Atomic and electronic structures of nitrogen vacancies in silicon nitride: Emergence of floating gap states

Abstract

We report the density functional calculations with the hybrid approximation to the exchange-correlation energy that clarify the atomic and electronic structures of the N vacancy (${\mathrm{V}}_{\mathrm{N}}$) in ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$. We find that the gap states induced by the Si dangling bonds around ${\mathrm{V}}_{\mathrm{N}}$ show interesting interplay between the spin splitting and the Jahn-Teller splitting depending on their charges. More surprisingly, we find that a peculiar electron state distributed in the internal space of the host SiN is hidden in the conduction bands and converted to a localized floating state in the fundamental energy gap due to the presence of ${\mathrm{V}}_{\mathrm{N}}$. This theoretical finding indicates ${\mathrm{V}}_{\mathrm{N}}$ being multiply charged from $+1$ to $\ensuremath{-}5$: The charge states from $+1$ to $\ensuremath{-}3$ are stable at respective Fermi-level positions in the gap, whereas the states $\ensuremath{-}4$ and $\ensuremath{-}5$ are metastable for the Fermi level near the conduction band bottom. A possibility of multilevel memory function of ${\mathrm{V}}_{\mathrm{N}}$ in SiN is suggested.