-\chapter{Molecular dynamics simulations}
+\chapter{Silicon carbide precipitation simulations}
The molecular dynamics (MD) technique is used to gain insight into the behavior of carbon existing in different concentrations in crystalline silicon on the microscopic level at finite temperatures.
Both, quantum-mechanical and classical potential molecular dynamics simulations are performed.
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.
+Due to promising advantages over the Tersoff potential the bond order potential of Erhart and Albe is used.
A time step of one fs is set.
\subsection{Simulations at temperatures used in ion beam synthesis}
$V_2$ approximately corresponds to the volume of a minimal 3C-SiC precipitate.
$V_3$ is approximately the volume containing the necessary amount of silicon atoms to form such a precipitate, which is slightly smaller than $V_2$ due to the slightly lower silicon density of 3C-SiC compared to c-Si.
The two latter insertion volumes are considered since no diffusion of carbon atoms is expected within the simulated period of time at prevalent temperatures.
-{\color{red}Todo: Refere to diffusion simulations and Mattoni paper.}
+This is due to the overestimated activation energies for carbon diffusion as pointed out in section \ref{subsection:defects:mig_classical}.
For rectangularly shaped precipitates with side length $L$ the amount of carbon atoms in 3C-SiC and silicon atoms in c-Si is given by
\begin{equation}
N_{\text{Carbon}}^{\text{3C-SiC}} =4 \left( \frac{L}{a_{\text{SiC}}}\right)^3
The insertion is realized in a way to keep the system temperature constant.
In each of 600 insertion steps 10 carbon atoms are inserted at random positions within the respective region, which involves an increase in kinetic energy.
Thus, the simulation is continued without adding more carbon atoms until the system temperature is equal to the chosen temperature again, which is realized by the thermostat decoupling excessive energy.
-Every inserted carbon atom must exhibit a distance greater or equal than 1.5 \AA{} to present neighboured atoms to prevent too high temperatures.
+Every inserted carbon atom must exhibit a distance greater or equal than 1.5 \AA{} to present neighboured atoms to prevent too high forces to occur.
Once the total amount of carbon is inserted the simulation is continued for 100 ps followed by a cooling-down process until room temperature, that is $20\, ^{\circ}\mathrm{C}$ is reached.
Figure \ref{fig:md:prec_fc} displays a flow chart of the applied steps involved in the simulation sequence.
\begin{figure}[!ht]
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 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, such conformational chamges are very unlikely to happen.
+Thus, such conformational changes are 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.
+Investigating the corresponding coordinates of the atoms it turns out that concatenated and differently oriented C-Si \hkl<1 0 0> dumbbell interstitials constitute configurations yielding separations of C atoms by this distance.
In 3C-SiC the same distance is also expected for nearest neighbour silicon atoms.
The bottom of figure \ref{fig:md:pc_si-si_c-c} shows the radial distribution of Si-Si bonds together with a reference graph for pure c-Si.
Indeed non-zero $g(r)$ values around 0.31 nm are observed while the amount of Si pairs at regular c-Si distances of 0.24 nm and 0.38 nm decreases.
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}.
\subsection{Limitations of conventional MD and short range potentials}
+\label{subsection:md:limit}
At first the formation of an amorphous SiC-like phase is unexpected since IBS experiments show crystalline 3C-SiC precipitates at prevailing temperatures.
On closer inspection, however, reasons become clear, which are discussed in the following.
In addition to the time scale limitation, problems attributed to the short range potential exist.
The sharp cut-off funtion, which limits the interacting ions to the next neighboured atoms by gradually pushing the interaction force and energy to zero between the first and second next neighbour distance, is responsible for overestimated and unphysical high forces of next neighboured atoms \cite{tang95,mattoni2007}.
+This is supported by the overestimated activation energies necessary for C diffusion as investigated in section \ref{subsection:defects:mig_classical}.
Indeed it is not only the strong C-C bond which is hard to break inhibiting carbon diffusion and further rearrengements.
This is also true for the low concentration simulations dominated by the occurrence of C-Si dumbbells spread over the whole simulation volume.
