Skip to main content
Log in

The effect of impurity position and doping concentration on the binding energies and total optical absorption coefficients in a \({\delta }\)-doped quantum well

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

Abstract

In this present work, for different impurity position and ionized doping concentrations, we have theoretically investigated the linear, third-order nonlinear, and total optical absorption coefficients corresponding to the \((1\rightarrow 2)\) intersubband transitions between the ground and first-excited conduction band states in a single \(\delta \)-doped GaAs well, with and without the presence of a donor impurity. Impurity binding energies were calculated using the effective-mass and parabolic band approximations within a variational scheme. The linear, third-order nonlinear, and total optical absorption coefficients for the intersubband transitions are calculated within the compact density matrix approach. The obtained results show that adding an impurity positioned at the symmetry center of the well, as well as the increase in the ionized donor concentrations, shifts the total optical absorption coefficients to higher photon energies. However, the off-center positions of impurities together with the varying ionized donor concentrations lead to blue or red shifts in relation to the values of binding energies. The results in this study may be useful for the design and applications of the devices based on the \(\delta \)-doped structures.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability Statement

This manuscript has associated data in a data repository. [Authors comment: All data, figures and the program are available. The corresponding author will provide all files upon request.]

References

  1. G. Bastard, Hydrogenic impurity states in a quantum well. Surf. Sci. 113, 165–169 (1982)

    Article  ADS  Google Scholar 

  2. R.L. Greene, K.K. Bajaj, Energy levels of hydrogenic impurity states in GaAs-Ga1-xAlxAs quantum well structures. Solid State Commun. 45, 825–829 (1983)

    Article  ADS  Google Scholar 

  3. E.C. Niculescu, Donor impurity in a finite parabolic quantum well. Phys. Lett. A 213, 85–88 (1996)

    Article  ADS  Google Scholar 

  4. E.C. Niculescu, L.M. Burileanu, A. Radu, Density of impurity states of shallow donors in a quantum well under intense laser field. Superlattices Microstruct. 44, 173–182 (2008)

    Article  ADS  Google Scholar 

  5. S. Baskoutas, A.F. Terzis, Binding energy of hydrogenic impurity states in an inverse parabolic quantum well under static external fields. Eur. Phys. J. B 69, 237–244 (2009)

    Article  ADS  Google Scholar 

  6. M.G. Barseghyan, A. Hakimyfard, S.Y. Lopez, C.A. Duque, A.A. Kirakosyan, Hydrostatic pressure, temperature and electric field effects on donor binding energy in Poschl-Teller quantum well. Phys. E 43, 529–533 (2010)

    Article  Google Scholar 

  7. V. Akimov, V. Tulupenko, C.A. Duque, A.L. Morales, R. Demediuk, A. Tiutiunnyk, D. Laroze, V. Kovalov, D. Sushchenko, Background impurities and a delta-doped QW Part I: center doping. Semicond. Sci. Technol. 34, 125009 (2019)

    Article  ADS  Google Scholar 

  8. M.E. Mora-Ramos, L.M. Gaggero-Sager, C.A. Duque, Binding energy of a donor impurity in GaAs \(\delta \)-doped systems under electric and magnetic fields, and hydrostatic pressure. Phys. E 44, 1335–1341 (2012)

    Article  Google Scholar 

  9. O. Oubram, O. Navarro, L.M. Gaggero-Sager, J.C. Martínez-Orozco, I. Rodriguez-Vargas, The hydrostatic pressure effects on intersubband optical absorption of n-type \(\delta \)-doped quantum well in GaAs. Solid State Sci. 14, 440–444 (2012)

    Article  ADS  Google Scholar 

  10. H. Dakhlaoui, S. Almansour, E. Algrafy, Effect of Si \(\delta \)-doped layer position on optical absorption in GaAs quantum well under hydrostatic pressure. Superlattice. Microst. 77, 196–208 (2015)

    Article  ADS  Google Scholar 

  11. K.A. Rodriguez-Magdaleno, J.C. Martinez-Orozco, I. Rodriguez-Vargas, M.E. Mora-Ramos, C.A. Duque, High-pressure effects on the intersubband optical absorption coefficient and relative refractive index change in an asymmetric double \(\delta \)- doped GaAs quantum well. Phys. status solidi B 252, 683–688 (2015)

    Article  ADS  Google Scholar 

  12. J.G. Rojas-Briseno, J.C. Martinez-Orozco, I. Rodriguez-Vargas, M.E. Mora-Ramos, C.A. Duque, Nonlinear absorption coefficient and relative refraction index change for an asymmetrical double \(\delta \)-doped quantum well in GaAs with a Schottky barrier potential. Phys. B 424, 13–19 (2013)

    Article  ADS  Google Scholar 

  13. H. Noverola-Gamas, L.M. Gaggero-Sagerz, O. Oubram, Optical absorption coefficient in n-type double \(\delta \)-doped layers GaAs quantum wells. Int. J. Modern Phys. B 33(1950215), 1–11 (2019)

    Google Scholar 

  14. E. Ozturk, Y. Ozdemir, Linear and nonlinear intersubband optical absorption coefficient and refractive index change in n-type \(\delta \)-doped GaAs structure. Opt. Commun. 294, 361–367 (2013)

