Cu-based interconnections are fabricated in a semiconductor device by depositing a thin film of Cu or Cu alloy on a dielectric film by sputtering, the dielectric film having trenches and/or via holes at least one groove and being arranged on or above a substrate, and carrying out high temperature and high pressure treatment to thereby embed the Cu or Cu alloy into the trenches and/or via holes, in which the sputtering is carried out at a substrate temperature of −20° C. to 0° C. using, as a sputtering gas, a gaseous mixture containing hydrogen gas and an inert gas in a ratio in percentage of 5:95 to 20:80.