The bonds of these C-Si pairs are also affected by the cut-off artifact preventing carbon diffusion and agglomeration of the dumbbells.
On the other hand, during implantation, the actual temperature inside the implantation volume is definetly higher than the experimentally determined temperature tapped from the surface of the sample.
\subsection{Increased temperature simulations}
+\label{subsection:md:inct}
Due to the limitations of short range potentials and conventional MD as discussed above elevated temperatures are used in the following.
The simulation sequence and other parameters aside system temperature remain unchanged as in section \ref{subsection:initial_sims}.
However, since the quality value does not account for bond lengthes, bond angles, crystallinity or the stacking sequence high values of $Q$ not necessarily correspond to structures close to 3C-SiC.
Structures that look promising due to high quality values need to be further investigated by other means.
+\subsubsection{Low carbon concetration simulations}
+
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm]{tot_pc_thesis.ps}\\
Similarly the peaks at 0.335 nm and 0.386 nm shrink in contrast to a new peak forming at 0.372 nm as can be seen in the yellow shaded region.
Obviously the structure obtained from the $450\,^{\circ}\mathrm{C}$ simulations, which is dominated by the existence of \hkl<1 0 0> C-Si dumbbells transforms into a different structure with increasing simulation temperature.
Investigations of the atomic data reveal substitutional carbon to be responsible for the new Si-C bonds.
-The peak at 0.197 nm corresponds to the distance of a substitutional carbon to the next neighboured silicon atoms.
-The one at 0.372 is the distance of the substitutional carbon atom to the second next silicon neighbour along the \hkl<1 1 0> direction.
+The peak at 0.197 nm corresponds to the distance of a substitutional carbon atom to the next neighboured silicon atoms.
+The one at 0.372 nm is the distance of a substitutional carbon atom to the second next silicon neighbour along a \hkl<1 1 0> direction.
Comparing the radial distribution for the Si-C bonds at $2050\,^{\circ}\mathrm{C}$ to the resulting Si-C bonds in a configuration of a substitutional carbon atom in crystalline silicon excludes all possibility of doubt.
The resulting bonds perfectly match and, thus, explain the peaks observed for the increased temperature simulations.
To conclude, by increasing the simulation temperature, the \hkl<1 0 0> C-Si dumbbell characterized structure transforms into a structure dominated by substitutional C.
Since the expected distance of these Si pairs in 3C-SiC is 0.308 nm the existing SiC structures embedded in the c-Si host are stretched.
In the upper part of figure \ref{fig:md:tot_c-c_si-si} the C-C radial distribution is shown.
-With increasing temperature a decrease of the amount of next neighboured C pairs can be observed.
+The total amount of C-C bonds with a distance inside the displayed separation range does not change significantly.
+Thus, even for elevated temperatures agglomeration of C atoms neccessary to form a SiC precipitate does not take place within the simulated time scale.
+However, with increasing temperature a decrease of the amount of next neighboured C pairs can be observed.
This is a promising result gained by the high temperature simulations since the breaking of these diomand and graphite like bonds is mandatory for the formation of 3C-SiC.
A slight shift towards higher distances can be observed for the maximum above 0.3 nm.
-Arrows with dashed lines mark C-C distances resulting from \hkl<1 0 0> dumbbell combinations while the arrows with the solid line mark distances arising from combinations of substitutional C.
+Arrows with dashed lines mark C-C distances resulting from \hkl<1 0 0> dumbbell combinations while the arrows with solid lines mark distances arising from combinations of substitutional C.
The continuous dashed line corresponds to the distance of a substitutional C with a next neighboured \hkl<1 0 0> dumbbell.
By comparison with the radial distribution it becomes evident that the shift accompanies the advancing transformation of \hkl<1 0 0> dumbbells into substitutional C.
Next to combinations of two substitutional C atoms and two \hkl<1 0 0> dumbbells respectively also combinations of \hkl<1 0 0> dumbbells with a substitutional C atom arise.
Again, this is a quite promising result, since the C atoms are taking the appropriate coordination as expected in 3C-SiC.
However, this is contrary to the initial precipitation model proposed in section \ref{section:assumed_prec}, which assumes that the transformation into 3C-SiC takes place in a very last step once enough C-Si dumbbells agglomerated.
