Pore sizes and their depth distributions in advanced low-k (ALK) films fabricated using plasma-enhanced chemical vapor deposition were determined using monoenergetic positron beams. The measurement of the energy distributions of annihilation γ-rays and the positron lifetime spectra of the ALK films before and after thin TaN atomic layer deposition showed that Ta atoms diffused into the films. As a result, mean pore size decreased, with the number of larger pores decreasing preferentially. From the measurements of the electron momentum distribution, we found that almost all the inner walls of pores were covered by Ta for the ALK film without pretreatment before TaN deposition. The penetration of Ta into the film, however, was suppressed by plasma treatment using an Ar/N2 or Ar/H2 gas mixture, where the Ar/N2-plasma treatment more effectively blocked Ta diffusion than the Ar/H2-plasma treatment. Through this work, we have demonstrated that monoenergetic positron beams are a powerful tool for characterizing capped porous films and the trapping of metallic atoms by pores.