The transient conductance response of the same TiO 2 memristor is first utilized to model STP changes in synapses, as shown on Fig. 2a,b. Figure 2c shows the voltage pulse pattern used to produce these responses (see supplementary material Figure S3 for a detailed description of the experimental setup used here that evolved into the one described in66). Each voltage pulse induces an increase in the conductance of the device, which then tends to slowly decay to its original state. Subsequent pulses have a similar effect that however depend on the previous resistive state of the device, the conductance peaks can be lower or higher in magnitude than the first peak, similar to short term plasticity mechanisms, as observed in biological synapses41.

Figure 2 A single memristor functioning both as a facilitating and saturated synapse. Shown are: (a) repeated STP-F and (b) STP-S post-synaptic response with simulation of the contributions of each pulse to a pre-synaptic neuron’s membrane potential with τ = 50 ms and appropriate STP model fitting (details in supplementary materials), (c) illustrates the pre-synaptic pulsing sequence applied to the memristive synaptic mimic; (d,e) delineate the corresponding occurrence probability of STP-F and STP-S events with respect to G 0 , while (f) presents measured transient conductance drift invoked by a train of three pulses (width = 10 μs, t int = 200 ms, t rec = 20 s), repeated 20 times. Full size image

In particular, the form of short-term plasticity emulated with this device is “short-term facilitation”. Figure 2a,b show two different cases of facilitation: in Fig. 2a we reproduce the classical form of short-term facilitation (here denoted as STP-F), where each input pulse has the effect of increasing the conductance, including its peak response. At the arrival of the first pulse the memristive conductance increases from the base line (blue line) allowing current to pass through to the neuron, causing an increase on the membrane potential of the connected neuron, shown by the black solid line. On the second spike, the conductance transiently increases even more and so at the third spike, leading to a behavior akin to short-term potentiation, where the synaptic efficacy transiently changes in short time scales. The observed phenomenon is clearly non-linear and cannot be explained by the linear summation of the input signals. We have deliberately chosen a fast membrane potential time constant so that no residuals are remaining from the previous spikes, demonstrating that each spike indeed contributes to the membrane voltage by a different amount. Modeling the measured conductance peaks by a reduced version of the Tsodyks-Markram model67 (see supplementary section), verified quantitatively the equivalence with biological synapses and also revealed that the time constants involved in the process are close to typical biological values. At a subset of our experiments, particularly when the initial conductance of the material is a relatively higher state, the same protocol will lead to a transient conductance at the second and third spike clearly lower than the initial one. We call this phenomenon saturation (STP-S) and we provide a hypothesis of how this deviation from the typically observed response of the memristors occurs. We argue that with every pulse, the potential alignment of filaments comprising of reduced TiO 2 leads to a higher conductive state, following the model presented in Fig. 1b. In the case where the provided energy does not exceed the instantaneous E i that would cause the device to undergo LTP or LTD (in the case of a significant energetic overshoot), such a transition is revertible and after a transient the conductance returns to its initial state. However, if the provided energy will be (is about to be) dissipated via an existing (partially formed) filament, at the same time annihilating it, we will most likely observe saturation in the response, as shown in Fig. 2b. We argue that the exhibited STP-S response stems from the mobility saturation of the available ionic resources (mainly O−2 vacancies) in the vicinity of a partially reduced TiO 2−x volume, i.e. a partially formed filament, particularly when the device has been previously stimulated. Clearly, a finite number of mobile resources exist within the volume of interest that can play a role in reducing TiO 2 from insulating towards (semi-) metallic phases, i.e. towards forming a conductive filament. And as single devices could in principle host multiple filaments46 within their functional cores, alike short-term plasticity phenomena can be triggered across a wide conductance spectrum (see Figure S8 in supplementary material).

In a concurrent experiment, the same device was subjected to a train of 3 consecutive voltage pulses of −4 V, 10 μs wide and inter-pulse interval t int = 400 ms. This sequence was repeated 600 times with a recovery interval between sequences t rec = 10 s, to allow for the device’s state being restored. The pre-stimuli initial conductance was found to vary within 2.85 and 3.1 μS. This range was divided into 17 equal conductance bins with STP-F and STP-S events discriminated (as in Fig. 2a,b) and plotted with respect to the device’s initial conductance (Figure S9). It is interesting to note that during the experiment the initial conductance range increased to values above 2.95 μS, possibly due to the partial formation of a new stable filament. This effect yielded a new equilibrium conductance at which the device could settle. Nonetheless, for both stable-state conditions, STP-S events are more likely to manifest at higher conductance levels than STP-F events, as shown by the corresponding probabilities of STP-F (Fig. 2d) and STP-S (Fig. 2e) occurrences. This illustrates the strong probabilistic switching nature that under the classical ReRAM context will contribute substantially to the devices unreliability.

In relation to the occurrence of the STP events presented in Fig. 2d,e, we have recorded all events of a single device when repeatedly excited with a stimulating scheme comprising three voltage pulses of 4 V, 10 μs wide, t int = 200 ms and t rec = 20 s, as illustrated in Fig. 2f. Facilitating (depressing-like) events have been colored mapped with blue (red), following a simple qualitative rule: if the initial conductance of the device is smaller (larger) than the immediate post-stimuli conductance then this event is considered as STP-F (STP-S). Initially, a steadily increase in the memristor’s conductance is observed. When however a critically high conductance is reached, depressing-like events are activated to restore the low conductance level; this trend occurs consistently when observed over a long period of time.

We further studied the effect of the amplitude and rate of the stimulating scheme in controlling the short-term dynamics of our prototypes. Figure 3a shows the transient conductance change for a two-pulses (spikes) input for inter-spike intervals ranging from 20 ms up to 200 ms. This change is recoverable after a period of time as measurements after 1–120 s show (see also supplementary material Figure S10). A clear correlation is found between the conductance decay and the interpulse timing, with the decay time constant being smaller for lower pulsing rates, as also illustrated in Fig. 3a. This adheres with the notion that when repeated training of an event occurs within a short period of time it becomes more difficult to forget this event. Details about the fitting and parameter extraction methods are found in the supplementary material. Figure 3b depicts the contribution of each pulse stimulus to the device’s conductance as a function of the stimulus amplitude; large amplitudes contribute a higher conductance modulation. The volatile behavior of our prototypes can be reproduced by an equivalent SPICE circuit model that we have presented previously68, as demonstrated for example in Fig. 3c.