From 1c9d7b21ee314037c34aefef556255eedf8eb0a1 Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 1 Jun 2011 11:44:55 +0200 Subject: [PATCH] baecker --- posic/thesis/defects.tex | 36 ++++++------ posic/thesis/md.tex | 95 ++++++++++++-------------------- posic/thesis/summary_outlook.tex | 28 +++++++++- 3 files changed, 81 insertions(+), 78 deletions(-) diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex index b8a58fb..424d798 100644 --- a/posic/thesis/defects.tex +++ b/posic/thesis/defects.tex @@ -105,7 +105,7 @@ In the first two pico seconds, while kinetic energy is decoupled from the system The formation energy of \unit[4.48]{eV} is determined by this low kinetic energy configuration shortly before the relaxation process starts. The \si{} atom then begins to slowly move towards an energetically more favorable position very close to the tetrahedral one but slightly displaced along the three coordinate axes. The formation energy of \unit[3.96]{eV} for this type of interstitial is equal to the result for the hexagonal one in the original work \cite{albe_sic_pot}. -Obviously the authors did not carefully check the relaxed results assuming a hexagonal configuration. +Obviously, the authors did not carefully check the relaxed results assuming a hexagonal configuration. In Fig. \ref{fig:defects:kin_si_hex} the relaxation process is shown on the basis of the kinetic energy plot. \begin{figure}[tp] \begin{center} @@ -1091,9 +1091,9 @@ As a result, C defect agglomeration indeed is expected, but only a low probabili %\end{figure} % Table~\ref{tab:defects:c-s} lists the energetic results of \cs{} combinations with the initial \ci{} \hkl[0 0 -1] DB. -For \cs{} 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 \ci{} \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. +For \cs{} located at position 1 and 3, the configurations $\alpha$ and A correspond to the naive relaxation of the structure by substituting the Si atom by a C atom in the initial \ci{} \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 $\beta$ and B respectively. +Fig.~\ref{fig:093-095} and \ref{fig:026-128} show structures A, B and $\alpha$, $\beta$ together with the barrier of migration for the A to B and $\alpha$ to $\beta$ 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 @@ -1113,7 +1113,7 @@ Present results show a difference in energy of states A and B, which exactly mat % mattoni: A favored by 0.4 eV - NO, it is indeed B (reinforce Song and Capaz)! % % AB transition -The migration barrier ss 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. +The migration barrier is 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! @@ -1121,12 +1121,12 @@ Obviously, either the CRT algorithm fails to seize the actual saddle point struc % a b \begin{figure}[tp] \begin{center} -\includegraphics[width=0.7\textwidth]{026-128.ps} +\includegraphics[width=0.7\textwidth]{comb_mig_026-128_vasp.ps} \end{center} \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. +Configuration $\alpha$ 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. @@ -1136,10 +1136,10 @@ This finding is in good agreement with a combined ab initio and experimental stu % 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}. +Configurations $\alpha$, A and B are not affected by spin polarization and show zero magnetization. +Mattoni et~al.~\cite{mattoni2002}, in contrast, find configuration $\beta$ 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, is obtained with zero magnetization and an increase in configurational energy by \unit[0.2]{eV}. +Indeed, investigating the migration path from configurations $\alpha$ to $\beta$ and, in doing so, reusing the wave functions of the previous migration step the final structure, i.e. configuration $\beta$, is 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. % @@ -1176,18 +1176,18 @@ Fig.~\ref{fig_defects:245csub} lists the remaining configurations and binding en % 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. +The energetically most favorable configuration (configuration $\beta$) 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 respective 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 next most favored configuration, i.e. \cs{} located at position 2, into configuration a and b are investigated, which show activation energies above \unit[2.2]{eV} and \unit[2.5]{eV}. -The respective barriers and structures are shown in Fig.~\ref{fig:051-xxx}. -Again, the non-magnetic configuration is obtained. -If not forced by the CRT algorithm, the structures beyond \perc{50} displacement of the transition into configuration a would likewise settle into configuration b. +Pathways starting from the next most favored configuration, i.e. \cs{} located at position 2, into configuration $\alpha$ and $\beta$ are investigated, which show activation energies above \unit[2.2]{eV} and \unit[2.5]{eV}. +The respective barriers and structures are displayed in Fig.