Electron states in a crystal with impurity levels near the band edge

The electron states in a crystal in the presence of impurity levels near the band edge are investigated. The density of states in various spectral ranges, including the transition region between the band and fluctuation states, is found by employing the technique of group expansion of the Green's function in terms of interacting-impurity-center complexes. Broadening of individual two-particle levels determining the density of states near the band edge is investigated. Criteria that the density of fluctuation states in this range is either a smooth function or possesses a fine structure are found. Long-range interaction of impurities is considered. The localization of the fluctuation states and the mobility threshold are discussed.