Internal transitions of acceptors confined in delta-doped GaAs/AlAs multiple quantum wells

We have investigated experimentally and theoretically the influence of the quantum confinement effect on internal transitions of shallow beryllium acceptors in both bulk GaAs and a series of delta-doped GaAs/AlAs multiple quantum well samples with well width ranging from 30 to 200 angstrom. A series of beryllium delta-doped GaAs/AlAs multiple-quantum wells with the doping at the well centre and a single epilayer of GaAs uniformly Be doped were grown by molecular beam epitaxy. Far-infrared absorptions were measured at 4.2 K for all samples. Three principal absorption lines were observed clearly, which correspond to acceptor state transitions from the ground state 1s(3/2) (Gamma(6) + Gamma(7)) to the three excited odd-parity states 2p(3/2) (Gamma(6) + Gamma(7)), 2p(5/2) (Gamma(6) + Gamma(7)) and 2p(5/2) Gamma(7), respectively. The photoluminescence spectra were measured at 4, 20, 40, 80 and 120 K, respectively. The two-hole transition of the acceptor-bound exciton from the ground state, 1S(3/2) (Gamma(6)), to the excited state, 2S(3/2) (Gamma(6)), has been clearly observed. A variational principle is presented to obtain the 2p-1s and 2s-1s transition energies of quantum-confined beryllium acceptors as a function of the well width. It is found that the acceptor internal transition energy increases with decreasing quantum-well width, and the experimental results are in good agreement with the theoretical calculation.