~\ref{fig:051-xxx}. +For the transition into configuration $\beta$, as before, the non-magnetic configuration is obtained. +If not forced by the CRT algorithm, the structures beyond \perc{50} and below \perc{90} displacement of the transition approaching configuration $\alpha$ would settle into configuration $\beta$. \begin{figure}[tp] \begin{center} \includegraphics[width=0.7\textwidth]{comb_mig_051-xxx_conf.ps} \end{center} -\caption{Migration barrier and structures of the transition of a configuration equivalent to the one of the initial \hkl<1 0 0> \ci{} DB with \cs{} located at position 2 into the a and b configurations.} +\caption{Migration barrier and structures of the transition of a configuration equivalent to the one of the initial \hkl<0 0 -1> \ci{} DB with \cs{} located at position 2 into the $\alpha$ and $\beta$ configurations.} \label{fig:051-xxx} \end{figure} Although lower than the barriers for obtaining the ground state of two C$_{\text{i}}$ defects, the activation energies are yet considered too high. @@ -1457,6 +1457,7 @@ These results support the above assumptions of an increased entropic contributio % link to migration of \si{}! The possibility for separated configurations of \cs{} and \si{} becomes even more likely if one of the constituents exhibits a low barrier of migration. In this case, the \si{} is assumed to constitute the mobile defect compared to the stable \cs{} atom. +Thus, migration paths of \si{} are investigated in the following excursus. Acoording to Fig.~\ref{fig:defects:si_mig1}, an activation energy of \unit[0.67]{eV} is necessary for the transition of the \si{} \hkl[0 -1 1] to \hkl[1 1 0] DB located at the neighbored Si lattice site in \hkl[1 1 -1] direction. \begin{figure}[tp] \begin{center} @@ -1468,6 +1469,7 @@ Acoording to Fig.~\ref{fig:defects:si_mig1}, an activation energy of \unit[0.67] \end{figure} The barrier, which is even lower than the one for \ci{}, indeed indicates highly mobile \si. In fact, a similar transition is expected if the \si{} atom, which does not change the lattice site during transition, is located next to a \cs{} atom. +Due to the low barrier the initial separation of the \cs{} and \si{} atom are very likely to occur. Further investigations revealed transition barriers of \unit[0.94]{eV} for the Si$_{\text{i}}$ \hkl[1 1 0] DB to the hexagonal Si$_{\text{i}}$, \unit[0.53]{eV} for the Si$_{\text{i}}$ \hkl[1 1 0] DB to the tetrahedral Si$_{\text{i}}$ and \unit[0.35]{eV} for the hexagonal Si$_{\text{i}}$ to the tetrahedral Si$_{\text{i}}$ configuration. The respective configurational energies are shown in Fig.~\ref{fig:defects:si_mig2}. \begin{figure}[tp] @@ -1479,7 +1481,7 @@ The respective configurational energies are shown in Fig.~\ref{fig:defects:si_mi \label{fig:defects:si_mig2} \end{figure} The obtained activation energies are of the same order of magnitude than values derived from other ab initio studies \cite{bloechl93,sahli05}. -The low barriers indeed enable configurations of separated \cs{} and \si{}. +The low barriers indeed enable configurations of further separated \cs{} and \si{} atoms by the highly mobile \si{} atom departing from the \cs{} defect as observed in the previously discussed MD simulation. % kept for nostalgical reason! diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex index 70aaba1..edd41ec 100644 --- a/posic/thesis/md.tex +++ b/posic/thesis/md.tex @@ -416,67 +416,8 @@ Results gained in this chapter show preferential occupation of Si lattice sites Thus, it is concluded that increased temperatures is not exclusively usefull to accelerate the dynamics approximatively describing the structural evolution. Moreover it can be considered a necessary condition to deviate the system out of equilibrium enabling the formation of 3C-SiC, which is obviously realized by a successive agglomeration of \cs{}. - -\section{Conclusions concerning the SiC conversion mechanism} - -MD simulations at temperatures used in IBS result in structures that are dominated by the C$_{\text{i}}$ \hkl<1 0 0> DB and its combinations if C is inserted into the total volume. -Incorporation into volumes $V_2$ and $V_3$ leads to an amorphous SiC-like structure within the respective volume. -To compensate overestimated diffusion barriers, simulations at accordingly increased temperatures are performed. -No significant change is observed for high C concentrations. -The amorphous phase is maintained. -Due to the incorporation of a huge amount of C into a small volume within a short period of time, damage is produced, which obviously decelerates structural evolution. -For the low C concentrations, time scales are still too low to observe C agglomeration sufficient for SiC precipitation, which is attributed