Semiconductor wafers are leveled by position-dependent measurement of a wafer-characterizing parameter to determine the position-dependent value of this parameter over an entire surface of the semiconductor wafer, etching the entire surface of the semiconductor wafer simultaneously under the action of an etching medium with simultaneous illumination of the entire surface, the material-removal etching rate dependent on the light intensity at the surface of the semiconductor wafer, the light intensity being established in a position-dependent manner such that the differences in the position-dependent values of the parameter measured in step a) are reduced by the position-dependent material-removal rate. Semiconductor wafers with improved flatness and nanotopography, and SOI wafers with improved layer thickness homogeneity are produced by this process.