A method for manufacturing a membrane assembly for EUV lithography, the method including: providing a stack including a membrane layer between a supporting substrate and an attachment substrate, wherein the supporting substrate includes an inner region and a border region; processing the stack, including selectively removing the inner region of the supporting substrate, to form a membrane assembly comprising: a membrane formed from at least the membrane layer; and a support holding the membrane, the support formed at least partially from the border region of the supporting substrate. The attachment substrate can be bonded to the rest of the stack.