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A reflective mask for extreme ultraviolet (EUV) lithography consists of a multilayer-coated substrate called a mask blank, and a patterned absorber layer on top. Local irregularity in the multilayer can disrupt the amplitude and/or phase of the reflected wave, thereby degrading the aerial image. Such defects are the most serious problem in mask fabrication because they are virtually impossible to repair. The multilayer coatings are currently inspected with visible-light scatter tools taking advantage of a high throughput. However, it is still unclear whether all the critical defects can be detected by visible/UV light, though a considerable effort is being put into improving the sensitivity. Another option is inspection using the EUV light. A possible at-wavelength inspection tool based on dark field imaging is schematically shown. In this tool, the scattered light from a defect is focused onto a detector by a magnifying optics, while the specular light is blocked. The sensitivity of the tool is closely related to the intensity of the collectable scattered light. This paper presents simulation of EUV scattering by multilayer defects from a viewpoint of mask blank inspection. We deal with a Gaussian-shaped phase defect in a Mo/Si multilayer. The simulation procedure has two steps. First, the electromagnetic field scattered from the defect is calculated by solving Maxwell's equations with a time-domain finite-element method. A graded-material-properties technique is used to reduce the error associated with finite-element discretization. Then, the resultant near field is extrapolated to the far field using the Kirchhoff diffraction formula. We performed two-dimensional simulations for line defects. The mask blank is illuminated by a TE plane wave with a wavelength of 13.5 nm. We will also discuss the effects of defect height on the scattering.