Polar optical phonon modes of a wurtzite ZnO/MgZnO multi-shell spherical quantum dot

Based on the macroscopic dielectric continuum model and Loudon´s uniaxial crystal model, the phonon modes of a wurtzite quasi-O-dimensional (QOD) multi-shell spherical quantum dot (QD) are derived and studied. Via solving Laplace equations under the spheniodal coordinates, the analytical and unified phonon states and dispersive equations are derived. Numerical analysis on a wurtzite three-layer ZnO/Mg_0.2Zn_0.8O/MgO QD is performed. The two-mode behavior of Mg_0.2Zn_0.8O ternary compounds is taken into account. The frequency ranges of the full phonon modes of the ZnO/ Mg_0.2Zn_0.8O /MgO QDs are analyzed and discussed. It is found that there are two types of dispersive phonon modes, i.e. quasi-confined (QC), and the interface optical (IO) phonon modes coexisting in QOD wurtzite ZnO/ Mg_0.2Zn_0.8O/MgO QD structures. Moreover, the QC modes also have three types of forms, i.e. QCⁱ (vibration waves located in the central ZnO material), QCⁱⁱ (vibration waves located in the Mg_0.2Zn_0.8O material) and QC^i-ii (vibration waves located both in the ZnO and Mg_0.2Zn_0.8O materials). The IO modes appear only in one frequency range. The QCⁱ modes exist in two frequency ranges, while the QCⁱⁱ and Qc^i-ii modes may appear in three frequency ranges. The analytical phonon states and dispersive equations obtained here are quite useful for further investigating Raman spectra of phonons and other relative properties of wurtzite multi-shell QOD QD systems.