The impact of the electric field on the photoionization cross section, polarizability, and donor impurity binding energy in multilayered spherical quantum dot

In the present paper, we look at how the applied electric field (EF) and structure sizes affect the shallow donor impurity binding energy (Eb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{\mathrm{b}}$$\end{document}), polarizability (Pα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P}_{\alpha }$$\end{document}) and photoionization cross section (PCS) of multilayer spherical quantum dots (MSQDs). The structure's wave functions and eigenvalues are calculated using the finite-element method (FEM) and in the framework of the effective mass approximation. The obtained numerical results show that the system sizes (core radius and well width) and the external EF have a considerable influence on the Eb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{\mathrm{b}}$$\end{document} of shallow donor impurity, polarizability as well as on the dependence of the PCS on the incident photon energy.