In manufacturing a semiconductor integrated circuit device, an interconnect trench and a contact hole are formed in an interlayer insulating film formed over a first-level interconnect on a semiconductor substrate, a barrier film is formed inside of the trench and contact hole so that its film thickness increases from the center of the bottom of the hole toward the sidewalls all around the bottom of the contact hole, a copper film is formed over the barrier film, and a second-level interconnect and a connector portion (plug) are formed by polishing by CMP. In this way, the geometrically shortest pathway of an electrical current flowing from the second-level interconnect toward the first-level interconnect through a connector portion (plug) does not coincide with a thin barrier film portion which has the lowest electrical resistance, so that the current pathway can be dispersed and a concentration of electrons does not occur readily.