An open source software package to compare and extend effective mass models of the phosphorus 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 have put together an open source software package to explore the limits of the effective mass model. In this package, we construct states using envelope functions expanded in freely extensible basis sets equipped with tunable parameters. Additionally, a full consideration of the effect of symmetry is applied to this basis set. This robust basis set allows us to compute arbitrarily precise approximate eigenstates of the effective mass Hamiltonian as confirmed by near zero values of the energy variance. We can, in principle, closely approximate the exact electronic structure of the donor in the context of effective mass for a broad class of model potentials, which in turn allows us to evaluate and compare extant and new effective 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.