Investigation of the Electronic Structure in GaAs/AlxGa1-xAs Quantum Dots with Four Electrons

In this paper, a detailed analysis of the electronic structure of four-electron quantum dots is performed with finite confinement potential by a modified variational optimization approach based mainly on the quantum genetic algorithm and the Hartree-Fock-Roothaan method. For the ground and higher excited configurations, our analysis covers a range of parameters like the average energies of ground and excited states, singlet and triplet state energies, orbital energies, and two-electron Coulomb and exchange interaction energies. One-electron kinetic energy, the Coulomb potential energy between electrons and impurity, the confinement potential energy for the electrons, and the probability of finding an electron inside or outside the quantum well are also studied. The results demonstrate that both spatial confinement and the height of the potential barrier have a pronounced effect on all energies in the strong and intermediate confinement regions, but this influence weakens significantly in large dot radii. The most substantial difference between singlet and triplet energies occurs in the 1s²2s2p configurations, with this difference decreasing in higher configurations. Significant increases in the 1s and 2s orbital energies are observed at the dot radii where the 2p, 3d, and 4f electrons from the outermost orbit begin to penetrate the well.