Interaction-induced threshold singularities in tunneling via localized levels

The current-voltage characteristic of the tunnel junction with a localized impurity level in the dielectric layer is studied. We take into account the fact that the electron tunneling from the level to the lead is accompanied by the formation of a positively charged hole bound to the impurity. The Coulomb interaction of electrons with the hole leads to power-law singularities in the transition rate, analogous to those arising in the problem of x-ray-absorption edges in metals. They manifest themselves in I-V characteristic as I∼(V-${\mathit{V}}_{\mathrm{th}}$${)}^{\mathrm{-}\mathrm{\alpha }}$θ(V-${\mathit{V}}_{\mathrm{th}}$), the exponent α being small when the spacing between impurity and junction leads is greater than the Fermi wavelength ${\lambda }_{\mathit{F}}$. Predicted dependences are most likely to be observed in junctions with leads made of a heavily doped semiconductor or in GaAs heterostructures, where the spacing may be of the order of ${\lambda }_{\mathit{F}}$.