Deterministic mechanisms of spiking in diffusive memristors
Introduction
Memristors attract a lot of attention from the scientific community because of many useful features at very compact sizes and very low power consumption. An “ideal” memristor, suggested as a theoretical abstraction by Chua in 1971 [1], replaces an electrical circuit of about 15 transistors along with other active and passive elements, whereas contemporary physical realizations of memristors are comparable in size with a single transistor on a silicon wafer [2], [3]. The small size of the device and a rich set of nonlinear characteristics pose memristors among top ranked base elements for hardware implementation of artificial neural networks. In these kinds of networks, one has to implement electronic synapses and neurons, and memristors can serve as both of those [4], [5], [6], [7].
Because of the aforementioned reasons, memristors are also perfect for other high tech fields, including computer memory [8], encrypted communications [9], [10], [11], etc. Nowadays, many types of the device implementation are under investigation [12], [13], [14], [15], [16], [17]. In general, the memristor is a two-terminal device with resistance (memristance) depending on some internal parameter, which is controllable by total current (or charge) flowing through it. Thus, so-called nonvolatile memristors [18] offer an electronic analog to biological synapses. Complementary, volatile memristors [16], can be used to construct an electronic equivalent of biological neurons. Recently, memristor-based neurons demonstrated spiking with various biomimetic properties such as tonic spiking, bursting, spike frequency adaptation, refractory period, threshold variability, and so on [19].
There are many different realizations of volatile memristors based on various physical principles. For instance, the NbO-based memristor switches between high- and low-resistive states via phase transitions of channels, which connect memristive terminals, from an insulating state to a metallic one [20]. Another new type of a volatile memristor, the so-called diffusive memristor [21], switches due to diffusion of Ag-metallic nanoclusters in SiO from one memristor terminal to the other, forming a bridge between the terminals. The dynamics of this memristor is rich and complex because of the combination of nanomechanical (Ag-cluster motion), thermal, and electrical degrees of freedom [18]. Moreover, the diffusive memristor allows for emulating both short- and long-term plasticity of biological synapses, which makes it more advanced in comparison with other memristive systems [21].
Artificial neurons, based on various types of available volatile memristors [19], [20], can exhibit quite regular, deterministic spiking, which makes them very promising for oscillator-based computing [22], a new computational paradigm relying on accurate frequency and phase relationships between coupled oscillators. However, the artificial neurons based on diffusive memristors [21] show quite random spiking regimes, which causes a number of questions regarding their usage as main elements for oscillator-based computing. On the other hand, it is well known that biological neurons and especially synapses are very noisy by nature [23], so some stochasticity of basic elements of artificial spiking neural networks can be considered as an advantage in implementing brain-inspired intelligent systems. In fact, adding randomization at different stages of data processing by widely used artificial neural networks improves their characteristics during both training and working phases [24], [25], [26], [27].
Even though we have in mind complex ensembles of memristors, each single element should be analyzed and described well. In this paper, we investigate nanomechanical and electrical properties of a diffusive memristor, neglecting its stochasticity. We use the same model of a neuron, based on the diffusive memristor, as in Ref. [28], but the thermal noise is removed from the consideration and the memristor potential profile is changed significantly. Thus, we analyze the main spiking mode of the deterministic system of ordinary differential equations using the theory of bifurcations. We found out that even the simplified model is capable of exhibiting non-trivial behavior, which can be observed in more complicated models and in real devices, so our findings give a reference on how to tune a diffusive memristor to operate in a preferable way.
The presented model parameters were adjusted in accordance with the measured characteristics of diffusive memristors fabricated by our experimental group.
Section snippets
Artificial neuron model
The most common [29] neuromorphic circuit for an artificial neuron consists of a volatile memristor with a capacitor in parallel and a load resistor in series (see inset in Fig. 1). If DC voltage is applied, the system demonstrates oscillations of different nature depending on voltage, as described in Ref. [28]. In this work, we consider a diffusive memristor with Ag nanoclusters (hereafter, particles or nanoparticles) diffusing between two terminals and forming some particle distribution,
Memristor’s current-voltage characteristic
The suggested shape of the potential was motivated by the experimental observation of hysteresis in current-voltage () curves in both current- and voltage-driven modes of volatile memristors [35], [36], [37]. This observation implies the co-existence of both - and -types of the Negative Differential Resistance (NDR) within the same characteristic of the devices (similar phenomenon was observed in semiconductors [38]). This is an important feature of memristors, which predefines
Spiking
The electric circuit presented in Fig. 1 can be called an “artificial neuron” due to its ability of generating short impulses, similar to spikes of real biological nerve cells. Spiking in the memristor-based circuit resembles the well known Pearson-Anson effect [39] discovered first in a similar circuit, where a neon bulb was used instead of the memristor. In our case, the physical mechanism can be explained in a following way. From the beginning, when , the nanoparticle sits in the right
Bifurcation analysis
To reveal the instabilities leading to the onset of self-sustained oscillations in the memristive circuit shown in Fig. 1 we performed a bifurcation analysis of the model (2) summarized in Fig. 2b, which presents a two-parameter bifurcation diagram. Here, the green curve corresponds to the values of the parameters and for which the system demonstrates the Andronov-Hopf bifurcation. The red line represents a global bifurcation associating with appearance or disappearance of periodic
Experimental evidence
To make sure that our model grasps qualitatively the electric properties of real devices we compare the curves obtained in our simulations with experimentally measured ones.
The diffusive memristor samples were prepared using magnetron sputtering technique. 50 nm Pt bottom electrode was deposited on p-type Si (100) wafer, followed by co-sputtering Ag and SiO to obtain a nominal thickness of 100 nm. The layers were deposited by RF sputtering for SiO and DC sputtering for Ag, respectively.
Conclusion
We studied the deterministic mechanisms responsible for the onset of oscillatory regimes in the diffusive memristor with a pinning center. For this purpose, we modified the model of diffusive memristors describing the experiments in [11], [18], [21] by introducing the potential with pinning and by neglecting temperature-driven noise. The obtained model demonstrates the current-voltage characteristics similar to ones measured in real devices. In particular, the model reproduces the coexistence
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work was supported by The Engineering and Physical Sciences Research Council (EPSRC) (grant No EP/S032843/1).
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