to the slow phase space propagation inherent to MD in general. -However, a phase transition of the C$_{\text{i}}$-dominated into a clearly C$_{\text{s}}$-dominated structure is observed. -The amount of substitutionally occupied C atoms increases with increasing temperature. -Isolated structures of stretched SiC adjusted to the c-Si host with respect to the lattice constant and alignement are formed. -Entropic contributions are assumed to be responsible for these structures at elevated temperatures that deviate from the ground state at 0 K. - -Results of the MD simulations at different temperatures and C concentrations can be correlated to experimental findings. -IBS studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates \cite{kimura82,eichhorn02}. -In particular, the restructuring of strong C-C bonds is affected \cite{deguchi92}. -These bonds preferentially arise if additional kinetic energy provided by an increase of the implantation temperature is missing to accelerate or even enable atomic rearrangements. -This is assumed to be related to the problem of slow structural evolution encountered in the high C concentration simulations. -The insertion of high amounts of C into a small volume within a short period of time resulting in essentially no time for the system to rearrange. -% rt implantation + annealing -Furthermore, C implanted at room temperature was found to be able to migrate towards the surface and form C-rich clusters in contrast to implantations at elevated temperatures, which form stable epitaxially aligned 3C-SiC precipitates \cite{serre95}. -In simulation, low temperatures result in configurations of highly mobile \ci{} \hkl<1 0 0> DBs whereas elevated temperatures show configurations of \cs{}, which constitute an extremely stable configuration that is unlikely to migrate. -Indeed, in the optimized recipe to form 3C-SiC by IBS \cite{lindner99}, elevated temperatures are used to improve the epitaxial orientation together with a low temperature implant to destroy stable SiC nanocrystals at the interface, which are unable to migrate during thermal annealing resulting in a rough surface. -Furtermore, the improvement of the epitaxial orientation of the precipitate with increasing temperature in experiment perfectly conforms to the increasing occurrence of \cs{} in simulation. -At elevated temperatures, implanted C is therefore expected to occupy substitutionally usual Si lattice sites right from the start. - -Thus, elevated temperatures are considered to constitute a necessary condition to deviate the system from equilibrium, as it is the case in IBS. -It is concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.~\cite{nejim95}. -This agrees well with a previous results of the {\em ab initio} study on defects in C implanted Si, which show C$_{\text{s}}$ to occur in all probability. -However, agglomeration and rearrangement is enabled by mobile C$_{\text{i}}$, which has to be present at the same time and is formed by recombination of C$_{\text{s}}$ and Si$_{\text{i}}$. -In contrast to assumptions of an abrupt precipitation of an agglomerate of C$_{\text{i}}$ \cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}, however, structural evolution is believed to occur by a successive occupation of usual Si lattice sites with substitutional C. -This mechanism satisfies the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate, whereas there is no obvious reason for the topotactic orientation of an agglomerate consisting exclusively of C-Si dimers, which would necessarily involve a much more profound change in structure for the transition into SiC. - \ifnum1=0 -\section{Valuation of a practicable temperature limit} -\label{section:md:tval} - -The assumed applicability of increased temperature simulations as discussed above and the remaining absence of either agglomeration of substitutional C in low concentration simulations or amorphous to crystalline transition in high concentration simulations suggests to further increase the system temperature. -So far, the highest temperature applied corresponds to 95 \% of the absolute Si melting temperature, which is 2450 K and specific to the Erhart/Albe potential. -However, melting is not predicted to occur instantly after exceeding the melting point due to additionally required transition enthalpy and hysteresis behaviour. -To check for the possibly highest temperature at which a transition fails to appear plain Si is heated up using a heating rate of $1\,^{\circ}\mathrm{C}/\text{ps}$. -Fig.