% 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
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
However, the present study indicates a local minimum state for the BC defect if spin polarized calculations are performed resulting in a net magnetization of two electrons localized in a torus around the C atom.\r
Another DFT calculation without fully accounting for the electron spin results in the smearing of a single electron over two non-degenerate Kohn-Sham states and an increase of the total energy by \unit[0.3]{eV} for the BC configuration.\r
Regardless of the rather small correction due to the spin, the difference we found is much smaller (\unit[0.9]{eV}), which would nicely compare to experimental findings $(\unit[0.70-0.87]{eV})$\cite{lindner06,tipping87,song90} for the migration barrier.\r
-However, since the BC configuration constitutes a real local minimum another barrier exists which is about \unit[1.2]{eV} ($\unit[0.9]{eV}+\unit[0.3]{eV}$) in height.\r
+However, since the BC configuration constitutes a real local minimum another barrier exists which is about \unit[1.2]{eV} in height.\r
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 into a C$_{\text{i}}$ \hkl[0 -1 0] DB located at the next neighbored Si lattice site in \hkl[1 1 -1] direction.\r
Calculations in this work reinforce this path by an additional improvement of the quantitative conformance of the barrier height (\unit[0.9]{eV}) to experimental values.\r
A more detailed description can be found in a previous study\cite{zirkelbach10a}.\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
+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 systematically investigated configuration space.\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.?]{eV} is observed.}\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
% mattoni: A favored by 0.4 eV - NO, it is indeed B (reinforce Song and Capaz)!\r
%\r
% AB transition\r
-% ...\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
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 \unit[0.2]{eV}.\r
-Obviously a different energy minimum of the electronic system is obatined in that case showing a hysterisis behavior.\r
-However, since the total energy is lower for the magnetic result it is believed to constitute the real, i.e. global, minimum of the electronic minimization.\r
-\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
-However, migration barriers yielding\r
-...\r
\r
-% mig a-b\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 neighbor 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[2.2-3.5]{eV}.\r
+Although lower than the barriers for obtaining the ground state of two C$_{\text{i}}$ defects the activation energies are 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 neighbors 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-zero 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 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}.\r
+In total ten different configurations exist within the investigated range.\r
+Configuration \RM{1} constitutes the energetically most favorable structure exhibiting a formation energy of \unit[4.37]{eV}.\r
+Obviously the configuration of a \hkl[1 1 0] Si$_{\text{i}}$ DB and a next neighbored C$_{\text{s}}$ in the same direction as the alignment of the DB, as displayed in the bottom right of Fig.~\ref{fig:162-097}, enables the largest possible reduction of strain.\r
+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 DB atom closest to the C atom does no longer form bonds to its top Si neighbors but to the second next neighbored Si atom along \hkl[1 1 0].\r
+However, this 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.\r
+The transition involving the latter two configurations is shown in Fig.~\ref{fig:dc_si-s}.\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{162-097.ps}\r
+\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} is observed.}\r
+\label{fig:162-097}\r
+\end{figure}\r
+An activation energy as low as \unit[0.12]{eV} is necessary for the migration into the ground state configuration.\r
+Thus, the C$_{\text{i}}$ \hkl<1 0 0> DB configuration is assumed to occur more likely.\r
+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.\r
+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.\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
+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.\r
+The interaction of the defects is well approximated by a Lennard-Jones 6-12 potential, which was used for curve fitting.\r
+The binding energy quickly drops to zero with the fit estimating almost zero interaction at \unit[0.6]{nm}.\r
+This indicates a low interaction capture radius of the defect pair.\r
+In IBS highly energetic collisions are assumed to easily produce configurations of these defects with separation distances exceeding the capture radius.\r
+For this reason C$_{\text{s}}$ without a nearby interacting Si$_{\text{i}}$ DB, which are, 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.\r
+\r
+As mentioned above, configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ DBs might be especially important at higher temperatures due to the low activation energy necessary for its formation.\r
+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.\r
+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 the C$_{\text{s}}$ and Si$_{\text{i}}$ DB by more than 4 next neighbor distances realized in a repeated migration mechnism of annihilating and arising Si DBs.\r
+The atomic configurations for two different points in time are shown in Fig.~\ref{fig:md}.\r
+Si atoms 1 and 2, which form the initial DB, occupy usual Si lattice sites in the final configuration while atom 3 occupies an interstitial site.\r
+\begin{figure}\r
+\begin{minipage}{0.49\columnwidth}\r
+\includegraphics[width=\columnwidth]{md01.eps}\r
+\end{minipage}\r
+\begin{minipage}{0.49\columnwidth}\r
+\includegraphics[width=\columnwidth]{md02.eps}\\\r
+\end{minipage}\\\r
+\begin{minipage}{0.49\columnwidth}\r
+\begin{center}\r
+$t=\unit[2230]{fs}$\r
+\end{center}\r
+\end{minipage}\r
+\begin{minipage}{0.49\columnwidth}\r
+\begin{center}\r
+$t=\unit[2900]{fs}$\r
+\end{center}\r
+\end{minipage}\r
