A theoretical study of the effects of uniaxial stress and spatial dielectric functions on the density of states of shallow donor impurities in a GaAs quantum well dot of circular geometry

Authors

  • Fredrick Omboga Oketch Technical University of Mombasa
  • Hannington Odhiambo Oyoko Pwani University

DOI:

https://doi.org/10.31349/RevMexFis.70.030501

Keywords:

Density of impurity states; GaAs quantum well dot; spatial dielectric function; applied uniaxial stress

Abstract

In the present work, we have carried out a comparative study of the effects of uniaxial stress and spatial dielectric functions on the density of impurity states (DOIS) of shallow donor impurities in a GaAs  quantum well dot of circular cross-section. Using a trial wave function in the effective mass approximation, we carried out calculations for a range of binding energies of hydrogenic (dielectric constant) and non-hydrogenic (spatial dielectric functions) donors for various applied uniaxial stress and for different uniaxial lengths of the quantum dot. Our results show that, for a constant axial length of the quantum dot and constant uniaxial stress, the DOIS for the donor impurity is markedly enhanced for the non-hydrogenic donor impurity over that for purely hydrogenic donor impurity. At constant axial length, the applied uniaxial stress enhances the DOIS in both cases. The density of impurity states has also been studied for a constant applied uniaxial stress for different axial lengths of the quantum dot. Here, again, the DOIS increases with increasing axial length of the quantum dot. In fact, the enhanced DOIS is observed throughout the range of binding energies considered. These results show that not only does the DOIS vary with the applied uniaxial stress and spatial dielectric functions they are also different for various axial lengths of the quantum dot. These findings indicate that is  important to take into account the effect of applied uniaxial stress and spatial dielectric functions when performing experimental studies of electronic, optical and transport properties of such nanostructures as quantum dots.

References

P. Harrison, and A. Valavanis, Quantum wells, wires and dots: Theoretical and Computational Physics of Semiconductor Nanostructures (John Wiley & Sons, Mroziewicz, B., 2016)

G. Bastard, Hydrogenic impurity states in a quantum well: A simple model, Phys. Rev. B 24 (1981) 4714, https://doi.org/10.1103/PhysRevB.24.4714

W. T. Masselink, Yia-Chung Chang, and H. Morkoc, Binding energies of acceptors in GaAs-AlxGa1-xAs quantum wells, Phys. Rev. B 28 (1983) 7373, https://doi.org/10.1103/PhysRevB.28.7373

P. Csavinszky and A. M. Elabsy, Dielectric response to a donor ion in a Ga1-xAlxAs-GaAs-Ga1-xAlxAs quantum well of infinite depth, Phys. Rev. B 32 (1985) 6498, https://doi.org/10.1103/PhysRevB.32.6498

J. W. Brown and H. N. Spector, Hydrogen impurities in quantum well wires, J. Appl. Phys. 59 (1986) 1179, https://doi.org/10.1063/1.336555

P. Csavinszky and H. Oyoko, Binding energy of on-axis hydrogenic and nonhydrogenic donors in a GaAs/Ga1-xAlxAs quantum-well wire of circularcross section, Phys. Rev. B 43 (1991) 9262, https://doi.org/10.1103/PhysRevB.43.9262

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

H. Odhiambo Oyoko, C. A. Duque, and N. Porras-Montenegro, Theoretical study of the effect of applied stress on the binding energy of a donor impurity in GaAs quantum well dot within an infinite potential barrier, Indian J. Pure and Appl. Phys. 42 (2004) 908, http://nopr.niscpr.res.in/handle/123456789/9648

A. Tiutiunnyk et al., Electronic structure and optical properties of triangular GaAs/AlGaAs quantum dots: Exciton and impurity states, Phys. B: Condens. Matter 484 (2016) 95, https://doi.org/10.1016/j.physb.2015.12.045

A. M. Elabsy, Hydrostatic pressure dependence of binding energies for donors in quantum well heterostructures, Phys. Scr. 48 (1993) 376, https://doi.org/10.1088/0031-8949/48/3/019

