We have investigated experimentally and theoretically the effect of quantum confinement on the acceptor binding energy in the GaAs/AlAs multiple-quantum well system

respectively. The system represents the maximum possible confinement for the acceptor states in the valence band and thus the maximum possible tuning range for the 1s-2p transition of the acceptor. A series of Be delta-doped GaAs/AlAs multiple quantum wells with the doping at the well center were grown on a semi-insulating (100) GaAs substrate by molecular beam epitaxy. The quantum-well width ranges from 3 to 20 nm. Each of multiple-quantum well structures investigated contained a same 5 nm wide AlAs barrier

while every GaAs well layer was delta doped at the well center with Be acceptor atoms. The doping level was 5×10

10

/cm

2

. The photoluminescence spectra were measured at 4

20

40

80

120

and 200 K

respectively using Renishaw Raman imaging microscope. The optical excitation for photoluminescence experiments was provided by an argonion laser 514.5 nm. The excitation power was typically 5 mW. The two-hole transitions of the acceptor-bound exciton from the ground state

to the even-parity excited state

have been clearly observed. The acceptor binding energy of the shallow beryllium acceptor at the center of the multiple-quantum wells has been measured experimentally. Under the single-band effective mass and envelop function approximation

a variational calculation is presented to obtain the acceptor binding energy as a function of quantum-well width. We choose the produce of two terms as the trial wave function of a hole. The Bohr radius is employed as a variational parameter in order to minimize the total energy of the system. The total energy of the system can be solved for any choice of the Bohr radius by expanding the derivatives in finite differences and forming an iterative shooting algorithm. It is found that the experimental results are in good agreement with the theory.