Electronic structure models of phosphorusδ-doped silicon

We report a density-functional theory treatment of phosphorus $\ensuremath{\delta}$-doped silicon. Using large asymmetric unit cells with up to 800 atoms, we obtain first-principles doping potentials, band energies, and donor-electron distributions. The explicit and nonempirical description of both valence and donor electrons improves upon previous models of this system. The effects of overlapping $\ensuremath{\delta}$-doping potentials in smaller systems are adequately captured using a uniform band alignment shift.