Semiconductor wafers are cut from a crystal and subjected to a series of processing steps in which material is removed from a front side and a rear side of the semiconductor wafers, comprising the following processing steps: a mechanical processing step, an etching step in which the semiconductor wafers are oxidized and material is removed from the front side of the wafers with the aid of a gaseous etchant containing hydrofluoric acid at a temperature of 20 to 70° C., and a polishing step in which the front side of the semiconductor wafer is polished, the processing steps in which the front side of the semiconductor wafer is polished causing material removal which does not amount to more than 5 μm in total.