Transitions from the 1s ground state to 2s excited states of the Be-acceptor confined in GaAs/AIGaAs quantum wells (QWs) have been observed via two independent spectroscopic techniques: Two-hole transitions of the bound exciton (BE) measured in selective photoluminescence and Resonant Raman Scattering. The dependence of the 1s - 2s transition energy on the QW thickness (50 Å < Lz < 140 Å) has been studied for the case of acceptors in the center of the QW. The experimentally determined 1s - 2s transition energies have then been added to recently calculated binding energies for the 2s excited state in order to obtain the total binding energies for the acceptor at different confinements. The derived binding energies are finally compared with theoretical predictions. The same kind of measurements have been performed for a QW with a given thickness, but in which the position of the acceptor has been varied from the center to the edge of the QW.

The dependencies of the binding energies of the exciton bound to the investigated acceptor on the QW thickness and the position of the acceptor in the QW have also been studied. For the case of varying QW thickness, an almost linear relationship between the binding energies of the BE and the acceptor binding the exciton is found. This fact implies that a correspondence to Haynes' rule in bulk material could be applied to these QW systems, but in this case for the same acceptor at different binding energies due to the effect of varying confinement.