A method of fabricating a semiconductor device wherein leakage current of a capacitor is reduced is provided. The method comprises steps of forming a lower electrode the surface of a semiconductor substrate, forming a silicon nitride film over the lower electrode, applying a first heat treatment whereby the silicon nitride film is annealed in an atmosphere containing oxygen, forming a dielectric film containing alkaline earth metals over the silicon nitride film, applying a second heat treatment whereby the electric film is annealed in an atmosphere containing oxygen, and forming an upper electrode on the surface of the dielectric film.