Abstract: Epitaxial growth of gallium arsenide (GaAs) on a semiconductor material (e.g., Si) using quasi-van der Waals Epitaxy (QvdWE). Prior to GaAs growth a buffer layer (e.g., graphene) is deposited which relieves lattice mismatch/thermal expansion. The low energy of the graphene surface and the GaAs/graphene interface is overcome through an optimized growth technique to obtain an atomically smooth low-temperature GaAs nucleation layer. The disclosure can be applied to optimize epitaxial thin film growth of other materials, (e.g., III-V semiconductors, such as InP, GaSb) on Si using van der Waals buffer layers such as graphene.