A CVD reactor includes a gas inlet element for introducing a process gas into a process chamber arranged between a process chamber cover and a susceptor. The gas inlet element contains at least one metal surface that comes into contact with the process gas. The metal surface has a passivation layer which prevents the metal surface from flaking due to exposure to one or more reactive gases. Cooling channels are arranged such that the passivation layer is maximally heated to 100° C. in a cleaning step in which chlorine is introduced into the process chamber and the susceptor is heated to at least 700° C. At the same time, the passivation layer is formed by chemically reacting a metal-organic compound with the metal atoms of the metal surface. The cleaning gas inlet openings are arranged such that the cleaning gas comes into contact with the metal surface that has the passivation layer.