% additional stuff\r
\usepackage{miller}\r
\r
+% roman numbers\r
+\newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}\r
+\r
\begin{document}\r
\r
%\title{Mobility of Carbon in Silicon -- a first principles study}\r
Ionic relaxation was realized by the conjugate gradient algorithm.\r
Spin polarization has been fully accounted for.\r
\r
-Migration and recombination pathways have been ivestigated utilizing the constraint conjugate gradient relaxation technique (CRT)\cite{kaukonen98}.\r
+Migration and recombination pathways have been investigated utilizing the constraint conjugate gradient relaxation technique (CRT)\cite{kaukonen98}.\r
The defect formation energy $E-N_{\text{Si}}\mu_{\text{Si}}-N_{\text{C}}\mu_{\text{C}}$ is defined by chosing SiC as a particle reservoir for the C impurity, i.e. the chemical potentials are determined by the cohesive energies of a perfect Si and SiC supercell after ionic relaxation.\r
-The binding energy of a defect pair is given by the difference of the formation energy of the complex and the sum of the two separated defect configurations, i.e. energetically favorable configurations show binding energies below zero and non-interacting isolated defects would result in a binding energy of zero.\r
+The binding energy of a defect pair is given by the difference of the formation energy of the complex and the sum of the two separated defect configurations.\r
+Accordingly, energetically favorable configurations show binding energies below zero while non-interacting isolated defects result in a binding energy of zero.\r
\r
\section{Results}\r
\r
The investigations proceed with pairs of the ground state and, thus, most probable defect configurations that are believed to be fundamental in the Si to SiC transition.\r
\r
\subsection{Separated defects in silicon}\r
+\label{subsection:sep_def}\r
% we need both: Si self-int & C int ground state configuration (for combos)\r
\r
Several geometries have been calculated to be stable for individual intrinsic and C related defects in Si.\r
\begin{table*}\r
\begin{ruledtabular}\r
\begin{tabular}{l c c c c c c c c c}\r
- & Si$_{\text{i}}$ \hkl<1 1 0> DB & Si$_{\text{i}}$ H & Si$_{\text{i}}$ T & Si \hkl<1 0 0> DB & V & C$_{\text{s}}$ & C$_{\text{i}}$ \hkl<1 0 0> DB & C$_{\text{i}}$ \hkl<1 1 0> DB & C$_{\text{i}}$ BC \\\r
+ & Si$_{\text{i}}$ \hkl<1 1 0> DB & Si$_{\text{i}}$ H & Si$_{\text{i}}$ T & Si$_{\text{i}}$ \hkl<1 0 0> DB & V & C$_{\text{s}}$ & C$_{\text{i}}$ \hkl<1 0 0> DB & C$_{\text{i}}$ \hkl<1 1 0> DB & C$_{\text{i}}$ BC \\\r
\hline\r
Present study & 3.39 & 3.42 & 3.77 & 4.41 & 3.63 & 1.95 & 3.72 & 4.16 & 4.66 \\\r
\multicolumn{10}{c}{Other ab initio studies} \\\r
The atomic arrangement is shown in the bottom right of Fig.~\ref{fig:036-239}.\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 oriented along \hkl[0 1 0] at position 2 (\unit[-1.90]{eV}) into a \hkl[0 1 0] 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 \hkl[-1 0 0] DB located at position 2 (\unit[-0.36]{eV}).\r
+Investigating migration barriers enables to predict the probability of formation of defect complexes by thermally activated diffusion processes.\r
+% ground state configuration, C cluster\r
+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.\r
+In addition, the starting configuration exhibits a low binding energy (\unit[-1.90]{eV}) and is, thus, very likely to occur.\r
+However, a barrier height of more than \unit[4]{eV} was detected resulting in a low probability for the transition.\r
+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.\r
+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}).\r
Starting from this configuration, an activation energy of only \unit[1.2]{eV} is necessary for the transition into the ground state configuration.\r
The corresponding migration energies and atomic configurations are displayed in Fig.~\ref{fig:036-239}.\r
\begin{figure}\r
Thus, lower migration barriers are expected for pathways resulting in larger separations of the C$_{\text{i}}$ DBs.\r
% calculate?!? ... hopefully acknowledged by 188-225 calc\r
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.\r
-Configurations, which exhibit both, a low binding energy as well as targeting transitions with low activation energies are, thus, most probable C$_{\text{i}}$ complex structures.\r
-On the other hand, if elevated temperatures enable migrations with huge activation energies, the comparably small differences in configurational energy can be neglected resulting in an almost equal occupation of these configurations.\r
+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.\r
+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.\r
In both cases the configuration yielding a binding energy of \unit[-2.25]{eV} is promising.\r
