SEMICONDUCTOR PHYSICS

Shallow impurity states in AlxGa1-xAs cylindrical quantum wire

Zengru Zhao1, 2 and Gaofeng Wang2,

+ Author Affiliations

 Corresponding author: Wang Gaofeng, Email:gaofengwang1982@gmail.com

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Abstract: Polarons bound to a shallow Coulomb impurity center in cylindrical quantum wire is studied by a variational approach. The binding energies of the shallow impurity states in AlxGa1-xAs cylindrical quantum wire are calculated as functions of the composition x and the impurity position. It is confirmed that the binding energies are reduced obviously by the influence of the electron-phonon interaction and the binding energies are increased with increasing the composition x.

Key words: quantum wireelectron-phonon interactionimpurity states



[1]
Lin Z C, Lin S D. Lee C P. Ordering of stacked InAs/GaAs quantum-wires in InAlAs/InGaAs matrix on (100) InP substrates. Phys E, 2008, 40:512 doi: 10.1016/j.physe.2007.07.005
[2]
Wang S, Kang Y, Han C J. Transverse Stark effect in the optical absorption in a square semiconducting quantum wire. Journal of Semiconductors, 2013, 34:102001 doi: 10.1088/1674-4926/34/10/102001
[3]
Santhi M, Peter A J. The binding energy of excitons in a cylindrical quantum wire under the influence of laser field intensity. Physica E, 2010, 42:1643 doi: 10.1016/j.physe.2010.01.016
[4]
Graham A M, Corfdir P, Heiss M, et al. Exciton localization mechanisms in wurtzite/zinc-blende GaAs nanowires. Phys Rev B, 2013, 87:125304 doi: 10.1103/PhysRevB.87.125304
[5]
Zhao Z R, Liang X X. Stark effects on bound polarons in polar cylindrical quantum wires with finite confining potential. J Appl Phys, 2009, 105:083704 doi: 10.1063/1.3095509
[6]
Wang X F, Lei X L. Polar-optic phonons and high-field electron transport in cylindrical GaAs/AlAs quantum wires. Phys Rev B, 1994, 49:4780 doi: 10.1103/PhysRevB.49.4780
[7]
Li S S, Xia J B. Binding energy of a hydrogenic donor impurity in a rectangular parallelepiped-shaped quantum dot:quantum confinement and Stark effects. J Appl Phys, 2007, 101:093716 doi: 10.1063/1.2734097
[8]
Zhao C L, Cai C Y, Xiao J L. The influences of an anisotropic parabolic potential on the quantum dot qubit. Journal of Semiconductors, 2013, 34(11):112002 doi: 10.1088/1674-4926/34/11/112002
[9]
Yin J W, Li W P, Yu Y F. Properties of a polaron in a quantum dot:a squeezed-state variational approach. Journal of Semiconductors, 2013, 34(1):012001 doi: 10.1088/1674-4926/34/1/012001
[10]
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. Phys Rev B, 2005, 71:245324 doi: 10.1103/PhysRevB.71.245324
[11]
Bouhassoune M, Charrour R, Fliyou M, et al. Binding energy of shallow impurities in a polar quantum well wire. Phys B, 2001, 304:389 doi: 10.1016/S0921-4526(01)00391-X
[12]
Moukhliss S, Fliyou M, Sbai N E. Binding energy of the donor-confined LO phonon system in quantum well wire structures. Phys Status Solidi B, 1998, 206:593 doi: 10.1002/(ISSN)1521-3951
[13]
Pokatilov E P, Fomin V M, Balaban S N, et al. Impurity-bound hole polaron in a cylindrical quantum wire. Phys Status Solidi B, 1998, 210:879 doi: 10.1002/(ISSN)1521-3951
[14]
Osório F A P, Degani M H, Hipólito O. Bound impurity in GaAs-Ga1-κAlκAs quantum-well wires. Phys Rev B, 1988, 37:1402 doi: 10.1103/PhysRevB.37.1402
[15]
Xie H J, Chen B, Ma K. Bound polaron in a cylindrical quantum wire of a polar crystal. Phys Rev B, 2000, 61:4827 doi: 10.1103/PhysRevB.61.4827
[16]
Buonocore F, Ladonisi G, Ninno D, et al. Bound impurity in GaAs-Ga1-κAlκAs quantum-well wires. Phys Rev B, 2002, 65:205415 doi: 10.1103/PhysRevB.65.205415
[17]
Chen Y S, Shockley W, Reaeson G L. Lattice vibration spectra of GaAsxP1-x single crystals. Phys Rev, 1966, 151:648 doi: 10.1103/PhysRev.151.648
[18]
Bellessa J, Symonds C, Meynaud C, et al. Exciton/plasmon polaritons in GaAs/Al0.93Ga0.07As heterostructures near a metallic layer. Phys Rev B, 2008, 78:205326 doi: 10.1103/PhysRevB.78.205326
[19]
Reyes-Gomez E, Raigoza N, Oliveira L E. Effects of hydrostatic pressure and aluminum concentration on the conduction-electron g factor in GaAs-(Ga, Al)As quantum wells under in-plane magnetic fields. Phys Rev B, 2008, 77:115308 doi: 10.1103/PhysRevB.77.115308
[20]
Chang I F, Mitra S S. Long wavelength optical phonons in mixed crystals. Adv Phys, 1971, 20:359 doi: 10.1080/00018737100101271
[21]
Liang X X, Yang J S. Effective-phonon approximation of polarons in ternary mixed crystals. Solid State Commun, 1996, 100:629 doi: 10.1016/0038-1098(96)00480-2
[22]
Zhao Z R, Liang X X. On the ion-and electron-phonon interaction effects on impurity states in polar cylindrical quantum wires. J Appl Phys, 2008, 103:053704 doi: 10.1063/1.2844455
[23]
Platzman P. Ground-state energy of bound polarons. Phys Rev, 1962125:1961 doi: 10.1103/PhysRev.125.1961
[24]
Adachi S. GaAs, AlAs, and AlxGa1-xAs:material parameters for use in research and device applications. J Appl Phys, 1985, 58:R1 doi: 10.1063/1.336070
Fig. 1.  Binding energies of the impurity states with (solid lines) and without (dashed lines) phonon influence in Al$_{x}$Ga$_{1-x}$As quantum wire as a function of composition $x$ with $R$ $=$ 5, 10, 15 nm.

