A method for manufacturing a membrane assembly for EUV lithography, the method including: providing a stack including: at least one membrane layer supported by a planar substrate, wherein the planar substrate has an inner region and a border region around the inner region; and a first sacrificial layer between the planar substrate and the membrane layer; selectively removing the inner region of the planar substrate such that the membrane assembly has: a membrane formed from the at least one membrane layer, and a border holding the membrane, the border having the border region of the planar substrate and the first sacrificial layer situated between the border region and the membrane layer, wherein the selectively removing the inner region of the planar substrate includes using an etchant which has a similar etch rate for the membrane layer and its oxide and a substantially different etch rate for the first sacrificial layer.