Ab initio study of phosphorus donors acting as quantum bits in silicon nanowires

A phosphorus (P) donor has been extensively studied in bulk Si to realize the concept of Kane quantum computers. In most cases the quantum bit was realized as an entanglement between the donor electron spin and the nonzero nuclei spin of the donor impurity mediated by the hyperfine coupling between them. The donor ionization energies and the spin-lattice relaxation time limited the temperatures to a few kelvin in these experiments. Here, we demonstrate by means of ab initio density functional theory calculations that quantum confinement in thin Si nanowires (SiNWs) results in (i) larger excitation energies of donor impurity and (ii) a sensitive manipulation of the hyperfine coupling by external electric field. We propose that these features may allow to realize the quantum bit (qubit) experiments at elevated temperatures with a strength of electric fields applicable in current field-effect transistor technology. We also show that the strength of quantum confinement and the presence of strain induced by the surface termination may significantly affect the ground and excited states of the donors in thin SiNWs, possibly allowing an optical read-out of the electron spin.