The binding energy of an exciton bound to a neutral donor (D0,X) in a GaAs-AlxGa1-xAs quantum well is calculated variationally by using a two-parameter wave function. There is no artificial parameter added in our calculation. Our results agree fairly well with previous experimental results, except that our position of the binding energy maximum is at about 15

The energy of a biexciton in a GaAs–AlxGa1-xAs quantum well is calculated variationally by use of a two-parameter trial wave function. The calculated binding energy, relative to two well-separated excitons, is greater than that given previously by Kleinman [Phys. Rev. B 28, 871 (1983)]. Our binding energy takes its greatest value when the well width is approximately 10 Å. The ratio of the binding energy of a biexciton to that of an exciton for a range of well thickness (5–300Å) is found to be from 0.127 to 0.284, which agrees fairly well with previous experimental results. The results of our approach are compared with those of earlier theories.

The effect of a spatially dependent effective mass in a finite GaAs/AlxGa1-xAs parabolic quantum well on hydrogenic impurity ground state (1s) binding energies and transition energies between a 1s state and lowlying excited state (2p±-like) has been calculated, respectively, as a function of well width and impurity position by using the one-dimensional method. Our results are compared with Niculescu’s results of constant effective mass. We find that the 1s state binding energies and the 1s→2p± transition energies are greater than Niculescu results for the same well width, respectively. These results are obtained as the impurity is located at the well center. At the same time the well widths corresponding to maximum values of the 1s state binding energies and the 1s→2p± transition energies are less than those of Niculescu, respectively. The physical meaning of 1/(1-λ) is discussed.

The binding energies of a two-dimensional (2D) biexciton have been calculated variationally for all values of the effective electron-to-hole mass ratio σ by using a three-parameter wave function. The ratio of the binding energy of a 2D biexciton to that of a 2D exciton is found to be from 0.582 to 0.220. The results agree fairly well with previous experimental results. The results of this approach are compared with those of earlier theories.

The binding energies of excitons bound to neutral donors in two-dimensional (2D) semiconductors within the spherical-effective-mass approximation, wchich are nondegenerate energy bands, have been calculated by a variational method for a relevant range of the effective electron-to-hole mass ratioσ. The ratio of the binding energy of a 2D exciton bound to a neutral donor to that of a 2D neutral donor is found to be from 0.58 to 0.10. In the limit of vanishing σ and large σ, the results agree fairly well with previous experimental results. The results of this approach are compared with those of earlier theories.