-First of all it constitutes the second most energetically favorable structure.\r
-Secondly, a migration path with a barrier as low as \unit[?.?]{eV} exists starting from a configuration of largely separated defects exhibiting a low binding energy (\unit[-1.88]{eV}).\r
+First of all, it constitutes the second most energetically favorable structure.\r
+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}).\r
The migration barrier and correpsonding structures are shown in Fig.~\ref{fig:188-225}.\r
% 188 - 225 transition in progress\r
\begin{figure}\r
\includegraphics[width=\columnwidth]{188-225.ps}\r
-\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[?.?]{eV} is observed.}\r
+\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.}\r
\label{fig:188-225}\r
\end{figure}\r
-Finally, this type of defect pair is represented four times (two times more often than the ground state configuration) within the investigated configuration space.\r
+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.\r
The latter is considered very important for high temperatures, which is accompanied by an increase in the entropic contribution to structure formation.\r
Thus, C agglomeration indeed is expected but only a low probability is assumed for C clustering by thermally activated processes with regard to the considered period of time.\r
% ?!?\r
\end{figure}\r
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.\r
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 the \unit[1]{nm} mark.\r
+The interpolated graph suggests the disappearance of attractive interaction forces, which are proportional to the slope of the graph, inbetween the two lowest separation distances of the defects.\r
+This finding, in turn, supports the previously established assumption of C agglomeration and absence of C clsutering.\r
\r
\begin{table}\r
\begin{ruledtabular}\r
\subsection{C$_{\text{i}}$ next to C$_{\text{s}}$}\r
\r
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.\r
-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 a Si atom with C in the initial C$_{\text{i}}$ \hkl[0 0 -1] DB structure at positions 1 and 3 respectively.\r
+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.\r
However, small displacements of the involved atoms near the defect result in different stable structures labeled b and B respectively.\r
+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. \r
\r
% A B\r
+%./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\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{093-095.ps}\r
+\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 inbetween 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.}\r
+\label{fig:093-095}\r
+\end{figure}\r
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 next neighbor.\r
-By breaking a Si-Si in favor of a Si-C bond configuration B is obtained, which shows a twofold coordinated Si atom located inbetween two substitutional C atoms residing on regular Si lattice sites.\r
+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 inbetween two substitutional C atoms residing on regular Si lattice sites.\r
This configuration has been identified and described by spectroscopic experimental techniques\cite{song90_2} as well as theoretical studies\cite{leary97,capaz98}.\r
-Configuration B is found to constitute the energetically more favorable configuration.\r
+Configuration B is found to constitute the energetically slightly more favorable configuration.\r
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.\r
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.\r
% mattoni: A favored by 0.4 eV - NO, it is indeed B (reinforce Song and Capaz)!\r
%\r
% AB transition\r
-%Figure~\ref{fig:AB} displays the two configurations and migration barrier for the transition among the two states.\r
+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.\r
+Keeping in mind the formidable agreement of the energy difference with experiment, the overestimated activation energy is quite unexpected and disappointing.\r
+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.\r
+% not satisfactory!\r
\r
% a b\r
\begin{figure}\r
\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.}\r
\label{fig:026-128}\r
\end{figure}\r
-Configuration a is similar to configuration A except that the C$_{\text{s}}$ at position 1 is facing the C DB atom as a next neighbor resulting in the formation of a strong C-C bond and a much more noticeable perturbation of the DB structure.\r
+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 next neighbor resulting in the formation of a strong C-C bond and a much more noticeable perturbation of the DB structure.\r
Nevertheless, the C and Si DB atoms remain threefold coordinated.\r
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}).\r
-\r
-...\r
-\r