Fig. 2.  Binding energies of the impurity states with phonon influence in Al$_{x}$Ga$_{1-x}$As quantum wire as a function of the impurity position with $R$ $=$ 5, 10, 15 nm.

Fig. 3.  Renormalization masses of the electron by LO phonon (dashed line), both LO and IO phonons (solid line) in Al$_{x}$Ga$_{1-x}$As quantum wire as a function of composition with $R$ $=$ 5, 10, 15 nm.

[1]
Lin Z C, Lin S D. Lee C P. Ordering of stacked InAs/GaAs quantum-wires in InAlAs/InGaAs matrix on (100) InP substrates. Phys E, 2008, 40:512 doi: 10.1016/j.physe.2007.07.005
[2]
Wang S, Kang Y, Han C J. Transverse Stark effect in the optical absorption in a square semiconducting quantum wire. Journal of Semiconductors, 2013, 34:102001 doi: 10.1088/1674-4926/34/10/102001
[3]
Santhi M, Peter A J. The binding energy of excitons in a cylindrical quantum wire under the influence of laser field intensity. Physica E, 2010, 42:1643 doi: 10.1016/j.physe.2010.01.016
[4]
Graham A M, Corfdir P, Heiss M, et al. Exciton localization mechanisms in wurtzite/zinc-blende GaAs nanowires. Phys Rev B, 2013, 87:125304 doi: 10.1103/PhysRevB.87.125304
[5]
Zhao Z R, Liang X X. Stark effects on bound polarons in polar cylindrical quantum wires with finite confining potential. J Appl Phys, 2009, 105:083704 doi: 10.1063/1.3095509
[6]
Wang X F, Lei X L. Polar-optic phonons and high-field electron transport in cylindrical GaAs/AlAs quantum wires. Phys Rev B, 1994, 49:4780 doi: 10.1103/PhysRevB.49.4780
[7]
Li S S, Xia J B. Binding energy of a hydrogenic donor impurity in a rectangular parallelepiped-shaped quantum dot:quantum confinement and Stark effects. J Appl Phys, 2007, 101:093716 doi: 10.1063/1.2734097
[8]
Zhao C L, Cai C Y, Xiao J L. The influences of an anisotropic parabolic potential on the quantum dot qubit. Journal of Semiconductors, 2013, 34(11):112002 doi: 10.1088/1674-4926/34/11/112002
[9]
Yin J W, Li W P, Yu Y F. Properties of a polaron in a quantum dot:a squeezed-state variational approach. Journal of Semiconductors, 2013, 34(1):012001 doi: 10.1088/1674-4926/34/1/012001
[10]
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. Phys Rev B, 2005, 71:245324 doi: 10.1103/PhysRevB.71.245324
[11]
Bouhassoune M, Charrour R, Fliyou M, et al. Binding energy of shallow impurities in a polar quantum well wire. Phys B, 2001, 304:389 doi: 10.1016/S0921-4526(01)00391-X
[12]
Moukhliss S, Fliyou M, Sbai N E. Binding energy of the donor-confined LO phonon system in quantum well wire structures. Phys Status Solidi B, 1998, 206:593 doi: 10.1002/(ISSN)1521-3951
[13]
Pokatilov E P, Fomin V M, Balaban S N, et al. Impurity-bound hole polaron in a cylindrical quantum wire. Phys Status Solidi B, 1998, 210:879 doi: 10.1002/(ISSN)1521-3951
[14]
Osório F A P, Degani M H, Hipólito O. Bound impurity in GaAs-Ga1-κAlκAs quantum-well wires. Phys Rev B, 1988, 37:1402 doi: 10.1103/PhysRevB.37.1402
[15]
Xie H J, Chen B, Ma K. Bound polaron in a cylindrical quantum wire of a polar crystal. Phys Rev B, 2000, 61:4827 doi: 10.1103/PhysRevB.61.4827
[16]
Buonocore F, Ladonisi G, Ninno D, et al. Bound impurity in GaAs-Ga1-κAlκAs quantum-well wires. Phys Rev B, 2002, 65:205415 doi: 10.1103/PhysRevB.65.205415
