Bulk photovoltaic effect of LiNbO3:Fe and its small-polaron-based microscopic interpretation

Abstract

Based on recent experimental evidence on the electronic and optical properties of Fe${}_{\mathrm{Li}}^{2+}$ and Nb${}_{\mathrm{Nb}}^{4+}$ in LiNbO${}_{3}$:Fe, both strongly determined by their small polaron character, a microscopic model is presented accounting for the main features of the bulk photovoltaic effect (BPVE) in this material. The relative sizes of the components of the photovoltaic tensor are explained on an atomic basis. Optical small polaron transfer from Fe${}_{\mathrm{Li}}^{2+}$ to Nb${}_{\mathrm{Nb}}^{5+}$ conduction band states and the subsequent coherent bandlike electron transport, terminated by the formation of Nb${}_{\mathrm{Nb}}^{4+}$ free small polarons within about ${10}^{\ensuremath{-}13}$ s, characterize the first steps of the BPVE. These free polarons, transported by thermally activated incoherent hopping, are then trapped by deeper defects such as Nb${}_{\mathrm{Li}}^{5+}$ and Fe${}_{\mathrm{Li}}^{3+}$ impurities. The model allows us to explain the strong increase of the ionization probability of Fe${}_{\mathrm{Li}}^{2+}$ and the coherent transport length with photon energy. The low mobility of the Nb${}_{\mathrm{Nb}}^{4+}$ conduction polarons appears to be the reason for the high open-circuit photovoltaic fields attainable in LiNbO${}_{3}$.