A semiconductor wafer is guided in a cutout in a carrier while a thickness of the semiconductor wafer is reduced to a target thickness by material removal from the front and back surfaces simultaneously. The semiconductor wafer is machined until it is thinner than a carrier body and thicker than an inlay used to line the cutout in the carrier to protect the semiconductor wafer. The carrier is distinguished by the fact that the carrier body and the inlay have different thicknesses throughout the entire duration of the machining of the semiconductor wafer, the carrier body being thicker than the inlay, by from 20 to 70 μm. Themethod provides semiconductor wafers polished on both sides, having a front surface, a back surface and an edge, and a local flatness of the front surface, SFQRmax of less than 50 nm with an edge exclusion of R-2 mm and less than nm with an edge exclusion of R-1 mm, based on a site area of 26 by 8 mm.