\section{Denstiy functional theory}
\label{section:dft}
+\subsection{Hohenberg-Kohn theorem}
+
\subsection{Born-Oppenheimer (adiabatic) approximation}
-\subsection{Hohenberg-Kohn theorem}
+\subsection{Effective potential}
-\subsection{Exchange correlation}
+\subsection{Kohn-Sham system}
+
+\subsection{Approximations for exchange and correlation}
\subsection{Pseudopotentials}
+\section{Modeling of defects}
+\label{section:basics:defects}
+
+\section{Migration paths and diffusion barriers}
+\label{section:basics:migration}
+
The method without updating the constraints but still applying them to all atoms shows a delayed crossing of the saddle point.
This is understandable since the update results in a more aggressive advance towards the final configuration.
In any case the barrier obtained is slightly higher, which means that it does not constitute an energetically more favorable pathway.
-The method in which the constraints are only applied to the diffusing C atom and two Si atoms, ... {\color{red}in progress} ...
+The method in which the constraints are only applied to the diffusing C atom and two Si atoms, ... {\color{red}Todo: does not work!} ...
\subsection{Migration barriers obtained by classical potential calculations}
\label{subsection:defects:mig_classical}
As expected by the initialization conditions the two carbon atoms form a bond.
This bond has a length of 1.38 \AA{} close to the nex neighbour distance in diamond or graphite, which is approximately 1.54 \AA.
The minimum of binding energy observed for this configuration suggests prefered C clustering as a competing mechnism to the C-Si dumbbell interstitial agglomeration inevitable for the SiC precipitation.
-{\color{red}Todo: Activation energies to obtain separated C confs currently in progress - could be added in the combined defect migration chapter and mentioned here, too!}
+{\color{red}Todo: Activation energies to obtain separated C confs FAILED (again?) - could be added in the combined defect migration chapter and mentioned here, too!}
However, for the second most favorable configuration, presented in figure \ref{fig:defects:comb_db_01} a), the amount of possibilities for this configuration is twice as high.
In this configuration the initial Si (I) and C (I) dumbbell atoms are displaced along \hkl<1 0 0> and \hkl<-1 0 0> in such a way that the Si atom is forming tetrahedral bonds with two silicon and two carbon atoms.
The carbon and silicon atom constituting the second defect are as well displaced in such a way, that the carbon atom forms tetrahedral bonds with four silicon neighbours, a configuration expected in silicon carbide.
{\color{red}Todo: Mig of C-Si DB conf to or from C sub + Si 110 in progress.}
+{\color{red}Todo: Mig of Si DB located next to a C sub (also by MD!).}
+
\section{Migration in systems of combined defects}
As already pointed out in the previous section energetic carbon atoms may kick out silicon atoms from their lattice sites during carbon implantation into crystalline silicon.
\chapter{Review of the silicon carbon compound}
+\label{chapter:sic_rev}
-\section{Properties and applications of silicon carbide}
+\section{Structure, properties and applications of silicon carbide}
-The stoichiometric composition of silicon and carbon termed silicon carbide (SiC) is the only chemical stable compound in the C/Si system \cite{}.
+The phase diagram of the C/Si system is shown in figure~\ref{fig:sic:si-c_phase}.
+The stoichiometric composition of silicon and carbon termed silicon carbide (SiC) is the only chemical stable compound in the C/Si system \cite{scace59}.
+\begin{figure}[ht]
+\begin{center}
+\includegraphics[width=12cm]{si-c_phase.eps}
+\end{center}
+\caption[Phase diagram of the C/Si system.]{Phase diagram of the C/Si system \cite{scace59}.}
+\label{fig:sic:si-c_phase}
+\end{figure}
SiC was first discovered by Henri Moissan in 1893 when he observed brilliant sparkling crystals while examining rock samples from a meteor crater in Arizona.
He mistakenly identified these crystals as diamond.
Although they might have been considered \glqq diamonds from space\grqq{} Moissan identified them as SiC in 1904 \cite{moissan04}.
In mineralogy SiC is still referred to as moissanite in honor of its discoverer.
It is extremely rare and almost impossible to find in nature.
-\subsection{SiC polytypes}
-
Each of the four sp$^3$ hybridized orbitals of the Si atom overlaps with one of the four sp$^3$ hybridized orbitals of the four surrounding C atoms and vice versa.
This results in fourfold coordinated covalent $\sigma$ bonds of equal length and strength for each atom with its neighbours.
-
Although the local order of Si and C next neighbour atoms characterized by the tetrahedral bonding is the same, more than 250 different types of structures called polytypes of SiC exist \cite{fischer90}.
-The polytypes differ in the one-dimensional stacking sequence of identical, closed-packed SiC bilayers.
+The polytypes differ in the one-dimensional stacking sequence of identical, close-packed SiC bilayers.
+\begin{figure}[ht]
+\begin{center}
+\includegraphics[width=12cm]{polytypes.eps}
+\end{center}
+\caption{Stacking sequence of SiC bilayers of the most common polytypes of SiC (from left to right): 3C, 2H, 4H and 6H.}
+\label{fig:sic:polytypes}
+\end{figure}
+Figure~\ref{fig:sic:polytypes} shows the stacking sequence of the most common and technologically most important SiC polytypes, which are the cubic (3C) and hexagonal (2H, 4H and 6H) polytypes.
+
+\begin{table}[ht]
+\begin{center}
+\begin{tabular}{l c c c c c c}
+\hline
+\hline
+ & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
+\hline
+Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
+Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
+Break down field$^{\text{A}}$ [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
+Saturation drift velocity$^{\text{A}}$ [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
+Electron mobility$^{\text{B}}$ [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
+Hole mobility$^{\text{B}}$ [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
+Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption[Properties of SiC polytypes and other semiconductor materials.]{Properties of SiC polytypes and other semiconductor materials. Doping concentrations are $10^{16}\text{ cm}^{-3}$ (A) and $10^{17}\text{ cm}^{-3}$ (B) respectively. References: \cite{wesch96,casady96}. {\color{red}Todo: add more refs + check all values!}}
+\label{table:sic:properties}
+\end{table}
+Different polytypes of SiC exhibit different properties.
+Some of the key properties are listed in table~\ref{table:sic:properties} and compared to other technologically relevant semiconductor materials.
+Despite the low carrier mobilities for low electric fields SiC outperforms Si concerning all other properties.
+The wide band gap ... light emitting diodes ... first blue led ... but GaN direct band gap semiconductor ...
+However ... combine all electr properties ... high-* .. .devices diodes, inverters ...
+break down field and high thermal conductivity ... high-densea and high-power ...
+high saturation drift velocity high-frequency ...
+Mechanical stability almost like diamond ...
+Chemical inert, low neutron capture foobar ... radiation hardness
+
+Since in this work 3C-SiC unit cell ... two fcc lattices ...
+
\section{Fabrication of silicon carbide}
\section{Ion beam synthesis of cubic silicon carbide}
+\section{Substoichiometric concentrations of carbon in crystalline silicon}
+
\section{Assumed precipitation mechanism of cubic silicon carbide in silicon}
\label{section:assumed_prec}
-\section{Substoichiometric concentrations of carbon in crystalline silicon}
-
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