Although the Tersoff potential is one of the most widely used potentials, there are some shortcomings.
Describing the Si-Si interaction Tersoff was unable to find a single parameter set to describe well both, bulk and surface properties.
-Due to this and since the first approach labeled T1~\cite{tersoff_si1} turned out to be unstable~\cite{dodson87}, two further parametrizations exist, T2~\cite{tersoff_si2} and T3~\cite{tersoff_si3}.
+Due to this, and since the first approach labeled T1~\cite{tersoff_si1} turned out to be unstable~\cite{dodson87}, two further parametrizations exist, T2~\cite{tersoff_si2} and T3~\cite{tersoff_si3}.
While T2 describes well surface properties, T3 yields improved elastic constants and should be used for describing bulk properties.
However, T3, which is used in the Si/C potential, suffers from an underestimation of the dimer binding energy.
Similar behavior is found for the C-C interaction.
An activation energy of \unit[2.2]{eV} is necessary to reorientate the \hkl[0 0 -1] into the \hkl[1 1 0] DB configuration, which is \unit[1.3]{eV} higher in energy.
Residing in this state another \unit[0.90]{eV} is enough to make the C atom form a \hkl[0 0 -1] DB configuration with the Si atom of the neighbored lattice site.
In contrast to quantum-mechanical calculations, in which the direct transition is the energetically most favorable transition and the transition composed of the intermediate migration steps is very unlikely to occur, the just presented pathway is much more conceivable in classical potential simulations, since the energetically most favorable transition found so far is likewise composed of two migration steps with activation energies of \unit[2.2]{eV} and \unit[0.5]{eV}, for which the intermediate state is the BC configuration, which is unstable.
-Thus the just proposed migration path, which involves the \hkl[1 1 0] interstitial configuration, becomes even more probable than the initially proposed path, which involves the BC configuration that is, in fact, unstable.
+Thus, the just proposed migration path, which involves the \hkl[1 1 0] interstitial configuration, becomes even more probable than the initially proposed path, which involves the BC configuration that is, in fact, unstable.
Due to these findings, the respective path is proposed to constitute the diffusion-describing path.
The evolution of structure and configurational energy is displayed again in Fig.~\ref{fig:defects:involve110}.
\begin{figure}[tp]
The migration path is best described by the reverse process.
Starting at \unit[100]{\%}, energy is needed to break the bonds of Si atom 1 to its neighbored Si atoms as well as the bond of the C atom to Si atom number 5.
At \unit[50]{\%} displacement, these bonds are broken.
-Due to this and due to the formation of new bonds, e.g. the bond of Si atom number 1 to Si atom number 5, a less steep increase of configurational energy is observed.
+Due to this, and due to the formation of new bonds, e.g. the bond of Si atom number 1 to Si atom number 5, a less steep increase of configurational energy is observed.
In a last step, the just recently formed bond of Si atom number 1 to Si atom number 5 is broken up again as well as the bond of the initial Si DB atom and its Si neighbor in \hkl[-1 -1 -1] direction, which explains the repeated boost in energy.
Finally, the system gains some configurational energy by relaxation into the configuration corresponding to \unit[0]{\%} displacement.
%
Silicon carbide (SiC) has a number of remarkable physical and chemical properties that make it a promising new material in various fields of applications.
The high electron mobility and saturation drift velocity as well as the high band gap and breakdown field in conjunction with its unique thermal stability and conductivity unveil SiC as the ideal candidate for high-power, high-frequency and high-temperature electronic and optoelectronic devices exceeding conventional silicon based solutions~\cite{wesch96,morkoc94,casady96,capano97,pensl93}.
-Due to the large Si--C bonding energy, SiC is a hard and chemical inert material suitable for applications under extreme conditions and capable for microelectromechanical systems, both as structural material and as a coating layer~\cite{sarro00,park98}.
+Due to the large Si-C bonding energy, SiC is a hard and chemical inert material suitable for applications under extreme conditions and capable for microelectromechanical systems, both as structural material and as a coating layer~\cite{sarro00,park98}.
