Impurity band density of states in the atomic limit

Model calculations are presented for the density of states in the impurity band of a semiconductor. The calculations are based on the Hubbard model in the atomic (i.e., infinite U) limit and are thus appropriate to impurity concentration below the critical one for the metal–insulator transition. No ordering of the electron spin is assumed, instead all spin configurations are taken to be equally probable. The impurity distribution is taken to be random. Calculations are carried out with a Gaussian overlap integral as a function of impurity–impurity distance and with the transfer integral obtained from hydrogenic wave function. The first seven moments of the density of states distribution of the Gaussian model and the first six moments of the hydrogenic model are calculated using a diagrammatic method. We also discuss asymptotic expressions for the distribution in the high and low density limits. Intepolation methods to reconstruct the distribution from the moments are investigated. It is believed that the methods used are suitable for generalizations to more realistic model Hamiltonians.