Processes for making a membrane having a curved feature are disclosed. Recesses each in the shape of a reversed, truncated pyramid are formed in a planar substrate surface by KOH etching through a mask. An oxide layer is formed over the substrate surface. The oxide layer can be stripped leaving rounded corners between different facets of the recesses in the substrate surface, and the substrate surface can be used as a profile-transferring substrate surface for making a membrane having concave curved features. Alternatively, a handle layer is attached to the oxide layer and the substrate is removed until the backside of the oxide layer becomes exposed. The exposed backside of the oxide layer includes curved portions protruding away from the handle layer, and can provide a profile-transferring substrate surface for making a membrane having convex curved features.