A. L. Morales, A. Montes, S. Y. Lopez, and C. A. Duque, Simultaneous effects of hydrostatic stress and an electric field on donors in a GaAs-(Ga, Al)As quantum well, J. Phys.: Condens. Matter 14 (2002) 987, https://doi.org/10.1088/0953-8984/14/5/304

S. Y. Lopez, N. Porras-Montenegro, and C. A. Duque, Binding energy and density of shallow impurity states in GaAs- (Ga,Al)As quantum wells: effects of an applied hydrostatic stress, Semicond. Sci. Technol. 18 (2003) 718, https://doi.org/10.1088/0268-1242/18/7/322

N. Raigoza, A. L. Morales, A. Montes, N. Porras-Montenegro, and C. A. Duque, Stress effects on shallow-donor impurity states in symmetrical GaAs/AlxGa1-xAs double quantum wells, Phys. Rev. B 69 (2004) 045323, https://doi.org/10.1103/PhysRevB.69.045323

N. Raigoza, A. L. Morales, and C. A. Duque, Effects of hydrostatic pressure on donor states in symmetrical GaAsGa0.7Al0.3As double quantum wells, Phys. B: Cond. Matt. 363 (2005) 262, https://doi.org/10.1016/j.physb.2005.03.031

J. D. Correa, O. Cepeda-Giraldo, N. Porras-Montenegro, and C. A. Duque, Hydrostatic pressure effects on the donor impurity-related photoionization cross-section in cylindricalshaped GaAs/GaAlAs quantum well wires, Phys. Stat. Sol. (b) 241 (2004) 3311, https://doi.org/10.1002/pssb.200405225

E. Kasapoglu, H. Sari, M. Gunes, and I. Sökmen, The effect of hydrostatic pressure on optical transitions in quantumwell wires, Phys. B: Cond. Matt. 353 (2004) 345, https://doi.org/10.1016/j.physb.2004.10.021

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

A. J. Peter, The effect of hydrostatic pressure on binding energy of impurity states in spherical quantum dots, Phys. E: Low-dim. Syst. and Nanostructures 28 (2005) 225, https://doi.org/10.1016/j.physe.2005.03.018

C. A. Duque, N. Porras-Montenegro, Z. Barticevic, M. Pacheco, and L. E. Oliveira, Electron-hole transitions in selfassembled InAs/GaAs quantum dots: Effects of applied magnetic fields and hydrostatic pressure, Microelectronics Journal 36 (2005) 231, https://doi.org/10.1016/j.mejo.2005.04.001

H. Oyoko, Effect of Hermanson’s spatial dielectric function on donor impurity binding energy in a cylindrical cross-sectional GaAs/GaAlAs quantum well wires on infinite length, Indian J. Pure and Appl. Phys. 38 (2000) 512, http://nopr.niscpr.res.in/handle/123456789/26911

F. Oketch and H. Oyoko, A theoretical study of variation of photoionization cross section of donor impurities in a GaAs quantum dot of cylindrical geometry with incident photon frequency, donor location along the dot axis and applied uniaxial stress, Rev. Mex. Fis. 66 (2020) 35, https://doi.org/10.31349/revmexfis.66.35

F. Oketch and H. Oyoko, A theoretical study of the effects of Thomas-Fermi and Hermanson’s dielectric functions and temperature on photoionization crosssection of a donor impurity in GaAs quantum dots of circular and rectangular crosssections, Eur. Phys. J. B 95 (2022) 44, https://doi.org/10.1140/epjb/s10051-022-00301-4

F. Oketch, H. Oyoko and G. Amolo, A Study of the Effect of Hermanson’s Spatial Dielectric Function on the Photoionization Cross-Section of a Hydrogenic and a non-Hydrogenic Donor Impurity in a GaAs Quantum Dot of Cylindrical Geometry in the Region of Finite and Infinite Barrier Potentials, J. Korean Phys. Soc. 73 (2018) 928, https://doi.org/10.3938/jkps.73.928