-Liu et~al.\cite{liu02} propose a similar structure \unit[0.2]{eV} lower than configuration B, thus, constituting the ground state configuration.\r
-The structure labeld b indeed is the ground state configuration, in which the two C atoms form a \hkl[1 0 0] DB sharing the C$_{\text{s}}$ lattice site and the initial Si DB atom occupying the lattice site shared by the initial C$_{\text{i}}$ DB.\r
-\r
-Spin polarization for C-C Int resulting spin up electrons located as in the case of the Si 100 int.\r
+Again a single bond switch, i.e. the breaking of the bond of a 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.\r
+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.\r
+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.\r
+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}.\r
% mattoni: A favored by 0.2 eV - NO! (again, missing spin polarization?)\r
-\r
-% mig a-b\r
+A net magnetization of two spin up electrons, which are euqally localized as in the Si$_{\text{i}}$ \hkl<1 0 0> DB structure is observed.\r
+Configurations a, A and B are not affected by spin polarization and show zero magnetization.\r
+Mattoni et~al.\cite{mattoni2002}, in contrast, find configuration b less favorable than configuration A by \unit[0.2]{eV}.\r
+Next to differences in the XC-functional and plane-wave energy cut-off this discrepancy might be attributed to the missing accounting for spin polarization in their calculations, which -- as has been shown for the C$_{\text{i}}$ BC configuration -- results in an increase of configurational energy.\r
+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}.\r
+Obviously a different energy minimum of the electronic system is obatined indicating hysteresis behavior.\r
+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.\r
+%\r
+% a b transition\r
+A low activation energy of \unit[0.1]{eV} is observed for the a$\rightarrow$b transition.\r
+Thus, configuration a is very unlikely to occur in favor of configuration b.\r
+\r
+% repulsive along 110\r
+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.\r
+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.\r
+This finding agrees well with results by Mattoni et~al.\cite{mattoni2002}.\r
+% all other investigated results: attractive interaction. stress compensation.\r
+In contrast, all other investigated configurations show attractive interactions.\r
+The most favorable configuration is found for C$_{\text{s}}$ at position 3, which corresponds to the lattice site of one of the upper next 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.\r
+The substitution with C allows for most effective compensation of strain.\r
+This structure is followed by C$_{\text{s}}$ located at position 2, the next neighbour atom below the two Si atoms bound to the C$_{\text{i}}$ DB atom.\r
+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.\r
+The latter is partially compensated by the C$_{\text{s}}$ atom.\r
+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].\r
+\r
+% c agglomeration vs c clustering ... migs to b conf\r
% 2 more migs: 051 -> 128 and 026! forgot why ... probably it's about probability of C clustering\r
+Obviously agglomeration of C$_{\text{i}}$ and C$_{\text{s}}$ is energetically favorable except for seprations along one of the \hkl<1 1 0> directions.\r
+The eneregtically 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.\r
+Again, conclusions concerning the probability of formation are drawn by investigating migration paths.\r
+Since C$_{\text{s}}$ is unlikely to exhibit a low activation energy for migration the focus is on C$_{\text{i}}$.\r
+Pathways starting from the two next most favored configurations were investigated, all of them showing activation energies above \unit[2.?-2.?]{eV}.\r
+Although lower than the barriers for obtaining the ground state of two C$_{\text{i}}$ defects the activation energy is yet considered too high.\r
+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.\r
\r
\subsection{C$_{\text{i}}$ next to V}\r
\r
+In the last subsection configurations of a C$_{\text{i}}$ DB with C$_{\text{s}}$ occupying a vacant site created by the implantation process have been investigated.\r
+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.\r
+Resulting binding energies of a C$_{\text{i}}$ DB with a nearby vacancy are listed in the second row of Table~\ref{table:dc_c-sv}.\r
+All investigated structures are prefered compared to isolated largely separated defects.\r
+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.\r
+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.\r
+The ground state configuration is obtained for a V at position 1.\r
+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.\r
+The second most favored 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 neighbours present in the C$_{\text{i}}$ DB configuration.\r
