  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.
