A lithography mask structure is provided, including: a substrate; at least one reflective layer over the substrate; and an absorber film stack over the at least one reflective layer, the absorber film stack including a plurality of first film layers of a first material and at least one second film layer of a second material. The second material is different from the first material, and the second film layer(s) is interleaved with the plurality of first film layers. In one embodiment, the total thickness of the absorber film stack is less than 50 nm. In another embodiment, the reflectivity of the absorber film stack is less than 2% for a pre-defined wavelength of EUV light. In a further embodiment, the second film layer(s) prevents the average crystallite size of the first film layers from exceeding the thickness of the first film layers.