Vibration properties of propagating and half-space optical phonons in a wurtzite Q1D GaN-based quantum wire

By employing the dielectric continuum and Loundon's uniaxial crystal models, the propagating (PR) and half-space (HS) optical phonon modes and the corresponding Fröhlich electron-phonon interaction Hamiltonians in a quasi-one-dimensionality (Q1D) wurtzite quantum wire (QWR) are derived and studied. Numerical calculations on a wurtzite GaN/Al0.15Ga0.85N QWR are performed, and the discussions are mainly focused on the dependent relationships of the dispersion and electron-phonon coupling properties of PR and HS modes on the free wave-number kz in z-direction and the azimuthal quantum number m. The calculated results show that there usually exist infinite branches of PR modes in the wurtzite QWR systems for given kz and m. The total branch number of the PR modes will decrease as kz increases. The dispersive frequencies of the HS modes fall into two frequency ranges, i.e. a high-frequency range and a low-frequency range. For certain kz and m, there also are infinite branches of HS modes in the high-frequency range, and only finite branches of HS modes could exist in the low-frequency range. The behavior that the 0H HS mode reduces to the IO modes for a relatively large kz has been obviously observed. Once the frequency of the low-frequency HS modes is lower than the characteristic frequency ωtT,GaN, all the low-frequency HS phonon branches iL will respectively reduce to the corresponding PRi optical phonon branches. Moreover, the dispersive properties of the PR and HS modes in Q1D QWR and Q2D quantum well structures have been compared in detail. The profound physical reasons resulting in these features have also been analyzed in depth. At last, the coupling properties between an electron with PR and HS phonon modes are discussed in detail.