  Electroforming is used to initiate the memristive response in
metal/oxide/metal devices by creating a filamentary conduction path in the
oxide film. Here we use a simple photoresist-based detection technique to map
the spatial distribution of conductive filaments formed in Nb/NbOx/Pt devices,
and correlate these with current-voltage characteristics and in-situ
thermoreflectance measurements to identify distinct modes of electroforming in
low and high conductivity NbOx films. In low conductivity films the filaments
are randomly distributed within the oxide film, consistent with a field-induced
weakest-link mechanism, while in high conductivity films they are concentrated
in the center of the film. In the latter case the current-voltage
characteristics and in-situ thermoreflectance imaging show that electroforming
is associated with current bifurcation into regions of low and high current
density. This is supported by finite element modelling of the current
distribution and shown to be consistent with predictions of a simple core-shell
model of the current distribution. These results clearly demonstrate two
distinct modes of electroforming in the same materials system and show that the
dominant mode depends on the conductivity of the film, with field-induced
electroforming dominant in low conductivity films and current-bifurcation
induced electroforming dominant in high conductivity films. Finally, we
demonstrate S-type and snap-back negative differential resistance in the high
conductivity films and explain this behavior in terms of two-zone model.
