Polar optical phonon states and Fröhlich electron–phonon interaction Hamiltonians in a wurtzite nitride quantum dot

Within the framework of the macroscopic dielectric continuum model, the surface-optical-propagating (SO-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 SO-PR mixing modes are given. It is found that there are two types of SO-PR mixing phonon modes, i.e. ρ-SO/z-PR mixing modes and the z-SO/ρ-PR mixing modes existing in Q0D wurtzite QDs. And each SO-PR mixing modes also have symmetrical and antisymmetrical forms. Via the standard procedure of field quantization, the Fröhlich Hamiltonians of electron–(SO-PR) mixing phonons interaction are obtained. And the orthogonal relations of polarization eigenvectors for these SO-PR mixing modes are also displayed. Numerical calculations on a wurtzite GaN cylindrical QD are carried out. The results reveal that the dispersive frequencies of all the SO-PR mixing modes are the discrete functions of phonon wave-numbers and azimuthal quantum numbers. The behaviors that the SO-PR mixing phonon modes in wurtzite QDs reduce to the SO modes and PR modes in wurtzite quantum well (QW) and quantum well wire (QWR) systems are analyzed deeply from both of the viewpoints of physics and mathematics. The result shows 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 for further analyzing phonon influence on optoelectronics properties of wurtzite Q0D QD structures.