Advanced approximation for the probability of phonon-assisted tunneling between traps

An approximate analytical expression is proposed for calculating the probability of phonon-assisted tunneling of charge carriers between deep centers (traps) in dielectrics and wide-bandgap semiconductors. It is shown that the discrepancy between the proposed approximation and the exact integral expression is orders of magnitude smaller than that of the previously known approximation. It is demonstrated that, with the increasing electric field, it becomes energetically more favorable for the charge carrier, instead of direct energetic excitation, to transfer part of the potential energy to the phonon subsystem before the tunneling act.