The present invention relates to a method for fabricating a diffusion-barrier cap on a Cu-containing interconnect element that has crystallites of at least two different crystal orientations, comprises selectively incorporating Si into only a first set of crystallites with at least one first crystal orientation, employing first process conditions, and subsequently selectively forming a first adhesion-layer portion comprising CuSi and a first diffusion-barrier-layer portion only on the first set of crystallites, thus forming a first barrier-cap portion, and subsequently selectively incorporating Si into only the second set of crystallites, employing second process conditions that differ from the first process conditions, and forming a second barrier-cap portion comprising a Si-containing second diffusion-barrier layer portion on the second set of crystallites of the interconnect element. The processing improves the properties of the diffusion-barrier cap and secures a continuous formation of a diffusion-barrier layer on the interconnect element.