Effective bond-orbital model for shallow acceptors in
GaAs-Al_{x}Ga_{1-x}As quantum wells and superlattices.
G.T. Einevoll,
Department of Physics and Materials Research Laboratory,
University of Illinois at Urbana-Champaign, 1110 West Green Street,
Urbana, Illinois 61801;
Institutt for Fysikk, Norges Teknisk Høgskole,
Universitetet i Trondheim, 7034 Trondheim, Norway
Yia-Chung Chang,
Department of Physics and Materials Research Laboratory,
University of Illinois at Urbana-Champaign, 1110 West Green Street,
Urbana, Illinois 61801
Physical Review B 41, 1447-1460 (1990)
Abstract
The novel effective bond-orbital model (EBOM) is used to calculate
energies of shallow acceptors in GaAs-Al_{x}Ga_{1-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, the authors 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,
they 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.