中国物理B ›› 2006, Vol. 15 ›› Issue (5): 1101-1109.doi: 10.1088/1009-1963/15/5/040

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

张立   

  1. Department of Mechanism and Electronic, Panyu Polytechnic, Panyu 511483,China
  • 收稿日期:2005-10-29 修回日期:2006-03-01 出版日期:2006-05-20 发布日期:2006-05-20
  • 基金资助:
    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).

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

Zhang Li (张立)   

  1. Department of Mechanism and Electronic, Panyu Polytechnic, Panyu 511483,China
  • Received:2005-10-29 Revised:2006-03-01 Online:2006-05-20 Published:2006-05-20
  • Supported by:
    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).

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摘要： The polar interface optical (IO) and surface optical (SO) phonon modes and the corresponding Fr\"{o}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.

关键词: interface and surface optical phonons, multi-layer cylindrical heterostructures, wurtzite quantum wires

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.

Key words: interface and surface optical phonons, multi-layer cylindrical heterostructures, wurtzite quantum wires

中图分类号:  (Phonons or vibrational states in low-dimensional structures and nanoscale materials)

  • 63.22.-m
63.20.K- (Phonon interactions) 68.35.Ct (Interface structure and roughness) 68.35.Ja (Surface and interface dynamics and vibrations) 68.65.La (Quantum wires (patterned in quantum wells)) 71.38.Fp (Large or Fr?hlich polarons)