Dispersion relation of the optical phonon frequencies in AlN/GaN superlattices

摘要

In this work we study the dispersion relation of the phonon frequencies in heterojunctions composed by Ⅲ-V nitride materials (GaN and AlN). We are concerned with the superlattice structure, namely /substrate /AlN /Al_xGa_(1-x)N/GaN / Al_xGa_(1-x)N/ ..., where the substrate is here considered to be a transparent dielectric medium like sapphire. We make use of a model based on the Froehlich Hamiltonian, taking into account the macroscopic theory known as the continuum dielectric model. The optical phonon modes are modelled considering only the electromagnetic boundary conditions, in the absence of charge transfer between ions. Numerical results of the confined optical phonon dispersion are presented, characterizing three distinct optical phonon classes designated as interface (IF), half-space (HS) and propagating (PR) modes. Furthermore, due to the dielectric anisotropy presented in the nitride, some additional peculiarities will be presented, like dispersive confined modes.