implanting -> incorporation

[lectures/latex.git] / nlsop / nlsop_emrs_2004.tex

diff --git a/nlsop/nlsop_emrs_2004.tex b/nlsop/nlsop_emrs_2004.tex
index 221b6a8..a9c5d03 100644 (file)
--- a/nlsop/nlsop_emrs_2004.tex
+++ b/nlsop/nlsop_emrs_2004.tex
@@ -82,7 +82,7 @@ Before discussing the implementation some assumptions and approximations have to
 \]
 with $b_{ap}$, $a_{cp}$ and $a_{ap}$ being parameters of the simulation to weight the three different ways of amorphization. The probability of an amorphous volume turning crystalline should behave contrary to $p_{c \rightarrow a}$ and thus is assumed to $p_{a \rightarrow c} = 1 - p_{c \rightarrow a}$.
 
-Figure \ref{3} shows the target devided into $64 \times 64 \times 100$ volumes with a side length of $3 \, nm$. Each of it has a state (crystalline/amorphous) and keeps the local carbon concentration. The simulation algorithm consists of three parts, the amorphization/recrystallization process, the carbon-implanting process and finally the diffusion process.
+Figure \ref{3} shows the target devided into $64 \times 64 \times 100$ volumes with a side length of $3 \, nm$. Each of it has a state (crystalline/amorphous) and keeps the local carbon concentration. The simulation algorithm consists of three parts, the amorphization/recrystallization process, the carbon-incorporation process and finally the diffusion process.
 
 For the amorphization/recrystallization process, random coordinates are computed to specify the volume which is hit by an implanted carbon ion. The two random numbers corresponding to the $x$ and $y$ coordinates are generated with a uniform probability distribution, $p(x)dx=dx \textrm{, } p(y)dy=dy$. The random number corresponding to the $z$ coordinate is distributed according to the linear approximated nuclear stopping power, $p(z)dz=(a_{el} \times z+b_{el})dz$, where $a_{el}$ and $b_{el}$ are simulation parameters describing the nuclear energy loss. After calculating the local probability of amorphization of that volume $p_{c \rightarrow a}$, another random number decides, depending on the current state, whether the volume gets amorphous or recrystallized. This step is looped for the average hit per ion in the simulation window, counted by TRIM collision data.
 
@@ -93,7 +93,17 @@ Finally a standard diffusion algorithm is started, so the supersaturation of car
 \newpage
 
 \section{Results}
+Figure \ref{4} shows a comparison of a simulation result and a cross-sectional TEM snapshot of $180 \, keV$ implanted carbon in silicon at $150 \,^{\circ} \mathrm{C}$ with $4.3 \times 10^{17} cm^{-2}$. The depth the lamella structure is starting in ($300 \, nm$) and also the average length of these precipitates complies to that one of the experimental data. The arrays are ordered in uniform intervals. It can be seen that lamella selforganized structures can be reproduced by the simulation.
 
+Furthermore conditions for observing lamella structures can be specified. Figure \ref{5} shows two identical simulation cycles with diffusion in $z$-direction switched off and on. The lamella structures only appear when diffusion in $z$-direction \ldots
+
+TODO:\\
+- diffusion rate -> depth of lamella structures\\
+- complementary arrays of c/a precipitates for z and z+1\\
+- evt FFT bilder\\
+- summary\\
+
+\newpage
 
 \section{Conclusion}
 
@@ -131,4 +141,18 @@ Finally a standard diffusion algorithm is started, so the supersaturation of car
 \end{center}
 \end{figure}
 
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=15cm]{if_cmp2_e.eps}
+\caption[Comparison of a simulation result and a cross-sectional TEM snapshot of $180 \, keV$ implanted carbon in silicon at $150 \,^{\circ} \mathrm{C}$ with $4.3 \times 10^{17} cm^{-2}$]{} \label{4}
+\end{center}
+\end{figure}
+
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=15cm]{mit_ohne_diff.eps}
+\caption[Identical simulation cycles, with diffusion switched off (left) and on (right)]{} \label{5}
+\end{center}
+\end{figure}
+
 \end{document}