  In-situ thermo-reflectance imaging is used to show that the discontinuous,
snap-back mode of current-controlled negative differential resistance (CC-NDR)
in NbOx-based devices is a direct consequence of current localization and
redistribution. Current localisation is shown to result from the creation of a
conductive filament either during electroforming or from current bifurcation
due to the super-linear temperature dependence of the film conductivity. The
snap-back response then arises from current redistribution between regions of
low and high current-density due to the rapid increase in conductivity created
within the high current density region. This redistribution is further shown to
depend on the relative resistance of the low current-density region with the
characteristics of NbOx cross-point devices transitioning between continuous
and discontinuous snap-back modes at critical values of film conductivity,
area, thickness and temperature, as predicted. These results clearly
demonstrate that snap-back is a generic response that arises from current
localization and redistribution within the oxide film rather than a
material-specific phase transition, thus resolving a long-standing controversy.
