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Finite element method simulation of electronic and optical properties in multi-InAs/GaAs quantum dots

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Abstract

The Schrödinger equation, which describes the behaviour of an electron with a single dopant inside the system, has been constructed. It is composed of three InAs cubic quantum dots (CQDs) immersed in GaAs material under the influence of an electric field applied along the x-growth direction. The equation has been solved by the finite element method within effective mass approximation. Our investigation shows that in the absence of the electric field, the binding energy (BE) reaches its maximum value when the impurity is at the centre of the system, with two smaller peaks at the other quantum dots (QDs) and a minimum at the centre of the barriers. The BE changes considerably with the electric field, especially for large dots and barriers. Both the BE and the photoionization cross-section (PCS) can be tuned by adjusting the system's dimensions and the electric field. An increase in the dot width, barrier width along the x-axis, or the electric field results in a redshift of photoionization when the impurity is at the centre of the system. The amplitude of the PCS also changes significantly, becoming more pronounced as the dot width or electric field increases and exhibiting non-monotonic behaviour in the case of the barrier width.

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Data Availability Statement

The manuscript has associated data in a data repository. All the files with tables, figures, and codes are available. The corresponding author will provide all the files in case that they are requested.

References

  1. A. Fakkahi, M. Kirak, M. Jaouane, A. Sali, A. Ed-Dahmouny, K. El-Bakkari, R. Arraoui, The nonlinear optical rectification and second harmonic generation of a single electron confined in a multilayer spherical quantum dot. Opt. Quantum Electron. (2023). https://doi.org/10.1007/s11082-023-04730-y

    Article  Google Scholar 

  2. I. Mal, J. Jayarubi, S. Das, A.S. Sharma, A.J. Peter, D.P. Samajdar, Hydrostatic pressure dependent optoelectronic properties of InGaAsN/GaAs spherical quantum dots for laser diode applications. Phys. Status Solidi (2019). https://doi.org/10.1002/pssb.201800395

    Article  Google Scholar 

  3. A. Zounoubi, I. Zorkani, K. El Messaoudi, A. Jorio, Magnetic field effect on the polarizability of shallow donor in cylindrical quantum dot. Phys. Lett. A 312, 220–227 (2003). https://doi.org/10.1016/S0375-9601(03)00640-6

    Article  CAS  ADS  Google Scholar 

  4. A. Sali, A. Rezzouk, N. Es-Sbai, M.O. Jamil, The simultaneous effects of the wetting layer, intense laser and the conduction band non-parabolicity on the donor binding energy in a InAs/GaAs conical quantum dot using the numerical FEM. Indian J. Pure Appl. Phys. 57, 483–491 (2019)

    Google Scholar 

  5. Y. Chrafih, K. Rahmani, M. Khenfouch, I. Zorkani, GaAlAs/GaAs cubical inhomogeneous quantum dot (core/shell) under external excitations: the photoionization cross-section of donor impurity with the polaronic effect. J. Nanophotonics 14, 1 (2020). https://doi.org/10.1117/1.JNP.14.016001

    Article  Google Scholar 

  6. C.E. Soliverez, An effective Hamiltonian and time-independent perturbation theory. J. Phys. C Solid State Phys. 2, 301 (1969). https://doi.org/10.1088/0022-3719/2/12/301

    Article  Google Scholar 

  7. C.P. Hilton, W.E. Hagston, J.E. Nicholls, Variational methods for calculating exciton binding energies in quantum well structures. J. Phys. A. Math. Gen. 25, 2395–2401 (1992). https://doi.org/10.1088/0305-4470/25/8/046

    Article  CAS  ADS  Google Scholar 

  8. J.-L. Liu, J.-H. Chen, O. Voskoboynikov, A model for semiconductor quantum dot molecule based on the current spin density functional theory. Comput. Phys. Commun. 175, 575–582 (2006). https://doi.org/10.1016/j.cpc.2006.06.009

    Article  MathSciNet  CAS  ADS  Google Scholar 

  9. P.-O. Löwdin, I. Mayer, Some studies of the general Hartree-Fock method, in Advances in quantum chemistry. (Academic Press, 1992), pp.79–114

    Google Scholar 

  10. F.S. Levin, J. Shertzer, Finite-element solution of the Schrödinger equation for the helium ground state. Phys. Rev. A 32, 3285–3290 (1985). https://doi.org/10.1103/PhysRevA.32.3285