+This configuration is follwed by the structure, in which a vacant site is created at position 2.\r
+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.\r
+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.\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{314-539.ps}\r
+\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.}\r
+\label{fig:314-539}\r
+\end{figure}\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{059-539.ps}\r
+\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.}\r
+\label{fig:059-539}\r
+\end{figure}\r
+Activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} are observed.\r
+In the first case the Si and C atom of the DB move towards the vacant and initial DB lattice site respectively.\r
+In total three Si-Si and one more Si-C bond is formed during the transition.\r
+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.\r
+A net amount of five Si-Si and one Si-C bond are additionally formed during the transition.\r
+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}.\r
+In both cases, the formation of additional bonds is responsible for the vast gain in energy rendering almost impossible the reverse processes.\r
+\r
+In summary, pairs of C$_{\text{i}}$ DBs and Vs, like no other before, show highly attractive interactions for all investigated combinations indpendent of orientation and separation direction of the defects.\r
+Furthermore, small activation energies, even for transitions into the ground state exist.\r
+Based on these results, a high probability for the formation of C$_{\text{s}}$ must be concluded.\r
+\r
\subsection{C$_{\text{s}}$ next to Si$_{\text{i}}$}\r
\r
-Non-zeor temperature, entropy, spatial separation of these defects possible, indeed observed in ab initio MD run.\r
+As shown in section~\ref{subsection:sep_def} C$_{\text{s}}$ exhibits the lowest energy of formation.\r
+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.\r
+There are good reasons for the existence of regions exhibiting such configurations with regard to the IBS process.\r
+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, which lost almost all of its kinetic energy.\r
+Thus, configurations of C$_{\text{s}}$ and Si self-interstitials are investigated in the following.\r
+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$_{\text{s}}$.\r
+\r
+\begin{table}\r
+\begin{ruledtabular}\r
+\begin{tabular}{l c c c c c c}\r
+ & \hkl[1 1 0] & \hkl[-1 1 0] & \hkl[0 1 1] & \hkl[0 -1 1] &\r
+ \hkl[1 0 1] & \hkl[-1 0 1] \\\r
+\hline\r
+1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\\r
+2 & \RM{2} & \RM{6} & \RM{6} & \RM{2} & \RM{8} & \RM{5} \\\r
+3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\\r
+4 & \RM{4} & \RM{7} & \RM{9} & \RM{10} & \RM{10} & \RM{9} \\\r
+5 & \RM{5} & \RM{8} & \RM{6} & \RM{2} & \RM{6} & \RM{2} \\\r
+\end{tabular}\r
+\caption{Equivalent configurations labeld \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.}\r
+\label{table:dc_si-s}\r
+\end{ruledtabular}\r
+\end{table}\r
+\begin{table*}\r
+\begin{ruledtabular}\r
+\begin{tabular}{l c c c c c c c c c c}\r
+ & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & \RM{6} & \RM{7} & \RM{8} & \RM{9} & \RM{10} \\\r
+\hline\r
+$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\\r
+$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\\r
+$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\\r
+\end{tabular}\r
+\caption{Formation energies $E_{\text{f}}$, binding energies $E_{\text{b}}$ and C$_{\text{s}}$-Si$_{\text{i}}$ separation distances of the combinational C$_{\text{s}}$ and Si$_{\text{i}}$ configurations as defined in table \ref{table:dc_si-s}. Energies are given in eV while the separation is given in nm.}\r
+\label{table:dc_si-s_e}\r
+\end{ruledtabular}\r
+\end{table*}\r
+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}.\r
+Corresponding formation as well as binding energies and the C$_{\text{s}}$-Si$_{\text{i}}$ distances are listed in Table~\ref{table:dc_si-s_e}.\r
+\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{c_sub_si110.ps}\r
+\caption{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance. The binding energies of the defect pairs are well approximated by a Lennard-Jones 6-12 potential, which is used for curve fitting.}\r
+\label{fig:dc_si-s}\r
+\end{figure}\r
+\r
+Non-zero temperature, entropy, spatial separation of these defects possible, indeed observed in ab initio MD run.\r
\r
\section{Discussion}\r
+\r
Our calculations show that point defects which unavoidably are present after ion implantation significantly influence the mobility of implanted carbon \r
in the silicon crystal.\r
A large capture radius has been found for... \r
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\bibliographystyle{h-physrev3}\r
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