In a process for fabricating a membrane, including, on a substrate, a thin-film multilayer including a film of piezoelectric material placed between a top electrode film and a bottom electrode film and an elastic film supporting said piezoelectric film, the process includes: determining at least one concavity/convexity curvature of said membrane along an axis parallel to the plane of the films so that at least one inflection point is defined, said point allowing a first region and a second region, corresponding to a concave part and a convex part or vice versa, to be isolated; depositing, on the surface of the substrate, a thin-film multilayer including at least one film of piezoelectric material, one bottom electrode film and one top electrode film; and structuring at least one of the electrode films to define at least said first membrane region, in which an electric field perpendicular to the plane of the films may be applied, and at least said second region, in which an electric field parallel to the plane of the films may be applied.