\hline
& T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & BC \\
\hline
-\multicolumn{6}{c}{Present study} \\
+Present study & & & & & & \\
{\textsc posic} & 6.09 & 9.05$^*$ & 3.88 & 5.18 & 0.75 & 5.59$^*$ \\
{\textsc vasp} & Unstable & Unstable & 3.72 & 4.16 & 1.95 & 4.66 \\
-\multicolumn{6}{c}{Other studies} \\
+Other studies & & & & & & \\
Tersoff \cite{tersoff90} & 3.8 & 6.7 & 4.6 & 5.9 & 1.6 & 5.3 \\
{\em Ab initio} \cite{dal_pino93,capaz94} & - & - & x & - & 1.89 & x+2.1 \\
\hline
In addition, the energy level diagram shows a net amount of two spin up electrons.
% todo smaller images, therefore add mo image
-% todo migration of \si{}!
-
\section{Migration of the carbon interstitial}
\label{subsection:100mig}
Si atoms 1 and 2, which form the initial DB, occupy Si lattice sites in the final configuration while Si atom 3 is transferred from a regular lattice site into the interstitial lattice.
These results support the above assumptions of an increased entropic contribution to structural formation involving C$_{\text{s}}$ to a greater extent.
+
+% todo migration of \si{}!
+
+
% kept for nostalgical reason!
%\section{Migration in systems of combined defects}
Below, a spherical 3C-SiC precipitate enclosed in a c-Si surrounding is investigated by means of MD.
On the one hand, these investigations are meant to draw conclusions on the capabilities of the potential for modeling the respective tasks in the C/Si system.
-Since, on the other hand, properties of the 3C-SiC precipitate, the surrounding and the interface can be obtained, the calculations could be considered to constitute a first investigation rather than a test of the capabilities of the potential.
+Since, on the other hand, properties of the 3C-SiC precipitate, its surrounding as well as the interface can be obtained, the calculations could be considered to constitute a first investigation rather than a test of the capabilities of the potential.
+
+\subsubsection{Interfacial energy}
To construct a spherical and topotactically aligned 3C-SiC precipitate in c-Si, the approach illustrated in the following is applied.
A total simulation volume $V$ consisting of 21 unit cells of c-Si in each direction is created.
The amount of C atoms together with the observed lattice constant of the precipitate leads to a precipitate radius of \unit[29.93]{\AA}.
Thus, the interface tension, given by the energy of the interface devided by the surface area of the precipitate is \unit[20.15]{eV/nm$^2$} or \unit[$3.23\times 10^{-4}$]{J/cm$^2$}.
This value perfectly fits within the eperimentally estimated range of \unit[$2-8\times10^{-4}$]{J/cm$^2$} \cite{taylor93}.
-Thus, the EA potential is considered an appropriate choice for the current study properly describing the energetics of interfaces.
+Thus, the EA potential is considered an appropriate choice for the current study concerning the accurate description of the energetics of interfaces.
+Furthermore, since the calculated interfacial energy is located in the lower part of the experimental range, the obtained interface structure might resemble an authentic configuration of an energetically favorable interface structure of a 3C-SiC precipitate in c-Si.
% todo
% nice to reproduce this value!
+\subsubsection{Stability of the precipitate}
+
+To investigate the stability of the precipiate, which is assumed to be stable even at temperatures above the Si melting temperature, the configuration is heated up beyond the critical point, at which the Si melting transition occurs.
+For this, the transition point of c-Si needs to be evaluated first.
+According to the authors of the potential, the Si melting point is \degk{2450}.
+However, melting is not predicted to occur instantly after exceeding the melting point due to the additionally required transition enthalpy and hysteresis behaviour.
+To determine the transition point, c-Si is heated up using a heating rate of \unit[1]{$^{\circ}$C/ps}.
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{fe_and_t.ps}
+\end{center}
+\caption{Total energy and temperature evolution of c-Si at temperatures in the region around the melting transition.}
+\label{fig:simulation:fe_and_t}
+\end{figure}
+Fig.~\ref{fig:simulation:fe_and_t} shows the total energy and temperature evolution in the region around the transition temperature.
+Indeed, a transition and the accompanied critical behaviour of the total energy is first observed at approximately \degk{3125}, which corresponds to \unit[128]{\%} of the Si melting temperature.
+The difference in total energy is \unit[0.58]{eV} per atom corresponding to \unit[55.7]{kJ/mole}, which compares quite well to the Si enthalpy of melting of \unit[50.2]{kJ/mole}.
+
+The precipitate structure is heated up using the same heating rate.
+As can be seen in Fig.~\ref{fig:simulation:sic_melt}, which shows a cross-sectional image of the configuration at different temperatures, the precipitate is stable whereas melting of the surrounding Si host matrix starting at the interface region is observed.
+\begin{figure}[tp]
+\begin{center}
+\subfigure[]{\label{fig:simulation:sic_melt1}\includegraphics[width=7cm]{sic_prec/melt_01.eps}}
+\subfigure[]{\label{fig:simulation:sic_melt2}\includegraphics[width=7cm]{sic_prec/melt_02.eps}}
+\subfigure[]{\label{fig:simulation:sic_melt3}\includegraphics[width=7cm]{sic_prec/melt_03.eps}}
+\end{center}
+\caption{Cross section image of the 3C-SiC precipitate in c-Si at temperatures before (a), at the onset of (b) and after (c) the Si melting transition.}
+\label{fig:simulation:sic_melt}
+\end{figure}
+This is verified by the radial distribution function shown in Fig.~\ref{fig:simulation:pc_500-fin}, which displays configurations before and after the Si transition occurs.
