Study the energy states and absorption coefficients of quantum dots and quantum anti-dots with hydrogenic impurity under the applied magnetic field

Document Type : Articles


1 Department of Physics, Faculty of Sciences, Shiraz Branch, Islamic Azad University, Shiraz, Iran

2 Department of Physics, Lamerd Higher Education Center, Lamerd, Iran


In this work, the effect of magnetic field on
electronic spectra and absorption coefficient of πΊπ‘Žπ΄π‘ /
πΊπ‘Ž1−π‘₯ 𝐴𝑙π‘₯𝐴𝑠 spherical quantum dot (QD) and
πΊπ‘Ž1−π‘₯ 𝐴𝑙π‘₯𝐴𝑠/πΊπ‘Žπ΄π‘  spherical quantum anti-dot (QAD)
with hydrogenic impurity are reported both theoretically
and numerically. The theoretical results which are
obtained based on perturbation theory are in agreement
with numerical results, which are obtained by using the
finite difference method. Using numerical solutions,
energy eigenvalues and eigenfunctions of the Schrödinger
equation in these structures are obtained. The effects of
the magnetic field on1s→2p0 absorption coefficient and
also on 1s and 2p energy levels of the QD and the QAD
have been investigated. The wave functions and energies
of an electron in these spherical systems, have been
studied. The results clearly show that the energy levels
changes and absorption coefficients in the QD and QAD
models are significantly different. It is also observed
some new degeneracies are appeared in the QAD model
under the applied magnetic field.