    Article  CAS  ADS  Google Scholar 

  11. M. Jaouane, A. Ed-Dahmouny, A. Fakkahi, R. Arraoui, K. El-Bakkari, H. Azmi, A. Sali, F. Ungan, Investigation of nonlinear optical rectification within multilayer wurtzite InGaN/GaN cylindrical quantum dots under the impact of temperature and pressure. Opt. Mater. 147, 114711 (2024). https://doi.org/10.1016/j.optmat.2023.114711

    Article  CAS  Google Scholar 

  12. C. Heyn, C.A. Duque, Donor impurity related optical and electronic properties of cylindrical GaAs-AlGaAs quantum dots under tilted electric and magnetic fields. Sci. Rep. 10, 9155 (2020). https://doi.org/10.1038/s41598-020-65862-9

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  13. A. Sali, M. Fliyou, H. Satori, H. Loumrhari, Photoionization of impurities in quantum-well wires. Phys. Status Solidi 211, 661–670 (1999). https://doi.org/10.1002/(SICI)1521-3951(199902)211:2%3c661::AID-PSSB661%3e3.3.CO;2-H

    Article  CAS  Google Scholar 

  14. A. Sali, M. Fliyou, H. Satori, H. Loumrhari, The effect of a strong magnetic field on the binding energy and the photoionization process in quantum-well wires. J. Phys. Chem. Solids 64, 31–41 (2003). https://doi.org/10.1016/S0022-3697(02)00205-6

    Article  CAS  ADS  Google Scholar 

  15. A. Sali, H. Satori, M. Fliyou, H. Loumrhari, The photoionization cross-section of impurities in quantum dots. Phys. Status Solidi 232, 209–219 (2002). https://doi.org/10.1002/1521-3951(200208)232:2%3c209::AID-PSSB209%3e3.0.CO;2-O

    Article  CAS  Google Scholar 

  16. M. Jaouane, A. Sali, A. Fakkahi, R. Arraoui, F. Ungan, The effects of temperature and pressure on the optical properties of a donor impurity in (In, Ga)N/GaN multilayer cylindrical quantum dots. Micro Nanostruct. 163, 107146 (2022). https://doi.org/10.1016/j.spmi.2021.107146

    Article  CAS  Google Scholar 

  17. A. Fakkahi, A. Sali, M. Jaouane, R. Arraoui, A. Ed-Dahmouny, Study of photoionization cross section and binding energy of shallow donor impurity in multilayered spherical quantum dot. Phys. E Low Dimens. Syst. Nanostruct. 143, 115351 (2022). https://doi.org/10.1016/j.physe.2022.115351

    Article  CAS  Google Scholar 

  18. V. Holovatsky, M. Chubrey, O. Voitsekhivska, Effect of electric field on photoionisation cross-section of impurity in multilayered quantum dot. Superlattices Microstruct. 145, 106642 (2020). https://doi.org/10.1016/j.spmi.2020.106642

    Article  CAS  Google Scholar 

  19. V.V. Mitin, D.I. Sementsov, N.Z. Vagidov, Quantum Mechanics for Nanostructures (Cambridge University Press, 2010)

    Book  Google Scholar 

  20. G. Safarpour, M. Barati, A. Zamani, E. Niknam, Binding energy and optical properties of an off-center hydrogenic donor impurity in a spherical quantum dot placed at the center of a cylindrical nano-wire. J. Lumin. 145, 990–996 (2014). https://doi.org/10.1016/j.jlumin.2013.09.002

    Article  CAS  Google Scholar 

  21. M.G. Barseghyan, H.M. Baghramyan, D. Laroze, J. Bragard, A.A. Kirakosyan, Impurity-related intraband absorption in coupled quantum dot-ring structure under lateral electric field. Phys. E Low Dimens. Syst. Nanostruct. 74, 421–425 (2015). https://doi.org/10.1016/j.physe.2015.07.032

    Article  CAS  ADS  Google Scholar 

  22. R. Arraoui, A. Sali, A. Ed-Dahmouny, K. El-Bakkari, M. Jaouane, A. Fakkahi, The spatial electric field effect on the impurity binding energy and self-polarization in a double quantum dot. Eur. Phys. J. Plus. 137, 979 (2022). https://doi.org/10.1140/epjp/s13360-022-03193-6

