Subfilamentary Networks in Memristive Devices

Redox-based memristive devices are one of the most attractive emerging memory technologies in terms of scaling, power consumption and speed. In these devices, external electrical stimuli cause changes of the resistance of an oxide layer sandwiched between two metal electrodes. In the simplest application, the device can be set into a low resistance state (LRS) and reset into a high resistance state (HRS), which may encode a logical one and zero, respectively. The major obstacle delaying large-scale application, however, is the large cycle-to-cycle (C2C) and device-to-device (D2D) variability of both LRS and HRS resistance values. These variabilities describe the stochastic nature of the switching process within one cell, resulting in different resistances obtained for each switching cycle and different resistances obtained for different cells on the same chip.
The switching process in transition metal oxides is believed to be driven by the nanoscale motion of oxygen vacancies, which form a so-called conductive filament bridging the metal electrodes. Application of electric fields results in a change in the vacancy concentration and, as a result, of the resistance. Changes of the microscopic structure of a single conductive filament, which are suspected to cause the C2C variability in memristive devices, have not yet been directly observed in experiment.
In the present study we employed spectromicroscopic photoemission threshold analysis and operando XAS analysis on graphene/SrTiO₃/Nb:SrTiO₃ memristive devices to identify the microscopic origin of variability. We find that a change of the shape of the conductive filament or variations in the oxygen vacancy distribution within the filament are indeed responsible for the observed variability.
The device schematic of our model system and a representative I-V curve are shown in Figure 1a and b. We investigated these devices using photoelectron emission microscopy (PEEM) aiming at verifying the microscopic origin of the variability of the obtained resistance values. To this purpose, we carried out combined XPEEM measurements (Nanospectroscopy beamline at Elettra synchrotron laboratory, Trieste, Italy) and threshold photoemission PEEM measurements using illumination by a mercury lamp (NanoESCA at Forschungszentrum Jülich, Germany). For the threshold photoemission analysis, several devices were switched into the LRS or HRS using the quasistatic I-V sweeps shown in Figure 1in air and mounted into the PEEM for each separate switching step as no biasing is possible within this instrument, while the XPEEM measurements were performed operando employing the same Set and Reset operations within the instrument. 
A threshold photoemission PEEM image of a representative device in the LRS is shown in 1c. Within the rather homogeneous graphene area, a region with enhanced contrast is clearly visible. The intensity of this feature varies reversibly with the resistance state after additional Reset and Set operations (Figure 1c-f), substantiating the hypothesis that this feature is the conductive filament. In the LRS, the energy difference between the secondary electron cut-off and the Fermi level ΔΦ^F is significantly more negative than in the HRS due to the presence of oxygen vacancies which lower the Schottky barrier at the electrode/oxide interface. Coming back to the question of C2C variability, it is very obvious from this experiment that the microscopic details of the filament change from cycle to cycle, and may in turn be responsible for differences in the resistance. The shape of the filament and the photoemission threshold as well as the distribution of regions of different photoemission threshold within the filament are significantly different in each state (Insets of Figure 1c-f).

OperandoXPEEM analysis of a similar device shows a non-circular, irregular filament shape (Figure 2a-d) of approximately 200 nm in diameter. The filament exhibits an inhomogeneous oxygen vacancy concentration across and around its core, as is evident from the map of the O K-edge A/B₂ peak ratio plotted in Figure 2c-d, which is representative of the vacancy concentration. Within the filament, there are regions of very different (high or medium) vacancy concentration. On average, the oxygen vacancy concentration is higher in the LRS than in the HRS, as is evident from the reduced peak A in the O K-edge spectrum (Figure 2e-f).
This observation confirms that conductive filaments do not necessarily exhibit a symmetric shape with a homogeneous gradient from a high oxygen vacancy concentration in the center to a low concentration at the edge, but rather possess a fine structure with regions with higher and lower vacancy concentration. At the same time, many small regions of enhanced contrast appear upon repeated cycling (Figure 1e), indicating that a multitude of such reduced regions can develop, which can be thought of as pre-filaments. It is very likely that both – the appearance of multiple filaments and their complex shape –  are related to the presence of nanoscale subfilamentary structures. The weight of each sub-filament varies from cycle to cycle, giving rise to the variability.