Polar vibration spectra of interface optical phonons and electron-interface optical phonon interactions in a wurtzite GaN-AlN nanowire

Within the framework of the dielectric continuum model and Loudon's uniaxial crystal model, the interface optical (IO) phonon modes and their electron-phonon interaction Frohlich-type Hamiltonian in a wurtzite nanowire are derived and studied. Numerical calculations are performed for the dispersion of the IO phonons and their electron-phonon coupling functions in a chosen wurtzite GaN-AlN nanowire. Our results show that the dispersions of the two branches of the IO phonon modes are obvious only if the axial direction wave number k(z) or the azimuthal quantum number m is small. Typical features in the dispersion curves are evidenced which are due to the anisotropy effects of wurtzite crystals. When k(z) or m is small enough, the IO phonon modes will disappear in the wurtzite nanowire. Moreover, k(z) and m have the analogical influence on the dispersion frequency of the IO phonons, especially for large k(z) or m. The frequencies of the two branches of the IO phonon modes with large k(z) or m converge to the two definite limiting values, which are the same as in the wurtzite GaN-AlN single planar heterojunction. The mathematical and physical reasons have been analyzed in depth. Our calculations for the electron-phonon coupling functions indicate that the strength of the electron-phonon interactions with the high-frequency modes is one order of magnitude larger than that with the low-frequency modes. The long-wavelength IO phonons with small m are more important for the electron-phonon interactions in a wurtzite GaN-AlN nanowire.