Dispersive spectra and Frohlich electron-phonon interaction Hamiltonians of full polar optical phonon states in a wurtzite nitride nanowire: quantum size effect

Based on the dielectric continuum model and Loudon's uniaxial crystal model, the full polar optical phonon modes including the propagating (PR) modes, quasi-confined modes, half-space (HS) modes and interface optical modes in a quasi-one-dimensional (Q1D) wurtzite rectangular nanowire (NW) structure are deduced and analyzed. The analytical phonon states, their dispersion equations, polar polarization eigenvectors and Frohlich electron-phonon interaction Hamiltonians are derived. Numerical calculations of quantum size effect on the dispersive spectra for these modes are performed on a wurtzite GaN/Al0.15Ga0.85N rectangular wurtzite NW. The dispersive features of the four types of phonon modes are analyzed. The behavior of the PR modes reducing to the corresponding HS modes is 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 some yielding points in the dispersive curves of the PR modes. These observations and results reveal that the confined dimensionality and cross-sectional shape influence greatly the dispersive properties of phonon modes in wurtzite quantum confined systems.