quality investigations

diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index 4a7524e..648e5aa 100644 (file)
--- 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.
@@ -300,10 +300,22 @@ 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}