Its radiation hardness allows the operation as a first wall material in nuclear reactors~\cite{giancarli98} and as electronic devices in space~\cite{capano97}.
The realization of silicon carbide based applications demands for reasonable sized wafers of high crystalline quality.
Coherency is lost once the increasing strain energy of the stretched SiC structure surpasses the interfacial energy of the incoherent 3C-SiC precipitate and the Si substrate.
These two different mechanisms of precipitation might be attributed to the respective method of fabrication.
While in CVD and MBE surface effects need to be taken into account, SiC formation during IBS takes place in the bulk of the Si crystal.
-However, in another IBS study~\cite{nejim95} a topotactic transformation is proposed that is likewise based on the formation of substitutional C, which is accompanied by the emission of Si self-interstitial atoms that previously occupied the lattice sites and a compensating reduction of volume due to the lower lattice constant of SiC compared to Si.
+However, in another IBS study~\cite{nejim95}, a topotactic transformation is proposed that is likewise based on the formation of substitutional C, which is accompanied by the emission of Si self-interstitial atoms that previously occupied the lattice sites and a compensating reduction of volume due to the lower lattice constant of SiC compared to Si.
The atomic migration involved in such a transformation is not clear.
For several reasons, solving the controversial view of SiC precipitation in Si is of fundamental interest.
Si self-interstitials (Si$_{\text{i}}$), known as the transport vehicles for dopants~\cite{fahey89,stolk95}, get trapped by reacting with the carbon atoms~\cite{stolk97}.
Furthermore, carbon incorporated in silicon is being used to fabricate strained silicon~\cite{strane94,strane96,osten99} utilized in semiconductor industry for increased charge carrier mobilities in silicon~\cite{chang05,osten97} as well as to adjust its band gap~\cite{soref91,kasper91}.
-Thus the understanding of carbon in silicon either as an isovalent impurity as well as at concentrations exceeding the solid solubility limit up to the stoichiometric ratio to form silicon carbide is of fundamental interest.
+Thus, the understanding of carbon in silicon either as an isovalent impurity as well as at concentrations exceeding the solid solubility limit up to the stoichiometric ratio to form silicon carbide is of fundamental interest.
Due to the impressive growth in computer power on the one hand and outstanding progress in the development of new theoretical concepts, algorithms and computational methods on the other hand, computer simulations enable the modeling of increasingly complex systems.
Atomistic simulations offer a powerful tool to study materials and molecular systems on a microscopic level providing detailed insight not accessible by experiment.
The intention of this work is to contribute to the understanding of C in Si by means of atomistic simulations targeted on the task to elucidate the SiC conversion mechanism in silicon.
The outline of this work is as follows:
-In chapter~\ref{chapter:sic_rev} a review of the Si/C compound is given, including the very central discussion on two controversial precipitation mechanisms present in literature in section~\ref{section:assumed_prec}.
+In chapter~\ref{chapter:sic_rev}, a review of the Si/C compound is given, including the very central discussion on two controversial precipitation mechanisms present in literature in section~\ref{section:assumed_prec}.
Chapter~\ref{chapter:basics} introduces some basics and internals of the utilized atomistic simulations as well as special methods of application.
Details of the simulation and associated test calculations are presented in chapter~\ref{chapter:simulation}.
-In chapter~\ref{chapter:defects} results of investigations of single defect configurations, structures of combinations of two individual defects as well as some selected diffusion pathways in silicon are shown.
+In chapter~\ref{chapter:defects}, results of investigations of single defect configurations, structures of combinations of two individual defects as well as some selected diffusion pathways in silicon are shown.
These allow to draw conclusions with respect to the SiC precipitation mechanism in Si.
More complex systems aiming to model the transformation of C incorporated in bulk Si into a SiC nucleus are examined in chapter~\ref{chapter:md}.
Finally, a summary and concluding remarks are given in chapter~\ref{chapter:summary}.
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