Polar interface optical phonon states and their dispersive properties of a wurtzite GaN quantum dot: quantum size effect

Abstract

Based on the macroscopic dielectric continuum model, the interface-optical-propagating (IO-PR) mixing phonon modes of a quasi-zero-dimensional (Q0D) 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. ρ-IO/z-PR mixing modes and the z-IO/ρ-PR mixing modes existing in Q0D wurtzite QDs. Each IO-PR mixing mode also has symmetrical and antisymmetrical forms. Via a standard procedure of field quantization, the Fröhlich Hamiltonians of electron-(IO-PR) mixing phonons 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 on the dispersive properties of IO-PR mixing modes. The results reveal that both the radial-direction size and the axial-direction size have great effect 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" the behavior of wurtzite quantum confined structures have been explicitly observed in the systems. Moreover, the behaviors that the IO-PR mixing phonon modes in wurtzite Q0D QDs reduce to the IO modes and PR modes in wurtzite Q2D QW and Q1D QWR systems are profoundly analyzed both from the viewpoint of physics and mathematics. These results show that the present theories of polar mixing phonon modes in wurtzite cylindrical QDs are consistent with the phonon modes theories in wurtzite QWs and QWR systems. The analytical electron-phonon interaction Hamiltonians obtained here are useful in further analyzing the phonon effect on optoelectronic properties of wurtzite Q0D QD structures.