-{\color{red}Todo: Summarize again! Mention, that the agglomeration necessary in order to form 3C-SiC is missing.}
+To summarize, results of low concentration simulations show a phase transition in conjunction with an increase in temperature.
+The C-Si \hkl<1 0 0> dumbbell dominated struture turns into a structure characterized by the occurence of an increasing amount of substitutional C with respect to temperature.
+Although diamond and graphite like bonds are reduced no agglomeration of C is observed within the simulated time resulting in the formation of isolated structures of stretched SiC, which are adjusted to the c-Si host with respect to the lattice constant and alignement.
+It would be conceivable that by agglomeration of further substitutional C atoms the interfacial energy could be overcome and a transition into an incoherent SiC precipitate could occur.
+
+{\color{red}Todo: Results reinforce the assumption of an alternative precipitation model as already pointed out in the defects chapter.}
+
+\subsubsection{High carbon concetration simulations}
\begin{figure}[!ht]
\begin{center}
Figure \ref{fig:md:12_pc} displays the radial distribution for Si-C and C-C pairs obtained from high C concentration simulations at different elevated temperatures.
Again, in both cases, the cut-off artifact decreases with increasing temperature.
Peaks that already exist for the low temperature simulations get slightly more distinct for elevated temperatures.
-This is also true for peaks located past distances of next neighbours indicating an increase for the long range order.
+This is also true for peaks located past distances of next neighbours indicating an increase in the long range order.
However this change is rather small and no significant structural change is observeable.
-Due to the continuity of high amounts of damage investigations of atomic configurations below remain hard to identify even for the highest temperature.
-Other than in the low concentration simulations analyzed defect structures are no longer necessarily aligned to the primarily existing but succesively disappearing c-Si host matrix inhibiting or at least hampering their identification and classification.
+Due to the continuity of high amounts of damage atomic configurations remain hard to identify even for the highest temperature.
+Other than in the low concentration simulation analyzed defect structures are no longer necessarily aligned to the primarily existing but succesively disappearing c-Si host matrix inhibiting or at least hampering their identification and classification.
As for low temperatures order in the short range exists decreasing with increasing distance.
The increase of the amount of Si-C pairs at 0.186 nm could be positively interpreted since this type of bond also exists in 3C-SiC.
On the other hand the amount of next neighboured C atoms with a distance of approximately 0.15 nm, which is the distance of C in graphite or diamond, is likewise increased.
Thus, higher temperatures seem to additionally enhance a conflictive process, that is the formation of C agglomerates, instead of the desired process of 3C-SiC formation.
This is supported by the C-C peak at 0.252 nm, which corresponds to the second next neighbour distance in the diamond structure of elemental C.
-Investigating the atomic data indeed reveals two C atoms which are bound to and interconnect by a third C atom to be responsible for this distance.
+Investigating the atomic data indeed reveals two C atoms which are bound to and interconnected by a third C atom to be responsible for this distance.
The C-C peak at about 0.31 nm, wich is slightly shifted to higher distances (0.317 nm) with increasing temperature still corresponds quite well to the next neighbour distance of C in 3C-SiC as well as a-SiC and indeed results from C-Si-C bonds.
The Si-C peak at 0.282 nm, which is pronounced with increasing temperature is constructed out of a Si atom and a C atom, which are both bound to another central C atom.
This is similar for the Si-C peak at approximately 0.35 nm.
In this case, the Si and the C atom are bound to a central Si atom.
+To summarize, the amorphous phase remains though sharper peaks in the radial distributions at distances expected for a-SiC are observed indicating a slight acceleration of the dynamics due to elevated temperatures.
-Regarding these findings there is a clear evidence of the formation of an amorphous SiC-like phase for all high concentration simulations performed at various temperatures.
-No significant structural change is observed for elevated temperatures.
-However, with the disappearance of the peaks at the respective cut-off radii one limitation of the short range potential seems to be accomplished.
-In addition, sharper peaks in the radial distributions at distances that are also expected for a-SiC might indicate a slight acceleration of the dynamics carried out at elevated temperatures, that is an expeditious formation of a structure superiorly compareable to a-SiC.
