Processes for forming an actuator having a curved piezoelectric membrane are disclosed. The processes utilize a profile-transferring substrate having a curved surface surrounded by a planar surface to form the curved piezoelectric membrane. The piezoelectric material used for the piezoelectric actuator is deposited on at least the curved surface of the profile-transferring substrate before the profile-transferring substrate is removed from the underside of the curved piezoelectric membrane. The resulting curved piezoelectric membrane includes grain structures that are columnar and aligned, and all or substantially all of the columnar grains are locally perpendicular to the curved surface of the piezoelectric membrane.