Phonon states of polar mixing optical modes in wurtzite ZnO-based coupling quantum dots

•It is confirmed that there are four types of polar optical mixing phonon modes in ZnO-based CQDs.•Each type of the mixing phonon modes has two forms: symmetrical modes and antisymmetrical modes.•Analytical phonon states and dispersive equations of these modes are obtained.•Energy ranges of the polar mixing modes in the ZnO/MgO CQD are characterized.•Electron–phonon interaction Hamiltonians are deduced, which are useful for the investigation of polaronic effect.

Within the framework of the macroscopic dielectric continuum model and Loudon's uniaxial crystal model, the phonon modes of a wurtzite ZnO-based coupling quantum dots (CQDs) are deduced and studied. The analytical phonon states of phonon modes are given. It is found that there are four types of polar phonon modes, i.e. the z-IO/ρ-QC modes, z-PR/ρ-IO modes, z-QC/ρ-QC modes and z-HS/ρ-IO modes coexisting in the wurtzite ZnO-based cylindrical CQDs. The energy ranges of these polar mixing phonon modes are analyzed and discussed. It is found that the z-IO/ρ-QC and z-PR/ρ-IO modes only exist in one frequency range, while z-QC/ρ-QC and z-HS/ρ-IO modes may appear in three frequency ranges. Based on the orthonormality relationships and a standard procedure of field quantization, the Fröhlich electron–phonon interaction Hamiltonians are obtained. The analytical Hamiltonians of electron–phonon interaction obtained here are quite useful for further investigating phonon influence on optoelectronics properties of wurtzite ZnO-based CQD structures.