Low-temperature contribution to the resonant tunneling conductance of a disordered $N$–$I$–$N$ junction

A formula for the contribution $\Delta G^{\text{res}} (T)$ to the resonant tunneling conductance of the $N$–$I$–$N$ junction (where $N$ is a normal metal and $I$ is an insulator) with a weak (low impurity concentrations) structural disorder in the $I$ layer from the low-temperature “smearing” electron Fermi surfaces in its $N$ shores is obtained. It is shown that the temperature dependence $\Delta G^{\text{res}} (T)$ in such a “dirty” junction qualitatively differs from the corresponding dependence $\Delta G_0(T)$ in a “pure” (without resonant impurities in the $I$ layer) junction: $\Delta G^{\text{res}}(T) < 0$, $d(\Delta G^{\text{res}})/dT < 0$; $\Delta G_0(T) > 0$, $d(\Delta G_0)/dT > 0$, which can serve as an experimental test of the presence of impurity tunneling resonances in the disordered $I$ layer.