Polar optical phonon states and their degenerative behaviors of wurtziteZnO/MgZnOcoupling quantum dots

Abstract

Analytical polar optical phonon states in a wurtzite ZnO -based cylindrical coupling quantum dots (CQDs) with arbitrary number of quantum dots (QDs) are deduced and analyzed. It is found that there are four types of polar mixing optical phonon modes, i.e., the z-IO/ρ-QC modes, the z-PR/ρ-IO modes, the z-QC/ρ-QC modes and the z-HS/ρ-IO modes coexisting in the ZnO -based CQDs. Within the framework of the macroscopic dielectric continuum model, the dispersive equations are derived by using the transferring matrix method. And the Fröhlich electron–phonon interaction Hamiltonians are obtained via a standard procedure of field quantization. The relationships between the present ZnO -based CQDs and the ZnO -based quantum wells (QWs) or the nanowires (NWs) are analyzed, and the general features of phonon modes in ZnO -based low-dimensional quantum structures are concluded and discussed. Under certain conditions, the present theoretical results in wurtzite ZnO -based CQDs can be naturally degenerate into those in wurtzite ZnO -based single or double QDs, wurtzite NWs and QWs and even into cubic quantum confined structures. This just embodies the intrinsic consistency of phonon mode theories in low-dimensional confined systems with different confined dimensions. Due to the ternary mixing effect of MgxZn1-xO crystal, the dielectric functions of MgxZn1-xO crystals are quite complicated, and the phonon modes in ZnO -based quantum structures have both the features of phonon modes in anisotropic wurtzite confined systems and isotropic rock-salt crystal quantum systems. The characteristics of electron–phonon coupling strength in ZnO -based quantum systems are summarized. Very strong polaronic effect could be prognosticated and anticipated in ZnO -based low-dimensional quantum structures because of their quite large electron–phonon coupling constants. The theoretical results and conclusions described in this paper also can be looked on as a summary of phonon states and their general features in ZnO -based quantum confined systems.