Flexible approach to exciton binding energies in type-I and type-II quantum wells

We propose a method to calculate the exciton binding energies in type-I and type-II quantum wells by expanding the electron and hole envelope functions into Gaussian-type functions separately. We calculate the binding energies, wave functions, and overlap integrals of the type-I and type-II excitons in an AlAs/GaAs/AlAs single quantum well as a function of the GaAs-layer thickness. This calculation model avoids predetermined ''artificial'' trial wave functions, and the results exhibit reasonable changes of the exciton properties from the quantum-confined states to the bulk states with the decrease of the GaAs-layer thickness to zero. It is suggested that the binding energy of the type-II exciton exceeds that of the type-I exciton when the GaAs-layer thickness is less than 2 ML because of the wave-function penetration and the large X-valley effective mass. In addition, it is obtained that the overlap integral between the electron and hole of the type-II exciton remarkably decreases with the increase of the GaAs-layer thickness, resulting from the spatial separation of the electron and hole.