-In addition to the classical potential approach ...
-Highly accurate technique DFT, VASP code, VASP mods, tools in appendix ...
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-Determining the formation energies if defects is ...
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-Migration pathways were investigated using the , which is explained in cloder detail in ...
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+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}.