\section{Ab initio MD simulations}
+No pressure control, since VASP does not support this feature in MD mode.
+The time step is set to one fs.
+Explain some more parameters that differ from the latter calculations ...
+
Molecular dynamics simulations of a single, two and ten carbon atoms in $3\times 3\times 3$ unit cells of crytsalline silicon are performed.
\section{Classical potential MD simulations}
+In contrast to the quantum-mechanical MD simulations the developed classical potential MD code is able to do constant pressure simulations using the Berendsen barostat.
+The system pressure is set to zero pressure.
+Due to promising advantages over the Tersoff potential the bond order potential of Erhard and Albe is used.
+A time step of one fs is set.
+
\subsection{Initial simulations}
In initial simulations aiming to reproduce a precipitation process simulation volumes of $31\times 31\times 31$ unit cells are utilized.
These carbon atoms are assumed to form strong bonds.
This is supported by figure \ref{fig:md:energy_450} displaying the total energy of all three simulations during the whole simulation sequence.
A huge decrease of the total energy during carbon insertion is observed for the simulations with high carbon concentration in contrast to the $V_1$ simulation, which shows a slight increase.
-The difference in energy $\Delta$ growing within the carbon insertion process persists unchanged until the end of the simulation.
+The difference in energy $\Delta$ growing within the carbon insertion process up to a value of roughly 0.06 eV per atom persists unchanged until the end of the simulation.
Here is the problem.
The excess amount of next neighboured strongly bounded C-C bonds in the high concentration simulations make these configurations energetically more favorable compared to the low concentration configuration.
However, in the same way a lot of energy is needed to break these bonds to get out of the local energy minimum advancing towards the global minimum configuration.
Thus, this transformation is very unlikely to happen.
+This is in accordance with the constant total energy observed in the continuation step of 100 ps inbetween the end of carbon insertion and the cooling process.
+Obviously no energetically favorable relaxation is taking place at a system temperature of $450\,^{\circ}\mathrm{C}$.
The C-C peak at about 0.31 nm perfectly matches the nearest neighbour distance of two carbon atoms in the 3C-SiC lattice.
As can be seen from the inset this peak is also observed for the $V_1$ simulation.
For low concentrations of carbon, that is the $V_1$ simulation and early stages of the $V_2$ and $V_3$ simulations, analyses of configurations in which Si-Si distances around 0.3 nm appear and which are identifiable in regions of high disorder, which especially applies for the high concentration simulations, identify the \hkl<1 0 0> C-Si dumbbell to be responsible for stretching the Si-Si next neighbour distance.
This excellently agrees with the calculated value $r(13)$ in table \ref{tab:defects:100db_cmp} for a resulting Si-Si distance in the \hkl<1 0 0> C-Si dumbbell configuration.
-\subsection{Increased temperature simulations}
+\begin{figure}[!ht]
+\begin{center}
+ \includegraphics[width=12cm]{sic_prec_450_si-c.ps}
+\end{center}
+\caption{Radial distribution function of the Si-C distances for 6000 carbon atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of $450\,^{\circ}\mathrm{C}$ and cooled down to room temperature together with Si-C bonds resulting in a C-Si \hkl<1 0 0> dumbbell configuration.}
+\label{fig:md:pc_si-c}
+\end{figure}
+Figure \ref{fig:md:pc_si-c} displays the Si-C radial distribution function for all three insertion volumes together with the Si-C bonds as observed in a C-Si \hkl<1 0 0> dumbbell configuration.
+The first peak observed for all insertion volumes is at approximately 0.186 nm.
+This corresponds quite well to the expected next neighbour distance of 0.189 nm for Si and C atoms in 3C-SiC.
+By comparing the resulting Si-C bonds of a C-Si \hkl<1 0 0> dumbbell with the C-Si distances of the low concentration simulation it is evident that the resulting structure of the $V_1$ simulation is dominated by this type of defects.
+This is not surpsising, since the \hkl<1 0 0> dumbbell is found to be the ground state defect of a C interstitial in c-Si and for the low concentration simulations a carbon interstitial is expected in every fifth silicon unit cell only, thus, excluding defect superposition phenomena.
+The peak distance at 0.186 nm and the bump at 0.175 nm corresponds to the distance $r(3C)$ and $r(1C)$ as listed in table \ref{tab:defects:100db_cmp} and visualized in figure \ref{fig:defects:100db_cmp}.
+In addition it can be easily identified that the \hkl<1 0 0> dumbbell configuration contributes to the peaks at about 0.335 nm, 0.386 nm, 0.434 nm, 0.469 nm and 0.546 nm observed in the $V_1$ simulation.
+Not only the peak locations but also the peak widths and heights become comprehensible.
+The distinct peak at 0.26 nm, which exactly matches the cut-off radius of the Si-C interaction, is again a potential artifact.
-It is not only the C-C bonds which seem to be unbreakable.
+For high carbon concentrations, that is the $V_2$ and $V_3$ simulation, the defect concentration is likewiese increased and a considerable amount of damage is introduced in the insertion volume.
+The consequential superposition of these defects and the high amounts of damage generate new displacement arrangements for the C-C as well as for the Si-C pair distances, which become hard to categorize and trace and obviously lead to a broader distribution.
+Short range order indeed is observed but only hardly visible is the long range order.
+This indicates the formation of an amorphous SiC-like phase.
