Photovoltage from ferroelectric domain walls in BiFeO$_3$

It has been debated for a decade whether the photovoltage in BiFeO$_3$ originates in a bulk photovoltaic effect, a ferroelectric domain-wall effect, or a combination of both. In order to elucidate the role of ferroelectric domain walls for the photovoltaic effect in BiFeO$_3$, we calculated the photovoltage of a single ferroelectric domain wall stemming from photo-generated electron-hole pairs residing at the ferroelectric domain wall, using first-principles calculations based on density-functional theory. We find that at the ferroelectric domain walls the electron-hole pairs form an electric dipole layer resulting in a saw-tooth shaped electronic potential, hence creating a domain-wall driven voltage upon illumination. This domain-wall driven photovoltage in BiFeO$_3$ is smaller than the experimentally measured photovoltage for light intensities up to several tens of mW/cm$^2$, indicating that bulk effects, not domain-wall effects, dominate the photovoltaic effect in BiFeO$_3$ in this intensity range.