One aspect of the invention relates to a semiconductor component with cavity structure and a method for producing the same. The semiconductor component has an active semiconductor chip with the microelectromechanical structure and a wiring structure on its top side. The microelectromechanical structure is surrounded by walls of at least one cavity. A covering, which covers the cavity, is arranged on the walls. The walls have a photolithographically patterned polymer. The covering has a layer with a polymer of identical type. In one case, the molecular chains of the polymer of the walls are crosslinked with the molecular chains of the polymer layer of the covering layer to form a dimensionally stable cavity housing.