A dielectric mandrel structure is formed on a single crystalline semiconductor layer. An amorphous semiconductor material layer is deposited on the physically exposed surfaces of the single crystalline semiconductor layer and surfaces of the mandrel structure. Optionally, the amorphous semiconductor material layer can be implanted with at least one different semiconductor material. Solid phase epitaxy is performed on the amorphous semiconductor material layer employing the single crystalline semiconductor layer as a seed layer, thereby forming an epitaxial semiconductor material layer with uniform thickness. Remaining portions of the epitaxial semiconductor material layer are single crystalline semiconductor fins and thickness of these fins are sublithographic. After removal of the dielectric mandrel structure, the single crystalline semiconductor fins can be employed to form a semiconductor device.