    Article  CAS  Google Scholar 

  23. M. Jaouane, A. Fakkahi, A. Ed-Dahmouny, K. El-Bakkari, A.T. Tuzemen, R. Arraoui, A. Sali, F. Ungan, Modeling and simulation of the influence of quantum dots density on solar cell properties. Eur. Phys. J. Plus 138, 148 (2023). https://doi.org/10.1140/epjp/s13360-023-03736-5

    Article  CAS  Google Scholar 

  24. R. Ram-Mohan, Finite Element and Boundary Element Applications in Quantum Mechanics (Oxford University Press, 2002)

    Book  Google Scholar 

  25. A. Sali, H. Satori, The combined effect of pressure and temperature on the impurity binding energy in a cubic quantum dot using the FEM simulation. Superlattices Microstruct. 69, 38–52 (2014). https://doi.org/10.1016/j.spmi.2014.01.011

    Article  CAS  ADS  Google Scholar 

  26. A. Bera, M. Ghosh, Simultaneous influence of hydrostatic pressure and temperature on binding energy of impurity doped quantum dots in presence of noise. J. Alloys Compd. 695, 3054–3060 (2017). https://doi.org/10.1016/j.jallcom.2016.11.345

    Article  CAS  Google Scholar 

  27. A. Ghosh, A. Bera, M. Ghosh, Influence of binding energy on dipole moment, polarizability and self-polarization effect of impurity doped quantum dots: role of noise. Chem. Phys. Lett. 678, 119–122 (2017). https://doi.org/10.1016/j.cplett.2017.04.042

    Article  CAS  ADS  Google Scholar 

  28. D. González-Morales, A. Valencia, A. Díaz-Nuñez, Magnetic susceptibility of doped quantum dots: interplay between binding energy and noise. Biointerface Res. Appl. Chem. 10, 5376–5381 (2020). https://doi.org/10.33263/BRIAC103.376381

    Article  Google Scholar 

  29. S. Yılmaz, H. Şafak, R. Şahingoz, M. Erol, Photoionization cross section and refractive-index change of hydrogenic impurities in a CdS-SiO2 spherical quantum dot. Open Phys. (2010). https://doi.org/10.2478/s11534-009-0115-8

    Article  Google Scholar 

  30. A. Imran, J. Jiang, D. Eric, M.N. Zahid, M. Yousaf, Z.H. Shah, Optical properties of InAs/GaAs quantum dot superlattice structures. Res. Phys. 9, 297–302 (2018). https://doi.org/10.1016/j.rinp.2018.02.016

    Article  Google Scholar 

  31. L.-Z. Liu, J.-J. Liu, Hydrogenic-donor impurity states in coupled quantum disks in the presence of a magnetic field. J. Appl. Phys. (2007). https://doi.org/10.1063/1.2764232

    Article  Google Scholar 

  32. M. Jaouane, A. Sali, A. Ezzarfi, A. Fakkahi, R. Arraoui, Study of hydrostatic pressure, electric and magnetic fields effects on the donor binding energy in multilayer cylindrical quantum dots. Phys. E Low Dimens. Syst. Nanostruct. 127, 114543 (2021). https://doi.org/10.1016/j.physe.2020.114543

    Article  CAS  Google Scholar 

  33. E. Sadeghi, E. Naghdi, Effect of electric and magnetic fields on impurity binding energy in zinc-blend symmetric InGaN/GaN multiple quantum dots. Nano Converg. 1, 25 (2014). https://doi.org/10.1186/s40580-014-0025-3

    Article  CAS  PubMed  Google Scholar 

  34. A. Ed-Dahmouny, A. Sali, N. Es-Sbai, R. Arraoui, M. Jaouane, A. Fakkahi, K. El-Bakkari, C.A. Duque, Combined effects of hydrostatic pressure and electric field on the donor binding energy, polarizability, and photoionization cross-section in double GaAs/GaAlAs quantum dots. Eur. Phys. J. B. 95, 136 (2022). https://doi.org/10.1140/epjb/s10051-022-00400-2

