Binding energy in tuned quantum dots under an external magnetic field
Subject Areas : Journal of Optoelectronical NanostructuresMojtaba Servatkhah 1 , pariya Hashemi 2 , Rahele Pourmand 3
1 - Department of Physics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
2 - Department of Physics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
3 - Department of physics, Estahban higher educational center, Estahban, Iran
Keywords: Impurity, Quantum Dot, Binding energy,
Abstract :
The binding energy of a tuned quantum dot (QD) under an external magnetic field have been theoretically investigated. For this goal, the Schrödinger equation is analytically solved without and with considering the impurity term and the energy eigenvalues and eigenfunctions are analytically derived. Then, the binding of the tuned QD was studied considering the various parameters. We found that (i) the binding energy decrease with rising the potential range. (ii) The binding energy reduces with enhancing the potential depth. The depth and stretching range of the confinement potential have important effects on the binding energy of the tuned QD.The binding energy of a tuned quantum dot (QD) under an external magnetic field have been theoretically investigated. For this goal, the Schrödinger equation is analytically solved without and with considering the impurity term and the energy eigenvalues and eigenfunctions are analytically derived. Then, the binding of the tuned QD was studied considering the various parameters. We found that (i) the binding energy decrease with rising the potential range. (ii) The binding energy reduces with enhancing the potential depth. The depth and stretching range of the confinement potential have important effects on the binding energy of the tuned QD.
[1] Khanonkin I, Bauer S, Mikhelashvili V, Eyal O, Lorke M, Jahnke F, Reith
Maier J. P, Eisenstein G, On the principle operation of tunneling injection
quantum dot lasers. Prog Quant Electron 81 (2022) 100362.
https://doi.org/10.1016/j.pquantelec.2021.100362.
[2] Dusanowski L, Nawrath C, Portalupi S. L, Jetter M, Huber T, Klembt S
Michler P, Hofling S, Optical charge injection and coherent control of a
quantum-dot spin-qubit emitting at telecom wavelengths. Nature Commun 13
(2022) 748.
https://doi.org/10.1038/s41467-022-28328-2
[3] Ali A. A, Shaer A, Elsaid M, Simultaneous effects of Rashba, magnetic field
and impurity on the magnetization and magnetic susceptibility of a GaAs
semiconductor quantum ring. J Magn Magn Matter 556 (2022) 169435.
https://doi.org/10.1016/j.jmmm.2022.169435
[4] Thakur T, Szafran B, Aharonov-Bohm oscillations in phosphorene quantum
rings: Mass anisotropy compensation by confinement potential. Phys Rev B
105 (2022) 165309.
https://doi.org/10.1103/PhysRevB.105.165309
[5] Rastegar Sedehi H. R, Khordad R, Bahramiyan H, Optical properties and
diamagnetic susceptibility of a hexagonal quantum dot: impurity effect. Op
Quant Electron 53 (2021) 264.
https://doi.org/10.1007/s11082-021-02927-7
[6] Avazzadeh Z, Bahramiyan H, Khordad R, Mohammadi S. A, Diamagnetic
susceptibility of an off-center hydrogenic donor in pyramid-like and cone-like
quantum dots. Eur Phys J Plus 131 (2016) 121.
https://doi.org/10.1140/epjp/i2016-16121-8
[7] Nasrallah S, Sfina N, Said M, Electronic properties of intersubband transition
in (CdS/ZnSe)/BeTe quantum wells. Eur Phys J B 47 (2005) 167-170.
https://doi.org/10.1140/epjb/e2005-00323-0
[8] Imamura K, Sugiyama Y, Nakata Y, Muto S, Yokoyama N, New optical
memory structure using self-assembled InAs quantum dots. Jpn J Appl Phys
34 (1995) L1445.
https://doi.org/10.1143/JJAP.34.L1445.