-The increase in temperature leads to the occupation of new defect states, which is particularly evident for low carbon concentrations.
-The question remains whether these states are only occupied due to the additional supply of kinetic energy and, thus, have to be considered unnatural for temperatures applied in IBS or whether the increase in temperature indeed enabled infrequent transitions to occur much faster, thus, leading to the intended acceleration of the dynamics and weakening of the unphysical quirks inherent to the potential.
-{\color{red}Todo: Formation energy of C sub and nearby Si self-int, to see whether this is a preferable state!}
+Regarding the outcome of both, high and low concentration simulations at increased temperatures, encouraging conclusions can be drawn.
+With the disappearance of the peaks at the respective cut-off radii one limitation of the short range potential seems to be accomplished.
+In addition, sharper peaks in the radial distributions lead to the assumption of expeditious structural formation.
+The increase in temperature leads to the occupation of new defect states, which is particularly evident but not limited to the low carbon concentration simulations.
+The question remains whether these states are only occupied due to the additional supply of kinetic energy and, thus, have to be considered unnatural for temperatures applied in IBS or whether the increase in temperature indeed enables infrequent transitions to occur faster, thus, leading to the intended acceleration of the dynamics and weakening of the unphysical quirks inherent to the potential.
In the first case these occupied states would be expected to be higher in energy than the states occupied at low temperatures.
Since substitutional C without the presence of a Si self-interstitial is energetically more favorable than the lowest defect structure obtained without removing a Si atom, that is the \hkl<1 0 0> dumbbell interstitial, and the migration of Si self-interstitials towards the sample surface can be assumed for real life experiments \cite{}, this approach is accepted as an accelerated way of approximatively describing the structural evolution.
-{\color{red}Todo: If C sub and Si self-int is energetically more favorable, the migration towards the surface can be kicked out. Otherwise we should actually care about removal of Si! In any way these findings suggest a different prec model.}
+{\color{red}Todo: C sub and Si self-int is energetically less favorable! Maybe fast migration of Si (mentioned in another Todo)? If true, we have to care about Si removal in simulations? In any way these findings suggest a different prec model.}
+
+\subsection{Valuation of a practicable temperature limit}
+\label{subsection:md:tval}
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm]{fe_and_t.ps}
\end{center}
-\caption{Free energy and temperature plot of plain silicon in the region around the transition temperature.}
+\caption{Free energy and temperature evolution of plain silicon at temperatures in the region around the melting transition.}
\label{fig:md:fe_and_t}
\end{figure}
-The assumed applicability as discussed above and the remaining absence of either agglomeration of substitutional C in low concentration simulations or amorphous to crystalline transition in high concentration simulations suggests to further increase the system temperature.
-So far, the highest temperature applied corresponds to 95 \% of the absolute silicon melting temperature, which is 2450 K and specific to the Erhard/Albe potential.
+The assumed applicability of increased temperature simulations as discussed above and the remaining absence of either agglomeration of substitutional C in low concentration simulations or amorphous to crystalline transition in high concentration simulations suggests to further increase the system temperature.
+So far, the highest temperature applied corresponds to 95 \% of the absolute silicon melting temperature, which is 2450 K and specific to the Erhart/Albe potential.
However, melting is not predicted to occur instantly after exceeding the melting point due to additionally required transition enthalpy and hysteresis behaviour.
To check for the possibly highest temperature at which a transition fails to appear plain silicon is heated up using a heating rate of $1\,^{\circ}\mathrm{C}/\text{ps}$.
Figure \ref{fig:md:fe_and_t} shows the free energy and temperature evolution in the region around the transition temperature.
The difference in free energy is 0.58 eV per atom corresponding to $55.7 \text{ kJ/mole}$, which compares quite well to the silicon enthalpy of melting of $50.2 \text{ kJ/mole}$.
The late transition probably occurs due to the high heating rate and, thus, a large hysteresis behaviour extending the temperature of transition.
To avoid melting transitions in further simulations system temperatures well below the transition point are considered safe.
