Optical absorption spectrum in disordered semiconductor multilayers Alireza Saffarzadeh 1, 2, ∗ and Leili Gharaee 1 $^{1}$Department of Physics, Payame Noor University, Nejatollahi Street, 159995-7613 Tehran, Iran $^{2}$Computational Physical Sciences Laboratory, Department of Nano-Science, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran (Dated: October 29, 2018) The effects of chemical disorder on the electronic and optical properties of semiconductor alloy multilayers are studied based on the tight-binding theory and single-site coherent potential approx- imation. Due to the quantum confinement of the system, the electronic spectrum breaks into a set of subbands and the electronic density of states and hence the optical absorption spectrum become layer-dependent. We find that, the values of absorption depend on the alloy concentration, the strength of disorder, and the layer number. The absorption spectrum in all layers is broadened because of the influence of disorder and in the case of strong disorder regime, two optical absorption bands appear. In the process of absorption, most of the photon energy is absorbed by the interior layers of the system. The results may be useful for the development of optoelectronic nanodevices. Low-dimensional quantum structures, such as quan- tum wells and superlattices, wires and dots have at- tracted great interest in the last few years, due to their possible application in nanodevices [1]. Among these structures, multilayers and superlattices, with thickness of few nanometers, are of considerable experimental and theoretical interest because of their specific electronic and optical properties and many promising areas of applica- tions. For example, multilayer semiconductors are very useful for laser diodes, leading to low threshold current, high power, and weak temperature dependence devices [2]. and amalgamation types in a unified theory. In the per- sistence type, two exciton peaks corresponding to the two constituent substances are observed, as seen in al- kali halides with mixed halides such as KCl$_{1}$$_{−}$$_{x}$Br$_{x}$. In the amalgamation type, however, only one exciton state appears, which can be seen in alkali halides with mixed alkalis such as K$_{x}$Rb$_{1}$$_{−}$$_{x}$Cl. These two typical cases can be distinguished by a parameter which is the ratio of the difference of the atomic energies in the two constituent substances to the energy-band width. In the persistence type, this difference is large compared to the bandwidth and the electronic spectrum is split into two bands, while, when this ratio is small, the impurity band is united with the host band and in this case, which corresponds to the amalgamation type, a single band appears. We should note that the transition from the amalgamation type to the persistence type also depends on the value of impu- rity concentration [10]. It has been demonstrated that, by using semiconductor nanostructures instead of bulk structures, the threshold current may be reduced by more than ten times due to the abrupt energy dependence of the density of states in low-dimensional structures which can enhance the light amplification mechanisms and thus allows lasing to occur at lower currents [3]. Furthermore, the optical absorption in semiconductors which is governed by the electronic density of states, is strongly affected by the impurities [4– 6]. For instance, using a semiconducting alloy A$_{1}$$_{−}$$_{x}$B$_{x}$, composed of two semiconductors A and B with differ- ent band gap energies, one can tune the operation of an optical device at desired wavelength. There are many different theoretical approaches that can be used for studying the electronic properties of dis- ordered semiconductors (see for instance [7]). Among them, the coherent potential approximation (CPA) [7–9] is one of the most widely used methods to study chemi- cally disordered systems. In this approximation the mul- tiple scattering on a single site is taken into consideration and this approach is fairly good for any values of band- width and scattering potential. The aim of this work is to extend the CPA for the doped semiconductor multilayers to investigate the in- fluence of substitutional disorder on the local density of states (LDOS) and optical absorbtion spectrum in each layer of the system and in both the persistence and amal- gamation types. The paper is organized as follows: in Sec. II, by applying the single-site approximation to the layered structures in the presence of chemical disorder, we present our theory and derive equations for the LDOS According to the work of Onodera and Toyozawa [10, 11], the optical absorption spectra of substitutional binary solid solutions can be classified into persistence INTRODUCTION arXiv:1001.2000v3 [cond-mat.mes-hall] 2 Jun 2010 Based on the Onodera-Toyozawa theory and the CPA, optical properties of various disorder systems have been investigated [5, 6, 12–14]. Recently, Shinozuka et al. [5, 6] studied the effect of chemical disorder on the elec- tronic and optical properties of bulk, quantum well and wire systems within the CPA. Because of the absence of periodicity in the confinement directions in the quantum wells and wires, the electronic and optical properties of these systems become site-dependent. In their calcula- tions, however, such a dependence has not been included. This site-dependence may be important in operation of nanoscale devices and will be included in our calculations.