Methods of forming structures with electrical isolation. A dielectric layer is formed over a semiconductor substrate, openings are patterned in the dielectric layer that extend to the semiconductor substrate, and a semiconductor material is epitaxially grown from portions of the semiconductor substrate that are respectively exposed inside the openings. The semiconductor material, during growth, defines a semiconductor layer that includes first portions respectively coincident with the openings and second portions that laterally grow from the first portions to merge over a top surface of the dielectric layer. A modified layer containing a trap-rich semiconductor material is formed in the semiconductor substrate.