+In fact the resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modified Tersoff potential \cite{gao02}.
+
+So why is it amorphous?
+Experiments show crystalline 3C-SiC at the prevailing temperature.
+Short range bond order potentials show overestimated interactions.
+Indeed it is not only the C-C bonds which seem to be unbreakable.
Also the C-Si pairs, as observed in the low concentration simulations, are stuck.
This can be seen from the horizontal progress of the total energy graph in the continue-step.
-Higher time periods or alternatively higher temperatures to spped up the simulation are needed.
+Higher time periods wil not do the trick.
+Alternatively higher temperatures to speed up or actually make possible the precipitation simulation are needed.
+
{\color{red}Todo: Read again about the accelerated dynamics methods and maybe explain a bit more here.}
+Finally explain which methods will be applied in the following.
+
+\subsection{Increased temperature simulations}
+
\subsection{Simulations at temperatures exceeding the silicon melting point}
LL Cool J is hot as hell!
+\subsection{Constructed 3C-SiC precipitate in crystalline silicon}
+
+In the following a spherical 3C-SiC precipitate enclosed in a c-Si surrounding is constructed as it is expected from IBS experiments and from simulations that finally succeed simulating the precipitation event.
+On the one hand this sheds light on characteristic values like the radial distribution function or the total amount of energy for configurations that are aimed to be reproduced by simulation possibly enabling the prediction of conditions necessary for the simulation of the precipitation process.
+On the other hand, assuming a correct alignment of the precipitate with the c-Si matrix, investigations of the behaviour of such precipitates and the surrounding can be made.
+
+To construct a spherical 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 used.
+To obtain a minimal and stable precipitate 5500 carbon atoms are considered necessary.
+The initial precipitate configuration is constructed in two steps.
+In the first step the surrounding silicon matrix is created.
+This is realized by just skipping the generation of silicon atoms inside a sphere of radius $x$, which is the first unknown variable.
+The silicon lattice constant $a_{\text{Si}}$ of the surrounding c-Si matrix is assumed to not alter dramatically and, thus, is used for the initial lattice creation.
+In a second step 3C-SiC is created inside the empty sphere of radius $x$.
+The lattice constant $y$, the second unknown variable, is chosen in such a way, that the necessary amount of carbon is generated.
+This is entirely described by the system of equations \eqref{eq:md:constr_sic_01}
+\begin{equation}
+\frac{8}{a_{\text{Si}}^3}(
+\underbrace{21^3 a_{\text{Si}}^3}_{=V}
+-\frac{4}{3}\pi x^3)+
+\underbrace{\frac{4}{y^3}\frac{4}{3}\pi x^3}_{\stackrel{!}{=}5500}
+=21^3\cdot 8
+\label{eq:md:constr_sic_01}
+\text{ ,}
+\end{equation}
+which can be simplified to read
+\begin{equation}
+\frac{8}{a_{\text{Si}}^3}\frac{4}{3}\pi x^3=5500
+\Rightarrow x = \left(\frac{5500 \cdot 3}{32 \pi} \right)^{1/3}a_{\text{Si}}
+\label{eq:md:constr_sic_02}
+\end{equation}
+and
+\begin{equation}
+%x^3=\frac{16\pi}{5500 \cdot 3}y^3=
+%\frac{16\pi}{5500 \cdot 3}\frac{5500 \cdot 3}{32 \pi}a_{\text{Si}}^3
+%\Rightarrow
+y=\left(\frac{1}{2} \right)^{1/3}a_{\text{Si}}
+\text{ .}
+\label{eq:md:constr_sic_03}
+\end{equation}
+By this means values of 2.973 nm and 4.309 \AA{} are obtained for the initial precipitate radius and lattice constant of 3C-SiC.
+Since the generation of atoms is a discrete process with regard to the size of the volume the expected amounts of atoms are not obtained.
+However, by applying these values the final configuration varies only slightly from the expected one by five carbon and eleven silicon atoms, as can be seen in table \ref{table:md:sic_prec}.
+\begin{table}[!ht]
+\begin{center}
+\begin{tabular}{l c c c c}
+\hline
+\hline
+ & C in 3C-SiC & Si in 3C-SiC & Si in c-Si surrounding & total amount of Si\\
+\hline
+Expected & 5500 & 5500 & 68588 & 74088\\
+Obtained & 5495 & 5486 & 68591 & 74077\\
+Difference & 5 & 14 & -3 & 11\\
+\hline
+\hline
+\end{tabular}
+\caption{Comparison of the expected and obtained amounts of Si and C atoms by applying the values from equations \eqref{eq:md:constr_sic_02} and \eqref{eq:md:constr_sic_03} in the 3C-SiC precipitate construction approach.}
+\label{table:md:sic_prec}
+\end{center}
+\end{table}
+
+After the initial configuration is constructed some of the atoms located at the 3C-SiC/c-Si interface show small distances, which results in high repulsive forces acting on the atoms.
+Thus, the system is equilibrated using strong coupling to the heat bath, which is set to be $20\,^{\circ}\mathrm{C}$.
+Once the main part of th excess energy is carried out previous settings for the Berendsen thermostat are restored and the system is relaxed for another 10 ps.
+
+PC and energy of that one.
+
+Now let's see, whether annealing will lead to some energetically more favorable configurations.
+
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