We have used high-voltage
Kelvin probe force microscopy to map
the spatial distribution of electrical potential, dropped along curved
current-carrying conducting domain walls, in x-cut single-crystal
ferroelectric lithium niobate thin films. We find that in-operando potential profiles and extracted electric fields, associated with p–n junctions contained within the walls, can be
fully rationalized through expected variations in wall resistivity
alone. There is no need to invoke additional physics (carrier depletion
zones and space-charge fields) normally associated with extrinsically
doped semiconductor p–n junctions. Indeed,
we argue that this should not even be expected, as inherent Fermi
level differences between p and n regions, at the core of conventional p–n junction behavior, cannot occur in domain walls that are surrounded
by a common matrix. This is important for domain-wall nanoelectronics,
as such in-wall junctions will neither act as diodes nor facilitate
transistors in the same way as extrinsic semiconducting systems do.