Theoretical study of phosphorousδ-doped silicon for quantum computing

We present microscopic model calculations of phosphorous δ-doped silicon. Using the planar Wannier orbitals [Y. C. Chang and G. Li, Comput. Phys. Commun. 95, 158 (1996)] obtained based on the pseudopotential method, we calculate the electronic structures of a large slab (1000 ML) self-consistently (for doping electrons), taking into account both the long-range Coulomb potential in the direction perpendicular to the doping plane and the short-range interaction due to the $1∕4$ monolayer (ML) phosphor δ doping. Our results show that the Fermi level after doping is about 1000.3em0exmeV below silicon conduction band minimum (CBM). We also find that the short-range interaction due to P dopants only has a minor influence on the Fermi level.