\chapter{Point defects in silicon}
-Given the conversion mechnism of SiC in crystalline silicon introduced in \ref{section:assumed_prec} the understanding of carbon and silicon interstitial point defects in c-Si is of great interest.
+Given the conversion mechnism of SiC in crystalline silicon introduced in section \ref{section:assumed_prec} the understanding of carbon and silicon interstitial point defects in c-Si is of great interest.
Both types of defects are examined in the following both by classical potential as well as density functional theory calculations.
In case of the classical potential calculations a simulation volume of nine silicon lattice constants in each direction is used.
Calculations are performed in an isothermal-isobaric NPT ensemble.
Coupling to the heat bath is achieved by the Berendsen thermostat with a time constant of 100 fs.
The temperature is set to zero Kelvin.
-Pressure is controlled by a Berendsen barostat again using a time constant of 100 fs and a bulk modulus of 100 GPa for silicon.
+Pressure is controlled by a Berendsen barostat \cite{berendsen84} again using a time constant of 100 fs and a bulk modulus of 100 GPa for silicon.
To exclude surface effects periodic boundary conditions are applied.
Due to the restrictions in computer time three silicon lattice constants in each direction are considered sufficiently large enough for DFT calculations.
The ions are relaxed by a conjugate gradient method.
-The cell volume and shape is allowed to change using the pressure control algorithm of Parinello and Rahman \cite{}.
+The cell volume and shape is allowed to change using the pressure control algorithm of Parrinello and Rahman \cite{parrinello81}.
Periodic boundary conditions in each direction are applied.
All point defects are calculated for the neutral charge state.
This is nicely reproduced by the DFT calculations performed in this work.
It has turned out to be very difficult to capture the results of quantum-mechanical calculations in analytical potential models.
-Among the established analytical potentials only the EDIP \cite{} and Stillinger-Weber \cite{} potential reproduce the correct order in energy of the defects.
+Among the established analytical potentials only the EDIP \cite{bazant97,justo98} and Stillinger-Weber \cite{stillinger85} potential reproduce the correct order in energy of the defects.
However, these potenitals show shortcomings concerning the description of other physical properties and are unable to describe the C-C and C-Si interaction.
In fact the Erhard/Albe potential calculations favor the tetrahedral defect configuration.
The hexagonal configuration is not stable opposed to results of the authors of the potential \cite{albe_sic_pot}.
\caption{Kinetic energy plot of the relaxation process of the hexagonal silicon self-interstitial defect simulation using the Erhard/Albe classical potential.}
\label{fig:defects:kin_si_hex}
\end{figure}
-To exclude failures in the implementation of the potential or the MD code itself the hexagonal defect structure was double-checked with the PARCAS MD code \cite{}.
+To exclude failures in the implementation of the potential or the MD code itself the hexagonal defect structure was double-checked with the PARCAS MD code \cite{parcas_md}.
The same type of interstitial arises using random insertions.
In addition, variations exist in which the displacement is only along two \hkl<1 0 0> axes ($E_\text{f}=3.8\text{ eV}$) or along a single \hkl<1 0 0> axes ($E_\text{f}=3.6\text{ eV}$) successively approximating the tetdrahedral configuration and formation energy.
The existence of these local minima located near the tetrahedral configuration seems to be an artifact of the analytical potential without physical authenticity revealing basic problems of analytical potential models for describing defect structures.
A binding energy of -0.50 eV is observed.
{\color{red}Todo: Jahn-Teller distortion (vacancy) $\rightarrow$ actually three possibilities. Due to the initial defect, symmetries are broken. The system should have relaxed into the minumum energy configuration!?}
-{\color{blue}Todo: Si int + vac and C sub ...?
+{\color{blue}Todo: Si int + vac and C sub/int ...?
Investigation of vacancy, Si and C interstitital.
As for the ground state of the single Si self-int, a 110 is also assumed as the lowest possibility in combination with other defects (which is a cruel assumption)!
}
{\color{red}Todo: DB mig along 110 (at the starting of this section)?}
-{\color{red}Todo: Migration of Si int + vac and C sub ...?}
+{\color{red}Todo: Migration of Si int + vac and C sub/int ...?}
{\color{red}Todo: Model of kick-out and kick-in mechnism?}
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