Semiconductor wafer of monocrystalline silicon contain fluorine, the fluorine concentration being 1·1010 to 1·1016 atoms/cm3, and is free of agglomerated intrinsic point defects whose diameter is greater than or equal to a critical diameter. The semiconductor wafers are produced by providing a melt of silicon which is doped with fluorine, and crystallizing the melt to form a single crystal which contains fluorine within the range of 1·1010 to 1·1016 atoms/cm3, at a growth rate at which agglomerated intrinsic point defects having a critical diameter or larger would arise if fluorine were not present or present in too small an amount, and separating semiconductor wafers from the single crystal.