Effective mass approximation combined with three-dimensional simulations of multilayered spherical quantum dots (MSQDs) have been conducted using the finite element method in the presence of a magnetic field (Bz). The energy eigenvalues and wave functions are obtained by solving the time-independent Schrödinger equation for both cases, with and without a shallow donor impurity (DI). These results are then used to determine the donor binding energy (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$E_b$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mi>b</mi> </msub> </math></EquationSource> </InlineEquation>) and evaluate the photoionization cross-section (PCS). The key outcomes of the present investigation can be summarized as follows: the donor binding energy increases with the applied magnetic field, with the rate of enhancement strongly dependent on the structural parameters, including the core radius, well width, and barrier thickness. For all magnetic field strengths and geometric configurations considered, the photoionization cross-section (PCS) exhibits a pronounced blue shift as the magnetic field increases, owing to the corresponding increase in the donor binding energy. Furthermore, the PCS peak intensity generally reaches its maximum at (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\gamma = 4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>=</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>) for all values of the core, well, and shell dimensions, except for (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$T_{b1}=0.4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>T</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </math></EquationSource> </InlineEquation>), where an opposite trend is observed. In addition, increasing the aluminum concentration induces a further blue shift and significantly enhances the PCS peak intensity. This effect becomes more pronounced at higher magnetic field strengths, highlighting the combined influence of magnetic confinement and material composition on the optical response of the nanostructure. The present work provides insight into the electronic structure and optical transitions of MSQDs, which is important for designing tunable optoelectronic devices with highly controllable energy levels.

Computational Analysis of Magnetic-Field Effects on Donor States and Photoionization in GaAs/AlGaAs Multilayered Spherical Quantum Dots

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发表日期：

2026年7月16日

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A. Fakkahi,
P. Başer,
H. Azmi,
M. Jaouane,
A. Sali,
R. Arraoui

摘要

Effective mass approximation combined with three-dimensional simulations of multilayered spherical quantum dots (MSQDs) have been conducted using the finite element method in the presence of a magnetic field (B_z). The energy eigenvalues and wave functions are obtained by solving the time-independent Schrödinger equation for both cases, with and without a shallow donor impurity (DI). These results are then used to determine the donor binding energy ( $E_b$ $E_{b}$ ) and evaluate the photoionization cross-section (PCS). The key outcomes of the present investigation can be summarized as follows: the donor binding energy increases with the applied magnetic field, with the rate of enhancement strongly dependent on the structural parameters, including the core radius, well width, and barrier thickness. For all magnetic field strengths and geometric configurations considered, the photoionization cross-section (PCS) exhibits a pronounced blue shift as the magnetic field increases, owing to the corresponding increase in the donor binding energy. Furthermore, the PCS peak intensity generally reaches its maximum at ( $\gamma = 4$ $γ = 4$ ) for all values of the core, well, and shell dimensions, except for ( $T_{b1}=0.4$ $T_{b 1} = 0.4$ ), where an opposite trend is observed. In addition, increasing the aluminum concentration induces a further blue shift and significantly enhances the PCS peak intensity. This effect becomes more pronounced at higher magnetic field strengths, highlighting the combined influence of magnetic confinement and material composition on the optical response of the nanostructure. The present work provides insight into the electronic structure and optical transitions of MSQDs, which is important for designing tunable optoelectronic devices with highly controllable energy levels.