Disclosed herein is a method for the fabrication of a capacitor of semiconductor device, which is capable of increasing a charge storage capacitance of the capacitor while generation of leakage current in the capacitor. The method comprises the steps of: forming a ruthenium film as a lower electrode on a semiconductor substrate; forming a TaON film having a high dielectric constant on the ruthenium film; and forming a upper electrode on the TaON film.