| We use a density functional method with a local exchange-correlation energy to calculate the energy and density of bound multiexciton complexes attached to neutral donors in silicon and germanium, assigning electrons and holes separately to single-particle orbitals in agreement with the Kirczenow shell model.; We employ two primary methods of calculating BMEC energies and densities, both employing density functional theory: (1) A simple effective-mass theory, used for large complexes, and (2) a more accurate method, which we describe in detail, including details of band structure. We also briefly describe several variations of density functional theory and present the results of calculations incorporating these variations.; The calculated properties of large BMECs are in close agreement with equivalent properties of electron-hole droplets, while the energies of BMECs calculated by the second method predict recombination line positions close to the observed positions. In the case of all donors in germanium and for the (alpha)-series of phosphorus in silicon, the calculated and experimental positions of all spectral features differ by less than 1 meV.; The calculations employing variants of density functional theory, as well as calculations on a simplified model of a bound exciton, indicate that a density funtional theory, which (a) has no self-interaction correction, (b) is spin-independent, and (c) has a local exchange-correlation energy equal to that of an electron-hole gas, produces more accurate BMEC energies than alternative density functional methods or than the Hartree-Fock method. |
