+\newpage
+
+\section{Results}
+Figure \ref{c-xtem} shows a comparison of a simulation result and a XTEM bright-field image of silicon implanted at $150 \,^{\circ} \mathrm{C}$ with $180 \, keV$ $C^+$ ions at a dose of $4.3 \times 10^{17} cm^{-2}$. Significant lamellar structure formation is observed in the depth interval between $200$ and $300 \, nm$ (Figure 4b). This is nicely reproduced by the simulation result shown in Figure 4a. Even the average length of the precipitates complies to experimental data. The lamellae are arranged in uniform intervals. Obviously the simulation is able to reproduce lamellar, selforganized structures.
+
+Simulations with different model parameters allow to specify conditions for observing lamellar structures.
+
+First runs with a simplified version of the program have shown that it is essential to assume low amorphization probabilities to avoid to early complete amorphization of the whole cell ensemble. Instead small amorphization parameters $p_b$, $p_c$, $p_s$ and a large number of simulation steps are required to observe lamellar structures. This finding is an agreement to the fact that of the bais of the low nuclear energy deposition of the light carbon ions in silicon, amorphization would not be expected at all at this elevated target temperatures \cite{4} and thus carbon mediated amorphization has to be taken into account to explain the amorphization process.
+
+Figure \ref{zdiff} shows the results of two identical simulation runs with diffusion in $z$-direction switched off and on. The lamellar structures appear only if diffusion in $z$-direction is enabled. Amorphous volumes denude the neighbouring crystalline layers of carbon. In consequence the stability of such cells against recrystallization is enhanced, the probability to amorphizise crystalline cells in the same depth is increased and the amorphization in the carbon denuded cells and their lateral vicinity is decreased. This fortifies the formation of lamellar precipitates. The result hilights the importance of the selforganization process.
+
+In Figure \ref{diffrate} two simulation results with different diffusion rates are compared. Higher diffusion rates cause a larger depth domain of lamellar structure. This can be understood since higher diffusion rates result in amorphous volumes holding more carbon which consequently stabilizes the amorphous state. In case of slower diffusion rates (Figure 6b) the redistribution of carbon is too slow to allow for an effective agglomeration of carbon atoms in amorphous cells to stabilize the amorphous state against recrystallization. This results in a smaller total amount of amorphous material in Figure 6b compared to Figure 6a. The stabilization occurs only at a depth larger than $240 \, nm$ where the total concentration of carbon is high enough. The sufficient stabilization of amorphous volumes in this deeper depth zone enables also the more effective contribution of the stress mediated amorphization.
+
+Figure \ref{compl-str} shows the extension of amorphous lamellae in plain view for two consecutive slices $m$ and $m+1$ of the ensemble. It is obvious that amorphous and crystalline lamellae have a complementary arrangement in neighbouring slices (Figure 7a,b) which again is a result of the carbon accumulation in the amorphous lamellae. This can be clearly seen by comparison of the corresponding carbon maps in Figure 7c,d.
+
+%Finally fourier transformation was applied on experimental XTEM measurements and simulatin results. \ldots
+
+\newpage
+
+\section{Summary and conclusion}
+A simple model explaining the selforganization process of lamellar, amorphous precipitates was introduced. In addition the implementation of that model to reasonable simulation code was discussed. This simulation code is able to reproduce experimental results. Furthermore the formation of these lamellar structures get traceable by the simulation code. Necessary conditions, i.e. diffusion in $z$-direction can be stated. We found the diffusion rate to influence the depth distribution of lamellar precipitates. Not easily measurable information is gained by the simulation like the complementary configuration of amorphous and crystalline arrays in successive layers.
+
+\newpage
+
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