The width of scribe lines may be reduced in semiconductor devices by applying a process technique in which trenches may be formed first from the rear side on the basis of a required width of the corresponding trenches, while subsequently it may be cut into the substrate from the front side on the basis of a reduced thickness of the corresponding saw blades, thereby also enabling a reduction of the scribe line width. Furthermore, contamination of the front side, i.e., of the metallization system, may be reduced, for instance, by performing an optional intermediate cleaning process.