In one embodiment, a method of fabricating a MIM capacitor includes forming an interlayer insulating layer having a contact plug on a semiconductor substrate, forming an etch stop layer on the interlayer insulating layer, and forming a mold layer having an opening exposing the contact plug on the etch stop layer. Next, a first conductive layer for the lower electrode is formed on the sidewalls and the bottom of the opening, and a photoresistive layer is formed on the first conductive layer. The mold layer and the photoresistive layer are then removed, and a composite dielectric layer is formed on the lower electrode. A second conductive layer is then formed on the composite dielectric layer. The composite dielectric layer may be composed of an oxide hafnium (HfO2) dielectric layer and an oxide aluminum (Al2O3) dielectric layer, with the oxide hafnium dielectric layer having a thickness of about 20 Å to about 50 Å. The oxide aluminum dielectric layer is formed with a thickness determined by subtracting the thickness of the oxide hafnium dielectric layer from a composite dielectric layer thickness corresponding to an equivalent oxide dielectric layer thickness set to provide a predetermined capacitance of the capacitor.