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{pc_500-fin.ps}
+\end{center}
+\caption{Radial distribution of a 3C-SiC precipitate embedded in c-Si at temperatures below and above the Si melting transition point.}
+\label{fig:simulation:pc_500-fin}
+\end{figure}
+The precipitate itself is not involved in the transition, as indicated by the Si-C and C-C distribution, which essentially stays the same.
+It is only the c-Si surrounding undergoing a structural phase transition, which is very well reflected by the difference observed for the respective Si-Si distributions.
+The temperature of transition is determined to be around \degk{2840}.
+This is surprising since the melting transition of c-Si for the same heating conditions is expected at temperatures around \degk{3125} as discussed above.
+Obviously, the precipitate lowers the transition point of the surrounding c-Si matrix.
+This is indeed verified by the cross-sectional images of the configurations shown in Fig.~\ref{fig:simulation:sic_melt}.
+Melting of the Si surrounding in fact starts in the defective interface region of the 3C-SiC precipitate and the c-Si surrounding propagating outwards until the whole Si matrix is affected.
+
+\subsubsection{Concluding remarks}
+
+To conclude, the obtained results, particularly the accurate value of the interface energy, the Si enthalpy of melting as well as the stability of the 3C-SiC structure give quite a good feeling concerning the applicability of the potential.
+
%Since the precipitate configuration is artificially constructed, the resulting interface does not necessarily correspond to the energetically most favorable configuration or to the configuration that is expected for an actually grown precipitate.
%Thus, annealing steps are appended to the gained structure in order to allow for a rearrangement of the atoms of the interface.
%The precipitate structure is rapidly heated up to \unit[2050]{$^{\circ}$C} with a heating rate of approximately \unit[75]{$^{\circ}$C/ps}.
%\includegraphics[width=0.7\textwidth]{pc_500-fin.ps}
%\end{center}
%\caption{Radial distribution of a 3C-SiC precipitate embedded in c-Si at temperatures below and above the Si melting transition point.}
-%%\label{fig:simulation:pc_500-fin}
+%\label{fig:simulation:pc_500-fin}
%\end{figure}
%Investigating the radial distribution function shown in figure \ref{fig:simulation:pc_500-fin}, which shows configurations below and above the temperature of the estimated transition, indeed supports the assumption of melting gained by the total energy plot in Fig. \ref{fig:simulation:fe_and_t_sic}.
%However, the precipitate itself is not involved, as can be seen from the Si-C and C-C distribution, which essentially stays the same for both temperatures.
%Obviously the precipitate lowers the transition point of the surrounding c-Si matrix.
%This is indeed verified by visualizing the atomic data.
%% ./visualize -w 640 -h 480 -d saves/sic_prec_120Tm_cnt1 -nll -11.56 -0.56 -11.56 -fur 11.56 0.56 11.56 -c -0.2 -24.0 0.6 -L 0 0 0.2 -r 0.6 -B 0.1
-%\begin{figure}[t]
-%%\begin{center}
+%\begin{figure}[tp]
+%\begin{center}
%\begin{minipage}{7cm}
%\includegraphics[width=7cm,draft=false]{sic_prec/melt_01.eps}
%\end{minipage}
%\includegraphics[width=7cm,draft=false]{sic_prec/melt_03.eps}
%\end{minipage}
%\end{center}
-%\caption{Cross section image of atomic data gained by annealing simulations of the constructed 3C-SiC precipitate in c-Si at \unit[200]{ps} (top left), \unit[520]{ps} (top right) and \unit[720]{ps} (bottom).}
+%\caption{Cross section image of the precipitate configuration gained by annealing simulations of the constructed 3C-SiC precipitate in c-Si at \unit[200]{ps} (top left), \unit[520]{ps} (top right) and \unit[720]{ps} (bottom).}
%\label{fig:simulation:sic_melt}
%\end{figure}
%Fig. \ref{fig:simulation:sic_melt} shows cross section images of the atomic structures at different times and temperatures.
\chapter{Summary and conclusions}
\label{chapter:summary}
+In a short review of the C/Si compound and the fabrication of the technologically promising semiconductor SiC by IBS, two controversial assumptions of the precipitation mechanism of 3C-SiC in c-Si are elaborated.
+To solve this controversy and contribute to the understanding of SiC precipitation in c-Si, a series of atomistic simulations is carried out.
+In the first part, intrinsic and C related point defects in c-Si as well as some selected diffusion processes of the C defect are investigated by means of first-principles quatum-mechanical calculations based on DFT and classical potential calculations employing a Tersoff-like analytical bond order potential.
+Shortcomings of the computationally efficient though less accurate classical potential approach compared to the quantum-mechanical treatment are revealed.
+The study proceeds investigating combinations of defect structures and related diffusion processes exclusively by the first-principles method.
+The applicability of the utilized bond order potential for subsequent MD simulations is discussed.
+Conclusions on the precipitation based on the DFT results are drawn.
+In the second part, classical potential MD simulations are performed, which try to directly reproduce the precipitation.
+Next to the shortcomings of the potential, quirks inherent to MD are discussed and a workaround is proposed.
+Although direct formation of SiC fails to appear, the results suggest a mechanism of precipitation, which is consistent with previous quantum-mechanical conclusions as well as experimental findings.
+
+Obtained results
+
+
+
Experimental studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates \cite{kimura82,eichhorn02}.
In particular, restructuring of strong C-C bonds is affected \cite{deguchi92}, which preferentially arise if additional kinetic energy provided by an increase of the implantation temperature is missing to accelerate or even enable atomic rearrangements.
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