Electronic Structures of a Quantum Well of A1-xBx Alloy Semiconductor in the Coherent Potential Approximation

Abstract

We have theoretically studied the electronic and optical properties of a quantum well (QW) in which the well region is constructed from a binary alloy semiconductor A 1--x B x in the coherent potential approximation (CPA). A tight binding model is used for a single particle (electron, hole, Frenkel exciton) in the well composed by a rectangular array of N x  N y  N z sites. The effect of the diagonal randomness is reduced to the coherent potential S(E), which is assumed to be the same for all sites, and is selfconsistently determined with the average Green's function. For a slab (1, 1, N z ) and wire (1, N y , N z ), the density of states r(E) is composed of N z (or N y  N z ) subbands, each shows the two (one)-dimensional van-Hove singularity. When x (or 1 --x) is small, a B (A) impurity-band always appears at the lower (higher) energy side of the lowest (highest) host-band. As the well width becomes narrower and/or the dimensionality decreases, the boundary for D/t decreases which separates the amalgamation type and the persistence type.Introduction Alloy semiconductors are important materials for giving us a variety of electronic and optical properties. For example, a convenient way to produce an optical device with a desirable wavelength is by using an alloy semiconductor A 1--x B x from two semiconductors A and B which have different band gap energies. This method is called band-gap engineering, which now is a guiding principle in the semiconductor technology.Theory for random alloy systems has been developed in the late 1960s, and the coherent potential approximation (CPA) was proposed first for diagonal randomness [1-4] and then for off-diagonal randomness [5]. The theory of CPA succeeds in explaining two types of electronic properties in alloy systems. If the physical parameters of A and B are not very different, the electronic properties of A 1--x B x change continuously in response to the change in the concentration x. This is called the amalgamation type. On the other hand, if the differences are large, the properties show two components originated from each constituent although the system is homogeneous. This is called the persistence type. In covalent semiconductors, most of bulk alloy systems are found to be of the amalgamation type, which then shows the band-gap engineering is applicable. If an alloy semiconductor is used for a quantum well region of superlattice structures, however, there is no guarantee for being the amalgamation type, because the effect of randomness is considered to be enhanced by the low dimensionality and the confinement of the wave function. The purpose of the paper is to extend the CPA theory to quantum well structures of various dimensionalities and geometrical size, and give a theoretical guiding principle for the electronic properties of alloy quantum well systems.

Optical absorption spectrum in disordered semiconductor multilayers

“…( 10) is obtained, as it was assumed in Refs. [5,6]. In the present work, the behavior of this function in each layer of the system which depends on the number of layers, alloy concentration and the strength of scattering processes via the self-energy will be studied in Sec.…”

“…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][5][6]. For instance, using a semiconducting alloy A 1−x B x , composed of two semiconductors A and B with different band gap energies, one can tune the operation of an optical device at desired wavelength.…”

“…Based on the Onodera-Toyozawa theory and the CPA, optical properties of various disorder systems have been investigated [5,6,[12][13][14]. Recently, Shinozuka et al [5,6] studied the effect of chemical disorder on the electronic 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.…”

“…Based on the Onodera-Toyozawa theory and the CPA, optical properties of various disorder systems have been investigated [5,6,[12][13][14]. Recently, Shinozuka et al [5,6] studied the effect of chemical disorder on the electronic and optical properties of bulk, quantum well and wire systems within the CPA.…”

Electronic and optical spectra in a diluted magnetic semiconductor multilayer

“…In previous studies [21][22][23], by applying the single-site coherent potential approximation (CPA) [24] to semiconductor alloy multilayers, the effects of chemical (nonmagnetic) disorder on optical absorption spectrum were investigated. The results showed that, the photon absorption by the system is layer dependent and strongly changes by variation of the scattering-strength of the chemical impurities [21].…”