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.
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.
+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.
{\color{red}Todo: Formation energy of C sub and nearby Si self-int, to see whether this is a preferable state!}
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.}
+\subsection{Valuation of a practicable temperature limit}
+
\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.
+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 Erhard/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 $1\,^{\circ}\mathrm{C}/\text{ps}$.
\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.
+Before proceeding with simulations at temperatrures exceeding the silicon melting point 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 in simulating the precipitation event.
+On the one hand this sheds light on characteristic values like the radial distribution function or the total amount of free energy for such a configuration that is aimed to be reproduced by simulation.
+On the other hand, assuming a correct alignment of the precipitate with the c-Si matrix, properties of such precipitates and the surrounding as well as the interface can be investiagted.
+Furthermore these investigations might establish the prediction of conditions necessary for the simulation of the precipitation process.
-To construct a spherical 3C-SiC precipitate in c-Si, the approach illustrated in the following is applied.
+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 used.
To obtain a minimal and stable precipitate 5500 carbon atoms are considered necessary.
The initial precipitate configuration is constructed in two steps.
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