Activation energy of the hopping conductivity of the -doped semiconductor in the low-density limit

We consider the impurity band structure of a system of multiple donor sheets, spaced significantly farther apart than the average in-plane donor separation. In a low-density limit the overlap of the wave functions of neighboring donors is relatively small and the spread of the energy levels is governed by the Coulomb shifts produced by the charged acceptors and donors. The activation energy of the hopping conductivity in the regime of nearest-neighbor hopping is equal to the Fermi-level position with respect to the isolated donor level, which is calculated as a function of the two-dimensional concentration of donors and the interplane distance assuming that the small degree of compensation is provided by the acceptors, which are distributed randomly between the sheets.