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points with vanishing slope. In other words, there are states with zero group velocity which are responsible for the singularities in the LDOS of each layer and will be shown below in the case of x = 0 and x = 1. Since the behavior of electronic states and the modification of energy band due to the influence of chemical disorder play a significant role in determining the optical properties of the disordered system, the LDOS should be analyzed in detail. 

In Figs. 2 and 3 we plot the layer-dependence of LDOS and the optical absorption spectrum for Δ = 0 . 5 which corresponds to E$_{B}$ = − 3 t . Because of the symmetry of the system in the z -direction, the electronic states for the layers n =1 and n = 5, and also for n = 2 and n = 4 are similar to each other. For this reason, we have investi- gated our desired quantities in the layers n =1, 2, and 3. The figures show how the value of alloy concentration influences the g$_{n}$ ( ω ) and A$_{n}$ ( ω ). In the case of x = 0 and x = 1, the LDOS of all layers shows a steplike be- 

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havior for the states around the bottom and the top of the band, while, sharp features are observed for energies around the center of band. Both the steplike and sharp features (van-Hove singularities) in the LDOS, which cor- respond to the symmetry points of the 1BZ, comes from the two-dimensional nature of the multilayer. The posi- tion of sharp peaks in the electronic density of states is different in various layers due to the quantum confine- ment along the confined direction. With increasing x the electronic spectra are shifted to the low-energy side and the steplike behavior and sharp peaks gradually disap- peared. In the case of maximum disorder, i.e., at x = 0 . 5 the LDOS is completely symmetric with respect to the center of band. The steplike and sharp features in the localized states are reproduced for x > 0 . 5. Also, it is clear that, a cusp may appear in the LDOS, depending on the value of alloy concentration. This effect, which is related to the value of Δ, confirms that such electronic spectra belong to the amalgamation type. 

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