In a process for coating substrates 1, 35, for example aluminum ceramic plates 1 or polyimide films 35 with copper by means of a device including a direct current source 10 which is connected to a sputtering cathode 5, 30, 31 disposed in a process chamber 15, 15a, 32 which can be evacuated and this cathode electrically interacts with a copper target 3, 33, 34 which can be sputtered and the sputtered particles are deposited on the substrate 1, 35 whereby the argon gas can be introduced into the process chamber 15, 15a, 32 which can be evacuated, an oxygen inlet 20, 39 is provided in addition to the argon inlet 21, 40, whereby the supply of oxygen can be controlled via a valve 19, 43 inserted in the feed line 23, 39 and the amount of oxygen can be metered such that during a first process phase a copper oxide layer which functions as a bonding agent forms on the substrate 1, 35 and after adjusting the argon atmosphere in the process chamber 15, 15a, 32 pure copper is deposited as an electrically conductive layer.