In this work, a new description of interatomic interactions in the metal-silicon systems is developed. The new interatomic potential is based on a reformulation of the Embedded Atom Method (EAM) potential for metals and the Stillinger -- Weber (SW) potential for silicon in a compatible functional form. The potential incorporates a description of the angular dependence of the interatomic interaction into the framework of the EAM potential and, therefore, is dubbed Angular-dependent EAM (AEAM) potential. The first parameterization of the AEAM potential is carried out for the Si-Ge-Au system. The cross Si-Au and Ge-Au interactions are fitted to reproduce the energies and structural characteristics of several representative bulk structures and small clusters as obtained from density functional theory (DFT) calculations, as well as the enthalpy of mixing of the liquid AuSi alloy at 1500 K.; While the effect of substrate patterning on surface diffusion and induced self assembly of Ge islands during growth is a very complex one at the atomic scale, the fundamental processes responsible for the creation of preferred sites for nucleation of two-dimensional (2D) Ge islands during the initial stages of the deposition can be identified in atomic -- level computer modeling. To mimic FIB irradiation induced patterned surfaces, a set of representative surfaces that incorporate surface strains and chemical modification (intermixed Au and Si) are chosen. The diffusion pathways and activation energy barriers for Ge adatoms on these model surfaces are obtained using molecular dynamics (MD) simulations performed with the new AEAM potential. The diffusion data is used as an input in kinetic Monte Carlo (kMC) simulations to study the effects of chemical and strain-patterning on the initial stages (sub-monolayer) of the nucleation and growth of 2D Ge islands during MBE.; The kMC simulations of growth of Ge on chemically patterned Si(001) suggest that modification in the surface chemistry during patterning can be used to localize the nucleation of 2D Ge islands of during sub-monolayer growth. Modification of surface strains (strain patterning), on the other hand, does not play a decisive role in defining the nucleation density of 2D islands during sub-monolayer deposition of Ge films.
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