Example embodiments relate to masks for extreme-ultraviolet (extreme-UV) lithography and methods for manufacturing the same. An example embodiment includes a mask for extreme-UV lithography. The mask includes a substrate. The mask also includes a reflecting structure that is supported by the substrate in a use face and is reflection-effective for extreme-UV radiation impinging onto the reflecting structure from a side opposite the substrate. Further, the mask includes attenuating and phase-shifting portions that are distributed within the use face that are suitable for attenuating and phase-shifting extreme-UV radiation parts reflected by the mask through the portions such that an upper surface of the mask in the use face, formed partly by the portions on the side opposite the substrate, exhibits height variations at sidewalls of the portions that extend perpendicular to the use face. In addition, the mask includes a capping layer that covers at least the sidewalls of the portions.
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