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
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