~\ref{fig:md:fe_and_t} shows the free energy and temperature evolution in the region around the transition temperature. -Indeed a transition and the accompanying critical behaviour of the free energy is first observed at approximately 3125 K, which corresponds to 128 \% of the Si melting temperature. -The difference in free energy is 0.58 eV per atom corresponding to $55.7 \text{ kJ/mole}$, which compares quite well to the Si enthalpy of melting of $50.2 \text{ kJ/mole}$. -The late transition probably occurs due to the high heating rate and, thus, a large hysteresis behaviour extending the temperature of transition. -To avoid melting transitions in further simulations system temperatures well below the transition point are considered safe. -According to this study temperatures of 100 \% and 120 \% of the Si melting point could be used. -However, defects, which are introduced due to the insertion of C atoms are known to lower the transition point. -Indeed simulations show melting transitions already at the melting point whenever C is inserted. -Thus, the system temperature of 95 \% of the Si melting point is considered the maximum limit. -\begin{figure}[tp] -\begin{center} -\includegraphics[width=0.7\textwidth]{fe_and_t.ps} -\end{center} -\caption{Free energy and temperature evolution of plain Si at temperatures in the region around the melting transition.} -\label{fig:md:fe_and_t} -\end{figure} - \section{Long time scale simulations at maximum temperature} As discussed in section~\ref{section:md:limit} and~\ref{section:md:inct} a further increase of the system temperature might help to overcome limitations of the short range potential and accelerate the dynamics involved in structural evolution. @@ -530,3 +471,39 @@ Changes exist ... bridge to results after cooling down to 20 degree C. \fi +\section{Conclusions concerning the SiC conversion mechanism} + +MD simulations at temperatures used in IBS result in structures that are dominated by the C$_{\text{i}}$ \hkl<1 0 0> DB and its combinations if C is inserted into the total volume. +Incorporation into volumes $V_2$ and $V_3$ leads to an amorphous SiC-like structure within the respective volume. +To compensate overestimated diffusion barriers, simulations at accordingly increased temperatures are performed. +No significant change is observed for high C concentrations. +The amorphous phase is maintained. +Due to the incorporation of a huge amount of C into a small volume within a short period of time, damage is produced, which obviously decelerates structural evolution. +For the low C concentrations, time scales are still too low to observe C agglomeration sufficient for SiC precipitation, which is attributed to the slow phase space propagation inherent to MD in general. +However, a phase transition of the C$_{\text{i}}$-dominated into a clearly C$_{\text{s}}$-dominated structure is observed. +The amount of substitutionally occupied C atoms increases with increasing temperature. +Isolated structures of stretched SiC adjusted to the c-Si host with respect to the lattice constant and alignement are formed. +Entropic contributions are assumed to be responsible for these structures at elevated temperatures that deviate from the ground state at 0 K. + +Results of the MD simulations at different temperatures and C concentrations can be correlated to experimental findings. +IBS studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates \cite{kimura82,eichhorn02}. +In particular, the restructuring of strong C-C bonds is affected \cite{deguchi92}. +These bonds preferentially arise if additional kinetic energy provided by an increase of the implantation temperature is missing to accelerate or even enable atomic rearrangements. +This is assumed to be related to the problem of slow structural evolution encountered in the high C concentration simulations. +The insertion of high amounts of C into a small volume within a short period of time resulting in essentially no time for the system to rearrange. +% rt implantation + annealing +Furthermore, C implanted at room temperature was found to be able to migrate towards the surface and form C-rich clusters in contrast to implantations at elevated temperatures, which form stable epitaxially aligned 3C-SiC precipitates \cite{serre95}. +In simulation, low temperatures result in configurations of highly mobile \ci{} \hkl<1 0 0> DBs whereas elevated temperatures show configurations of \cs{}, which constitute an extremely stable configuration that is unlikely to migrate. +Indeed, in the optimized recipe to form 3C-SiC by IBS \cite{lindner99}, elevated temperatures are used to improve the epitaxial orientation together with a low temperature implant to destroy stable SiC nanocrystals at the interface, which are unable to migrate during thermal annealing resulting in a rough surface. +Furtermore, the improvement of the epitaxial orientation of the precipitate with increasing temperature in experiment perfectly conforms to the increasing occurrence of \cs{} in simulation. +At elevated temperatures, implanted C is therefore expected to occupy substitutionally usual Si lattice sites right from the start. + +Thus, elevated temperatures are considered to constitute a necessary condition to deviate the system from equilibrium, as it is the case in IBS. +It is concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.