  Transition metal oxides such as \ce{BiVO4} are promising materials as
photoelectrodes in solar-to-fuel conversion applications. However, their
performance is limited by the low carrier mobility (especially electron
mobility) due to the formation of small polarons. Recent experimental studies
show improved carrier mobility and conductivity by atomic dopings. We studied
the small polaron hopping mobility in pristine and doped \ce{BiVO4} by
combining Landau-Zener theory and kinetic Monte Carlo (kMC) simulation fully
from first-principles, and investigated the effect of dopant-polaron
interactions on the mobility. We found polarons are spontaneously formed at V
in both pristine and Mo/W doped \ce{BiVO4}, which can only be described
correctly by density function theory (DFT) with the Hubbard correction (DFT+U)
or hybrid exchange-correlation functional but not local or semi-local
functionals. We found DFT+U and dielectric dependant hybrid functional (DDH)
give similar electron hopping barriers, which are also similar between the room
temperature monoclinic phase and the tetragonal phase. The calculated electron
mobility agrees well with experimental values, which is around $10^{-4}$
cm$^2$V$^{-1}$s$^{-1}$. We found the electron polaron transport in \ce{BiVO4}
is neither fully adiabatic nor nonadiabatic, and the first and second nearest
neighbor hoppings have significantly different adiabacity in spite of similar
hopping barriers. We further computed polaron mobility in the presence of
different dopants and showed that Cr substitution of V is an electron trap
while Mo and W are "repulsive" centers, mainly due to the minimization of local
lattice expansion by dopants and electron polarons. The dopants with
"repulsive" interactions to polarons are promising for mobility improvement due
to larger wavefunction overlap and delocalization of locally concentrated
polarons.
