A sensor has a foundation wafer having a sensor chamber, at least one silicon-based micromechanical structure integrated with the sensor chamber of the foundation wafer, at least one covering that covers the foundation wafer in a region of the sensor chamber, the covering including a first layer which is a deposition layer and is permeable to an etching medium and reaction products, and a hermetically sealing second layer which is a sealing layer and located above the first layer, the deposition layer which is the first layer being permeable in a region of the sensor chamber to the etching medium and a reaction product, the deposition layer for being permeable having structures selected from the group consisting of etching openings, porous regions, and both.