A method for fabricating a capacitor for a semiconductor device is disclosed, which comprises the steps of: forming a storage node electrode on a semiconductor wafer, forming a dielectric layer made of a cyclic silicon nitride layer on the surface of the storage node electrode, and forming an upper electrode on the dielectric layer; lowering the thickness T_eff of the dielectric layer and improving leakage current characteristics through use of a cyclic Si₃N₄ or a cyclic SiO_xN_y (wherein x falls between 0.1 and 0.9 and y falls between 0.1 and 2), having a large oxidation resistance and high dielectric ratio, as a dielectric.