[9] E. Leobandung, L. Guo, S. Y. Chou, Single hole quantum dot transistors in
silicon. Appl. Phys. Lett. 67 (1995) 2338.
https://doi.org/10.1063/1.114337
[10] Durante F, Alves P, Karunasiri G, Hanson N, Byloos M, Liu H. C, Bezinger
A, Buchanan M, NIR, NWIR and LWIR quantum well infrared photodetector
using interband and intersubband transitions. Infrared Phys Technol 50 (2007)
182-186.
https://doi.org/10.1016/j.infrared.2006.10.021
[11] Khordad R, Optical properties of quantum wires: Rashba effect and external
magnetic field. J Lumin 134 (2013) 201.
https://doi.org/10.1016/j.jlumin.2012.08.047
[12] Lu L, Xie W, Hassanabadi H, The effects of intense laser on nonlinear
properties of shallow donor impurities in quantum dots with the Woods-Saxon
potential. J Lumin 131 (2011) 2538.
https://doi.org/10.1016/j.jlumin.2011.06.051
[13] Hashemi P, Servatkhah M, Pourmand R, The effect of Rashba spin-orbit
interaction on optical far-infrared transition of tuned quantum dot/ring
systems. Opt Quant Electron 53 (2021) 567.
https://doi.org/10.1007/s11082-021-03173-7
[14] Khordad R, Rastegar Sedehi H. R, Electrocaloric effect in quantum dots using
the non-extensive formalism. Opt Quant Electron 53 (2021) 264.
https://doi.org/10.1007/s11082-022-03902-6
[15] Ghanbari A, Khordad R, Bound states and optical properties for Derjaguin-
Landau-Verweij-Overbook potential. Opt Quant Electron 53 (2021) 152.
https://doi.org/10.1007/s11082-021-02797-z
[16] Sayrac M, Effects of applied external fields on the nonlinear optical
rectification, second, and third-harmonic generation in an asymmetrical semi
exponential quantum well. Opt Quant Electron 54 (2022) 52.
https://doi.org/10.1007/s11082-021-03425-6
[17] Holovatsky V, Chubrey M, Voitsekhivska O, Effect of electric field on
photoionization cross-section of impurity in multilayered quantum dot.
Superlatt Microstrut (2022) 107137.
[18] Sayari A, Servatkhah M, Pourmand R, Effects of electron-phonon interaction
and pressure on optical properties of wedge-shaped quantum dots. Physica B
628 (2022) 413631.
https://doi.org/10.1016/j.physb.2021.413631
[19] Servatkhah M, Pourmand R, Optical properties of a two-dimensional GaAs
quantum dot under strain and magnetic field. Eur Phys J Plus 135 (2020) 754.
https://doi.org/10.1140/epjp/s13360-020-00773-2
[20] Khordad R, Vaseghi B, Effects temperature, pressure and spin-orbit
interaction simultaneously on third harmonic generation of wedge-shaped
quantum dots. Chin J Phys 59 (2019) 473-480.
https://doi.org/10.1016/j.cjph.2019.04.005
[21] Kirak M, Magnetic and thermodynamic properties of GaAs quantum dot
confined by parabolic-inverse square plus Gaussian potential. J Magn Magn
Mater 536 (2021) 167481.
https://doi.org/10.1016/j.jmmm.2020.167481
[22] Khordad R, Bahramiyan H, Int J Mod Phys C 24 (2013) 1350041.
[23] Hayek L. A, Sandouqa A. S, Energy and binding energy of donor impurity in
quantum dot with Gaussian confinement. Superlatt Microstruct 85 (2015) 216.
https://doi.org/10.1016/j.spmi.2015.05.025
[24] Khordad R, Effect of temperature on the binding energy of excited states in a
ridge quantum wire. Physica E 41 (2009) 543-547.
https://doi.org/10.1016/j.physe.2008.10.004
[25] Ungan F, Bahar M. K, Pal S, Romas M. E. M, Electron-related nonlinear
optical properties of cylindrical quantum dot with the Rosen-Morse axial
potential. Commun Theor Phys 72 (2020) 075505.
https://doi.org/10.1088/1572-9494/ab8a1d
[26] Firoozi A, Mohammadi A, Khordad R, Jalali T, Q-BOR-FDTD method for
solving Schrodinger equation for rotationally symmetric nanostructures with
hydrogenic impurity. Phys Script 97 (2022) 025802.
https://doi.org/10.1088/1402-4896/ac48ac .
