5 FIG. 6: (Color online) The total optical absorption spectrum for two disordered semiconductor multilayers as a function of energy and alloy concentration. In (a) E$_{B}$ = − 3 t and in (b) E$_{B}$ = − 8 t . ω is measured in units of t . FIG. 5: (Color online) The same as Fig. 3 but for E$_{B}$ = − 8 t . the value of optical absorption in each layer depends on the layer number, and the interior layers play a major role in such a process. This feature, which has not been predicted in the previous studies [5, 6], is important in operation of semiconductor optoelectronic nanodevices. In a clean system, i.e., in the case of x = 0 or x = 1, A$_{n}$ ( ω ) shows sharp peaks at the edges of the subbands. However, in a system with substitutional disorder, the absorption peaks are broadened and their heights de- crease. Based on the behavior of electronic states, with increasing x , as shown in Fig. 3, the optical absorption spectrum shifts to the low-energy side, due to its depen- dence on the bottom energy of the subbands. The max- imum value of A$_{n}$ ( ω ) corresponds to the cases of x = 0 and x = 1, because the van Hove singularities for these values of x are significantly large. Thus, we can con- clude that, in doped semiconductor multilayers, impuri- ties with lower (higher) site energy in comparison with the energy of host atoms and with finite concentration x , decrease the strength of optical absorption, i.e., the height of peaks in A$_{n}$ ( ω ), and incident photons with low (high) energy are needed. To investigate the another aspect of the electronic and optical properties of the system, we have shown in Figs. 4 and 5, g$_{n}$ ( ω ) and A$_{n}$ ( ω ) for Δ = 1 . 33 which corresponds to E$_{B}$ = − 8 t . We can clearly see that a gap appears in the LDOS for each value of x ( = 0 , 1) and the electronic spectra split into two bands corresponding to the two constituent crystals; the lower- (higher-) energy band in this figure corresponds to the B ( A ) atoms. Accordingly, these electronic spectra belong to the persistence type. This gap opening is a consequence of scattering process of carriers by random distribution of the elements in the alloy, and its magnitude depends on the strength of dis- order. Our analysis of the behavior of LDOS is similar to that of Fig. 2. Another interesting feature is that optical absorption of the surface layers, i.e., layers n = 1 and n = N , is smaller than that of the interior layers, due to the in- fluence of surface states [compare the maximum value of A$_{1}$ ( ω ) with that of A$_{2}$ ( ω ) and A$_{3}$ ( ω ) at the lowest ener- gies in Fig. 3]. This indicates that in multilayer systems, Fig. 5 clearly indicates that in the case of strong dis- order regime, A$_{n}$ ( ω ) consists of two bands and the spec- trum stretches toward the higher-energy side. With in- creasing x , the optical absorption spectrum of the A -type