\chapter{Introduction}

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}.
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.
Despite the tremendous progress achieved in the fabrication of high purity SiC employing techniques like the modified Lely process for bulk crystal growth~\cite{tairov78,tsvetkov98} or chemical vapor deposition (CVD) and molecular beam epitaxy (MBE) for homo- and heteroepitaxial growth~\cite{kimoto93,powell90,fissel95}, available wafer dimensions and crystal qualities are not yet sufficient.

Another promising alternative to fabricate SiC is ion beam synthesis (IBS).
High-dose carbon implantation at elevated temperatures into silicon with subsequent annealing results in the formation of buried SiC layers~\cite{borders71,reeson87}.
A two-temperature implantation technique was proposed to achieve single crystalline, epitaxial SiC layers and a sharp SiC/Si interface~\cite{lindner99,lindner99_2,lindner01,lindner02}.

Although high-quality SiC can be achieved by means of IBS, the precipitation mechanism is not yet fully understood.
High resolution transmission electron microscopy studies indicate the formation of C-Si interstitial complexes sharing conventional silicon lattice sites (C-Si dumbbells) during the implantation of carbon in silicon.
These C-Si dumbbells agglomerate and once a critical radius is reached, the topotactic transformation into a SiC precipitate occurs~\cite{werner97,lindner01}.
In contrast, investigations of strained Si$_{1-y}$C$_y$/Si heterostructures formed by MBE~\cite{strane94,guedj98}, which incidentally involve the formation of SiC nanocrystallites, suggest an initial coherent precipitation by agglomeration of substitutional instead of interstitial C.
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.
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.
A better understanding of the supposed SiC conversion mechanism and related carbon-mediated effects in silicon will enable significant technological progress in SiC thin film formation on the one hand and likewise offer perspectives for processes which rely upon prevention of precipitation events for improved silicon based devices on the other hand.
Implanted carbon is known to suppress transient enhanced diffusion of dopant species like boron or phosphorus in the annealing step~\cite{cowern96}, which can be exploited to create shallow p-n junctions in submicron technologies.
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.
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}.
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.
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}.

