Film growth is characterized by the making and breaking of chemical bonds. Other interactions such as Van der Waals and electrostatic forces are secondary if not negligible. The primary purpose of this thesis is to provide an assessment on how epitaxial growth on an inert substrate, i.e. no dangling bonds, can proceed. This is done by calculating the adsorption energy of carbon (C), silicon (Si), and germanium (Ge) adatoms at different sites on graphene sheet and mapping their potential energy surface. We observe that adsorption energy of carbon on graphene is the strongest, 1.45 eV more than that of silicon and 1.56 eV more than germanium. The second part of this thesis is observing how C, Si and Ge dimers behave on graphene. Carbon dimer still displays the strongest interaction with graphene, yet the binding strength of germanium dimer surpasses that of silicon's in these dimer simulations. All calculations are done by the ab-initio density functional theory.
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