Fig. 6: Small polaron hopping.
From: Low-bias photoelectrochemical water splitting via mediating trap states and small polaron hopping
a Schematic small polaron hopping paths in the phosphorus-doped BiVO4 sample for DFT calculations. Only V (red) and phosphorus (purple) atoms are displayed in the schematic structure model. Atoms highlighted are within the supercell and the rest are in the neighbor cells. The colored arrows are the selected hopping paths in the calculations. b Hopping energy barriers in phosphorus-doped BiVO4 sample along the reaction coordination of different reactions paths. The dashed line represents the hopping barrier in pristine BiVO4. The below table shows the hopping barriers of different paths in phosphorus-doped BiVO4. c Schematic small polaron formation: Initial excitation of BiVO4 leads to a charge transfer transition from oxygen (light grey) to V atom (blue). The initial excited carriers undergo optical-phonon scattering, during which the charge can be trapped in a small polaron, resulting the lattice expansion. Adapted and reprinted with permission from Rettie, A. J. E., Chemelewski, W. D., Emin, D. & Mullins, C. B. Unravelling small-polaron transport in metal oxide photoelectrodes. J. Phys. Chem. Lett. 7, 471–479 (2016). Copyright 2016 American Chemical Society. d Schematic small polaron hopping between two identical V atoms in VO4 units with potential energy landscape. Solid circles indicate the polaron location. The dark and red dashed curves indicate adiabatic surfaces of BiVO4 and phosphorus-doped BiVO4 samples, respectively. Ea and Ea’ represents the polaron hopping energy barriers of BiVO4 and phosphorus doped BiVO4 samples. Adapted and reprinted with permission from Rettie, A. J. E., Chemelewski, W. D., Emin, D. & Mullins, C. B. Unravelling small-polaron transport in metal oxide photoelectrodes. J. Phys. Chem. Lett. 7, 471–479 (2016). Copyright 2016 American Chemical Society. e The potential energy surface for the ground and the photon excited states with polaron formation states and the corresponding re-excitation energy barriers (EST) for BiVO4 (solid red) and phosphorus-doped BiVO4 (dashed red) samples.
