Photoluminescence (PL) measurements were carried out on a Be-acceptor $\delta$-doped GaAs/Al${}_{0.33}$Ga${}_{0.67}$As heterostructure at 1.6 K at magnetic fields up to 5 T. The studied PL originated from the recombination of free electrons in a two-dimensional electron gas with holes captured on Be acceptors. The electron concentration on the first electric subband was estimated by an analysis of the evolution of Landau levels in the magnetic field. To find the concentration of electrons on the second electric subband we analyzed the PL intensity at zero magnetic field and compared it with calculations based on a spherical model of a shallow acceptor. Calculations carried out for different models of an acceptor-bound hole envelope wave function allow to discuss quantitatively the validity of approximations often used to describe free-to-bound ${\Gamma }_6\to {\Gamma }_8$ transitions.

• Received 23 April 2011

DOI:https://doi.org/10.1103/PhysRevB.83.245313