An improved and new process of fabricating high dielectric constant MIM capacitors. These high dielectric constant MIM capacitor met all of the stringent requirements needed for both for both RF and analog circuit applications. For the high dielectric constant MIM capacitor, the metal is comprised of copper electrodes in a dual damascene process. The dielectric constant versus the total thickness of super lattices is controlled by the number of layers either 4/4, 2/2, and 1/1 artificial layers. Hence thickness of the film can be easily controlled. Enhancement of dielectric constant is because of interface. Dielectric constants near 900 can be easily achieved for 250 Angstrom thick super lattices. MBE, molecular beam epitaxy or ALCVD, atomic layer CVD techniques is used for this type layer growth process.