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 properties of a hydrogenic impurity in a parabolic GaAs quantum-well wire in the presence of the magnetic field are investigated using the finite-difference method within the quasi-one-dimensional effective potential model. The magnetic effects on the energies and binding energies of the ground and lowest excited states of a hydrogenic impurity in a parabolic GaAs quantum-well wire are studied for various parabolic potentials. The calculated results indicate that the interplay of the spatial confinement and the magnetic confinement of electrons in the quantum-well wires leads to complicated binding energies of the hydrogenic impurity, and high magnetic fields significantly increase the binding energies of the hydrogenic impurity in the case of weak spatial confinement.

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 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

Using a two-parameter wave function, we calculate variationally the binding energy of an exciton bound to an ionized donor impurity (D+, X) in GaAs-AlxGa1−xAs quantum wells for the values of the well width from 10 to 300A, when the dopant is located in the center of the well and at the edge of the well. The theoretical results confirm that the previous experimental speculation proposed by Reynolds et al. [Phys. Rev. B 40, 6210 (1989)] is the binding energy of D+, X for the dopant at the edge of the well. In addition, we also calculate the center-of-mass wave function of the exciton and the average interparticle distances. The results are discussed in detail.

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.

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.

Using a simple two-parameter wavefunction, we calculate variationally the binding energy of positively and negatively charged excitons in GaAs/AlxGa1-xAs quantum wells for well widths from 10 to 300A. We consider the effect of effective mass, dielectric constant mismatch in the two materials, and the whole correlation among the particles. The results are discussed and compared in detail with previous experimental and theoretical results, which show fair agreement with them.

The effect of a spatially dependent effective mass in a finite GaAs/AlxGa1-xAs parabolic quantum well with a magnetic field on hydrogenic impurity ground state (1s) binding energies, and lowly excited state (2p

In the effective-mass approximation, using a simple two-parameter wave function and a one-dimensional (1D) equivalent potential model, we calculate variationally the binding energy of an exciton bound to a neutral donor (D0,X) in finite GaAs-AlxGa1−xAs quantum well wires (QWWs). At the wire width of 25 A, the binding energy has a peak value, which is also at the position of the peak of the exciton binding energy, and the center-of-mass wave functions of excitons reaches the most centralized distribution. In addition, the changing tendency of the average interparticle distance as the wire width is reverse to that of the binding energy.