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Advanced Theory and Simulations

Optical Properties of Three‐Electron GaAs/AlxGa1−xAs QDs with Finite Confinement Potential

Yusuf Yakar, Bekir Çakır, Ayhan Özmen

Published Aug 14, 2024• 3 citations
Publisher

Abstract

Abstract In the case of finite confinement potential, the average energies and corresponding wave functions for the 1s2nl configurations, in which nl = 2s, 2p, 3d, and 4f, of three‐electron GaAs/AlxGa1−xAs quantum dot with and without impurity are computed by using a new variational approach which is a combination of Quantum Genetic Algorithm procedure and Hartree–Fock–Roothaan method. Using the calculated average energies and wave functions, a detailed investigation of the linear, third‐order nonlinear and total absorption coefficients (ACs) and the refractive index changes (RICs) for the quantum dot is performed, and the obtained results are presented as a function of dot radius and photon energies. The results show that the dot radius, the impurity charge, and the height of potential barrier have a strong influence on the average energies and absorption spectra of the system. As the potential barrier height increases, the peak positions of the ACs and RICs shift toward higher energy, and there is a significant increase in the amplitudes of the absorption spectra as the potential barrier height increases. In addition, the electron wave functions begin to enter the quantum well at smaller dot radii with increasing barrier height.

DOI
10.1002/adts.202400515

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Abstract In the case of finite confinement potential, the average energies and corresponding wave functions for the 1s2nl configurations, in which nl = 2s, 2p, 3d, and 4f, of three‐electron GaAs/AlxGa1−xAs quantum dot with and without impurity are computed by using a new variational approach which is a combination of Quantum Genetic Algorithm procedure and Hartree–Fock–Roothaan method. Using the calculated average energies and wave functions, a detailed investigation of the linear, third‐order nonlinear and total absorption coefficients (ACs) and the refractive index changes (RICs) for the quantum dot is performed, and the obtained results are presented as a function of dot radius and photon energies. The results show that the dot radius, the impurity charge, and the height of potential barrier have a strong influence on the average energies and absorption spectra of the system. As the potential barrier height increases, the peak positions of the ACs and RICs shift toward higher energy, and there is a significant increase in the amplitudes of the absorption spectra as the potential barrier height increases. In addition, the electron wave functions begin to enter the quantum well at smaller dot radii with increasing barrier height.
The study presents results of the linear and non-linear optical properties of GaAs quantum dots. The reported work aims to provide new results of the quantum dot optical properties confined in Hua plus modified Eckart (HPME) potential. To obtain analytical expressions for the energy eigenvalues and the wave functions, we solved the time-independent Schrödinger equation for the HPME potential by using the parametric Nikiforov-Uvarov (NU) method. Investigation of the linear, third-order nonlinear, and total absorption coefficients and refractive index changes was done with the help of the density matrix approach. The results showed that the energy decreases in a linear manner as the potential parameter, V0. Also, it is observed that as the barrier slope increases, the peaks of the linear, third-order linear, and total absorption coefficient tend to higher values of energy. Furthermore, as the barrier slope increases, the change in refractive indices increases, and their positions shift to higher energies. Additionally, an increase in the structure parameters and optical intensity greatly influences the absorption coefficients and the refractive index changes of the quantum dots.
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In this work, the energy levels and wave functions of the pyramidal quantum dot (PQD) are numerically calculated using the finite element method. Then, the refractive index changes (RICs) and absorption coefficients (ACs) are determined. To this goal, we have used the compact-density matrix method. Numerical results have been presented for the GaAs/Al[Formula: see text]Ga[Formula: see text]As pyramid quantum dot. It is found that the change of structural parameters like quantum dot sizes has an important influence on energy levels, wave functions, and optical properties of PQD. With increasing the height of PQD, the Acs, and RICs increase and shift toward higher energies.
In this present study, we have theoretically investigated the effect of applied external electric field and non-resonant intense laser field, as well as the adjustable physical parameters (A, M, and η) of the system, on the linear and nonlinear of GaAs/GaAlAs cylindrical quantum dot. The confinement potential of the quantum dot is composed of the axial potential with a Razavy-type quantum well in the z-direction, and the cylindrical-type potential in the radial direction. To achieve this goal, the wave functions, and the corresponding eigenvalues of the electron are investigated by resolving the time-independent Schrödinger equation using the diagonalisation technique in terms of the effective mass approximation. The linear and nonlinear optical properties’ expressions have been calculated with the help of the compact density matrix method. Our numerical results show that by changing the A, M, and η parameters, we can see a blueshift or redshift in the total optical absorption coefficients (TOACs) and relative refractive index changes (RRICs). Additionally, they are redshifted, and their extrema increase as the radius increases. The increase in electric field or laser field intensities generates a strong displacement of the resonant peak position towards the higher energies, diminishes the TOACs magnitude, and shrinks RRICs extrema. The model potential used in the computation is important, and the study of it will be practical in the development and research of nanostructures systems.
Optical properties of quantum well nanostructure for typical GaAs/AlxGa1-xAs are investigated in a new approach. By using the point canonical transformation method and numerical solution of the Schrödinger equation, the energy levels and wave functions of electrons in the quantum well confinement potential are calculated. Then, the effect of position-dependent effective mass on the intersubband optical absorption coefficient and the refractive index changes of the quantum well calculated by compact density matrix method, are studied. Results are compared with the case of constant mass. Our results show that with considering spatially varying electron effective mass linear and nonlinear optical properties increases and shifts toward the lower energies. Researches on this matter open a new field in fundamental and applied physics, and also offer a wide range of potential applications for photonic devices.
The linear and third-order nonlinear optical absorption coefficients (ACs) and the refractive index change (RIC) for a spherical quantum dot, having a hydrogenic impurity under an applied magnetic field have been theoretically studied. In numerical calculations, a variational scheme is adopted within effective mass approximation to determine the energy eigenvalues for the impurtiy. The variations of impurity binding energy with the dot radius, the linear and nonlinear ACs and RIC with the photon energy are investigated and effect of homogeneous magnetic field strength is discussed on these optical properties. It has been found that the binding energy, ACs and RIC are sensitively dependent on the magnetic field strength. Moreover, the calculated results also indicate that the absorption peak energies move to higher energies with increasing magnetic field.