Propagating optical-phonon modes and their electron-phonon interactions in wurtziteGaN∕AlxGa1−xNquantum wells

Abstract

The equation of motion for the $p$-polarization field in an arbitrary wurtzite multilayer heterostructure is solved for the propagating optical-phonon (POP) modes in the framework of the dielectric-continuum model and Loudon's uniaxial crystal model. The polarization eigenvector, the dispersion relation, and the electron-propagating-phonon (EPP) interaction Fr\ohlich-like Hamiltonian are derived. The analytical formulas can be directly applied to single heterojunctions, single and multiple quantum wells (QW's), and superlattices. The dispersion relations of the POP modes and the EPP coupling functions are investigated for a given $\mathrm{GaN}∕{\mathrm{Al}}_{0.15}{\mathrm{Ga}}_{0.85}\mathrm{N}$ single QW with full account of the strains of QW structures and the anisotropy effects of wurtzite crystals. We find that there are infinite POP branches, which can be denoted by a quantum number $n(n=1,2,\dots{})$, with definite symmetry with respect to the center of symmetry of the QW structure. The dispersion of the POP modes with smaller $n$ is more obvious than for larger $n$. Moreover, the modes with smaller $n$ are much more important for the EPP interactions than the modes with larger $n$. In most cases, it is enough to consider the modes with $n=1,2,\dots{},10$ for the EPP interactions in a single QW. The long-wavelength POP modes are much more important for the EPP interactions. Furthermore, the strain effects of the QW structures have a strong influence on the dispersion of the POP modes. The strength of the EPP interactions is markedly increased due to the strains of the QW structures.