Y. Liu, H. Xie, Y. Xing, Optical vibration modes in multi-layer quantum dots of polar ternary mixed crystals, Physica E, 121 (2020) 114124. Available:
[2] A. Ghadimi, M. Ahmadzadeh, Effect of Variation of Specifications of Quantum Well and Contact Length on Performance of Inp-Based Vertical Cavity Surface Emitting Laser (VCSEL), Journal of Optoelectronical Nanostructures, 5(1) (2020) 19–34.
[3] E. Kasapoglu, H. Sari, I. Sökmen, J.A. Vinasco, D. Laroze, C.A. Duque, Effects of intense laser field and position dependent effective mass in Razavy quantum wells and quantum dots, Physica E, 126 (2021) 114461.
[4] M. Servatkhah, Study of RbCl quantum pseudo-dot qubits using Shannon and Laplace entropies, Optical and Quantum Electronics, 52 (2020) 126. Available:
[5] F. Rahimi, T. Ghaffary, Y. Naimi, H. Khajehazad, Efect of magnetic feld on energy states and optical properties of quantum dots and quantum antidots, Optical and Quantum Electronics, 53(47) (2021) 1–16.
[6] R. Betancourt-Riera, R. Betancourt-Riera, L.A. Ferrer-Moreno, A.D. Sañu-Ginarte, Theory of electron Raman scattering in a semiconductor core/shell quantum well wire, Physica B, 563 (2019) 93–100. Available:
[7] Y. Naimi, J. Vahedi, M. R. Soltani, Effect of position-dependent effective mass on optical properties of spherical nanostructures, Optical and Quantum Electronics, 47 (2015) 2947-2956.
R. Yahyazadeh, Z. Hashempour, Numerical Modeling of Electronic and Electrical Characteristics of 𝐴𝑙0.3πΊπ‘Ž0.7𝑁/πΊπ‘Žπ‘ Multiple Quantum Well Solar Cells, Journal of Optoelectronical Nanostructures, 5(3) (2020) 81–101. Available:
[9] H. Bahramiyan, M. Servatkhah, Second and third harmonic generation of a hexagonal pyramid quantum dot: impurity position effect, Optical and Quantum Electronics, 47 (2015) 2747-2758. Avai`lable:
[10] S. Chaudhuri, Two-electron quantum dot in a magnetic field: Analytic solution for finite potential model, Physica E, 128 (2021) 114571.
[11] Y. Naimi, Refractive index changes of a donor impurity in spherical nanostructures: Effects of hydrostatic pressure and temperature, Phys. B, 428 (2013) 43–47.
[12] H. Bahramiyan, S. Bagheri, Linear and nonlinear optical properties of a modified Gaussian quantum dot: pressure, temperature and impurity effect, journal of optoelectronical nanostructures, 3 (3) (2018) 79-100.
[13] L. StevanoviΔ‡, N. FilipoviΔ‡, V. PavloviΔ‡, Effect of magnetic field on absorption coefficients, refractive index changes and group index of spherical quantum dot with hydrogenic impurity, Journal of Luminescence, Optical Materials, 91 (2019) 62–69.
[14] F. Rahimi, T. Ghaffary, Y. Naimi, H. Khajehazad, Study of the Spin-Orbit Interaction Effects on Energy Levels and the Absorption Coefficients of Spherical Quantum Dot and Quantum Anti-Dot under the Magnetic Field, journal of optoelectronical nanostructures, 6 (2) (2021) 55-74. Available:
[15] M. Rezvani Jalal, M. Habibi, Simulation of Direct Pumping of Quantum Dots in a Quantum Dot Laser, journal of optoelectronical nanostructures, 2 (2) (2017) 61-69.
[16] S. Sakiroglu, D. Gul Kilic, U. Yesilgul, F. Ungan, E. Kasapoglu, H. Sari, I. Sokmen, Intense laser field effects on the third-harmonic generation in a quantum pseudodot system, Physica B, 521 (2017) 215–220.
[17] F. Hakimian, M.R. Shayesteh, M.R. Moslemi, Proposal for Modeling of FWM Efficiency of QD-SOA Based on the Pump/Probe Measurement Technique, journal of optoelectronical nanostructures, 5 (4) (2020) 49-65.
[18] R. Khordad, M. Servatkhah, Study of entanglement entropy and exchange coupling in two-electron coupled quantum dots, Optical and Quantum Electronics, 49 (2017) 217.
[19] I. Karabulut, H. S ¸afak, M. Tomak, Excitonic effects on the nonlinear optical properties of small quantum dots, J. Phys. D: Appl. Phys, 41 (2008) 155104.
[20] G.V.B. de Souza, A. Bruno-Alfonso, Finite-difference calculation of donor energy levels in a spherical quantum dot subject to a magnetic field, Physica E, 66 (2015) 128–132. Available:
[21] 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, Physica E, 127 (2021) 114543.
[22] K.L. Jahan, A. Boda, I.V. Shankar, Ch. N. Raju, A. Chatterjee, Magnetic field effect on the energy levels of an exciton in a GaAs quantum dot: Application for excitonic lasers, Sci Rep, 8 (2018) 5073. Available:
S. M. Bilankohi, M. Ebrahimzadeh, T. Ghaffary, Study of the properties of Au/Ag core/shell nanoparticles and its application, Indian Journal of Science and Technology, 8 (2015) 31-33.
[24] K. Khordad, Temperature effect on the threshold frequency of absorption in a quantum pseudodot, Physica, B 406 (2011) 620-623.
[25] M. Choubani, R.B. Mahrsia, L. Bouzaiene, H. Maaref, Nonlinear optical rectification in vertically coupled InAs/GaAs quantum dots under electromagnetic fields, pressure and temperature effects, J. Luminesc, 144 (2013) 158-162.
Available: [26] H. Khajehazad, T. Ghaffary, M. Ebrahimzadeh, Microwave Absorption Properties of Fe2O3/Paraffin Wax Nanocomposite, Asian J. Chem., 25(13) 7651-7652, (2013).
[27] F. Rahmani, J. Hasanzadeh, Investigation of the Third-Order Nonlinear Optical Susceptibilities and Nonlinear Refractive Index In Pbs/Cdse/Cds Spherical Quantum Dot, journal of optoelectronical nanostructures, 3 (1) (2018) 65-78.
[28] X.F. Yan, Q. Chen, W. Pei, J.Z. Peng, Magnetic field dependence of the electronic and optical properties of silicene quantum dots, Solid State Communications, 327 (2021) 114219.
[29] Y. Naimi, A.R. Jafari, Optical properties of quantum dots versus quantum antidots: Effects of hydrostatic pressure and temperature, Journal of Computational Electronics, 13 (2014) 666-672. Available:
[30] E.B. Al, E. Kasapoglu, S. Sakiroglu, H. Sari, I. Sokmen, C.A. Duque,
Binding energies and optical absorption of donor impurities in spherical quantum dot under applied magnetic field, Physica E, 119 (2020) 114011.
[31] B. ÇakΔ±r, Y. Yakar, A. Özmen, Investigation of Magnetic Field Effects on Binding Energies in Spherical Quantum Dot with Finite Confinement Potential, Chemical Physics Letters, 684 (2017) 250–256.
[32] A. Abramowitz, I. Stegun, Handbook of Mathematical Function with Formulas Graphs and Mathematical Tables, (1964), pp. 505–509. US GPO, Washington, D.C.
[33] Y. Naimi, A.R. Jafari, Oscillator strengths of the intersubband electronic transitions in the multi-layered nano-antidots with hydrogenic impurity, J. Comput. Electron, 11(2012) 414-420.
[34] A.R. Jafari, Y. Naimi, Linear and nonlinear optical properties of multi-layered spherical nano-systems with donor impurity in the center, J. Comput. Electron, 12 (2013) 36-42.
[35] S. M. Bilankohi, M. Ebrahimzadeh, T. Ghaffary, M. Zeidiyam, Scattering, Absorption and Extinction Properties of Al/TiO2 Core/Shell Nanospheres, Indian Journal of Science and Technology, 8 (2015) 1-4
[36] M. Servatkhah, R. Pourmand, Optical properties of a two-dimensional GaAs quantum dot under strain and magnetic field, The European Physical Journal Plus,135 (2020) 754. Available: