三元混晶矩形量子线的表面光学声子模
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摘要
运用改进的无规元素等位移模型和玻恩-黄近似,结合介电连续模型,研究了三元混晶矩形量子线系统的表面光学声子模.以AlxGa1-xAs和ZnxCd1-xSe为例,获得了表面光学声子模的色散关系以及表面光学声子模的频率随混晶组分和量子线结构的变化关系.结果表明:与二元晶体量子线不同,在三元混晶量子线系统中存在四支表面光学声子模,这四支表面光学声子模的频率曲线位于三元混晶的体纵、横光学声子的频率区间内,且其能量随混晶组分和量子线结构的变化而呈非线性变化.三元混晶的"单模"和"双模"性也在色散曲线中体现出来.
Surface optical phonons in freestanding rectangular quantum wire systems of polar ternary mixed crystals are investigated with the modified random-element-isodisplacement model and the Born-Huang approximation based on the dielectric continuum model.The numerical results of the surface optical phonon frequencies as functions of the wave-vector,composition x,and geometric structures of the quantum wires in AlxGa1-xAs and ZnxCd1-xSe quantum wire systems are obtained and discussed.It is shown that different from quantum wire systems of binary crystals,there are four branches of surface optical phonon modes in quantum wire systems of polar ternary mixed crystals to localize in the frequency regions between the bulk longitudinal and transversal optical phonons in ternary mixed crystal,and the surface optical phonon modes non-linearly change in frequency with the composition and the geometric structures of rectangular quantum wire systems of polar ternary mixed crystals.The effects of " one mode" and "two mode" behaviors of the ternary mixed crystals are shown in the dispersion curves.
Surface optical phonons in freestanding rectangular quantum wire systems of polar ternary mixed crystals are investigated with the modified random-element-isodisplacement model and the Born-Huang approximation based on the dielectric continuum model.The numerical results of the surface optical phonon frequencies as functions of the wave-vector,composition x,and geometric structures of the quantum wires in AlxGa1-xAs and ZnxCd1-xSe quantum wire systems are obtained and discussed.It is shown that different from quantum wire systems of binary crystals,there are four branches of surface optical phonon modes in quantum wire systems of polar ternary mixed crystals to localize in the frequency regions between the bulk longitudinal and transversal optical phonons in ternary mixed crystal,and the surface optical phonon modes non-linearly change in frequency with the composition and the geometric structures of rectangular quantum wire systems of polar ternary mixed crystals.The effects of " one mode" and "two mode" behaviors of the ternary mixed crystals are shown in the dispersion curves.
引文
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[4] Xie H J,Chen C Y,Ma B K.Bound polaron in a cylindrical quantum wire of a polar crystal[J].Phys Rev B,2000,61(7):4827-4834.
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[16] Zhang L.Interface-phonon modes in quasi-one-dimensional wurtzite rectangular quantum wires[J].Commun Theor Phys,2006,46(6):1109-1112.
[17] Zhang L,Shi J J.Polar interface optical phonon modes and Fr9hlich electron-phonon interaction Hamiltonians in wurtzite quantum well wires[J].Semicond Sci Technol,2005,20(6):592-600.
[18] 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].Phys Rev B,2005,71(24):245324(1-9).
[19] Zhang L.Polar interface and surface optical vibration spectra in multi-layer wurtzite quantum wires:transfer matrix method[J].Chin Phys,2006,15(5):1101-1109.
[20] Chang I F,Mitra S S.Long wavelength optical phonons in mixed crystals[J].Adv Phys,1971,20(85):539-404.
[21] Born M,Huang K.Dynamical Theory of Crystal Lattices[M].New York:Oxford University Press,1954:82-86.
[22] Liang X X,Ban S L.Optical vibration modes and electron-phonon interaction in ternary mixed crystals of polar semiconductors[J].Chin Phys,2004,13(1):71-81.
[23] Liang X X,Yang J S.Effective-phonon approximation of polarons in ternary mixed crystals[J].Solid State Commum,1996,100(9):629-634.
[24] Adachi S.GaAs,AlAs and AlxGa1-x As material parameters for use in research and device applications[J].J Appl Phys,1985,58(3):R1-R29.
[25] Yu S,KIim K W,Bergman L,et al.Long-wavelength optical phonons in ternary nitride-based crystals[J].Phys Rev B,1998,58(23):15283-15287.
[26] Strites S,Morkoc H.GaN,AlN,and InN:A review[J].J Vac Sci Technol B,1992,10(4):1237-1266.
