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

Abstract

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 Fr\"ohlich-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.