Electronic Contribution to the Elastic Constants in Strained Layer Quantum Dot Superlattices of Non-Parabolic Semiconductors with Graded Interfaces

Abstract

Most papers in the area of semiconductor superlattices (SLs) are based on the assumption that the interface between the layers are sharply defined with the zero thickness so as to be devoid of any interface effects. The advanced experimental techniques may produce SL with physical interface between the two materials crystallographically abrupt, but the bonding environment of the atoms adjoining these interface will change at least on an atomic scale as the potential form changes from a well (barrier) to a barrier (well), an intermediate potential region exists for the charge carriers. Thus, the influence of the finite thickness of the interface on the carrier dispersion law becomes very important. In this paper we study the electronic contribution to the elastic constants in strained layer quantum dot superlattices of non-parabolic semiconductors with graded structures and compare the same with that of the constituent materials, by formulating the appropriate dispersion laws. It is found, taking InSb/GaSb quantum dot strained superlattices of non-parabolic semiconductors as an example, that the carrier contribution to the second-and third-order elastic constants oscillates with the electronic concentration together with the fact that the nature of oscillations are totally dispersion relation dependent. We have also suggested an experimental method for determining the electronic contribution to the elastic constants in quantum-confined materials having arbitrary carrier energy spectra. In addition, the well-known results for bulk specimens of wide-gap stress free materials have been obtained as special cases from our generalized formulation under certain limiting conditions.