A study of two confined electrons using the Woods-Saxon potential

In this paper, we studied two electrons confined in a quantum dot with the Woods-Saxon potential by using the method of numerical diagonalization of the Hamiltonian matrix within the effective-mass approximation. The great advantage of our methodology is that it enables confinement regimes by varying two parameters in the model potential. A ground-state behavior (singlet -> triplet state transitions) as a function of the strength of a magnetic field has been investigated. We found that the confinement barrier size and the barrier inclination of a Woods-Saxon potential are important for the singlet-triplet oscillation of a two-electron quantum dot. Based on the computed energies and wavefunctions, the linear and nonlinear optical absorption coefficients have been examined between the (1)S state (L=0) and the 1P state (L=1). The results are presented as a function of the incident photon energy for the different values of the barrier size and height. It is found that the optical properties of the two-electron system in a quantum dot are strongly affected by the barrier height and size.