Abstract The polar interface optical (IO) and surface optical (SO) phonon modes and the corresponding Fr?hlich 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.
Received: 29 October 2005
Revised: 01 March 2006
Accepted manuscript online:
PACS:
63.22.-m
(Phonons or vibrational states in low-dimensional structures and nanoscale materials)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 60276004 and 60390073) and the Natural Science Foundation of Guangzhou Education Bureau, China (Grant No 2060).
Cite this article:
Zhang Li (张立) Polar interface and surface optical vibration spectra in multi-layer wurtzite quantum wires: transfer matrix method 2006 Chinese Physics 15 1101
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