Using multivalley effective mass theory to probe the phosphorous donor effective potential in silicon

Multivalley effective mass (MEM) theories combine physical intuition with an efficient use of computational resources. However, the most appropriate form of effective potential to use with MEM theory remains an open question. Here we develop an MEM theory for an electron confined to a phosphorus donor in Silicon, and explore the most useful form of effective potential that would allow us to accurately predict both spectrum and wavefunction of the electron. We employ a variational method with a freely extensible set of symmetrized Gauss- or Slater-type atomic basis states, with representatives from all five irreducible representations of the T_d point-symmetry group. We employ stochastic optimization to complete both variational minimization and model parameter fitting, which allows for parameter spaces of large dimensionality. We consider an effective potential with tetrahedrally symmetric central cell corrections and a dynamic dielectric, as well as exchange-correlation effects, and we also explore effects of external perturbations such as an applied electric field. Our investigation here lays a solid foundation for studies of electronic states and interactions of multiple donors.