    Article  CAS  ADS  Google Scholar 

  35. H. Azmi, N. Amri, K. El-Bakkari, M. Jaouane, A. Fakkahi, A. Sali, R. Arraoui, A. Ed-Dahmouny, Hydrostatic pressure, electric field, non-parabolicity and polaronic mass effects on the donor binding energy in a semimagnetic double quantum well. Eur. Phys. J. Plus. 138, 952 (2023). https://doi.org/10.1140/epjp/s13360-023-04603-z

    Article  CAS  Google Scholar 

  36. L. Belamkadem, O. Mommadi, R. Boussetta, S. Chouef, M. Chnafi, A. El Moussaouy, J.A. Vinasco, D. Laroze, C.A. Duque, C. Kenfack-Sadem, R.M. Keumo Tsiaze, F.C. Fobasso Mbognou, A. Kerkour El-Miad, The intensity and direction of the electric field effects on off-center shallow-donor impurity binding energy in wedge-shaped cylindrical quantum dots. Thin Solid Films 757, 139396 (2022). https://doi.org/10.1016/j.tsf.2022.139396

    Article  CAS  ADS  Google Scholar 

  37. L. Shi, Z.W. Yan, M.W. Meng, Binding energy and photoionization cross section of hydrogenic impurities in elliptic cylindrical core/shell quantum dots under a non-axial electric field. Superlattices Microstruct. 150, 106818 (2021). https://doi.org/10.1016/j.spmi.2021.106818

    Article  CAS  Google Scholar 

  38. R. Arraoui, A. Sali, A. Ed-Dahmouny, M. Jaouane, A. Fakkahi, Polaronic mass and non-parabolicity effects on the photoionization cross section of an impurity in a double quantum dot. Superlattices Microstruct. 159, 200 (2021). https://doi.org/10.1016/j.spmi.2021.107049

    Article  CAS  Google Scholar 

  39. M. Jaouane, A. Sali, A. Fakkahi, R. Arraoui, A. Ed-Dahmouny, F. Ungan, Photoionization cross section of donor single dopant in multilayer quantum dots under pressure and temperature effects. Phys. E Low Dimens. Syst. Nanostruct. 144, 115450 (2022). https://doi.org/10.1016/j.physe.2022.115450

    Article  CAS  Google Scholar 

  40. L.M. Burileanu, Photoionization cross-section of donor impurity in spherical quantum dots under electric and intense laser fields. J. Lumin. 145, 684–689 (2014). https://doi.org/10.1016/j.jlumin.2013.08.043

    Article  CAS  Google Scholar 

  41. M. Jaouane, K. El-Bakkari, E.B. Al, A. Sali, F. Ungan, Linear and nonlinear optical properties of CdSe/ZnTe core/shell nanostructures with screened modified Kratzer potential. Eur. Phys. J. Plus. 138, 319 (2023). https://doi.org/10.1140/epjp/s13360-023-03934-1

    Article  CAS  Google Scholar 

  42. M. Jaouane, A. Sali, E. Kasapoglu, F. Ungan, Tuning of nonlinear optical characteristics of a cylindrical quantum dot by external fields and structure parameters. Philos. Mag. 103, 693–711 (2023). https://doi.org/10.1080/14786435.2023.2171499

    Article  CAS  ADS  Google Scholar 

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Authors and Affiliations

  1. Laboratory of Solid-State Physics (LPS), Department of Physics, Faculty of Science Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, 1796, Fez, Morocco

    M. Jaouane, R. Arraoui, A. Fakkahi, K. El-Bakkari, H. Azmi & A. Sali

  2. SIGER Laboratory, Faculty of Sciences and Technology, Sidi Mohamed Ben Abdellah University, 2202, Fez, Morocco

    A. Ed-Dahmouny

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  1. M. Jaouane
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Contributions

The contributions of the authors are as follows: MJ worked on numerical computations, programming codes, and outcomes analysis. RA participated in formal analysis and developed the theory. AS proposed the problem, coordinated with coauthors, and revised the manuscript. AE-D, AF, KE-B, and HA focused on the scientific analysis and text production.

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Correspondence to M. Jaouane.

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Jaouane, M., Arraoui, R., Ed-Dahmouny, A. et al. Finite element method simulation of electronic and optical properties in multi-InAs/GaAs quantum dots. Eur. Phys. J. Plus 139, 222 (2024). https://doi.org/10.1140/epjp/s13360-024-05029-x

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