Processes for making a profile-transferring substrate surface and membranes having curved features are disclosed. A profile-transferring substrate surface having a curved feature is created by isotropic plasma etching through a shadow mask. The shadow mask has a through hole which has a lower portion adjacent to the bottom surface of the shadow mask and an upper portion that is above and narrower than the lower portion. The isotropic plasma etching through the shadow mask can create a curved dent in a planar substrate in a central portion of an area enclosed by the bottom opening. After the shadow mask is removed. A uniform layer of material deposited over the exposed surface of the substrate will include a curved feature at the location of the curved dent in the substrate surface.