Vibration spectra of polar mixing optical phonon states and Frohlich electron-phonon coupling behaviors in a wurtzite ZnO quantum dot

Based on the dielectric continuum model and Loudon’s uniaxial crystal model, the interface-opticalpropagating (IO-PR) mixing phonon states of a quasi-zero-dimensional (Q0D) wurtzite cylindrical quantum dot (QD) are investigated. 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 coexisting in Q0D wurtzite QDs. Numerical calculation on a wurtzite ZnO QD shows that the dispersion frequencies of the mixing modes are discrete functions of the azimuthal quantum number and axial wave-number. The calculated results agree well with the recent experimental spectra in ZnO QDs. An abnormal electron-phonon coupling strength is observed with the increase of the azimuthal quantum number and the order of phonon modes, which is attributed to the modulation effect of anisotropic dielectric functions of wurtzite ZnO crystal. The analytical Fr¨olich-like Hamiltonian of electron-phonon interaction obtained here is quite useful for further analyzing phonon influence on optoelectronics properties of wurtzite Q0D QD structures. The present results can be reduced naturally to those of wurtzite quantum wires or quantum wells as the height or radius of cylindrical QD approaches infinity. This supports the validity and unity of phonon modes theories in wurtzite lowdimensional quantum systems.