A semiconductor device has an MIS (metal-insulating film-semiconductor) structure, and a film mainly containing Al, O, and N atoms is used on a semiconductor. Alternatively, a semiconductor device has an MIS structure, and a film mainly containing Al, O, and N atoms is provided as a gate insulating film on a channel region between a source and a drain. Characteristics required of a gate insulating film of a 0.05 μm-gate-length-generation semiconductor transistor are satisfied. In particular, no fixed charge is included in the film, and impurity diffusion is reduced.