The structures and methods described above provide mechanisms to improve interconnect reliability and resistivity. The interconnect reliability and resistivity are improved by using a composite barrier layer, which provides good step coverage, good copper diffusion barrier, and good adhesion with adjacent layers. The composite barrier layer includes an ALD barrier layer to provide good step coverage. The composite barrier layer also includes a barrier-adhesion-enhancing film, which contains at least an element or compound that contains Mn, Cr, V, Ti, or Nb to improve adhesion. The composite barrier layer may also include a Ta or Ti layer between the ALD barrier layer and the barrier-adhesion-enhancing layer.