Atomistic tight-binding Hartree-Fock calculations of multielectron configurations in P-doped silicon devices: wavefunction reshaping

Donor-based quantum devices in silicon are attractive platforms for universal quantum computing and analog quantum simulations. The nearly-atomic precision in dopant placement promises great control over the quantum properties of these devices. We present atomistic calculations and a detailed analysis of many-electron states in a single phosphorus atom and selected phosphorus dimers in silicon. Our self-consistent method involves atomistic calculations of the electron energies utilizing representative tight-binding Hamiltonians, computations of Coulomb and exchange integrals without any reference to an atomic orbital set, and solutions to the associated Hartree-Fock equations. First, we assess the quality of our tight-binding Hartree-Fock protocol against Configuration-Interaction calculations for two electrons in a single phosphorus atom, finding that our formalism provides an accurate estimation of the electron-electron repulsion energy requiring smaller computational boxes and single-electron wavefunctions. Then, we compute charging and binding energies in phosphorus dimers observing their variation as a function of impurity-impurity separation. Our calculations predict an antiferromagnetic ground state for the two-electron system and a weakly bound three-electron state in the range of separations considered. We rationalize these results in terms of the single-electron energies, charging energies, and the wavefunction reshaping.