Methods and techniques for fabricating layered structures, such as capacitive micromachined ultrasound transducers, as well as the structures themselves. The layered structure has a membrane that includes a polymer-based layer and a top electrode on the polymer-based layer. The membrane is suspended over a closed cavity and may be actuated by applying a voltage between the top electrode and a bottom electrode that may be positioned along or be a bottom of the closed cavity. The layered structure may be fabricated using a wafer bonding process.