Various embodiments of fabricated crystalline-based structures for the electronics, optoelectronics and optics industries are disclosed. Each of these structures is created in part by cleaving a donee layer from a crystalline donor, such as a micaceous/lamellar mass comprising a plurality of lamelliform sheets separable from each other along relatively weak cleavage planes. Once cleaved, one or more of these lamelliform sheets become the donee layer. The donee layer may be used for a variety of purposes, including a crystalline layer for supporting heteroepitaxial growth of one or more semiconductor layers thereon, an insulating layer, a barrier layer, a planarizing layer and a platform for creating useful structures, among others.