Large-scale atomistic density functional theory calculations of phosphorus-doped silicon quantum bits

Abstract

We present density functional theory calculations of phosphorus dopants in bulk silicon and of several properties relating to their use as spin qubits for quantum computation. Rather than a mixed pseudopotential or a Heitler-London approach, we have used an explicit treatment for the phosphorus donor and examined the detailed electronic structure of the system as a function of the isotropic doping fraction, including lattice relaxation due to the presence of the impurity. Doping electron densities (ρ doped − ρ bulk ) and spin densities (ρ ↑ − ρ ↓ ) are examined in order to study the properties of the dopant electron as a function of the isotropic doping fraction. Doping potentials (V doped − V bulk ) are also calculated for use in calculations of the scattering cross-sections of the phosphorus dopants, which are important in the understanding of electrically detected magnetic resonance experiments. We find that the electron density around the dopant leads to non-spherical features in the doping potentials, such as trigonal lobes in the (001) plane at energy scales of +12 eV near the nucleus and of -700 meV extending away from the dopants. These features are generally neglected in effective mass theory and will affect the coupling between the donor electron and the phosphorus nucleus. Our density functional calculations reveal detail in the densities and potentials of the dopants which are not evident in calculations that do not include explicit treatment of the phosphorus donor atom and relaxation of the crystal lattice. These details can also be used to parameterize tight-binding models for simulation of large-scale devices.

Host isotope mass effects on the hyperfine interaction of group-V donors in silicon

“…Rigorous evaluation of our experimental findings requires further theoretical research involving advanced methods. 35,36 In conclusion, we have revealed the host isotope mass effects on the hyperfine interaction of group-V donors from the variation in the ENDOR spectra of various isotopically engineered Si crystals. The relative intensities of the split ENDOR compoents for all the group-V donors are explained by a negative linear dependence of the hyperfine parameter A on the average Si isotope mass M NN at the four nearest-neighbor sites to the donor.…”

Multivalley effective mass theory simulation of donors in silicon

“…Near the donor, the local potential deviates from this simple 1/r behavior, as a result of reduced dielectric screening from the silicon lattice and complex reorganization of the local electronic structure. 8,43 To describe this effect, we include a central cell correction U cc (r), such that the full donor impurity potential takes the form U (r) = U c (r)+U cc (r). Due to the tetrahedral symmetry of the covalent bonding between the donor and the neighboring silicon atoms in the lattice, we allow for the central cell correction U cc (r) to be tetrahedrally symmetric, to be contrasted with the more restrictive spherical symmetry assumed in previous studies.…”

Simulated doping of Si from first principles using pseudoatoms

“…If the latter case is of interest, it is necessary to use real atoms, within a supercell large enough to avoid spurious interaction between impurities (see, e.g., Refs. 11,55,and 56). Such systems are, with no exception, equivalent to very heavily doped systems, owing to the severe practical limitations on feasible supercell sizes.…”