It is generally accepted that the charge transport in dielectrics is governed by coulombic trap ionization due to a barrier lowering in high electric fields (Frenkel effect). In this paper, the charge transport mechanism in Si 3 N 4 and nonstoichiometric silicon rich SiN x is experimentally studied and quantitatively analyzed with five theoretical models: Frenkel model of Coulomb traps ionization, Hill-Adachi model of overlapping Coulomb traps, Shklovskii-Efros percolation model, Makram-Ebeid and Lannoo model of multiphonon isolated traps ionization and Nasyrov-Gritsenko model of phonon-assisted electron tunneling between nearby traps. It is shown that the charge transport in Si 3 N 4 and SiN x is qualitatively described by Frenkel effect, but Frenkel effect predicts an enormously low attempt to escape factor value. The charge transport at traps energies W t = 1.6 eV and W opt = 3.2 eV in Si 3 N 4 and SiN x can be described by an increase in traps concentration in the framework of Makram-Ebeid and Lannoo model and Nasyrov-Gritsenko model. The Makram-Ebeid and Lannoo model quantitatively describes the charge transport in Si 3 N 4 and SiN x with low silicon enrichment. The charge transport in nonstoichiometric SiN x with high silicon enrichment is well explained by Nasyrov-Gritsenko model.