  A simple means of detecting and spatially mapping volatile and nonvolatile
conductive filaments in metal/oxide/metal cross-point devices is introduced and
its application demonstrated. The technique is based on thermal discolouration
of a thin photoresist layer deposited on the top electrode of the cross-point
device and relies on the increase in temperature produced by local Joule
heating of an underlying conductive filament. Finite element modelling of the
temperature distribution and its dependencies shows that the maximum
temperature at the top-electrode/photoresist interface is particularly
sensitive to the top-electrode thickness. The technique is demonstrated on NbOx
based metal-oxide-metal cross-point devices with a 25 nm thick top (Pt)
electrode, where it is used to undertake a statistical analysis of the filament
location as a function of device area. This shows that filament formation is
heterogeneous. The majority of filaments form preferentially along the
top-electrode edge and the fraction of these increases with decreasing device
area. Transmission electron microscopy of the top and bottom electrode edges is
used to explain this observation and suggests that it is due to a reduction in
the effective oxide thickness in this region.
