Tersoff indeed predicts a metastable BC configuration.
However, it is not in the correct order and lower in energy than the \ci{} \hkl<1 1 0> DB.
Quantum-mechanical results of this configuration are discussed in more detail in section \ref{subsection:bc}.
-In another {\em ab inito} study, Capaz~et~al. \cite{capaz94} in turn found BC configuration to be an intermediate saddle point structure of a possible migration path, which is \unit[2.1]{eV} higher than the \ci{} \hkl<1 0 0> DB structure.
+In another {\em ab inito} study, Capaz~et~al.~\cite{capaz94} in turn found the BC configuration to be an intermediate saddle point structure of a possible migration path, which is \unit[2.1]{eV} higher than the \ci{} \hkl<1 0 0> DB structure.
This is assumed to be due to the neglection of the electron spin in these calculations.
Another {\textsc vasp} calculation without fully accounting for the electron spin results in the smearing of a single electron over two non-degenerate states for the BC configuration.
This problem is resolved by spin polarized calculations resulting in a net spin of one accompanied by a reduction of the total energy by \unit[0.3]{eV} and the transformation into a metastable local minimum configuration.
\caption[Structure, charge density isosurface and Kohn-Sham level diagram of the bond-centered interstitial configuration.]{Structure, charge density isosurface and Kohn-Sham level diagram of the bond-centered interstitial configuration. Gray, green and blue surfaces mark the charge density of spin up, spin down and the resulting spin up electrons in the charge density isosurface, in which the carbon atom is represented by a red sphere. In the energy level diagram red and green lines mark occupied and unoccupied states.}
\label{img:defects:bc_conf}
\end{figure}
-In the BC insterstitial configuration the interstitial atom is located inbetween two next neighbored Si atoms forming linear bonds.
+In the BC insterstitial configuration the interstitial atom is located in between two next neighbored Si atoms forming linear bonds.
In a previous study this configuration was found to constitute an intermediate saddle point configuration determining the migration barrier of one possibe migration path of a \ci{} \hkl<1 0 0> DB configuration into an equivalent one \cite{capaz94}.
This is in agreement with results of the EA potential simulations, which reveal this configuration to be unstable relaxing into the \ci{} \hkl<1 1 0> configuration.
However, this fact could not be reproduced by spin polarized {\textsc vasp} calculations performed in this work.
As will be shown in subsequent migration simulations the same would happen to structures where the C atom is displaced along the migration direction, which approximately is the \hkl[1 1 0] direction.
These relaxations indicate that the BC configuration is a real local minimum instead of an assumed saddle point configuration.
Fig. \ref{img:defects:bc_conf} shows the structure, charge density isosurface and Kohn-Sham levels of the BC configuration.
+In fact, the net magnetization of two electrons is already suggested by simple molecular orbital theory considerations with respect to the bonding of the C atom.
The linear bonds of the C atom to the two Si atoms indicate the $sp$ hybridization of the C atom.
Two electrons participate to the linear $\sigma$ bonds with the Si neighbors.
The other two electrons constitute the $2p^2$ orbitals resulting in a net magnetization.
Figures \ref{fig:defects:cp_00-1_0-10_mig} and \ref{fig:defects:cp_00-1_ip0-10_mig} show the migration barriers of the \ci{} \hkl<0 0 -1> to \hkl<0 -1 0> DB transition.
In the first case, the transition involves a change in the lattice site of the C atom whereas in the second case, a reorientation at the same lattice site takes place.
In the first case, the pathways for the two different time cosntants look similar.
-A local minimum exists inbetween two peaks of the graph.
+A local minimum exists in between two peaks of the graph.
The corresponding configuration, which is illustrated for the results obtained for a time constant of \unit[1]{fs}, looks similar to the \ci{} \hkl<1 1 0> configuration.
Indeed, this configuration is obtained by relaxation simulations without constraints of configurations near the minimum.
Activation energies of roughly \unit[2.8]{eV} and \unit[2.7]{eV} are needed for migration.
Although classical potential simulations reproduce the same order in energy of the \ci{} \hkl<1 0 0> and \hkl<1 1 0> DB interstitial configurations as obtained by more accurate quantum-mechanical calculations, the obtained migration pathways and resulting activation energies differ to a great extent.
On the one hand, the most favorable pathways differ.
-On the other hand, the activation energies obtained by classical potential simulations are tremendously overestimated by a factor of 2.4 to 3.5.
+However, the pathway, which is considered most probable in the classical potential treatment, exhibits the same starting and final configuration of the DB structure as well as the change in orientation during migration as obtained by quantum-mechanical calculations.
+On the other hand, the activation energy obtained by classical potential simulations is tremendously overestimated by a factor of 2.4 to 3.5.
+The overestimated barrier is due to the short range character of the potential, which drops the interaction to zero within the first and next neighbor distance.
+Since the total binding energy is accommodated within a short distance, which according to the universal energy relation would usually correspond to a much larger distance, unphysical high forces between two neighbored atoms arise.
+This is explained in more detail in a previous study \cite{mattoni2007}.
Thus, atomic diffusion is wrongly described in the classical potential approach.
The probability of already rare diffusion events is further decreased for this reason.
However, agglomeration of C and diffusion of Si self-interstitials are an important part of the proposed SiC precipitation mechanism.
Thus, a serious limitation that has to be taken into account for appropriately modeling the C/Si system using the otherwise quite promising EA potential is revealed.
Possible workarounds are discussed in more detail in section \ref{section:md:limit}.
-\section{Combination of point defects}
+\section{Combination of point defects and related diffusion processes}
The study proceeds with a structural and energetic investigation of pairs of the ground-state and, thus, most probable defect configurations that are believed to be fundamental in the Si to SiC conversion.
Investigations are restricted to quantum-mechanical calculations.
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.
-\subsection{Diffusion processes among configurations of \ci{} pairs}
+%\subsection{Diffusion processes among configurations of \ci{} pairs}
+To draw further conclusions on the probability of C clustering, transitions into the ground-state configuration are investigated.
Based on the lowest energy migration path of a single \ci{} \hkl<1 0 0> DB, the configuration, in which the second \ci{} 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 smooth transition path is not found.
Fig.~\ref{fig:defects:050} shows the relaxed structure of a vacancy created at position 5.
The Si DB atom is largely displaced along \hkl[1 1 0] and somewhat less along \hkl[0 0 -1], which corresponds to the direction towards the vacancy.
The \si DB atom approaches Si atom number 1.
-Indeed, a non-zero charge density is observed inbetween these two atoms exhibiting a cylinder-like shape superposed with the charge density known from the DB itself.
+Indeed, a non-zero charge density is observed in between these two atoms exhibiting a cylinder-like shape superposed with the charge density known from the DB itself.
Strain reduced by this huge displacement is partially absorbed by tensile strain on Si atom number 1 originating from attractive forces of the C atom and the vacancy.
A binding energy of \unit[-0.50]{eV} is observed.
\section{Conclusions concerning the SiC conversion mechanism}
+\ifnum1=0
+
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, are 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$_{\text{i}}$.
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
Thus, elevated temperatures might lead to thermodynamically unstable configurations of C$_{\text{s}}$ and a remaining Si atom in the near interstitial lattice, which is supported by the result of an {\em ab initio} molecular dynamics run.
%Thus, due to missing attractive interaction forces driving the system to form C-Si \hkl<1 0 0> dumbbell interstitial complexes substitutional C, while thermodynamically not stable, constitutes a most likely configuration occuring in IBS, a process far from equlibrium.
+\fi
+
% todo
% maybe move above stuff to conclusion chapter, at least shorten!
% see remember in sic chapter
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