Effective bond-orbital model for acceptor states in semiconductors and quantum dots

The effective bond-orbital model (EBOM) is introduced as a new way of calculating binding energies of acceptors in semiconductors and semiconductor heterostructures. The method combines the virtues of the effective-mass theory (k.p) and tight-binding methods. It is especially useful for shallow acceptors in heterostructures, where a proper effective-mass treatment is extremely complicated, while EBOM is straightforward to apply. The method is first applied to single acceptors in bulk Si and GaAs, where large-size clusters with cubic symmetry including up to 438 000 lattice sites are used in the calculations. A scaling approximation that reduces the sizes of the clusters required in the calculations is introduced to handle excited acceptor states with large spatial extensions. Comparisons with previous calculations and experimental values for acceptor binding energies show that the EBOM results are as accurate as or better than results from effective-mass calculations. The EBOM is also applied to a double acceptor in GaAs, where a prediction of the energy of an excited state is in good agreement with the experimental value. As an illustration of the method applied to heterostructures, we calculate the ground-state energies of spherical quantum dots (GaAs-${\mathrm{Al}}_{0.3}$ ${\mathrm{Ga}}_{0.7}$As) with and without acceptors in the center.