Semiconductor device having a capacitance element and method of manufacturing the same

A dielectric film is formed by depositing an amorphous strontium oxide film to a thickness of one to several atomic layers on a first electrode layer, then depositing an amorphous titanium oxide film to a thickness of one to several atomic layers on the amorphous strontium oxide film, and then heat-treating a laminated film of the amorphous strontium oxide film and the amorphous titanium oxide film at a temperature close to a crystallization start temperature, thereby converting the laminated film to a single-layer amorphous strontium titanate film containing a plurality of crystal grains therein. The laminated film may have a plurality of amorphous strontium oxide films and a plurality of amorphous titanium oxide films that are alternately laminated. A semiconductor device includes a capacitor having as its dielectric film a single-layer amorphous strontium titanate film containing a plurality of crystal grains therein.