Effective bond-orbital model for shallow acceptors in GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells and superlattices

The novel effective bond-orbital model (EBOM) is used to calculate energies of shallow acceptors in GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells and superlattices. The model is tight-binding-like, and the interactions between bond orbitals located at sites in the face-centered-cubic lattice are fitted to make EBOM predict the right band structure close to the valence-band edge. Symmetry-adapted functions consisting of proper linear combinations of bond orbitals located at sites in the vicinity of the acceptor impurity are used as basis functions in variational calculations of energies of acceptor states. First, we calculate energies of both ${\Gamma }_6$ (heavy-hole) and ${\Gamma }_7$ (light-hole) ground states and first even-parity excited states for C and Be acceptors centered in the well material of single quantum wells. When comparing EBOM results with results from previous multiband effective-mass calculations, we generally find good agreement for the ground-state energies and the corresponding binding energies, while the estimates for the excited states vary substantially. Comparisons with recent experiments, where two independent experimental techniques are used to measure energies of transitions involving the excited states, favor the EBOM results. The deviations of the effective-mass results are thought to reflect inherent shortcomings in the effective-mass method, absent in the EBOM, namely the calculational difficulty of properly incorporating position-dependent material parameters and the practical limitations on the flexibility of trial wave functions in actual calculations. Finally, the EBOM is used to calculate binding energies of acceptors in superlattices. Up to 11 wells are included in the model for the thinnest superlattices in which coupling of adjacent wells is essential. In order to compare with recent photoluminescence experiments on C acceptors in narrow-barrier superlattices, the corresponding EBOM calculations for both well- and barrier-centered acceptors in superlattices are performed.