Disclosed are a repairable photomask structure and extreme ultraviolet (EUV) photolithography methods. The structure includes a multilayer stack, a protective layer above the stack and a light absorber layer above the protective layer. The stack includes alternating layers of high and low atomic number materials and a selected one of the high atomic number material layers is different from the others such that it functions as an etch stop layer. This configuration allows the photomask structure to be repaired if/when defects are detected near exposed surfaces of the multilayer stack following light absorber layer patterning. For example, when a defect is detected near an exposed surface of the stack in a specific opening in the light absorber layer, the opening can be selectively extended down to the etch stop layer or all the openings can be extended down to the etch stop layer in order to remove that defect.