The charge transport and trap nature responsible for the leakage current through thermally cured methyl‐terminated organosilicate low‐κ dielectric films are studied. It is found that the Frenkel emission does not describe correctly the charge transport in the studied films. The charge transport occurs via the phonon‐assisted electron tunneling between neutral traps as described in the Nasyrov–Gritsenko model. The obtained thermal trap energy value 1.2 eV is close to that for the oxygen divacancy (SiSiSi cluster) in SiO2. The electron energy loss spectra, photoluminescence excitation of 2.7 eV blue band spectra, and data from the simulation within the density functional theory for the model SiCOH low‐κ structure confirm the presence of oxygen vacancy and divacancy in the studied films. The thermal trap energy value estimated as half the Stokes shift of the blue luminescence also gives a value close to 1.2 eV. It proves the correctness of the Nasyrov–Gritsenko model for describing the charge transport mechanism and the conclusion that oxygen divacancies are traps responsible for the leakage current in the studied low‐κ films.