Methods of forming a self-aligned, selective semiconductor on insulator (SOI) structure and a related structure are disclosed. In one embodiment, a method includes providing a substrate; forming a gate structure over a channel within the substrate; recessing a portion of the substrate adjacent the channel; forming an insulating layer on a bottom of the recessed portion; and forming a semiconductor material above the insulating layer. An upper surface of the semiconductor material may be sloped. A MOSFET structure may include a substrate; a channel; a source region and a drain region adjacent the channel; a gate structure above the channel and the substrate; a shallow trench isolation (STI) distal from the gate structure; a selectively laid insulating layer in at least one of the source region and the drain region; and an epitaxially grown semiconductor material above the selectively laid insulating layer.