Current-controlled negative differential resistance has significant potential as a fundamental building block in brain-inspired neuromorphic computing. However, achieving desired negative differential resistance characteristics, which is crucial for practical implementation, remains challenging due to little consensus on the underlying mechanism and unclear design criteria. Here, we report a material-independent model of current-controlled negative differential resistance to explain a broad range of characteristics, including the origin of the discontinuous snap-back response observed in many transition metal oxides. This is achieved by explicitly accounting for a non-uniform current distribution in the oxide film and its impact on the effective circuit of the device, rather than a material-specific phase transition. The predictions of the model are then compared with experimental observations to show that the continuous S-type and discontinuous snap-back characteristics serve as fundamental building blocks for composite behaviour with higher complexity. Finally, we demonstrate the potential of our approach for predicting and engineering unconventional compound behaviour with novel functionality for emerging electronic and neuromorphic computing applications.

In-situ thermo-reflectance imaging is used to show that the discontinuous, snap-back mode of current-controlled negative differential resistance (CC-NDR) in NbO x -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 NbO x 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 longstanding controversy.Current-controlled negative differential resistance (NDR) is observed in a wide range of amorphous transition metal oxides (e.g. TiO x 1 , TaO x 2 , VO x 3 and NbO x 4,5 ) and is being used to fabricate devices for brain-inspired computing, including: trigger comparators 6 , self-sustained and chaotic oscillators 7-10 , threshold logic devices 11,12 and the emulation of biological neuronal dynamics 13,14 . In their simplest form such devices consist of simple metal-oxidemetal structures and exhibit a smooth transition from positive to negative differential resistance under current-controlled operation (hereafter referred to as S-type NDR) due to a rapid increase in device conductance, as shown in Figure 1a. In general this can arise from electronic, thermal or a combination of electronic and thermal processes but for amorphous

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/NbO x /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 NbO x 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 modeling 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 material 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.

Reactive metal electrodes (Nb, Ti, Cr, Ta, and Hf) are shown to play an important role in controlling the volatile switching characteristics of metal/Nb2O5/Pt devices. In particular, devices are shown to exhibit stable threshold switching under negative bias but to have a response under positive bias that depends on the choice of metal. Three distinct responses are highlighted: Devices with Nb and Ti top electrodes are shown to exhibit stable threshold switching with symmetric characteristics for both positive and negative polarities; devices with Cr top electrodes are shown to exhibit stable threshold switching but with asymmetric hysteresis windows under positive and negative polarities; and devices with Ta and Hf electrodes are shown to exhibit an integrated thresholdmemory (1S1M) response. Based on thermodynamic data and lumped element modelling these effects are attributed to the formation of a metal-oxide interlayer and its response to field-induced oxygen exchange. These results provide important insight into the physical origin of the switching response and pathways for engineering devices with reliable switching characteristics.

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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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Dual phase (DP) steels containing four different amounts of martensite ranging from 42 to 72 vol.-% have been developed from 0 . 42 wt-% carbon normalised steel by intercritical heat treatment at a xed temperature of 740°C but varying holding times followed by water quenching. Mechanical properties of dual phase steels with increasing volume fraction of martensite have been investigated highlighting the effect of martensite content. The macrohardness has been found to increase with increasing martensite content in dual phase steel. The yield and tensile strengths have been found to increase with increasing amount of martensite whereas the percentage elongation and the percentage area reduction have been found to decrease. This has been attributed to the presence of hard and brittle martensite phase, which increases the strength at the expense of ductility. The mode of fracture has been found to change from purely ductile to mixed (ductilezbrittle) as the martensite volume fraction increases from 42 to 72% in dual phase steels. Friction and wear properties under dry sliding conditions have also been found to improve with increasing martensite volume fraction in dual phase steels. The applications of medium carbon DP steels in the eld of mineral processing and mining have been discussed.MST/5974