[2] Stroscio M A,Kim K W,Littlejohn M A,et al.Polarization eigenvectors of surface-optical phonon modes in a rectangular quantum wire[J].Phys Rev B,1990,42(2):1488-1491.
[3] Wang X F,Lei X L.Polar-optic phonons and high-field electron transport in cylindrical GaAs/AlAs quantum wires[J].Phys Rev B,1994,49(7):4780-4789.
[4] Xie H J,Chen C Y,Ma B K.Bound polaron in a cylindrical quantum wire of a polar crystal[J].Phys Rev B,2000,61(7):4827-4834.
[5] Xie H J,Chen C Y,Ma B K.The bound polaron in a cylindrical quantum well wire with a finite confining potential[J].J Phys:Condens Matter,2000,12(40):8623-8640.
[6] Zhang L.Polar oscillations of interface and surface optical phonons in free-standing cylindrical quantum-well wires[J].Commun Theor Phys,2004,42(3):459-466.
[7] Zhang L,Xie H J.Interface and surface optical phonons in a free-standing GaAs/AlxGa1-xAs cylindrical quantumwell wire[J].Physica B,2005,363(1-4):146-157.
[8] Brancus D E N,Ion L.Full optical phonon spectrum and Fr9hlich Hamiltonian in wurtzite-type free-standing quantum well wires[J].Phys Rev B,2007,76(15):155304(1-12).
[9] Zhang L.Full polar optical phonon states and dispersive spectra of a wurtzite GaN/AlN rectangular quantum wire[J].Turk J Phys,2012,36:398-414.
[10] Constantinou N C,Ridley B K.Guided and interface LO phonons in cylindrical GaAs/AlxGa1-xAs quantum wires[J].Phys Rev B,1990,41(15):10627-10631.
[11] Zhu B F.Optical-phonon modes and Fr9hlich potential in one-dimensional quantum-well wires[J].Phys Rev B,1991,44(4):1926-1929.
[12] Comas F,Trallero-Giner C,Cantarero A.Optical phonons and electron-phonon interaction in quantum wires[J].Phys Rev B,1993,47(12):7602-7605.
[13] Knipp P A,Reinecke T L.Interface phonons of quantum wires[J].Phys Rev B,1992,45(16):9091-9102.
[14] Enderlein R.Optical-phonon modes of circular quantum wires[J].Phys Rev B,1993,47(4):2162-2175.
[15] Zhang L.Polar quasi-confined optical phonon modes in wurtzite quasi-one-dimensional GaN/AlxGa1-xN quantum well wires[J].Chinese Journal of Semiconductors,2006,27(10):1717-1724.
[16] Zhang L.Interface-phonon modes in quasi-one-dimensional wurtzite rectangular quantum wires[J].Commun Theor Phys,2006,46(6):1109-1112.
[17] Zhang L,Shi J J.Polar interface optical phonon modes and Fr9hlich electron-phonon interaction Hamiltonians in wurtzite quantum well wires[J].Semicond Sci Technol,2005,20(6):592-600.
[18] 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].Phys Rev B,2005,71(24):245324(1-9).
[19] Zhang L.Polar interface and surface optical vibration spectra in multi-layer wurtzite quantum wires:transfer matrix method[J].Chin Phys,2006,15(5):1101-1109.
[20] Chang I F,Mitra S S.Long wavelength optical phonons in mixed crystals[J].Adv Phys,1971,20(85):539-404.
[21] Born M,Huang K.Dynamical Theory of Crystal Lattices[M].New York:Oxford University Press,1954:82-86.
[22] Liang X X,Ban S L.Optical vibration modes and electron-phonon interaction in ternary mixed crystals of polar semiconductors[J].Chin Phys,2004,13(1):71-81.
[23] Liang X X,Yang J S.Effective-phonon approximation of polarons in ternary mixed crystals[J].Solid State Commum,1996,100(9):629-634.
[24] Adachi S.GaAs,AlAs and AlxGa1-x As material parameters for use in research and device applications[J].J Appl Phys,1985,58(3):R1-R29.
[25] Yu S,KIim K W,Bergman L,et al.Long-wavelength optical phonons in ternary nitride-based crystals[J].Phys Rev B,1998,58(23):15283-15287.
[26] Strites S,Morkoc H.GaN,AlN,and InN:A review[J].J Vac Sci Technol B,1992,10(4):1237-1266.