Channel-to-substrate leakage in a FinFET device is prevented by inserting an insulating layer between the semiconducting channel (fin) and the substrate during fabrication of the device. Similarly, source/drain-to-substrate leakage in a FinFET device is prevented by isolating the source/drain regions from the substrate by inserting an insulating layer between the source/drain regions and the substrate. Forming such an insulating layer isolates the conduction path from the substrate both physically and electrically, thus preventing current leakage. In an array of semiconducting fins made up of a multi-layer stack, the bottom material is removed, thus yielding a fin array that is suspended above the silicon surface. A resulting gap underneath the remaining top fin material is then filled with oxide to better support the fins and to isolate the array of fins from the substrate.