Binding Energy Of Positively Charged Acceptors In Germanium - A Green’s Function Monte Carlo Calculation

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Abstract Spectroscopic measurements of germanium crystals have revealed some of the characteristics of impurity complexes which can be explained in terms of charge acceptors interacting with surrounding holes to form so-called pseudoatoms. With suitable modifications, these complexes can be treated in the same way as real atoms and ions by conventional quantum methods, as described in earlier work, and by QMC methods as described first in this paper. The complexes of interest include double acceptor impurities Be and Zn binding three holes and quadruple acceptors binding four holes, equivalent to negatively charged infinite-mass nuclei (of charge -Z) surrounded by positively charged holes (of charge +1). with use of effective masses for the holes, an effective dielectric constant, and a modification of Fermi statistics to allow four holes in ls orbitals, these systems may be treated as simple atoms and ions in diffusion QMC with importance sampling. The systems treated were equivalent to nodeless H-, He+, He, He-, Li+, Li, and Li-. Both variational and diffusion calculations used the same trial wavefunctions, which were symmetrized ls orbital products with added correlation terms linear in the interelectron distances. For the one- and two-hole systems, the energies could be deduced from the analogous systems. For these the diffusion QMC calculations gave equivalent results. In all cases the diffusion calculations gave slightly lower energies than the variational calculations. In comparisons with experiment, agreement was good for double acceptors and poor for triple acceptors, for which the pseudoatom model was judged to be inadequate.