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\title{Modelling of a selforganization process leading to periodic arrays of nanometric amorphous precipitates by ion irradiation}

\author{F. Zirkelbach, M. Häberlen, J.K.N. Lindner and B. Stritzkeri}
%\from{Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany}

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\begin{center}
 {\Large\bf
  Modelling of a selforganization process leading to periodic arrays of nanometric amorphous precipitates by ion irradiation
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 }
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\begin{center}
 {\large
  F. Zirkelbach, M. Häberlen, J. K. N. Lindner and B. Stritzker
  \par
 }
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 {\scriptsize
  Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany
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 }
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{\bf
 Abstract
}

We developed a Monte-Carlo-Simulation code based on a simple model that tries to explain the selforganization process leading to periodic arrays of nanometric amorphous precipitates by ion irradiation. In the present work we focus on high-dose carbon implantation into silicon. Due to the compressive stress caused by amorphous $SiC_x$ on the $Si$ host lattice,  which is relaxing in vertical direction as this process occurs near the target surface, preferential amorphization of the stressed regions between amorphous inclusions during continued implantation is taking place. This, together with the diffusion of carbon into the amorphous volumes, to reduce the carbon supersaturation in the crystalline volumes leads to a uniform configuration of amorphous, lamella preciptates with high carbon concentration. The simulation is able to reproduce results gained by cross-sectional TEM meassurements of high-dose carbon implanted silicon. Adjusting the simulation parameters we found a configuration matching the depth distribution and the average length of these amorphous arrays. Furthermore conditions can be specified as a necessity for the selforganization process and information about the configuration in the layers of the target, which is not easily measurable is obtained.

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\section{Introduction}
Formation of nanometric selforganized ordered amorphous lamella precipitates is observed at certain conditions at high-dose implantation of impurity atoms. The present work focuses on high-dose carbon implantation into silicon. Typical doses are $1-10 \times 10^{17} cm^{-2}$ with an ion energy of $180 keV$. Temperatures below $400 \, ^{\circ} \mathrm{C}$ are needed. A model describing the selforganization process will be introduced, followed by a review of the implementation of the simulation code. Results of the Monte-Carlo-Simulation will be compared to cross-sectional TEM measurements. Necessary conditions for observing lamella precipitates are named and some additional, difficult to measure information like the carbon distribution and amorphous/crystalline structure in the layers of the target were obtained.

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\section{Model}
A model describing the formation \ldots %;)

\section{Simulation}

\section{Results}

\section{Conclusion}

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\begin{thebibliography}{20}
 \bibitem{1} J.K.N. Lindner, Appl. Phys. A 77 (2003) 27-38.
 \bibitem{2} M. Häberlen, J.K.N. Lindner, B. Stritzker, Nucl. Instr. and Meth. B 216 (2004) 36-40.
\end{thebibliography}

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