Membranes for EUV lithography are disclosed. In one arrangement, a membrane has a stack having layers in the following order: a first capping layer including an oxide of a first metal; a base layer including a compound having a second metal and an additional element selected from the group consisting of Si, B, C and N; and a second capping layer including an oxide of a third metal, wherein the first metal is different from the second metal and the third metal is the same as or different from the first metal.