A method for fabricating low k and ultra-low k multilayer interconnect structures on a substrate includes: a set of interconnects separated laterally by air gaps; forming a support layer in the via level of a dual damascene structure that is only under the metal line; removing a sacrificial dielectric through a perforated bridge layer that connects the top surfaces of the interconnects laterally; performing multilevel extraction of a sacrificial layer; sealing the bridge in a controlled manner; and decreasing the effective dielectric constant of a membrane by perforating it using sub-optical lithography patterning techniques.