A dielectric in an integrated circuit is formed by creating oriented cylindrical voids in a conventional dielectric material. Preferably, voids are formed by first forming multiple relatively long, thin carbon nanotubes perpendicular to a surface of an integrated circuit wafer, by depositing a conventional dielectric on the surface to fill the area between the carbon nanotubes, and by then removing the carbon nanotubes to produce voids in place of the carbon nanotubes. A layer of dielectric and voids thus formed can be patterned or otherwise processed using any of various conventional processes. The use of a conventional dielectric material having numerous air voids substantially reduces the dielectric constant, leaving a dielectric structure which is both structurally strong and can be constructed compatibly with conventional processes and materials.