Substrate with multilayer reflective film, reflective mask blank, reflective mask, and method for manufacturing semiconductor device

The purpose of the present invention is to provide a substrate with a multilayer reflective film, which is used for producing a reflective mask blank and a reflective mask that have a multilayer reflective film that has a high reflectance with respect to exposure light and a low background level during defect inspection. Therefore, the substrate with the multilayer reflective film according to the present invention is provided with a multilayer reflective film for reflecting exposure light, the multilayer reflective film comprising a multilayer film in which low-refractive-index layers and high-refractive-index layers are alternately laminated on the substrate, the multilayer reflective film contains molybdenum (Mo) and at least one additive element selected from the group consisting of nitrogen (N), boron (B), carbon (C), zirconium (Zr), oxygen (O), hydrogen (H), and deuterium (D), and the multilayer reflective film has a crystallite size of 2.5 nm or less as calculated from the diffraction peak of Mo (110)