Skip to main content
SpringerLink
Log in

The spatial electric field effect on the impurity binding energy and self-polarization in a double quantum dot

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

This paper provides a theoretical investigation of the binding energy \(E_{{\text{b}}}\) and self-polarization of a hydrogenic shallow donor impurity located in a \({\text{GaAs}} - {\text{Ga}}_{1 - x} {\text{Al}}_{x} {\text{As}}\) double quantum dot under the influence of the spatial electric field. The variational approach within the effective mass approximation is used to solve the Schrödinger equation. The main contributions reveal that the effect of the spatial electric field on the impurity binding energy is less presented compared to the applied electric field in the x-direction. Also, the binding energy and the self-polarization are significantly affected by the spatial electric field strength \(\left( F \right)\), the impurity position \(\left( {x_{0} } \right)\), and the barrier width. In the absence of the spatial electric field, the self-polarization is an odd function with respect to the barrier center having two small peaks. Moreover, our findings show that for different impurity locations, the angles of the spatial electric field components θ and φ affect dramatically the binding energy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data Availability Statement

The corresponding author will provide all the files in case they are requested. This manuscript has associated data in a data repository. [Authors’ comment: The comments in this section are summaries of the findings reached from all of the research included in the ‘Results and Discussions’ section and do not arise from earlier work, thus no citations are required.]

References

  1. A. Tartakovskii, Quantum Dots: Optics, Electron Transport and Future Applications (2012). https://doi.org/10.1017/CBO9780511998331

  2. 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  ADS  Google Scholar 

  3. A. Montes, C.A. Duque, N. Porras-Montenegro, Density of shallow-donor impurity states in rectangular cross section GaAs quantum-well wires under applied electric field. J. Phys. Condens. Matter. 10, 5351–5358 (1998). https://doi.org/10.1088/0953-8984/10/24/012

    Article  ADS  Google Scholar 

  4. A. Sali, J. Kharbach, A. Rezzouk, M. Ouazzani Jamil, The effects of polaronic mass and conduction band non-parabolicity on a donor binding energy under the simultaneous effect of pressure and temperature basing on the numerical FEM in a spherical quantum dot. Superlattices Microstruct. 104, 93–103 (2017). https://doi.org/10.1016/j.spmi.2017.02.014

    Article  ADS  Google Scholar 

  5. S.O. Oluwatobi, E.H.M. Sakho, P. Sundararajan, L. Thabang, Ternary Quantum Dots Synthesis, Properties, and Applications. Woodhead Publishing Series in Electronic and Optical Materials (Woodhead Publishing, Sawston, 2021)

    Google Scholar 

  6. R. Hanson, L.P. Kouwenhoven, J.R. Petta, S. Tarucha, L.M.K. Vandersypen, Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007). https://doi.org/10.1103/RevModPhys.79.1217

    Article  ADS  Google Scholar 

  7. F. Abualnaja, W. He, M. Jones, Z. Durrani, Device fabrication for investigating Maxwell’s Demon at room-temperature using double quantum dot transistors in silicon. Micro Nano Eng. 14, 100114 (2022). https://doi.org/10.1016/j.mne.2022.100114

    Article  Google Scholar 

  8. 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  Google Scholar 

  9. C. Heyn, C.A. Duque, Donor impurity related optical and electronic properties of cylindrical GaAs-AlxGa1−x As quantum dots under tilted electric and magnetic fields. Sci. Rep. 10, 1–18 (2020). https://doi.org/10.1038/s41598-020-65862-9

    Article  Google Scholar 

  10. A. Fakkahi, A. Sali, M. Jaouane, R. Arraoui, Hydrostatic pressure, temperature, and electric field effects on the hydrogenic impurity binding energy in a multilayered spherical quantum dot. Appl. Phys. A Mater. Sci. Process. 127, 1–9 (2021). https://doi.org/10.1007/s00339-021-05055-x

    Article  Google Scholar 

  11. 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 

  12. E. Kasapoglu, F. Ungan, H. Sari, I. Sökmen, M.E. Mora-Ramos, C.A. Duque, Donor impurity states and related optical responses in triangular quantum dots under applied electric field. Superlattices Microstruct. 73, 171–184 (2014). https://doi.org/10.1016/j.spmi.2014.05.023

    Article  ADS  Google Scholar 

  13. E. Kasapoglu, F. Ungan, C.A. Duque, U. Yesilgul, M.E. Mora-Ramos, H. Sari, I. Sökmen, The effects of the electric and magnetic fields on the nonlinear optical properties in the step-like asymmetric quantum well. Phys. E Low-Dimens. Syst. Nanostruct. 61, 107–110 (2014). https://doi.org/10.1016/j.physe.2014.03.024

