X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Fthesis%2Fmd.tex;h=c26717895ac52e0bda4a9d8e6cb828866b8a7309;hb=b4d7c0b64e8ccb8cbf8ab1850a1a1bda5c28c560;hp=4a7524ea5c966cc333d049d8028affef695dbcac;hpb=dc8c4ad6e5ce70527a1e97f63e35ed31753fa0b5;p=lectures%2Flatex.git

diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index 4a7524e..c267178 100644
--- a/posic/thesis/md.tex
+++ b/posic/thesis/md.tex
@@ -286,7 +286,7 @@ Structures that look promising due to high quality values need to be further inv
 \includegraphics[width=12cm]{tot_pc_thesis.ps}\\
 \includegraphics[width=12cm]{tot_ba.ps}
 \end{center}
-\caption[Si-C radial distribution and quality evolution for the low concentration simulations at different elevated temperatures.]{Si-C radial distribution and quality evolution for the low concentration simulations at different elevated temperatures. All structures are cooled down to $20\,^{\circ}\mathrm{C}$. The grey line shows resulting Si-C bonds in a configuration if substitutional C in c-Si (C$_\text{sub}$) at zero temperature. Arrows in the quality plot mark the end of carbon insertion and the start of the cooling down step.}
+\caption[Si-C radial distribution and quality evolution for the low concentration simulations at different elevated temperatures.]{Si-C radial distribution and quality evolution for the low concentration simulations at different elevated temperatures. All structures are cooled down to $20\,^{\circ}\mathrm{C}$. The grey line shows resulting Si-C bonds in a configuration of substitutional C in c-Si (C$_\text{sub}$) at zero temperature. Arrows in the quality plot mark the end of carbon insertion and the start of the cooling down step. A fit function according to equation \eqref{eq:md:fit} shows the estimated evolution of quality in the absence of the cooling down sequence.}
 \label{fig:md:tot_si-c_q}
 \end{figure}
 Figure \ref{fig:md:tot_si-c_q} shows the radial distribution of Si-C bonds for different temperatures and the corresponding quality evolution as defined earlier for the low concentration simulaton, that is the $V_1$ simulation.
@@ -300,19 +300,52 @@ Investigations of the atomic data reveal substitutional carbon to be responsible
 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.
 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 observe for the increased temperature simulations.
+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.
 
-This is also reflected in the qualities obtained for different temperatures.
+This is also reflected in the quality values obtained for different temperatures.
+While simulations at $450\,^{\circ}\mathrm{C}$ exhibit 10 \% of fourfold coordinated carbon simulations at $2050\,^{\circ}\mathrm{C}$ exceed the 80 \% range.
+Since substitutional carbon has four next neighboured silicon atoms and is the preferential type of defect in elevated temperature simulations the increase of the quality values become evident.
+The quality values at a fixed temperature increase with simulation time.
+After the end of the insertion sequence marked by the first arrow the quality is increasing and a saturation behaviour, yet before the cooling process starts, can be expected.
+The evolution of the quality value of the simulation at $2050\,^{\circ}\mathrm{C}$ inside the range in which the simulation is continued at constant temperature for 100 fs is well approximated by the simple fit function
+\begin{equation}
+f(t)=a-\frac{b}{t} \text{ ,}
+\label{eq:md:fit}
+\end{equation}
+which results in a saturation value of 93 \%.
+Obviously the decrease in temperature accelerates the saturation and inhibits further formation of substitutional carbon.
+Conclusions drawn from investigations of the quality evolution correlate well with the findings of the radial distribution results.
 
 \begin{figure}[!ht]
 \begin{center}
 \includegraphics[width=12cm]{tot_pc2_thesis.ps}\\
 \includegraphics[width=12cm]{tot_pc3_thesis.ps}
 \end{center}
-\caption[C-C and Si-Si radial distribution for the low concentration simulations at different elevated temperatures.]{C-C and Si-Si radial distribution for the low concentration simulations at different elevated temperatures. All structures are cooled down to $20\,^{\circ}\mathrm{C}$.}
+\caption[C-C and Si-Si radial distribution for the low concentration simulations at different elevated temperatures.]{C-C and Si-Si radial distribution for the low concentration simulations at different elevated temperatures. All structures are cooled down to $20\,^{\circ}\mathrm{C}$. Arrows with dashed lines mark C-C distances of \hkl<1 0 0> dumbbell combinations and those with solid lines mark C-C distances of combinations of substitutional C. The dashed line corresponds to the distance of a substitutional C with a next neighboured \hkl<1 0 0> dumbbell.}
 \label{fig:md:tot_c-c_si-si}
 \end{figure}
+The formation of substitutional carbon also affects the Si-Si radial distribution displayed in the lower part of figure \ref{fig:md:tot_c-c_si-si}.
+Investigating the atomic strcuture indeed shows that the peak arising at 0.325 nm with increasing temperature is due to two Si atoms directly bound to a C substitutional.
+It corresponds to the distance of second next neighboured Si atoms along a \hkl<1 1 0>-equivalent direction with substitutional C inbetween.
+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.
+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.
+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.
+In addition, structures form that result in distances residing inbetween the ones obtained from combinations of mixed defect types and the ones obtained by substitutional C configurations, as can be seen by quite high g(r) values to the right of the continuous dashed line and to the left of the first arrow with a solid line.
+For the most part these structures can be identified as configurations of one substitutional C atom with either another C atom that basically occupies a Si lattice with a Si interstitial residing in the very next surrounding or a C atom that nearly occupies a Si lattice site forming a defect other than the \hkl<1 0 0>-type with the Si atom.
+Again, this is a quite promising result since the ...
+Both cases ...
+Might be due to other defects compensatig strain by pushing them together.
+Actually promising result, since the structure is right and even the lengthes begin to compare.
+Structures with 3 C which are right in place are observable.
+Hmm ... foo.
 
 \subsection{Constructed 3C-SiC precipitate in crystalline silicon}