A method for manufacturing a HEMT device includes forming, on a heterostructure, a dielectric layer, forming a through opening through the dielectric layer, and forming a gate electrode in the through opening. Forming the gate electrode includes forming a sacrificial structure, depositing by evaporation a first gate metal layer layer, carrying out a lift-off of the sacrificial structure, depositing a second gate metal layer by sputtering, and depositing a third gate metal layer. The second gate metal layer layer forms a barrier against the diffusion of metal atoms towards the heterostructure.