Interface optical-phonon modes and electron–interface-phonon interactions in wurtzite GaN/AlN quantum wells

Abstract

Based on the dielectric-continuum model and Loudon's uniaxial crystal model, the equation of motion for the p-polarization field in an arbitrary wurtzite multilayer heterostructure is solved exactly for the interface optical-phonon modes. The polarization eigenvector, the dispersion relation, and the electron--interface-phonon interaction Fr\"ohlich-like Hamiltonian are derived using the transfer-matrix method. The analytical formulas can be directly applied to single heterojunctions, single and multiple quantum wells (QW's), and superlattices. Considering the strains of QW structures and the anisotropy effects of wurtzite crystals, the dispersion relations of the interface phonons and the electron--interface-phonon coupling strengths are investigated for GaN/AlN single and coupled QW's. We find that there are four (eight) interface optical-phonon branches with definite symmetry with respect to the symmetric center of a single (coupled) QW. Typical features in the dispersion curves are evidenced which are due to the anisotropy effects of wurtzite crystals. The lower-frequency modes are much more important for the electron--interface-phonon interactions than the higher-frequency modes. For the lower-frequency interface phonons, the intensity of the electron-phonon interactions is reduced due to the strain effects of the QW structures. For the higher-frequency interface modes, the influence of the strains on the electron-phonon interactions can be ignored.