    Article  ADS  Google Scholar 

  14. H.O. Oyoko, N. Porras-Montenegro, S.Y. López, C.A. Duque, Comparative study of the hydrostatic pressure and temperature effects on the impurity-related optical properties in single and double GaAs-Ga1-xAlxAs quantum wells. Phys. Status Solidi Curr. Top. Solid State Phys. 4, 298–300 (2007). https://doi.org/10.1002/pssc.200673259

    Article  ADS  Google Scholar 

  15. O. Akankan, I. Erdogan, H. Akbas, Spatial electric field effect on the self-polarization in GaAs/AlAs square quantum-well wires. Phys. E Low-Dimens. Syst. Nanostruct. 35, 217–221 (2006). https://doi.org/10.1016/j.physe.2006.07.035

    Article  ADS  Google Scholar 

  16. E. Sadeghi, Study of the effect of spatial electric field on the energy levels in a GaAs/AlAs cubic quantum dot. Phys. E Low-Dimens. Syst. Nanostruct. 41, 365–367 (2009). https://doi.org/10.1016/j.physe.2008.08.056

    Article  ADS  Google Scholar 

  17. B. Vaseghi, G. Rezaei, V. Azizi, F. Taghizadeh, Simultaneous effects of spatial electric field and spinorbit interaction on the cubic quantum dot energy levels. Phys. E Low-Dimens. Syst. Nanostruct. 43, 1080–1083 (2011). https://doi.org/10.1016/j.physe.2011.01.004

    Article  ADS  Google Scholar 

  18. R.L. Restrepo, G.L. Miranda, C.A. Duque, M.E. Mora-Ramos, Simultaneous effects of hydrostatic pressure and applied electric field on the impurity-related self-polarization in GaAs/Ga1-xAlxAs multiple quantum wells. J. Lumin. 131, 1016–1021 (2011). https://doi.org/10.1016/j.jlumin.2011.01.014

    Article  Google Scholar 

  19. H.O. Oyoko, C.A. Duque, N. Porras-Montenegro, Uniaxial stress dependence of the binding energy of shallow donor impurities in GaAs-(Ga, AI)As quantum dots. J. Appl. Phys. 90, 819–823 (2001). https://doi.org/10.1063/1.1372976

    Article  ADS  Google Scholar 

  20. S. Adachi, GaAs, AlAs, and AlxGa1-xAs. J. Appl. Phys. (1985). https://doi.org/10.1063/1.336070

    Article  Google Scholar 

  21. S. Ves, K. Strössner, C.K. Kim, M. Cardona, Dependence of the direct energy gap of GaP on hydrostatic pressure. Solid State Commun. 55, 327–331 (1985). https://doi.org/10.1016/0038-1098(85)90618-0

    Article  ADS  Google Scholar 

  22. O. Akankan, A study of the effect of spatial electric field on the binding energy and polarization of a donor impurity in a GaAs/AlAs tetragonal quantum dot (TQD). Superlattices Microstruct. 55, 45–52 (2013). https://doi.org/10.1016/j.spmi.2012.11.014

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  24. J.J. Liu, M. Shen, S.W. Wang, The influence of compressive stress on shallow-donor impurity states in symmetric GaAs-Ga1-xAlxAs double quantum dots. J. Appl. Phys. 101, 1–6 (2007). https://doi.org/10.1063/1.2717584

    Article  Google Scholar 

  25. 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, 107049 (2021). https://doi.org/10.1016/j.spmi.2021.107049

    Article  Google Scholar 

  26. E. Iqraoun, A. Sali, K. El-Bakkari, M.E. Mora-Ramos, C.A. Duque, Binding energy, polarizability, and diamagnetic response of shallow donor impurity in zinc blende GaN quantum dots. Superlattices Microstruct. 107142, 1 (2022). https://doi.org/10.1016/j.spmi.2021.107142

    Article  Google Scholar 

  27. E. Iqraoun, A. Sali, A. Rezzouk, E. Feddi, F. Dujardin, M.E. Mora-Ramos, C.A. Duque, Donor impurity-related photoionization cross section in GaAs cone-like quantum dots under applied electric field. Philos. Mag. 97, 1445–1463 (2017). https://doi.org/10.1080/14786435.2017.1302613

    Article  ADS  Google Scholar 

  28. S.E. Okan, I. Erdoǧan, H. Akbaş, Anomalous polarization in an electric field and self-polarization in GaAs/AlAs quantum wells and quantum well wires. Phys. E Low-Dimens. Syst. Nanostruct. 21, 91–95 (2004). https://doi.org/10.1016/j.physe.2003.08.072

    Article  ADS  Google Scholar 

  29. G.X. Wang, L.L. Zhang, H. Wei, External electric field effect on shallow donor impurity states in zinc-blende InxGa1- xN/GaN symmetric coupled quantum dots. Adv. Condens. Matter Phys. (2017). https://doi.org/10.1155/2017/5652763

