A substrate surface is coated with a permeation barrier of inorganic material, which is vaporized from a crucible in a vacuum chamber evacuated to at least 10.sup.-3 mbar and precipitated on the substrate surface.An ionizing electron beam of low energy is thus passed through the gas phase of inorganic material with formation of a plasma, preferably in the direction running approximately parallel to the substrate surface.At least one low voltage electron beam gun with assigned electrode is incorporated in the vacuum chamber between the crucible and the substrate support.The main application is for coating plastic films for the packaging industry.