J. D. Correa, N. Porras-Montenegro and C. A. Duque, Donorrelated photoionization cross-section of GaAs-(Ga, Al)As quantum dots: hydrostatic pressure effects, Phys. stat. sol. (b) 241 (2004) 2440, https://doi.org/10.1002/pssb.200404908

B. Welber, M. Cardona, C. K. Kim, and S. Rodriguez, Dependence of the direct energy gap of GaAs on hydrostatic pressure, Phys. Rev. B 12 (1975) 5729, https://doi.org/10.1103/PhysRevB.12.5729

D. E. Aspnes, GaAs lower conduction-band minima: Ordering and properties, Phys. Rev. B 14 (1976) 5331, https://doi.org/10.1103/PhysRevB.14.5331

S. Adachi, GaAs, AlAs, and AlxGa1-xAs: Material parameters for use in research and device applications, J. Appl. Phys. 58 (1985) R1, https://doi.org/10.1063/1.336070

M. E. Mora-Ramos, S. Y. Lopez and C. A. Duque, Γ − X mixing in GaAs- Ga1-xAlxAs quantum wells under hydrostatic pressure, Eur. Phys. J. B 62 (2008) 257, https://doi.org/10.1140/epjb/e2008-00161-6

H. Odhiambo Oyoko, The Effect of Uniaxial Stress on the Density of States of Shallow Donor Impurities in GaAs Quantum Wells, Phys. Scr. 66 (2002) 94, https://doi.org/10.1238/Physica.Regular.066a00094

P. Csavinszky and H. Oyoko, Binding energies of on-axis hydrogenic and nonhydrogenic donors in GaAs/Ga1-x AlxAs, Journal of Mathematical Chemistry 9 (1992) 197, https://doi.org/10.1007/BF01165147

H. Odhiambo Oyoko, N. Porras-Montenegro, S. Y. Lopez and C. A. Duque, Comparative study of the hydrostatic pressure and temperature effects on the impurity-related optical properties in single and double GaAs-Ga1-x AlxAs quantum wells, Phys. stat. sol(c) 4 (2007) 298, https://doi.org/10.1002/pssc.200673259

A. Sivakami, M. Mahendran, Hydrostatic pressure and conduction band non-parabolicity effects on the impurity binding energy in a spherical quantum dot, Phys. B: Cond. Matt. 405 (2010) 1403, https://doi.org/10.1016/j.physb.2009.12.008

A. Sivakami, V. Gayathri, Hydrostatic pressure and temperature dependence of dielectric mismatch effect on the impurity binding energy in a spherical quantum dot, Superlatt. Microstruct. 58 (2013) 218, https://doi.org/10.1016/j.spmi.2013.03.002

X. Hu et al., Photoluminescence of InAs/GaAs quantum dots under direct twophoton excitation, Sci. Rep. 10 (2020) 10930, https://doi.org/10.1038/s41598-020-67961-z

S. Zhu, Y. Song, X. Zhao, J. Shao, J. Zang, and B. Yang, The photoluminescence mechanism in carbon dots (graphene quantum dots, carbon nanodots, and polymer dots): Current state and future perspective, Nano Res. 8 (2015) 355, https://doi.org/10.1007/s12274-014-0644-3

F. Liu et al., Highly Luminescent Phase-Stable CsPbI3 Perovskite Quantum Dots Achieving Near 100% Absolute Photoluminescence Quantum Yield, ACS Nano 11 (2017) 10373, https://doi.org/10.1021/acsnano.7b05442

Downloads

Published

2024-05-01

How to Cite

[1]
F. O. Oketch and Hannington Odhiambo Oyoko, “A theoretical study of the effects of uniaxial stress and spatial dielectric functions on the density of states of shallow donor impurities in a GaAs quantum well dot of circular geometry”, Rev. Mex. Fís., vol. 70, no. 3 May-Jun, pp. 030501 1–, May 2024.