• Chinese Journal of Quantum Electronics
  • Vol. 39, Issue 4, 632 (2022)
Li Zhang1、* and Qi Wang2
Author Affiliations
  • 1[in Chinese]
  • 2[in Chinese]
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    DOI: 10.3969/j.issn.1007-5461.2022.04.019 Cite this Article
    Zhang Li, Wang Qi. Frohlich electron-phonon interaction Hamiltonian in GaN nanowires with triangular cross-section[J]. Chinese Journal of Quantum Electronics, 2022, 39(4): 632 Copy Citation Text show less
    References

    [1] Han W Q, Fan S S, Li Q Q, et al. Synthesis of gallium nitride nanorods through a carbon nanotube-confined reaction [J]. Science, 1997, 277(5330): 1287-1289.

    [2] Tanaka T, Uchida K, Kawanaka S, et al. Stimulated emission from rectangular cross-sectional GaN optical waveguides by photo-pumping and stripe design of optical waveguides formed with a selectively grown GaInN/GaN buried heterostructure [J]. Solid-State Electronics, 1997, 41(2): 255-261.

    [3] Liu B D, Bando Y, Tang C C, et al. Quasi-aligned single-crystalline GaN nanowire arrays [J]. Applied Physics Letters, 2005, 87(7): 073106.

    [4] Seo M K, Yang J K, Jeong K Y, et al. Modal characteristics in a single-nanowire cavity with a triangular cross section [J]. Nano Letters, 2008, 8(12): 4534-4538.

    [5] Zhang L. Dispersive spectra and scattering rates of interface optical phonon modes in a wurtzite GaN-based step quantum well with strong built-in electric field [J]. The Journal of Light Scattering, 2016, 28(2): 131-139.

    [7] Xie H J, Chen C Y, Ma B K. Bound polaron in a cylindrical quantum wire of a polar crystal [J]. Physical Review B, 2000, 61(7): 4827-4834.

    [8] Zhang L, Shi J J, Tansley T L. Polar vibration spectra of interface optical phonons and electron-interface optical phonon interactions in a wurtzite GaN-AlN nanowire [J]. Physical Review B, 2005, 71(24): 245324.

    [9] Zhang L, Shi J J. Dispersive spectra and Frohlich electron-phonon interaction Hamiltonians of full polar optical phonon states in a wurtzite nitride nanowire: Quantum size effect [J]. Semiconductor Science and Technology, 2012, 27(5): 055006.

    [10] Li W K, Blinder S M. Particle in an equilateral triangle: Exact solution of a nonseparable problem [J]. Journal of Chemical Education, 1987, 64(2): 130-132.

    [11] Li W K, Blinder S M. Solution of the Schrodinger equation for a particle in an equilateral triangle [J]. Journal of Mathematical Physics, 1985, 26(11): 2784-2786.

    [12] Pinsky M A. The eigenvalues of an equilateral triangle [J]. SIAM Journal on Mathematical Analysis, 1980, 11(5): 819-827.

    [13] McCartin B J. Eigenstructure of the equilateral triangle, part II: The Neumann problem [J]. Mathematical Problems in Engineering, 2002, 8: 591873.

    [14] McCartin B J. Eigenstructure of the equilateral triangle, part I: The dirichlet problem [J]. SIAM Review, 2003, 45(2): 267-287.

    [15] Práger M. Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle [J]. Applications of Mathematics, 1998, 43(4): 311-320.

    [16] Práger M. Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case [J]. Applications of Mathematics, 2001, 46(3): 231-239.

    [17] Freitas P. Upper and lower bounds for the first Dirichlet eigenvalue of a triangle [J]. Proceedings of the American Mathematical Society, 2006, 134(7): 2083-2089.

    [18] Shi J J. Interface optical-phonon modes and electron-interface-phonon interactions in wurtzite GaN/AlN quantum wells [J]. Physical Review B, 2003, 68(16): 165335.

    [19] Mori N, Ando T. Electron-optical-phonon interaction in single and double heterostructures [J]. Physical Review B, 1989, 40(9): 6175-6188.

    [20] Zhang L, Shi J J. Influence of surface optical phonons on exciton binding energies of a quasi-one-dimensional wurtzite GaN-based nanowire: Quantum size effect [J]. Journal of Applied Physics, 2013, 113(9): 093710.

    Zhang Li, Wang Qi. Frohlich electron-phonon interaction Hamiltonian in GaN nanowires with triangular cross-section[J]. Chinese Journal of Quantum Electronics, 2022, 39(4): 632
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