Stark effect of confined shallow levels in phosphorus-doped silicon nanocrystals

Abstract

By envelope-function approximation, we computed the effect of confinement in spherical P-doped Si nanocrystals in a uniform electric field without adjustable parameters. Based on nanocrystal size, we can distinguish several regimes. For a radius $R$ that is larger than ${R}_{t}$ $({R}_{t}\ensuremath{\sim}21\text{ }\text{nm})$ the ground state is ionized at a critical electric field, ${\mathcal{E}}_{cr}$, by tunneling from a $1s$-like state, localized at the impurity, to a $2p$-like state, localized to the well that is formed by the electric field and the potential barrier that is generated by the embedding matrix at the nanocrystal surface. For smaller nanocrystals, for which ${R}_{sp}<R<{R}_{t}$ $({R}_{sp}\ensuremath{\sim}7\text{ }\text{nm})$, there is a range of electric fields in which the ground state is formed by the hybridization of the impurity states and surface-well states. Further, within this hybridization range, there is a value of the electric field at which the ground $1s$-like state and the excited $2{p}_{0}$ state have the same hyperfine coupling. Based on these findings, we envisage a quantum computing scheme in which qubits shuttling relies on excited states when an electric field is applied.