Monocrystalline silicon semiconductor wafers have a front side and a rear side, and a denuded zone which extends from the front side to the rear side as far as a depth which between a center and an edge of the semiconductor wafer on average is not less than 8 μm and not more than 18 μm, and having a region adjoining the denuded zone having BMDs whose density at a distance of 30 μm from the front side is not less than 2×109 cm−3. The semiconductor wafers are produced by a method comprising providing a substrate wafer of monocrystalline silicon and an RTA treating the substrate wafer, the treatment subdivided into a first thermal treatment of the substrate wafer in an atmosphere consisting of argon and into a second thermal treatment of the substrate wafer in an atmosphere consisting of argon and ammonia.