Optical Γ₆ → Γ₈ Free-to-Bound Transitions in Acceptor δ-Doped Single Heterostructure - Theoretical Analysis

A theoretical analysis was carried out of an optical transition observed in high-quality GaAs/AlGaAs heterostructures δ-doped with shallow acceptors. The transition involves a 2D electron and a 3D acceptor-localized hole. The wave functions of a bulk Be acceptor were calculated within the spherical model with both the s-like and d-like parts of the envelope taken into account. The electron envelope wave functions resulted from self-consistent calculations of the electrostatic potential and were dependent on the 2D electron concentration, $n_s$. We show that: (i) including the d-like part of the acceptor envelope relaxes the selection rules of free-to-bound transitions at k=0;(ii) in the magnetic field, the selection rules depend on the number of the electron Landau level;(iii) the ratio of the intensity of the strongest transitions in both circular polarizations is essentially different from 3:1, and strongly depends on $n_s$. These results show that a description that neglects the d-like part of the acceptor envelope is both qualitatively and quantitatively unjustified.