Etching openings are provided in a membrane above an etched-out cavity, only at a distance of at most one tenth of the diameter of the member away from the edge of the cavity. For production, a poly layer is applied to a sacrificial layer composed of SiO2 and is provided with rows of etching holes, through which channels are etched out in the sacrificial layer. The poly layer is oxidized and is made smooth by means of a planarization layer. Etching holes are produced in the edge region of the membrane layer. The sacrificial layer is removed over the entire area of the cavity which is to be produced, with the etching medium propagating sufficiently quickly through the channels.