which form the initial DB, occupy Si lattice sites in the final configuration while Si atom 3 is transferred from a regular lattice site into the interstitial lattice.
-\begin{figure}
-\begin{minipage}{0.49\columnwidth}
-\includegraphics[width=\columnwidth]{md01.eps}
-\end{minipage}
-\begin{minipage}{0.49\columnwidth}
-\includegraphics[width=\columnwidth]{md02.eps}\\
-\end{minipage}\\
-\begin{minipage}{0.49\columnwidth}
-\begin{center}
-$t=\unit[2230]{fs}$
-\end{center}
-\end{minipage}
-\begin{minipage}{0.49\columnwidth}
-\begin{center}
-$t=\unit[2900]{fs}$
-\end{center}
-\end{minipage}
-\caption{Atomic configurations of an ab initio molecular dynamics run at \unit[900]{$^{\circ}$C} starting from a configuration of C$_{\text{s}}$ located next to a Si$_{\text{i}}$ \hkl[1 1 0] DB (atoms 1 and 2). Equal atoms are marked by equal numbers. Bonds are drawn for substantial atoms only.}
-\label{fig:md}
-\end{figure}
+Furthermore, the interaction strength, i.e. the absolute value of the binding energy, quickly drops to zero with increasing separation distance as can be seen in Fig.~\ref{fig:dc_si-s}.
+The interaction of the defects is well approximated by a Lennard-Jones (LJ) 6-12 potential, which is used for curve fitting.
+Unable to model possible positive values of the binding energy, i.e. unfavorable configurations, located to the right of the minimum, the LJ fit should rather be thought as a guide for the eye describing the decrease of the interaction strength, i.e. the absolute value of the binding energy, with increasing separation distance.
+The LJ fit estimates almost zero interaction already at \unit[0.5-0.6]{nm}, indicating a low interaction capture radius of the defect pair.
+In IBS separations exceeding this capture radius are easily produced.
+For these reasons, it must be concluded that configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ instead of the thermodynamically stable C$_{\text{i}}$ \hkl<1 0 0> DB play a decisive role in IBS, a process far from equilibrium.
+Indeed, in a previous study, an ab initio molecular dynamics run at \unit[900]{$^{\circ}$C} results in a separation of the C$_{\text{s}}$ and Si$_{\text{i}}$ DB located right next to each other \cite{zirkelbach11}.
+
+To summarize, these obtained results suggest an increased participation of C$_{\text{s}}$ already in the initial stages of precipitation under IBS conditions.
+
+\section{Large scale empirical potential MD results}
-\section{Discussion}
+\section{Summary and discussion}
Obtained results for separated point defects in Si are in good agreement to previous theoretical work on this subject, both for intrinsic defects\cite{leung99,al-mushadani03} as well as for C point defects\cite{dal_pino93,capaz94}.
The ground state configurations of these defects, i.e. the Si$_{\text{i}}$ \hkl<1 1 0> and C$_{\text{i}}$ \hkl<1 0 0> DB, have been reproduced and compare well to previous findings of theoretical investigations on Si$_{\text{i}}$\cite{leung99,al-mushadani03} as well as theoretical\cite{dal_pino93,capaz94,burnard93,leary97,jones04} and experimental\cite{watkins76,song90} studies on C$_{\text{i}}$.
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