Bimodal hole transport in bulk BiVO 4 from computation
We report first principles and mesoscale kinetic simulations of intrinsic electron and hole transport in stoichiometric monoclinic BiVO 4 (BVO). A main finding is that hole transport is bimodal: there are fast hole hops within VO 4 tetrahedra that are not ‘transport-efficient’ and slower hole hops across VO 4 tetrahedra that are ‘transport-efficient’. This bimodality in hole transport may explain the slow transport/high recombination characteristics of BVO. In this work, polaron hops were described via the two-state Marcus/Holstein model of V V –V IV and O I –O II interchanges for electron and hole polarons respectively. The relevant parameters in the theory were obtained using the density functional theory DFT+U method. Hopping activation energies were combined with Einstein diffusion theory to yield mobility as well as with kinetic Monte Carlo (KMC) modeling. All unique nearest neighbor electron and hole hopping processes were characterized. For V-to-V hops of electron polarons, we obtained activation energies of ~0.37 eV that compare well with the experimental activation energy of ~0.30 eV for drift mobility. Electron polarons remain localized on single sites along the hopping pathways before hopping via tunneling, suggestive of small non-adiabatic coupling and a diabatic character consistent with V-to-V electron transfer through space (no bridge linkers). These simulations yield a small electron transport anisotropy, with transport in the (a,b) plane being faster than along the c direction by a factor of ~2. For hole polarons our calculations support the character of small polarons localized on O atoms as well. Some nearest neighbor hole hops have a diabatic character, while other nearest neighbor hops are adiabatic and phonon-assisted with an Arrhenius thermal dependence. Hops through O–V–O bridges and through space have low activation barriers (~0.17 eV and ~0.25 eV) while hops through O–Bi–O bridges have higher activation barriers (~0.37 eV and higher). The mobility is gated by the slower transport across VO 4 tetrahedra through O–Bi–O bridges owing to the underlying BVO lattice network. Hole mobility is determined to be about one order of magnitude larger than electron mobility consistent with THz spectroscopy measurements. Here, this work sets the foundation to address facet selectivity of charge carriers in shape and size-tailored crystals.