+\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$_{\text{i}}$ DB (atoms 1 and 2). Equal atoms are marked by equal numbers. Blue lines correpsond to bonds, which are drawn for substantial atoms.}\r
+\label{fig:md}\r
+\end{figure}\r
\r
\section{Discussion}\r
\r
+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}.\r
+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$_{\text{i}}$.\r
+A quantitatively improved activation energy of \unit[0.9]{eV} for a qualitatively equal migration path based on studies by Capaz et.~al.\cite{capaz94} to experimental values\cite{song90,lindner06,tipping87} ranging from \unit[0.70-0.87]{eV} reinforce their derived mechanism of diffusion for C$_{\text{i}}$ in Si.\r
+\r
+The investigation of defect pairs indicates a general trend of defect agglomeration mainly driven by the potential of strain reduction.\r
+Obtained results for the most part compare well with results gained in previous studies\cite{leary97,capaz98,mattoni2002,liu02} and show an astnishingly good agreement with experiment\cite{song90}.\r
+Configurations involving two C impurities indeed exhibit the ground state for structures consisting of C-C bonds, which are responsible for the vast gain in energy.\r
+However, based on investigations of possible migration pathways, these structures are less likely to arise than structures, in which both C atoms are interconnected by another Si atom, which is due to high activation energies of the respective pathways or alternative pathways with less high activation energies, which, however, involve intermediate unfavorable configurations.\r
+Thus, agglomeration of C$_{\text{i}}$ is expected while the formation of C-C bonds is assumed to fail to appear by thermally activated diffusion processes.\r
+\r
+In contrast, C$_{\text{i}}$ and V were found to efficiently react with each other exhibiting activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} resulting in C$_{\text{s}}$ configurations.\r
+In addition, a highly attractive interaction exhibiting a large capture radius was observed, effective independent of the orientation and the direction of separation of the defects.\r
+Thus, the formation of C$_{\text{s}}$ is very likely to occur.\r
+Comparatively high energies necessary for the reverse process reveal this configuration to be extremely stable.\r
+\r
+Investigating configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ formation energies higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB were obtained keeping up previously derived assumptions concerning the ground state of C$_{\text{i}}$ in otherwise perfect Si.\r
+However, a small capture radius was identified for the respective interaction that might prevent the recombination of defects exceeding a separation of \unit[0.6]{nm} into the ground state configuration.\r
+In addition, a rather small activation energy of \unit[0.77]{eV} allows for the formation of a C$_{\text{s}}$-Si$_{\text{i}}$ pair originating from the C$_{\text{i}}$ \hkl<1 0 0> DB structure by thermally activated processes.\r
+Thus, elevated temperatures might lead to configurations of C$_{\text{s}}$ and a remaining Si atom in the near interstitial lattice, which is supported by the result of the molecular dynamics run.\r
+\r
+These findings allow to draw conclusions on the mechanisms involved in the process of SiC conversion in Si.\r
+Agglomeration of C$_{\text{i}}$ is energetically favored and enabled by a low activation energy for migration.\r
+Although ion implantation is a process far from thermodynamic equlibrium, which might result in phases not described by the Si/C phase diagram, i.e. a C phase in Si, high activation energies are believed to be responsible for a low probability of the formation of C clusters.\r
+\r
+Unrolling these findings on the initially stated controversy present in the precipitation model, an increased participation of C$_{\text{s}}$ already in the initial stage must be assumed.\r
+Thermally activated C$_{\text{i}}$ might turn into C$_{\text{s}}$.\r
+The associated emission of Si$_{\text{i}}$ serves two needs, as a vehicle for other C$_{\text{s}}$ and as a supply of Si atoms needed elsewhere to form the SiC structure.\r
+As for the vehicle, Si$_{\text{i}}$ is believed to react with C$_{\text{s}}$ turning it into a highly mobile C$_{\text{i}}$ again, allowing for the rearrangement of the C atom.\r
+The rearrangement is crucial to end up in a configuration of C atoms only occupying substitutionally the lattice sites of one of the fcc lattices that build up the diamond lattice as expected in 3C-SiC.\r
+On the other hand the conversion of some region of Si into SiC by substitutional C is accompanied by a reduction of the volume since SiC exhibits a \unit[20]{\%} smaller lattice constant than Si.\r
+The reduction in volume is compensated by excess Si$_{\text{i}}$ serving as building blocks for the surrounding Si host or a further formation of SiC.\r
+\r
+It is, thus, concluded that precipitation occurs by a successive agglomeration of C$_{\text{s}}$.\r
+However, the process is governed by both, C$_{\text{s}}$ accompanied by Si$_{\text{i}}$ as well as C$_{\text{i}}$.\r
+... HIER WEITER ...\r
+By this, explains the alignment of the \hkl(h k l) lattice planes of the precipitate and the substrate.\r
+No contradiction to ... has Si int ... nice to explain cloudy TEM images indicating atoms in interstitial lattice.\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
Especially vacancies.... \r
\r
\r
+C$_{\text{s}}$ must be attributed an important role in SiC formation ...\r
+\r
+Spin polarized ... Si or C-C show qualitatively other defect structure than C-Si , in which the C forms almot colinear bond and Si remains 120 ... COOL!\r
+\r
\section{Summary}\r
In summary, we have shown that ...\r
\r
+Interactions ... improved by migration paths and acivation energies ... probability ...\r
+\r
+\r
% ----------------------------------------------------\r
\section*{Acknowledgment}\r
We gratefully acknowledge financial support by the Bayerische Forschungsstiftung (DPA-61/05) and the Deutsche Forschungsgemeinschaft (DFG SCHM 1361/11).\r
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\end{document}\r
\r
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