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.

Phonon States and Dispersive Spectra of Polar Optical Phonons in Quasi-One-Dimensional Nanowires of Wurtzite ZnO and Zinc-Blend MgO Semiconductors

Within the framework of the macroscopic dielectric continuum model and Loudon＇s uniaxial crystal model, the phonon modes of a wurtzite/zinc-blende one-dimensional （1D） cylindrical nanowire （NW） are derived and studied. The analytical phonon states of phonon modes are given. It is found that there exist two types of polar phonon modes, i.e. interface optical （IO） phonon modes and the quasi-confined （QC） phonon modes existing in 1D wurtzite/zinc-blende NWs. Via the standard procedure of field quantization, the Fr6hlich electron-phonon interaction Hamiltonians are obtained. Numerical calculations of dispersive behavior of these phonon modes on a wurtzite/zinc-blende ZnO/MgO NW are performed. The frequency ranges of the IO and QC phonon modes of the ZnO/MgO NWs are analyzed and discussed. It is found that the IO modes only exist in one frequency range, while QC modes may appear in three frequency ranges. The dispersive properties of the IO and QC modes on the free wave-number kz and the azimuthal quantum number m are discussed. The analytical Hamiltonians of electron-phonon interaction obtained here are quite useful for further investigating phonon influence on optoelectronics properties of wurtzite/zinc-blende 1D NW structures.