Abstract: A composite structure comprises a receiver substrate having at least one cavity defined in the substrate and devoid of solid material or filled with a sacrificial solid material, a single-crystal semiconductor layer disposed on the receiver substrate, the layer having a free surface over the entire extent of the structure and a thickness between 0.1 micron and 100 microns, and a piezoelectric layer secured to the single-crystal semiconductor layer and located between the single-crystal semiconductor layer and the receiver substrate. A device is based on a movable membrane above a cavity, and is formed from the composite structure. A method is used to fabricate the composite structure.