Quasi-confined optical phonon modes in a free-standing GaN nanowire with ring geometry

Within the framework of the dielectric continuum model and Loudons uniaxial crystal model, the quasi-confined (QC) phonon modes and corresponding Fröhlich-like Hamiltonian in GaN nanowires with ring geometry are investigated. The dispersion relations and electron-QC phonon coupling strength are calculated numerically. Results reveal that the dispersions of the QC modes are obvious only when the wave number kz and the azimuthal quantum number m are small. Meanwhile, the behaviors of QC modes reducing to surface optical phonon modes are observed. Moreover, the lower-order QC modes in the higher frequency region make more contributions to the electron-QC phonon coupling strengths. Furthermore, the electron-QC coupling functions sometimes can get the maximum value at certain kz and m, which is attributed to the “modulating” effect of the dielectric functions ratio (ϵz/ϵt) due to the anisotropy of the wurtzite nitride crystals.

► Dispersions of the QC phonon modes are obvious when kz and m are small.
► The QC modes reduce to SO modes due to the anisotropic effect of wurtzite crystal.
► The lower-order QC+ modes are much more important to the coupling strength.
► The electron-QC coupling functions sometimes have the maximum value.