    Article  ADS  Google Scholar 

  15. E. Ozturk, Nonlinear intersubband absorption and refractive index change in n-type \(\delta \)-doped GaAs for different donor distributions. Eur. Phys. J. Plus 130(1), 1–11 (2015)

    Article  Google Scholar 

  16. D. Ahn, Intersubband transitions in a \(\delta \)-doped semiconductor with an applied electric field: Exact solutions. Phys. Rev. B 48, 7981–7985 (1993)

    Article  ADS  Google Scholar 

  17. J.C. Martinez-Orozco, K.A. Rodriguez-Magdaleno, J.R. Suarez-Lopez, C.A. Duque, R.L. Restrepo, Absorption Coefficient and Relative Refractive Index Change for a double \(\delta \)-doped GaAs MIGFET-like structure: Electric and Magnetic field effects. Superlattices Microstruct. 92, 166–173 (2016)

    Article  ADS  Google Scholar 

  18. E. Kasapoglu, S. Sakiroglu, I. Sokmen, R.L. Restrepo, M.E. Mora-Ramos, C.A. Duque, The effects of the electric and intense laser field on the binding energies of donor impurity states (1s and 2p\(\pm \)) and optical absorption between the related states in an asymmetric parabolic quantum well. Opt. Mater. 60, 318–323 (2016)

    Article  ADS  Google Scholar 

  19. E.B. Al, E. Kasapoglu, S. Sakiroglu, C.A. Duque, I. Sokmen, Binding energy of donor impurity states and optical absorption in the Tietz-Hua quantum well under an applied electric field. J. Mol. Struct. 1157, 288–291 (2018)

    Article  ADS  Google Scholar 

  20. A.L. Vartanian, A.L. Asatryan, L.A. Vardanyan, Influence of image charges on the impurity-related optical properties of near-surface quantum wells under a transverse electric field. Physi. E Low-dimensional Syst. Nanostruct. 113, 115–120 (2019)

    Article  ADS  Google Scholar 

  21. G. Weber, Density of states and optical-absorption spectra of shallow impurities in quantum wells under the influence of a longitudinal electric field. Phys. Rev. B 41, 10043–10048 (1990)

    Article  ADS  Google Scholar 

  22. H.O. Oyoko, N. Porras-Montenegro, S.Y. Lopez, 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. Stat. Sol. 4, 298–300 (2007)

    Google Scholar 

  23. L.E. Oliveira, R. Perez-Alvarez, Optical-absorption spectra associated with impurities in a GaAs-(Ga, Al)As quantum well. Phys. Rev. B 40, 10460–10468 (1989)

    Article  ADS  Google Scholar 

  24. N. Raigoza, A.L. Morales, C.A. Duque, Infinite potential barrier and hydrostatic pressure effects on impurity-related optical absorption spectra in gaas double quantum wells. Braz. J. Phys. 36, 350–353 (2006)

    Article  ADS  Google Scholar 

  25. R.L. Restrepo, A.L. Morales, J.C. Martínez-Orozco, H.M. Baghramyan, M.G. Barseghyan, M.E. Mora-Ramos, C.A. Duque, Impurity-related nonlinear optical properties in delta-doped quantum rings: Electric field effects. Phys. B Phys. Condens. Matter 453, 140–145 (2014)

    Article  ADS  Google Scholar 

  26. L. Ioriatti, Thomas-Fermi theory of \(\delta \)-doped semiconductor structures: Exact analytical results in the high-density limit Phys. Rev. B 41, 8340–8344 (1990)

    Article  Google Scholar 

  27. A. Blom, M.A. Odnoblyudov, I.N. Yassievich, K.-A. Chao, Donor states in modulation-doped SiÕSiGe heterostructures. Phys. Rev. B 68(165338), 1–16 (2003)

    Google Scholar 

  28. F. Ungan, E. Kasapoglu, H. Sari, I. Sökmen, Inter-sub-band transitions and binding energies of donor impurities in a modulation-doped quantum well in the presence of electric field. Superlattices Microstruct. 46, 864–871 (2009)

    Article  ADS  Google Scholar 

  29. A.L. Saraiva, A. Baena, M.J. Calderón, B. Koiller, Theory of one and two donors in silicon. J. Phys. Condens. Matter 27, 154208 (2015)

    Article  ADS  Google Scholar 

  30. H. Yildirim, M. Tomak, Nonlinear optical properties of a Pöschl-Teller quantum well. Phys. Rev. B 72(115340), 1–6 (2005)

    Google Scholar 

  31. A. Keshavarz, M.J. Karimi, Linear and nonlinear intersubband optical absorption in symmetric double semi-parabolic quantum wells. Phys. Lett. A 374, 2675–2680 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aysevil Salman Durmuşlar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Salman Durmuşlar, A., Turkoglu, A., Mora-Ramos, M.E. et al. The effect of impurity position and doping concentration on the binding energies and total optical absorption coefficients in a \({\delta }\)-doped quantum well. Eur. Phys. J. Plus 136, 372 (2021). https://doi.org/10.1140/epjp/s13360-021-01370-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-01370-7

Navigation