A study of an exciton in a quantum dot with Woods–Saxon potential

A theoretical study of an exciton confined in a quantum dot with the Woods–Saxon potential is presented. The great advantage of our methodology is that it enables confinement regimes by varying two parameters in the model potential. Calculations are made by using the method of the numerical diagonalization of the Hamiltonian matrix within the effective-mass approximation. The binding energies of the ground (L=0L=0) and first excited (L=1L=1) states are obtained as functions of the dot radius. Based on the computed energies and wave functions, the linear, the third-order nonlinear and the total optical absorption coefficients have been examined between the ground and the first excited states. The results are presented as a function of the incident photon energy for the different values of the dot radius and the barrier slope. It is found that the binding energy and the optical properties of the excitons in a quantum dot are strongly affected by the dot radius and the barrier slope of the confinement potential.