The electronic structure of Group V dopants in silicon -- The requirements for a realistic DFT model

Typical concentrations of Group V donors in Si wafers used in experiment are up to 10$^{18}$ cm$^{-3}$. In contrast, the simulation cell in a typical atomistic simulation would contain a few hundred Si atoms and one or two dopants. That is equivalent to concentrations on the order of at least 10$^{20}$ cm$^{-3}$. We investigate the effect of donor concentration on the electronic structure of doped bulk silicon in density functional simulations (DFT) using the linear scaling DFT code Conquest on very large cells, and the cell sizes required to model the metal-semiconductor transition correctly.