Transfer matrix theory for the optical absorption spectrum of mixed crystals

We study the density of states and optical absorption spectrum of linear mixed crystals in the one- dimensional alloy transfer matrix approximation. Local modes, which are present in the single impurity limit, develop into collective modes by merging into a band as the impurity concentration increases. The composition dependence of local and collective like optical absorption peaks is discussed, and we show that qualitatively different behaviours are obtained for single band and split bands type density of states.