[27] Bose C, Perturbation calculation of impurity states in spherical quantum dots
with parabolic confinement. Physica E 4 (1999) 180-184.
https://doi.org/10.1016/S1386-9477(99)00010-7
[28] Ikhdair S. M, Sever R, Approximate eigenvalue and eigenfunction solutions
for the generalized Hulthen potential with any angular momentum. J Math
Chem 42 (2007) 461-471.
https://doi.org/10.1007/s10910-006-9115-8
[29] Bose C, Sarkar C. K, Perturbation calculation of donor states in spherical
quantum dots. Solid State Electron 42 (1998) 1661-1663.
https://doi.org/10.1016/S0038-1101(98)00126-9
[30] Elward J. M, Chakraborty A, Effect of dot size on exciton binding energy and
electron-hole recombination probability in CdSe quantum dots. J Chem
Theory Comput 9 (2013) 4351-4359.
https://doi.org/10.1021/ct400485s
[31] Merchancano S. T. P, Marinez L. E. B, The binding energy of donor impurities
in GaAs quantum dots under the pressure effect. Rev Mex de Fis 53 (2007)
470-474.
[32] Mikhail I. F. I, El Sayed S. B. A, Exact and variational calculations of a
hydrogenic impurity binding energy in a multilayered spherical quantum dot.
Physica E 43 (2011) 1371.
https://doi.org/10.1016/j.physe.2011.03.007
[33] Hashemi P, ServatkhahM, Pourmand R, Opt Commun 506 (2022) 127551.
[34] Jahan K. L, Boda A, Shankar I. V, Raju Ch. N, Chatterjee A, Magnetic field
effect on the energy levels on an exciton in a GaAs quantum dot: Application
for excitonic lasers. Sci Report 8 (2018) 5073.
https://doi.org/10.1038/s41598-018-23348-9
[35] Ghanbari A, Khordad R, Taghizadeh F, Influence of Coulomb term on thermal
properties of fluorine. Chem Phys Lett 801 (2022) 139725.
https://doi.org/10.1016/j.cplett.2022.139725
[36] Sadeghi E, Naghdi E, Effect of electric and magnetic field on impurity binding
energy in zinc-blend symmetric InGaN/GaN multiple quantum dots. Nano
Converg 1 (2014) 25. https://doi.org/10.1186/s40580-014-0025-3.
[37] Chen T, Xie W, Liang S, Optical and electronic properties of a two-
dimensional quantum dot with an impurity. J Lumin 139 (2013) 64-68.
https://doi.org/10.1016/j.jlumin.2013.02.030
[38] Dong S. H, Lozada-Cassou M, Yu J, Angeles F. J, Rivera A. L, Hidden
symmetries and thermodynamic properties for a harmonic oscillator plus an
inverse square potential. Int J Quant Chem 107 (2007) 366-371.
https://doi.org/10.1002/qua.21103
[39] Mikhail I. F. I, Shafee A. M, Optical absorption in a disk-shaped quantum dot
in the presence of an impurity. Physica B 507 (2017) 142.
https://doi.org/10.1016/j.physb.2016.11.027
[40] Ghanbari A, Khordad R, Taghizadeh F, Nasirizadeh I, Edet C. O, Ali N,
Impurity effect on thermal properties of tuned quantum dot/ring systems.
Chem Phys Lett 806 (2022) 140000.
https://doi.org/10.1016/j.cplett.2022.140000
[41] Pal S, Ghosh M, Duque C. A, Impurity related optical properties in tuned
quantum dot/ring systems. Philos Mag 99 (2019) 2457.
https://doi.org/10.1080/14786435.2019.1619949.