J. Semicond. > Volume 36 > Issue 3 > Article Number: 032003

Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field

Yun Kang , Sheng Wang , and Xianli Li

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Abstract: Using the finite element method, we investigate the lowest and first few excited state energies in a two-dimensional GaAs quantum ring (QR) with a hydrogenic donor impurity and effective mass approximation under a uniform magnetic field perpendicular to the ring plane. We study in detail the dependence of the energy spectrum with different angular momentum on the inner radius, the outer radius and width of the QR, the magnetic field and impurity position. The results reveal that the electron energies increase with the inner radius while decrease with the outer radius and width of the QR; for a fixed ring, the magnetic field induces the increase of the electron energies. Moreover, the existence of impurity reduces energy levels, and the energy levels depend highly on the impurity position, which decreases as the impurity is far away from the center of the QR. Also, the dependence of the angular momentum on the energy spectrum is analyzed in detail.

Key words: quantum ringhydrogenic donor impuritymagnetic fieldelectron energy states

Abstract: Using the finite element method, we investigate the lowest and first few excited state energies in a two-dimensional GaAs quantum ring (QR) with a hydrogenic donor impurity and effective mass approximation under a uniform magnetic field perpendicular to the ring plane. We study in detail the dependence of the energy spectrum with different angular momentum on the inner radius, the outer radius and width of the QR, the magnetic field and impurity position. The results reveal that the electron energies increase with the inner radius while decrease with the outer radius and width of the QR; for a fixed ring, the magnetic field induces the increase of the electron energies. Moreover, the existence of impurity reduces energy levels, and the energy levels depend highly on the impurity position, which decreases as the impurity is far away from the center of the QR. Also, the dependence of the angular momentum on the energy spectrum is analyzed in detail.

Key words: quantum ringhydrogenic donor impuritymagnetic fieldelectron energy states



References:

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[1]

Sidor Y, Partoens B, Peeters F M. Exciton in a quantum wire in the presence of parallel and perpendicular magnetic fields[J]. Phys Rev B, 2005, 71: 165323.

[2]

Villamil P, Cabra C, Porras-Montenegro N. Polaron effects on the energy of a hydrogenic donor impurity in GaAs—(Ga, Al)As quantum-well wires[J]. Microelectron J, 2008, 39: 466.

[3]

Perez-Merchancano S T, Franco R, Silva-Valencia J. Impurity states in a spherical GaAs—Ga1-xAlxAs quantum dots: effects of hydrostatic pressure[J]. Microelectron J, 2008, 39: 383.

[4]

Boz F K, Aktas S. Magnetic field effect on the binding energy of a hydrogenic impurity in coaxial GaAs/AlxGa1-xAs quantum well wires[J]. Superlattices and Microstructures, 2005, 37: 281.

[5]

Xia C X, Jiang F C, Wei S Y. Hydrogenic impurity in zinc-blende GaN/AlGaN quantum dot[J]. Microelectron J, 2007, 38: 663.

[6]

Wang S, Wei G Z, Han Y. Stark effect dependence on hydrogenic impurities in GaAs parabolic quantum-well wires[J]. Commun Theory Phys, 2009, 52: 953.

[7]

Wang S, Wei G Z, Yi G Y. Binding energies of hydrogenic impurities on-center and off-center in cylindrical quantum dots under electric and magnetic fields[J]. Int J Mod Phys B, 2010, 24: 4293.

[8]

Peter A J. Hydrogenic impurities in cylindrical quantum wires in the presence of a magnetic field[J]. Physica E, 2007, 39: 115.

[9]

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]. J Appl Phys, 2007, 101: 93716.

[10]

Zounoubi A, Zorkani I, Messaoudi K E. Magnetic field effect on the polarizability of shallow donor in cylindrical quantum dot[J]. Phys Lett A, 2003, 312: 220.

[11]

Manaselyan A K, Kirakosyan A A. Effect of the dielectric-constant mismatch and magnetic field on the binding energy of hydrogenic impurities in a spherical quantum dot[J]. Physica E (Amsterdam), 2004, 22: 825.

[12]

Manaselyan A K, Kirakosyan A A. Barrier penetration in Kane type semiconductor nanostructures[J]. Physica E (Amsterdam), 2005, 28: 452.

[13]

Mano T, Kuroda T, Sanguinetti S. Self-assembly of concentric quantum double rings[J]. Nano Lett, 2005, 5: 425.

[14]

Kazaryan E M, Shahnazaryan V A, Sarkisyan H A. Optical interband absorption and Stark shift in a quantum ring on a sphere[J]. Opt Commun, 2004, 315: 253.

[15]

Rodríguez-Prada F, García L F, Mikhailov I D. One-electron quantum ring of non-uniform thickness in magneticfield[J]. Physica E, 2014, 56: 393.

[16]

Dahan P, Malits P. Effect of symmetry on the electronic properties of arbitrarily shaped quantum rings in a magneticfield[J]. Physica E, 2014, 56: 165.

[17]

Wang G X, Zhang P. Hydrogenic impurity binding energy in self-assembled GaAs/Ga1-xAlxAs quantum rings[J]. J Appl Phys, 2008, 103: 063713.

[18]

Lee C M, Li J Q, Ruan W Y. Energy spectra of a magnetic quantum ring with an off-center impurity[J]. Commun Theory Phys, 2006, 45: 737.

[19]

Bruno-Alfonso A, Latgé A. Semiconductor quantum rings: shallow-donor levels[J]. Phys Rev B, 2000, 61: 15887.

[20]

Li H T, Liu L Z, Liu J J. Electronic states of elliptical quantum rings subjected to a magnetic field[J]. Chin Phys Lett, 2008, 11: 4101.

[21]

Jia B Y, Yu Z Y, Liu Y M. Donor-bound electron states in a two-dimensional quantum ring under uniform magnetic field[J]. Chin Phys B, 2011, 6: 067301.

[22]

Wang N, Liu D, Kong X J. Biexciton energies in concentric double quantum rings[J]. J Appl Phys, 2013, 113: 053714.

[23]

Jin M G, Xie W F, Chen T R. Photoionization cross section in a two-dimensional quantum ring with a donor impurity[J]. Superlattices and Microstructures, 2013, 62: 59.

[24]

Sato N, Iwata S. Application of finite-element method to the two-dimensional Schrodinger equation[J]. Journal of Computational Chemistry, 1988, 9: 222.

[25]

Joseph P, George R. Accuracy of a hybrid finite-element method for solving a scattering Schrödinger equation[J]. Phys Rev E, 2012, 86: 066707.

[26]

Amado M, Lima R P A, Santander C G. Donor-bound electrons in quantum rings under magnetic fields[J]. Phys Rev B, 2007, 76: 073312.

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Y Kang, S Wang, X L Li. Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field[J]. J. Semicond., 2015, 36(3): 032003. doi: 10.1088/1674-4926/36/3/032003.

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Manuscript received: 06 August 2014 Manuscript revised: Online: Published: 01 March 2015

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