The connection between noncentrosymmetric materials structure, electronic structure, and bulk photovoltaic performance remains not well understood. In particular, it is still unclear which photovoltaic (PV) mechanism(s) are relevant for the recently demonstrated visible-light ferroelectric photovoltaic (K,Ba)(Ni,Nb)O$_{3-delta}$. In this paper, we study the bulk photovoltaic effect (BPVE) of (K,Ba)(Ni,Nb)O$_{3-delta}$ and KNbO$_{3}$ by calculating the shift current from first principles. The effects of structural phase, lattice distortion, oxygen vacancies, cation arrangement, composition, and strain on BPVE are systematically studied. We find that (K,Ba)(Ni,Nb)O$_{3-delta}$ has a comparable BPVE with that of the broadly explored BiFeO$_{3}$, but for a much lower photon energy. In particular, the Glass coefficient of (K,Ba)(Ni,Nb)O$_{5}$ in a simply layered structure can be as large as 12 times that of BiFeO$_{3}$. Furthermore, the nature of the wavefunctions dictates the eventual shift current yield, which can be significantly affected and engineered by changing the O vacancy location, cation arrangement, and strain. This is not only helpful for understanding other PV mechanisms that relate to the motion of the photocurrent carriers, but also provides guidelines for the design and optimization of PV converters.
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