CONFINEMENT ENERGY OF QUANTUM DOTS AND THE BRUS EQUATION
Keywords:Confinement Energy, Quantum Dots, Brus Equation, Spherical Potential Well, Schrodinger Equation, Spherical Bessel Differential Equation
A review of the ground state confinement energy term in the Brus equation for the bandgap energy of a spherically shaped semiconductor quantum dot was made within the framework of effective mass approximation. The Schrodinger wave equation for a spherical nanoparticle in an infinite spherical potential well was solved in spherical polar coordinate system. Physical reasons in contrast to mathematical expediency were considered and solution obtained. The result reveals that the shift in the confinement energy is less than that predicted by the Brus equation as was adopted in most literatures.
Abramowitz, M., & Stegun, I. (1970). Handbook of mathematical functions with formulas, Graphs and mathematical tables. National bureau of standards.
Brus, L.E., (1984). Electron-electron and electron-hole interactions in small semiconductor crystallite: The size dependence of the lowest excited electronic state. J. Chem. Phys. 80, 4403. Retrieved on 18th June, 2020 from http://dx.doi.org/10.1063//1.447218.
Chukwuocha, E.O., Onyeaju, M.C., & Harry, .S.T., (2012) Theoretical Studies on the Effect of Confinement on Quantum Dots using the Brus Equation. World Journal of Condensed Matter Physics, Vol.2(2), 96-100, USA. Retrieved online on 15th June, 2020 from http://dx.doi.org/10.4236/wjcmp.2012.2017.
Chukwuocha, E.O., & Onyeaju, M.C., (2012). Effect of Quantum Confinement 0n the Wavelength of CdSe, ZnS and GaAS Quantum Dots (QD). International Journal of Scientific & Technology Research. Vol. 1, No. 7.
Davies, J.H., (2005). The Physics of Low-Dimensional Semiconductors: An introduction (6th reprint ed.). New York: Cambridge University Press.
Delerue, C. & Lannoo, M., (2004). Nanostructures: Theory and Modelling. India: Springer. DOI: https://doi.org/10.1007/978-3-662-08903-3
Dey, S., Swargiary, D., Chakraborty, K., Dasgupta, D., Bordoloi, D., Saikia, R., N .…. Choudhury, S. (2012). The Confinement Energy of Quatum Dots. Retrieved on 19th June, 2020 from https://arxiv.org>pdf
Esaki, L., & Tsu, R., (1970). Superlattice and Negative differential conductivity in semiconductors. IBM Journal of Research and Developments. Retrieved on 15th June, 2020 from ieeexplore.iee.org DOI: https://doi.org/10.1147/rd.141.0061
Fox, M., & Ispasoiu, R., (2017). Quantum Wells, Superlattices, and Bandgap Engineering. In: Kasap., & Capper, P. (eds). Springer Handbook of Electronic and Photonic Materials. Springer Handbook, Springer, Cham.
Gupta, J.B., (2014). Electronic devices and Circuits. India: S.K. Kataria &Sons.
Ikeri, H.I., Onyia, A.I., & VwaVware, O.J., (2019). The Dependence of Confinement energy on the size of Quantum dots. International Journal of Scientific Research in Physics and Applied Sciences, Vol.7, issue 2, pp27-33. Retrieved on 19th June 2020 from https://doi.org/10.26438/ijsrpas/v7i2.2730. DOI: https://doi.org/10.26438/ijsrpas/v7i2.2730
Kayanuma, Y., (1988). Quantum Size Effects of Interacting Electrons and Holes in Semiconductor Microcrystals with Spherical shape. Phys. Rev. B 38, 9797 – 9805. DOI: https://doi.org/10.1103/PhysRevB.38.9797
Pillai, S.O., (2010). Solid State Physics (6th ed.). New-Delhi: New age International.
Pohl, U.W., (2013). Epitaxy of semiconductors: Introduction to Physical Principles Berlin: Springer. DOI: https://doi.org/10.1007/978-3-642-32970-8_1
Weber, H.J., & Arfken, G.B., (2003). Essential Mathematical methods for Physicist. Academic press, USA.
Yu, P.Y. & Cardona, M., (2005). Fundamentals of Semiconductors: Physics and Material Properties (3rd). New York: Springer. DOI: https://doi.org/10.1007/b137661