A New Method for the Electronic Structure of Random Lattice —the Coexistence of the Local and the Band Character—

Abstract

A new method to obtain the Green’s function of a mixed crystal is studied in the tight binding approximation. The crystal is devided into cells and the Green’s function in a cell is obtained for each atomic arrangement in it. In that process the effects of the other cells are approximated by their average which is determined self-consistently.
The numerical results are obtained for the one dimensional model. The peaks due to the localized levels of the clusters appear in the state density curve for the smaller concentrations. They coalesce with the increase of the concentration and the overall structure nears to that of a virtual lattice, if the atomic energy difference is small. It is found that the virtual crystal model holds well in the middle of the band. The optical absorption curve is calculated in this model.