Charge transport in most dielectrics (excluding thermal oxide on Si) is controlled by built charge inside dielectric due to captured electrons or holes on traps. Therefore the current dependence on applied voltage and temperature is determined by trap ionization mechanism. In present time widely accepted model for trap ionization is Frenkel effect. However, our experiments with charge transport in Si₃N₄ show the unphysical low attempt to escape factor and enormously large effective tunnel electron mass obtained by experiment data fitting within this model. To explain the charge transport in Si₃N₄ we propose the alternative multi-phonon model of trap ionization. According to the theory of multi-phonon processes the probability P of trap ionization is given by the following equation

Here W_opt, W_t are the optical and thermal energies of trap ionization, W_ph is the phonon energy. This model gives a good agreement with experiment for Si₃N₄. We suppose that multi-phonon model of trap ionization can be general model for most dielectrics including high-K dielectrics, such as Ta₂O₅, Ba_xSr_1-xTiO₃ etc. Our simulations of SONOS EEPROM memory show that replacing of top SiO₂ by high-k dielectrics (Al₂O₃, ZrO₂) leads to the decreasing of write/erase programming voltage and/or reduces programming pulse duration.