It will likewise offer perspectives for processes that rely upon prevention of precipitation events, e.g. the fabrication of strained pseudomorphic Si$_{1-y}$C$_y$ heterostructures\cite{strane96,laveant2002}.
Atomistic simulations offer a powerful tool to study materials on a microscopic level providing detailed insight not accessible by experiment.
-HIER WEITER ...
-Relevant structures consisting of $\approx 10^4$ atoms for the nanocrystal and even more atoms for a reasonably sized Si host matrix are too large to be completely described by high accuracy quantum mechanical methods.
-Directly modelling the dynamics of the processes mentioned above almost inevitably requires the atomic interaction to be described by less accurate though computationally more efficient classical potentials.
+In particular, molecular dynamics (MD) constitutes a suitable technique to investigate the dynamical and structural properties of some material.
+Modelling the processes mentioned above requires the simulation of a large amount of atoms ($\approx 10^5-10^6$), which inevitably dictates the atomic interaction to be described by computationally efficient classical potentials.
+These are, however, less accurate compared to quantum-mechnical methods and theire applicability for the description of the physical problem has to be verified first.
The most common empirical potentials for covalent systems are the Stillinger-Weber\cite{stillinger85} (SW), Brenner\cite{brenner90}, Tersoff\cite{tersoff_si3} and environment-dependent interatomic potential (EDIP)\cite{bazant96,bazant97,justo98}.
-Until recently\cite{lucas10}, a parametrization to describe the C-Si multicomponent system within the mentioned interaction models did only exist for the Tersoff\cite{tersoff_m} and related potentials, e.g. the one by Gao and Weber\cite{gao02}.
-Whether such potentials are appropriate for the description of the physical problem has, however, to be verified first by applying classical and quantum-mechanical methods to relevant processes that can be treated by both methods.
-For instance, a comparison of empirical potential molecular dynamics (MD) and density functional theory (DFT) calculations showed that SW is best suited for simulations of dislocation nucleation processes\cite{godet03} and threshold displacement energy calculations\cite{holmstroem08} in Si important in ion implantation, while the Tersoff potential yielded a qualitative agreement for the interaction of Si self-interstitials with substitutional C\cite{mattoni2002}.
-Antisite pairs and defects in SiC have been investigated, both classically\cite{posselt06,gao04} employing the Gao/Weber potential\cite{gao02} and quantum-mechanically\cite{rauls03a,gao07,gao2001,bockstedte03}, which, both, agree very well with experimental results\cite{gali03,chen98,weber01}.
+Until recently\cite{lucas10}, a parametrization to describe the C-Si multicomponent system within the mentioned interaction models did only exist for the Tersoff\cite{tersoff_m} and related potentials, e.g. the one by Gao and Weber\cite{gao02} as well as the one by Erhart and Albe\cite{albe_sic_pot}.
+All these potentials are short range potentials employing a cut-off function, which drops the atomic interaction to zero inbetween the first and second next neighbor distance.
+In a combined ab initio and empirical potential study it was shown that the Tersoff potential properly describes binding energies of combinations of C defects in Si\cite{mattoni2002}.
+However, investigations of brittleness in covalent materials\cite{mattoni2007} identified the short range character of these potentials to be responsible for overestimated forces necessary to snap the bond of two next neighbored atoms.
+In a previous study\cite{zirkelbach10a} we approved ... influence on migration ... crucial for problem under study.
+However ... considered good, especially non-zero temperatures(?) ...
+
+HIER WEITER ...
+
An extensive comparison\cite{balamane92} concludes that each potential has its strengths and limitations and none of them is clearly superior to others.
Despite their shortcomings these potentials are assumed to be reliable for large-scale simulations\cite{balamane92,huang95,godet03} on specific problems under investigation providing insight into phenomena that are otherwise not accessible by experimental or first principles methods.
Remaining shortcomings have frequently been resolved by modifying the interaction\cite{tang95,gao02a,mattoni2007} or extending it\cite{devanathan98_2} with data gained from ab initio calculations\cite{nordlund97}.
-In this work, the applicability of a Tersoff-like bond order potential\cite{albe_sic_pot} to basic processes involved in the initially mentioned SiC precipitation mechanism has been investigated by comparing results gained by classical and ab initio calculations.
-In the following a comparative investigation of density functional theory studies and classical potential calculations of the structure, energetics and mobility of carbon defects in silicon is presented.
+In this work, a combined ab initio and empirical potential simulation study on the initially mentioned SiC precipitation mechanism has been performed.
+High accurate quantum-mechanical results have been used to identify shortcomings of the classical potentials, which then are taken into account in these type of simulations.
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\section{Methodology}