A wiring structure of a semiconductor device buries an aperture, for example, a contact hole or via hole. The wiring structure includes a semiconductor substrate, an insulating layer formed on the semiconductor substrate and having an aperture formed therein, a diffusion barrier film formed on the inner sidewalls of the aperture and which has a smooth surface without having grain boundaries made of a refractory metal or refractory metal compound, and a metal layer formed on the diffusion barrier film. The metal layer formed on the smooth sidewalls of the diffusion barrier film is made of a uniformly and continuously formed aluminum film having an excellent step coverage. Accordingly, the method for forming the wiring structure effectively buries a contact hole having a high aspect ratio and enhances the reliability of a manufactured device.