Polar interface and surface optical vibration spectra in multi-layer wurtzite quantum wires： transfer matrix method

The polar interface optical （IO） and surface optical （SO） phonon modes and the corresponding Froehlich electron phonon-interaction Hamiltonian in a freestanding multi-layer wurtzite cylindrical quantum wire （QWR） are derived and studied by employing the transfer matrix method in the dielectric continuum approximation and Loudon＇s uniaxial crystal model. A numerical calculation of a freestanding wurtzite GaN/AlN QWR is performed. The results reveal that for a relatively large azimuthal quantum number m or wave-number kz in the free z-direction, there exist two branches of IO phonon modes localized at the interface, and only one branch of SO mode localized at the surface in the system. The degenerating behaviours of the IO and SO phonon modes in the wurtzite QWR have also been clearly observed for a small kz or m. The limiting frequency properties of the IO and SO modes for large kz and m have been explained reasonably from the mathematical and physical viewpoints. The calculations of electron-phonon coupling functions show that the high-frequency IO phonon branch and SO mode play a more important role in the electron phonon interaction.

Polar interface and surface optical vibration spectra in multi-layer wurtzite quantum wires:transfer matrix method

The polar interface optical (IO) and surface optical (SO) phonon modes andthe corresponding Fr"{o}hlich electron--phonon--interaction Hamiltonian in afreestanding multi-layer wurtzite cylindrical quantum wire (QWR) are derivedand studied by employing the transfer matrix method in the dielectriccontinuum approximation and Loudon's uniaxial crystal model. A numericalcalculation of a freestanding wurtzite GaN/AlN QWR is performed. The resultsreveal that for a relatively large azimuthal quantum number m or wave-numberk_z in the free z-direction, there exist two branches of IO phonon modeslocalized at the interface, and only one branch of SO mode localized at thesurface in the system. The degenerating behaviours of the IO and SO phononmodes in the wurtzite QWR have also been clearly observed for a smallk_z or m. The limiting frequency properties of the IO and SO modes forlarge k_z and m have been explained reasonably from the mathematical andphysical viewpoints. The calculations of electron--phonon coupling functionsshow that the high-frequency IO phonon branch and SO mode play a moreimportant role in the electron--phonon interaction.