For future generation high-speed LSI devices, copper interconnection with low dielectric constant (low-k) interlayer films is required to decrease RC(R: interconnect resistance, C: interlayer dielectric capacitance) delay. Recently, a new process for low-k films, utilizing dual frequency plasma enhanced chemical vapor deposition (PECVD) with source gas of polysiloxane, has been developed for copper damascene integration. To characterize microstructures in the PECVD grown low-k films, we have carried out positron-positronium lifetime measurements with a slow positron beam. We have found sub-nanometer-sized voids and clear relation between the void size and dielectric constant.