Vibrating modes and dispersive spectra of full polar optical phonons in wurtzite GaN/AlGaN rectangular nanowires

Abstract

By employing the dielectric continuum model and Loudon’s uniaxial crystal model, the full polar optical phonon modes including the propagating (PR) modes, the quasi-confined (QC) modes, the half-space (HS) modes, and the interface optical (IO) modes in a quasi-one-dimensional (Q1D) wurtzite rectangular nanowire (NW) structure are deduced and analyzed. The analytical phonon states, their dispersion equations and polarization eigenvectors are derived. Numerical calculations for the dispersive spectra of these phonon modes are performed on a wurtzite GaN/Al0.15Ga0.85N rectangular wurtzite NW. The behavior of the PR modes reducing to the HS modes with the same order are observed clearly in the dispersive curves of these modes, which reveals that the present theories of phonon modes are self-consistency and correct for the description of phonon modes in wurtzite Q1D rectangular NW. Moreover, there are a series of yielding points in the dispersive curves of the PR modes. These observations and results reveal that the confined dimensionality and cross-section shape influence greatly the dispersive properties of phonon modes in wurtzite quantum confined systems.