a process for epitaxially coating the front surface of a semiconductor wafer in a cvd reactor , the front surface of the semiconductor wafer being exposed to a process gas which contains a source gas and a carrier gas , and the back surface of the semiconductor wafer being exposed to a displacement gas , wherein the displacement gas contains no more than 5 % by volume of hydrogen , with the result that diffusion of dopants out of the back surface of the semiconductor wafer , which is intensified by hydrogen , is substantially avoided . with this process , it is possible to produce a semiconductor wafer with a substrate resistivity of ≦ 100 mωcm and a resistivity of the epitaxial layer of & gt ; 1 ωcm without back - surface coating , the epitaxial layer of which semiconductor wafer has a resistance inhomogeneity of & lt ; 10 %.