Quantum size and dielectric effects of polar optical phonon spectra in wurtzite nitride quantum dots

Abstract

Based on the macroscopic dielectric continuum model, the interface-optical-propagating (IO-PR) mixing phonon modes of a quasi-zero-dimensional wurtzite cylindrical quantum dot (QD) structure are derived and studied. The analytical phonon states of IO-PR mixing modes are given. It is found that there are two types of IO-PR mixing phonon modes, i.e., the ρ-IO/z-PR mixing modes and the z-IO/ρ-PR mixing modes, existing in wurtzite QDs. Each IO-PR mixing mode also has symmetrical and antisymmetrical forms. Via a standard procedure of field quantization, the Frohlich Hamiltonians of the electron-(IO-PR) mixing phonon interaction are obtained. The orthogonal relations of polarization eigenvectors for these IO-PR mixing modes are also displayed. Numerical calculations for a wurtzite GaN cylindrical QD are focused on the quantum size effect and the dielectric effect on the dispersive properties of IO-PR mixing modes. The results reveal that both the radial-direction size and the axial-direction size as well as the dielectric matrix have great influence on the dispersive frequencies of the IO-PR mixing phonon modes. The limiting features of dispersive curves of these phonon modes are discussed in depth. The phonon modes' reducing behavior of wurtzite quantum confined structures has been found in the systems. Moreover, the behaviors that the IO-PR mixing phonon modes in wurtzite QDs reduce to the IO modes and the PR modes in wurtzite quantum well and quantum wire systems are analyzed deeply from the viewpoints of both physics and mathematics. These results show that the present theories of polar mixing phonon modes in wurtzite cylindrical QDs are consistent with the phonon mode theories in wurtzite quantum wells and quantum wire systems.