The use of atomic layer deposition (ALD) to form a dielectric layer of zirconium nitride (Zr.sub.3N.sub.4) and zirconium oxide (ZrO.sub.2) and a method of fabricating such a dielectric layer produces a reliable structure for use in a variety of electronic devices. Forming the dielectric structure includes depositing zirconium oxide using atomic layer deposition using precursor chemicals, followed by depositing zirconium nitride using precursor chemicals, and repeating. Alternatively, the zirconium nitride may be deposited first followed by the zirconium nitride, thus providing a different work function. Such a dielectric may be used as the gate insulator of a MOSFET, a capacitor dielectric, or a tunnel gate insulator in memories, because the high dielectric constant (high-k) of the film provides the functionality of a thinner silicon dioxide film, and because of the reduced leakage current of the physically thicker dielectric layer when compared to an electrically equivalent thickness of silicon dioxide.