The dipole model of narrowing of the energy gap between the Hubbard bands in slightly compensated semiconductors

A model of the narrowing of the energy gap between the Hubbard bands (the A ⁰ and A ⁺ bands for acceptors and the D ⁰ and D ^? bands for donors) with increasing concentration of hydrogen-like dopants at low concentrations of the compensating impurity is suggested. The width of the impurity bands is assumed to be small compared to the gap between them. It is taken into account that the local Coulomb interaction between the ions of an electric dipole formed as a result of transition of a hole (electron) between two electrically neutral dopant atoms induces a decrease in the band gap. The calculated thermal activation energies of hopping transitions of holes (electrons) between the impurity bands are in agreement with the experimental data for slightly compensated p-Si:B, p-Ge:Ga, and n-Ge:Sb crystals.