An efficient method of fabricating a high-quality heteroepitaxial microstructure having a smooth surface. The method includes detaching a layer from a base structure to provide a carrier substrate having a detached surface, and then forming a heteroepitaxial microstructure on the detached surface of the carrier substrate by depositing an epitaxial layer on the detached surface of a carrier substrate. Also included is a heteroepitaxial microstructure fabricated from such method.