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A simple means of detecting and spatially mapping volatile and nonvolatileconductive filaments in metal/oxide/metal cross-point devices is introduced andits application demonstrated. The technique is based on thermal discolourationof a thin photoresist layer deposited on the top electrode of the cross-pointdevice and relies on the increase in temperature produced by local Jouleheating of an underlying conductive filament. Finite element modelling of thetemperature distribution and its dependencies shows that the maximumtemperature at the top-electrode/photoresist interface is particularlysensitive to the top-electrode thickness. The technique is demonstrated on NbOxbased 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 filamentlocation as a function of device area. This shows that filament formation isheterogeneous. The majority of filaments form preferentially along thetop-electrode edge and the fraction of these increases with decreasing devicearea. Transmission electron microscopy of the top and bottom electrode edges isused to explain this observation and suggests that it is due to a reduction inthe effective oxide thickness in this region.

Detection and spatial mapping of conductive filaments in metal/oxide/metal cross-point devices