Disclosed are embodiments of a semiconductor structure, a design structure for the semiconductor structure and a method of forming the semiconductor structure. The embodiments reduce harmonics and improve isolation between the active semiconductor layer and the substrate of a semiconductor-on-insulator (SOI) wafer. Specifically, the embodiments incorporate a trench isolation region extending to a fully or partially amorphized region of the wafer substrate. The trench isolation region is positioned outside lateral boundaries of at least one integrated circuit device located at or above the active semiconductor layer of the SOI wafer and, thereby improves isolation. The fully or partially amorphized region of the substrate reduces substrate mobility, which reduces the charge layer at the substrate/BOX interface and, thereby reduces harmonics. Optionally, the embodiments can incorporate an air gap between the wafer substrate and integrated circuit device(s) in order to further improve isolation.