We report photoluminescence studies of internal transitions of shallow Be acceptors in bulk GaAs and a series of S-doped GaAs/ALAs multiple quantum well samples with well width ranging from 3 to 20nm. A series of Be S-doped GaAs/ AlAs multiple-quantum wells with the doping at the well center and a single epilayer of GaAs uniformly Be doped were grown by molecular beam epitaxy. The photoluminescence spectra were measured at 4,20,40, 80, and 120K, respectively. A two-hole transition of the acceptor-bound exciton from the ground state, 1S3/2 （/8）, to the first-excited state, 2S3/2 （Г6） , has been clearly observed. A variational principle is presented to obtain the 2s-1s transition energies of quantum confined Be acceptors as a function of the well width under the single-band effective mass and envelop function approximations. It is found that the acceptor transition energy increases with decreasing quantum-well width, and the experimental results agree well with the theoretical calculation.
