+\label{chapter:basics}
+
+In the following the simulation methods used within the scope of this study are introduced.
+Enabling the investigation of the evolution of structure on the atomic scale, molecular dynamics (MD) simulations were chosen in order to model the behavior and precipitation of C introduced into an initially crystalline Si environment.
+To be able to model systems with a large amount of atoms computational efficient classical potentials to describe the interaction of the atoms are most often used in MD studies.
+For reasons of flexibility in executing this non-standard task and in order to be able to use a novel interaction potential \cite{albe_sic_pot} an appropriate MD code called {\textsc posic}\footnote{{\textsc posic} is an abbreviation for {\bf p}recipitation {\bf o}f {\bf SiC}}\footnote{Source code: http://www.physik.uni-augsburg.de/\~{}zirkelfr/posic/posic.tar.bz2} including a library collecting respective MD subroutines was developed from scratch.
+The basic ideas of MD in general and the adopted techniques as implemented in {\em posic} in particular are outlined in section \ref{section:md}, while the functional form and derivative of the employed classical potential is presented in appendix \ref{app:d_tersoff}.
+An overview of the most important tools within the MD package is given in appendix \ref{app:code}.
+Although classical potentials are often most successful and at the same time computationally efficient in calculating some physical properties of a particular system, not all of its properties might be described correctly due to the lack of quantum-mechanical effects.
+Thus, in order to obtain more accurate results quantum-mechanical calculations from first principles based on density functional theory (DFT) were performed.
+The Vienna {\em ab initio} simulation package ({\textsc vasp}) \cite{kresse96} is used for this purpose.
+The relevant basics of DFT are described in section \ref{section:dft} while an overview of utilities mainly used to create input or parse output data of {\textsc vasp} is given in appendix \ref{app:code}.
+The gain in accuracy achieved by this method, however, is accompanied by an increase in computational effort constraining the system to be described to be much smaller in size.
+Thus, investigations based on DFT are restricted to single defects or combinations of two defects in a rather small Si supercell, their structural relaxation as well as some selected diffusion processes.
+Next to the structure, defects can be characterized by the defect formation energy, a scalar indicating the costs necessary for the formation of the defect, which is explained in section \ref{section:basics:defects}.
+The method used to investigate migration pathways to identify the prevalent diffusion mechanism is introduced in section \ref{section:basics:migration} and modifications to the {\textsc vasp} code implementing this method are presented in appendix \ref{app:patch_vasp}.
+
+\section{Molecular dynamics simulations}
+\label{section:md}