-Thus, in the following system temperatures of 100 \% and 120 \% of the silicon melting point are used.
-
-\subsection{Constructed 3C-SiC precipitate in crystalline silicon}
-
-{\color{red}Todo: We want to know where we want to go ...}
-
-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]
+According to this study temperatures of 100 \% and 120 \% of the silicon melting point could be used.
+However, defects, which are introduced due to the insertion of C atoms are known to lower the transition point.
+Indeed simulations show melting transitions already at the melting point whenever C is inserted.
+Thus, a system temperature of 95 \% of the silicon melting point is used in the following.
+
+\subsection{Long time scale simulations at maximum temperature}
+
+HERE: Quality evolution showed that without cooling it could have increased ... mention that, while at temperatures already simulated, the time time scale is extended! ...
+
+As discussed in section \ref{subsection:md:limit} and \ref{subsection:md:inct} a further increase of the system temperature might help to overcome limitations of the short range potential and accelerate the dynamics involved in structural evolution.
+A maximum temperature to avoid melting is determined in section \ref{subsection:md:tval} to be 120 \% of the Si melting point but due to defects lowering the transition point a maximum temperature of 95 \% of the Si melting temperature is considered usefull.
+This value is almost equal to the temperature of $2050\,^{\circ}\mathrm{C}$ already used in former simulations.
+Thus, this approach reduces to the application of longer time scales.
+Super!
+
+Next to a longer time scale of simulating at maximum temperature a few more changes are applied.
+In the following simulations the system volume, the amount of C atoms inserted and the shape of the insertion volume are modified from the values used in the first MD simulations.
+To speed up the simulation the initial simulation volume is reduced to 21 Si unit cells in each direction and 5500 inserted C atoms in either the whole volume or in a sphere with a radius of 3 nm corresponding to the size of a precipitate consisting of 5500 C atoms.
+The 100 ps sequence after C insertion intended for structural evolution is exchanged by a 10 ns sequence, which is hoped to result in the occurence of infrequent processes.
+The return to lower temperatures is considered seperately.
+
+\begin{figure}[!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}
+\includegraphics[width=12cm]{fe_100.ps}
+\includegraphics[width=12cm]{q_100.ps}
\end{center}
-\end{table}
+\caption[Evolution of the free energy and quality of a simulation at 100 \% of the Si melting temperature.]{Evolution of the free energy and quality of a simulation at 100 \% of the Si melting temperature. Matt colored parts of the graphs represent the C insertion sequence.}
+\label{fig:md:exceed100}
+\end{figure}
+\begin{figure}[!ht]
+\begin{center}
+\includegraphics[width=12cm]{fe_120.ps}
+\includegraphics[width=12cm]{q_120.ps}
+\end{center}
+\caption[Evolution of the free energy and quality of a simulation at 120 \% of the Si melting temperature.]{Evolution of the free energy and quality of a simulation at 120 \% of the Si melting temperature. Matt colored parts of the graphs represent the C insertion sequence.}
+\label{fig:md:exceed120}
+\end{figure}
+Figure \ref{fig:md:exceed100} and \ref{fig:md:exceed120} show the evolution of the free energy per atom and the quality at 100 \% and 120 \% of the Si melting temperature.
+
+{\color{red}Todo: Melting occurs, show and explain it and that it's due to the defects created.}
+
+{\color{red}Todo: Due to melting, after insertion, simulation is continued NVE, so melting hopefully will not occur, before it will be cooled down later on.}
-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.
+{\color{red}Todo: In additions simulations at 95 \% of the Si melting temperature are started again for longer times.}
-PC and energy of that one.
+\subsection{Further accelerated dynamics approaches}
-Now let's see, whether annealing will lead to some energetically more favorable configurations.
+{\color{red}Todo: self-guided MD!}
-Estimate surface energy ...
+{\color{red}Todo: other approaches?}
-\subsection{Simulations at temperatures exceeding the silicon melting point}
+{\color{red}
+Todo: ART MD?
+Also, how about forcing a migration of a $V_2$ configuration to a constructed prec configuration, detrmine the maximum saddle point and let the simulation run.
+}
-LL Cool J is hot as hell!