The invention relates to a process for producing a semiconductor wafer by double-side grinding of the semiconductor wafer, in which the semiconductor wafer is simultaneously ground on both sides, first by rough-grinding and then by finish-grinding, using a grinding tool. The semiconductor wafer, between the rough-grinding and the finish-grinding, remains positioned in the grinding machine, and the grinding tool continues to apply a substantially constant load during the transition from rough-grinding to finish-grinding. The invention also relates to an apparatus for carrying out the process and to a semiconductor wafer having a local flatness value on a front surface of less than 16 nm in a measurement window of 2 mm×2 mm area and of less than 40 nm in a measurement window of 10 mm×10 mm area.