    Article  Google Scholar 

  30. K. El-Bakkari, A. Sali, E. Iqraoun, A. Ezzarfi, Polaron and conduction band non-parabolicity effects on the binding energy, diamagnetic susceptibility and polarizability of an impurity in quantum rings. Superlattices Microstruct. 148, 106729 (2020). https://doi.org/10.1016/j.spmi.2020.106729

    Article  Google Scholar 

  31. 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  Google Scholar 

  32. C.M. Duque, M.G. Barseghyan, C.A. Duque, Donor impurity in vertically-coupled quantum-dots under hydrostatic pressure and applied electric field. Eur. Phys. J. B. 73, 309–319 (2010). https://doi.org/10.1140/epjb/e2009-00433-7

    Article  ADS  Google Scholar 

  33. C. Xia, Z. Zeng, S. Wei, J. Wei, Shallow-donor impurity in vertical-stacked InGaN/GaN multiple-quantum wells: electric field effect. Phys. E Low-Dimens. Syst. Nanostruct. 43, 458–461 (2010). https://doi.org/10.1016/j.physe.2010.08.033

    Article  ADS  Google Scholar 

  34. G. Wang, X. Duan, W. Chen, The hydrogenic donor impurity binding energy of Quantum dot in the presence of an electric field, in Proceedings—2012 International Conference on Computer Science, Electronic Information Engineering. ICCSEE 2012, vol. 2 (2012), pp. 23–26. https://doi.org/10.1109/ICCSEE.2012.423

  35. E. Kasapoglu, The hydrostatic pressure and temperature effects on donor impurities in GaAs/Ga1—xAlxAs double quantum well under the external fields. Phys. Lett. Sect. A Gen. At. Solid State Phys. 373, 140–143 (2008). https://doi.org/10.1016/j.physleta.2008.10.080

    Article  Google Scholar 

  36. C. Xia, Z. Zeng, S. Wei, Barrier width dependence of the donor binding energy of hydrogenic impurity in wurtzite InGaN/GaN quantum dot. J. Appl. Phys. 106, 094301 (2009). https://doi.org/10.1063/1.3245335

    Article  ADS  Google Scholar 

  37. M. Ulas, I. Erdogan, E. Cicek, S.S. Dalgic, Self polarization in GaAs-(Ga, Al)As quantum well wires: electric field and geometrical effects. Phys. E Low-Dimens. Syst. Nanostruct. 25, 515–520 (2005). https://doi.org/10.1016/j.physe.2004.08.100

    Article  ADS  Google Scholar 

  38. I. Erdogan, S. Yavuz, Laser field effect on self-polarization of a donor impurity in a finite Ga1-xAlxAs/GaAs quantum well. Phys. B Condens. Matter. 609, 412728 (2021). https://doi.org/10.1016/j.physb.2020.412728

    Article  Google Scholar 

  39. I. Erdogan, O. Akankan, H. Akbas, Effects of hydrostatic pressure on the self-polarization in GaAs/Ga1-xAlxAs quantum wells under the electric field. Phys. E Low-Dimens. Syst. Nanostruct. 42, 136–140 (2009). https://doi.org/10.1016/j.physe.2009.09.014

    Google Scholar 

  40. E. Cicek, A.I. Mese, B. Ozkapi, I. Erdogan, Combined effects of the hydrostatic pressure and temperature on the self-polarization in a finite quantum well under laser field. Superlattices Microstruct. 155, 106904 (2021). https://doi.org/10.1016/j.spmi.2021.106904

    Article  Google Scholar 

  41. G. Rezaei, S. Mousavi, E. Sadeghi, External electric field and hydrostatic pressure effects on the binding energy and self-polarization of an off-center hydrogenic impurity confined in a GaAs/AlGaAs square quantum well wire. Phys. B Condens. Matter. 407, 2637–2641 (2012). https://doi.org/10.1016/j.physb.2012.04.014

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Solid Physics Laboratory, Department of Physics, Faculty of Sciences Dhar El Mehraz, Sidi Mohamed Ben Abdellah University, Dhar El Mahraz, B.P. 1796, Fez, Morocco

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

  2. Faculty of Sciences and Technique, Sidi Mohammed Ben Abdellah University, Route d’Imouzzer, B.P. 2202, Fez, Morocco

    A. Ed-Dahmouny

Authors
  1. R. Arraoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Sali
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Ed-Dahmouny
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. El-Bakkari
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Jaouane
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. A. Fakkahi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Arraoui.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arraoui, R., Sali, A., Ed-Dahmouny, A. et al. 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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-03193-6

Search

Navigation