Monocrystalline semiconductor wafers have defect-reduced regions, the defect-reduced regions having a density of GOI-relevant defects within the range of 0/cm2 to 0.1/cm2 and occupy overall an areal proportion of 10% to 100% of the planar area of the semiconductor wafer, wherein the remaining regions of the semiconductor wafer have a significantly higher defect density than the defect-reduced regions. The wafers may be produced by a method for annealing GOI relevant defects in the wafer, by irradiating defined regions of a side of the semiconductor wafer by laser wherein each location is irradiated with a power density of 1 GW/m2 to 10 GW/m2 for at least 25 ms, wherein the laser emits radiation of a wavelength above the absorption edge of the wafer semiconductor material and wherein the temperature of the wafer rises by less than 20 K as a result of irradiation.