On a first semiconductor material substrate, an overlying sacrificial layer formed of a second semiconductor material is deposited. In a first region, a first semiconductor material region is formed over the sacrificial layer. In a second region, a second semiconductor material region is formed over the sacrificial layer. The first semiconductor material region is patterned to define a first FinFET fin. The second semiconductor material region is patterned to define a second FinFET fin. The fins are each covered with a cap and sidewall spacer. The sacrificial layer formed of the second semiconductor material is then selectively removed to form an opening below each of the first and second FinFET fins (with those fins being supported by the sidewall spacers). The openings below each of the fins are then filled with a dielectric material that serves to isolate the semiconductive materials of the fins from the substrate.