Comparing effective mass models of the phoshorus donor in silicon

Evaluating effective mass models of an isolated phosphorus donor in silicon requires disentangling various sources of error. In an effort to suppress the error resulting from state approximation, we construct states using envelope functions expanded in freely extensible basis sets equipped with tunable parameters. This robust basis set allows us, in principle, to compute arbitrarily precise approximate eigenstates of the effective mass Hamiltonian as confirmed by near zero values of the energy variance. This means we can, in principle, closely approximate the exact electronic structure of the donor for a broad class of model potentials, which in turn allows us to evaluate and compare these potential models.

In this talk, we examine models of the donor atom's Coulomb potential considering the effects of a dielectric constant with dynamic response. Further, we go beyond the Coulomb potential and present phenomenological psuedopotentials to include exchange and correlation effects from the donor's valence electrons. Finally, we include symmetry breaking perturbations, in particular the effect of an external electric field upon the donor electron.