A process of fabricating high dielectric constant MIM capacitors. The high dielectric constant MIM capacitors are for both RF and analog circuit applications. For the high dielectric constant MIM capacitors, 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 artificial layers. Dielectric constants near 900 can be achieved for 250 Angstrom thick super lattices. MBE, molecular beam epitaxy or ALCVD, atomic layer CVD techniques are employed for the layer growth processes.