Studying the electronic states of semimagnetic-based double quantum wells (DQWs) is particularly intriguing due to the combined effects of quantum confinement and exchange interactions with localized magnetic ions. In such structures, the incorporation of Mn²⁺ ions introduce a spin-dependent potential through the exchange interaction, which alters the energy spectrum and lifts the spin degeneracy of electronic states. The double quantum well configuration enables the investigation of tunneling phenomena and the coupling between adjacent wells, providing a versatile system for analyzing the influence of structural parameters on carrier dynamics. In this work, we specifically investigated the effect of the DQW dimensions, namely, the well width and barrier thickness, on the electronic states by solving the transcendental equation within the effective mass approximation, using the trial wavefunction corresponding to the DQW system. The outcomes reveal that each parameter exerts a distinct influence: more precisely, the electronic state energies tend to increase with the increment of the barrier thickness, due to the reduction in tunneling probability, while they decrease with the increment of the well width, as a result of the weaker quantum confinement. Furthermore, the increase in the Manganese composition leads to a higher potential barrier, which enhances the quantum confinement and, consequently, results in an increase in the energies of the electronic states. In conclusion, these findings not only deepen our understanding of the electronic behavior in semimagnetic heterostructures but also offer practical guidance for tailoring quantum well architectures to meet specific functional requirements in advanced semiconductor technologies. Furthermore, these results are aligned with the findings reported in Refs. [1,2].

[1] T. Kamizato, M. Matsuura, Excitons in double quantum wells, Phys Rev B 40 (1998) 15–1989. https://doi.org/10.1103/PhysRevB.40.8378.

[2] J. Cen, K.K. Bajaj, Binding energies of excitons and donors in a double quantum well in a magnetic field, (1992).