~\cite{nejim95}. +This agrees well with a previous results of the {\em ab initio} study on defects in C implanted Si, which show C$_{\text{s}}$ to occur in all probability. +However, agglomeration and rearrangement is enabled by mobile C$_{\text{i}}$, which has to be present at the same time and is formed by recombination of C$_{\text{s}}$ and Si$_{\text{i}}$. +In contrast to assumptions of an abrupt precipitation of an agglomerate of C$_{\text{i}}$ \cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}, however, structural evolution is believed to occur by a successive occupation of usual Si lattice sites with substitutional C. +This mechanism satisfies the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate, whereas there is no obvious reason for the topotactic orientation of an agglomerate consisting exclusively of C-Si dimers, which would necessarily involve a much more profound change in structure for the transition into SiC. + +{\color{red}Si serves as vehicle, for stress compensation (vorallem stress, evtl auch schon vorher rausarbeiten!) and as Si supply for further SiC.} + diff --git a/posic/thesis/summary_outlook.tex b/posic/thesis/summary_outlook.tex index dd01f14..1725727 100644 --- a/posic/thesis/summary_outlook.tex +++ b/posic/thesis/summary_outlook.tex @@ -10,9 +10,33 @@ The applicability of the utilized bond order potential for subsequent MD simulat Conclusions on the precipitation based on the DFT results are drawn. In the second part, classical potential MD simulations are performed, which try to directly reproduce the precipitation. Next to the shortcomings of the potential, quirks inherent to MD are discussed and a workaround is proposed. -Although direct formation of SiC fails to appear, the results suggest a mechanism of precipitation, which is consistent with previous quantum-mechanical conclusions as well as experimental findings. +Although direct formation of SiC fails to appear, the obtained results indicate a mechanism of precipitation, which is consistent with previous quantum-mechanical conclusions as well as experimental findings. + +Quantum-mechanical results of intrinsic point defects in Si are in good agreement to previous theoretical work on this subject \cite{leung99,al-mushadani03}. +The \si{} \hkl<1 1 0> DB defect is reproduced as the ground-state configuration followed by the hexagonal and tetrahedral defect. +Spin polarized calculations are required for the \si{} \hkl<1 0 0> DB and vacancy whereas no other of the investigated intrinsic defects is affected. +For the \si{} \hkl<1 0 0> DB, the net spin up density is localized in two caps at each of the two DB atoms perpendicularly aligned to the bonds to the other two Si atoms. +For the vacancy, the net spin up electron density is localized in caps at the four surrounding Si atoms directed towards the vacant site. +Results obtained by calculations utilizing the classical EA potential yield formation energies, which are of the same order of magnitude. +However, EA predicts the tetrahedral configuration to be most stable. +The particular problem is due to the cut-off and the fact that the second neighbors are only slightly more distant than the first neighbors within the tetrahedral configuration. +Furthermore, the hexagonal defect structure is not stable opposed to results of the authors of the potential \cite{albe_sic_pot}. +The obtained structure after relaxation, which is similar to the tetrahedral configuration, has a formation energy equal to the one given by the authors for the hexagonal one. +Obviously, the authors did not check the structure after relaxation still assuming a hexagonal configuration. +The actual structure equals the tetrahedral configuration, which is slightly displaced along the three coordinate axes. +Variations exist with displacements along two or a single \hkl<1 0 0> direction indicating a potential artifact. +However, finite temperature simulations are not affected by this artifact due to a low activation energy necessary for a transition into the energetically more favorable tetrahedral configuration. +Next to the known problem of the underestimated formation energy of the tetrahedral configuration \cite{tersoff90}, the energetic sequence of the defect structures is well reproduced by the EA calculations. +Migration barriers of \si{} investigated by quantum-mechanical calculations are found to be of the same order of magnitude than values derived in other ab initio studies \cite{bloechl93,sahli05}. + +HIER WEITER + +Defects of C in c-Si are well described by both methods. + + + + -Obtained results -- 2.20.1