Finite difference calculation of optical properties of hydrogenic impurity in spherical quantum dot with parabolic confinement

Abstract

The optical properties of an electron with an impurity in a spherical quantum dot under parabolic confinement are studied and energies, wave functions, binding energies, radial matrix elements, polarizability, susceptibility and oscillator strength have been evaluated. The numerical method used is the finite difference method in the framework of the effective mass approximation. The variation of the energy levels and radial matrix elements have been studied as function of the radius of the GaAs sphere and also as function of the frequency of the harmonic oscillator potential or parabolic potential. In addition we have studied how polarizability, susceptibility and the oscillator strength vary as a function of dot radius and at different parabolic potential frequencies.

Temperature-Related Electronic Low-Lying States in Different Shapes In.1Ga.9N/GaN Double Quantum Wells under Size Effects

“…This effect has been investigated by Elabsy [9] and Nithiananthi and Jayakumar [10] in a 𝐺𝑎𝐴𝑠/𝐺𝑎 1−𝑥 𝐴𝑙 𝑥 𝐴𝑠 quantum well, and Khordad [11] in a V-groove 𝐺𝑎𝐴𝑠/𝐺𝑎 1−𝑥 𝐴𝑙 𝑥 𝐴𝑠 quantum wire. Recently, the electronic properties were examined using different methods: Variational approach [12][13][14][15], finite element method [16,17], finite difference method [18], matrix diagonalization method [19] and density functional theory [20]. However, few papers have dealt with the electronic properties of multiple low-dimensional systems in the presence of a hydrogenic donor impurity [21][22][23][24].…”

Impact of Applied Temperature and Hydrostatic Pressure on the Off-Center Donor Spectrum in Spherical Quantum Dot

“…Many theoretical studies using various approaches have been attached to the donor impurity states in low-dimensional quantum dots, such as the variational approach [5][6][7][8], the finite element method [9][10][11][12], and the finite difference method [13][14], which proceeds in two steps: (i) the derivation and division operators are decomposed into smaller parts. (ii) The numerical scheme used to solve the problem approaches convergence as the size of the nanostructures decreases.…”