Disposable gate structures and a planarization dielectric layer are formed over doped semiconductor material portions on a crystalline insulator layer. Gate cavities are formed by removing the disposable gate structures selective to the planarization dielectric layer. Doped semiconductor material portions are removed from underneath the gate cavities to provide pairs of source and drain regions separated by a gate cavity. Within a first gate cavity, a faceted crystalline dielectric material portion is grown from a physically exposed surface of the crystalline insulator layer, while a second gate is temporarily coated with an amorphous material layer. A contoured semiconductor region is epitaxially grown on the faceted crystalline dielectric material portion in the first gate cavity, while a planar semiconductor region is epitaxially grown in the second gate cavity. The semiconductor regions can provide at least one contoured channel region and at least one planar channel region.