A method of forming the fin structure that includes forming a replacement gate structure on a channel region of the at least one replacement fin structure; and forming an encapsulating dielectric encapsulating the replacement fin structure leaving a portion of the replacement gate structure exposed. The exposed portion of the replacement gate structure is etched to provide an opening through the encapsulating dielectric to the replacement fin structure. The replacement fin structure is etched selectively to the dielectric to provide a fin opening having a geometry dictated by the encapsulating dielectric. Functional fin structures of a second semiconductor material is epitaxially grown on the growth surface of the substrate substantially filling the fin opening.