Electron quasi-confined-optical-phonon interactions in wurtzite GaN/AlN quantum wells

The equation of motion for the p-polarization field in a wurtzite GaN/AlN multilayer heterostructure is solved for the quasi-confined-optical-phonon modes based on the dielectric-continuum model and Loudon's uniaxial crystal model. The polarization eigenvector, the dispersion relation of the quasi-confined-optical-phonon modes and the electron-quasi-confined-phonon interaction Fröhlich-like Hamiltonian are derived. The analytical formulas can be directly applied to single/multiple quantum wells (QW's) and superlattices. The electron-quasi-confined-phonon coupling functions are investigated for a given AlN/GaN/AlN single QW with full account of the strains of the QW structures and the anisotropy effect of wurtzite crystals. We find that there are two kinds of quasi-confined-optical-phonon modes in the GaN/AlN QW's: the GaN-layer quasi-confined-optical-phonon modes and the AlN-layer quasi-confined-optical-phonon modes. There are infinite quasi-confined-optical-phonon branches, labelled by a quantum number n (n=1,2,...), with definite symmetry with respect to the center of the AlN/GaN/AlN single QW for a given phonon wave number q. The dispersions of the quasi-confined-optical-phonon modes with smaller n are more obvious than the ones with larger n. Moreover, the modes with smaller n are much more important for their electron-quasi-confined-phonon interactions than those with larger n. In most cases, it is enough to consider the modes with n≤ 8 for the electron-quasi-confined-phonon interactions in a single GaN/AlN QW. The higher frequency modes are more significant than the lower ones. The long-wavelength quasi-confined-optical-phonon modes are much more important for the electron-quasi-confined-phonon interactions. The GaN-layer quasi-confined-optical-phonon energies and their electron-quasi-confined-phonon interaction strength are markedly increased due to the strains of the QW structures. The influence of the strains on the the AlN-layer electron-quasi-confined-phonon interactions can be ignored.