[17]
Chen Y S, Shockley W, Reaeson G L. Lattice vibration spectra of GaAsxP1-x single crystals. Phys Rev, 1966, 151:648 doi: 10.1103/PhysRev.151.648
[18]
Bellessa J, Symonds C, Meynaud C, et al. Exciton/plasmon polaritons in GaAs/Al0.93Ga0.07As heterostructures near a metallic layer. Phys Rev B, 2008, 78:205326 doi: 10.1103/PhysRevB.78.205326
[19]
Reyes-Gomez E, Raigoza N, Oliveira L E. Effects of hydrostatic pressure and aluminum concentration on the conduction-electron g factor in GaAs-(Ga, Al)As quantum wells under in-plane magnetic fields. Phys Rev B, 2008, 77:115308 doi: 10.1103/PhysRevB.77.115308
[20]
Chang I F, Mitra S S. Long wavelength optical phonons in mixed crystals. Adv Phys, 1971, 20:359 doi: 10.1080/00018737100101271
[21]
Liang X X, Yang J S. Effective-phonon approximation of polarons in ternary mixed crystals. Solid State Commun, 1996, 100:629 doi: 10.1016/0038-1098(96)00480-2
[22]
Zhao Z R, Liang X X. On the ion-and electron-phonon interaction effects on impurity states in polar cylindrical quantum wires. J Appl Phys, 2008, 103:053704 doi: 10.1063/1.2844455
[23]
Platzman P. Ground-state energy of bound polarons. Phys Rev, 1962125:1961 doi: 10.1103/PhysRev.125.1961
[24]
Adachi S. GaAs, AlAs, and AlxGa1-xAs:material parameters for use in research and device applications. J Appl Phys, 1985, 58:R1 doi: 10.1063/1.336070
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    Received: 03 January 2014 Revised: 04 March 2014 Online: Published: 01 August 2014

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      Zengru Zhao, Gaofeng Wang. Shallow impurity states in AlxGa1-xAs cylindrical quantum wire[J]. Journal of Semiconductors, 2014, 35(8): 082002. doi: 10.1088/1674-4926/35/8/082002 Z R Zhao, G F Wang. Shallow impurity states in AlxGa1-xAs cylindrical quantum wire[J]. J. Semicond., 2014, 35(8): 082002. doi: 10.1088/1674-4926/35/8/082002.Export: BibTex EndNote
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      Zengru Zhao, Gaofeng Wang. Shallow impurity states in AlxGa1-xAs cylindrical quantum wire[J]. Journal of Semiconductors, 2014, 35(8): 082002. doi: 10.1088/1674-4926/35/8/082002

      Z R Zhao, G F Wang. Shallow impurity states in AlxGa1-xAs cylindrical quantum wire[J]. J. Semicond., 2014, 35(8): 082002. doi: 10.1088/1674-4926/35/8/082002.
      Export: BibTex EndNote

      Shallow impurity states in AlxGa1-xAs cylindrical quantum wire

      doi: 10.1088/1674-4926/35/8/082002
      Funds:

      the Inner Mongolia Natural Science Foundation, China 2013MS0111

      Project supported by the Inner Mongolia Natural Science Foundation, China (No. 2013MS0111) and the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region (No. NJZZ14159)

      the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region NJZZ14159

      More Information
      • Corresponding author: Wang Gaofeng, Email:gaofengwang1982@gmail.com
      • Received Date: 2014-01-03
      • Revised Date: 2014-03-04
      • Published Date: 2014-08-01

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