Memristors for the Curious Outsiders

Recent Advances in Cerium Oxide-Based Memristors for Neuromorphic Computing

This review article attempts to provide a comprehensive review of the recent progress in cerium oxide (CeO2)-based resistive random-access memories (RRAMs). CeO2 is considered the most promising candidate because of its multiple oxidation states (Ce3+ and Ce4+), remarkable resistive-switching (RS) uniformity in DC mode, gradual resistance transition, cycling endurance, long data-retention period, and utilization of the RS mechanism as a dielectric layer, thereby exhibiting potential for neuromorphic computing. In this context, a detailed study of the filamentary mechanisms and their types is required. Accordingly, extensive studies on unipolar, bipolar, and threshold memristive behaviors are reviewed in this work. Furthermore, electrode-based (both symmetric and asymmetric) engineering is focused for the memristor's structures such as single-layer, bilayer (as an oxygen barrier layer), and doped switching-layer-based memristors have been proved to be unique CeO2-based synaptic devices. Hence, neuromorphic applications comprising spike-based learning processes, potentiation and depression characteristics, potentiation motion and synaptic weight decay process, short-term plasticity, and long-term plasticity are intensively studied. More recently, because learning based on Pavlov's dog experiment has been adopted as an advanced synoptic study, it is one of the primary topics of this review. Finally, CeO2-based memristors are considered promising compared to previously reported memristors for advanced synaptic study in the future, particularly by utilizing high-dielectric-constant oxide memristors.

Energy transport between heat baths with oscillating temperatures

Energy transport is a fundamental physical process that plays a prominent role in the function and performance of myriad systems and technologies. Recent experimental measurements have shown that subjecting a macroscale system to a time-periodic temperature gradient can increase thermal conductivity in comparison to a static temperature gradient. Here, we theoretically examine this mechanism in a nanoscale model by applying a stochastic Langevin framework to describe the energy transport properties of a particle connecting two heat baths with different temperatures, where the temperature difference between baths is oscillating in time. Analytical expressions for the energy flux of each heat bath and for the system itself are derived for the case of a free particle and a particle in a harmonic potential. We find that dynamical effects in the energy flux induced by temperature oscillations give rise to complex energy transport hysteresis effects. The presented results suggest that applying time-periodic temperature modulations is a potential route to control energy storage and release in molecular devices and nanosystems.

Proposal for Trapped-Ion Quantum Memristor

A quantum memristor combines the memristive dynamics with the quantum behavior of the system. We analyze the idea of a quantum memristor based on ultracold ions trapped in a Paul trap. Corresponding input and output memristor signals are the ion electronic levels populations. We show that under certain conditions the output/input dependence is a hysteresis curve similar to classical memristive devices. This behavior becomes possible due to the partial decoherence provided by the feedback loop, which action depends on previous state of the system (memory). The feedback loop also introduces nonlinearity in the system. Ion-based quantum memristor possesses several advantages comparing to other platforms-photonic and superconducting circuits-due to the presence of a large number of electronic levels with different lifetimes as well as strong Coulomb coupling between ions in the trap. The implementation of the proposed ion-based quantum memristor will be a significant contribution to the novel direction of "quantum neural networks".

Iontronic Neuromorphic Signaling with Conical Microfluidic Memristors

Experiments have shown that the conductance of conical channels, filled with an aqueous electrolyte, can strongly depend on the history of the applied voltage. These channels hence have a memory and are promising elements in brain-inspired (iontronic) circuits. We show here that the memory of such channels stems from transient concentration polarization over the ionic diffusion time. We derive an analytic approximation for these dynamics which shows good agreement with full finite-element calculations. Using our analytic approximation, we propose an experimentally realizable Hodgkin-Huxley iontronic circuit where micrometer cones take on the role of sodium and potassium channels. Our proposed circuit exhibits key features of neuronal communication such as all-or-none action potentials upon a pulse stimulus and a spike train upon a sustained stimulus.

Improved Performance of the Al2O3-Protected HfO2-TiO2 Base Layer with a Self-Assembled CH3NH3PbI3 Heterostructure for Extremely Low Operating Voltage and Stable Filament Formation in Nonvolatile Resistive Switching Memory

Herein, we report intriguing observations of an extremely stable nonvolatile bipolar resistive switching (NVBRS) memory device fabricated using HfO₂-TiO₂ topologically protected by Al₂O₃ as a stacked base layer for a CH₃NH₃PbI₃ (MAPI) electrolyte layer sandwiched between Ag and fluorine-doped tin oxide (FTO) electrodes. MAPI has been successfully synthesized by a rapid microwave-solvothermal (MW-ST) method within 10 min at 120 °C without requiring any inert gas atmosphere using low-cost precursors and solvents. Subsequently, MAPI powders are dissolved in aprotic solvents (DMF/DMSO = 8:2), and a spin-coated thin film is allowed to recrystallize upon annealing at 120 °C via a solution-based nanoscale self-assembly process. The fabricated memory device with the Ag/MAPI/Al₂O₃/TiO₂-HfO₂/FTO configuration shows an enhanced resistance ratio of 10⁵ for >10⁴ s at an extremely lower operating voltage (SET +0.2 V, RESET -0.2 V) when compared to that of the pristine MAPI device (±1 V, 10², 10⁴ s). We show that the memory device also exhibits a remarkable endurance of ≥3500 cycles due to the Al₂O₃ robust coating on the HfO₂-TiO₂ layer, facilitating prompt heterojunction formation. Thus, the adopted innovative strategies to prepare structurally and optically stable (∼1.5 years) MAPI under high-humid conditions could offer enhanced performance of NVBRS memory devices for medical, security, internet of things (IoT), and artificial intelligence (AI) applications.

Computational capacity of LRC, memristive, and hybrid reservoirs

Reservoir computing is a machine learning paradigm that uses a high-dimensional dynamical system, or reservoir, to approximate and predict time series data. The scale, speed, and power usage of reservoir computers could be enhanced by constructing reservoirs out of electronic circuits, and several experimental studies have demonstrated promise in this direction. However, designing quality reservoirs requires a precise understanding of how such circuits process and store information. We analyze the feasibility and optimal design of electronic reservoirs that include both linear elements (resistors, inductors, and capacitors) and nonlinear memory elements called memristors. We provide analytic results regarding the feasibility of these reservoirs and give a systematic characterization of their computational properties by examining the types of input-output relationships that they can approximate. This allows us to design reservoirs with optimal properties. By introducing measures of the total linear and nonlinear computational capacities of the reservoir, we are able to design electronic circuits whose total computational capacity scales extensively with the system size. Our electronic reservoirs can match or exceed the performance of conventional "echo state network" reservoirs in a form that may be directly implemented in hardware.

All-Printed Flexible Memristor with Metal–Non-Metal-Doped TiO2 Nanoparticle Thin Films

A memristor is a fundamental electronic device that operates like a biological synapse and is considered as the solution of classical von Neumann computers. Here, a fully printed and flexible memristor is fabricated by depositing a thin film of metal–non-metal (chromium-nitrogen)-doped titanium dioxide (TiO₂). The resulting device exhibited enhanced performance with self-rectifying and forming free bipolar switching behavior. Doping was performed to bring stability in the performance of the memristor by controlling the defects and impurity levels. The forming free memristor exhibited characteristic behavior of bipolar resistive switching with a high on/off ratio (2.5 × 10³), high endurance (500 cycles), long retention time (5 × 10³ s) and low operating voltage (±1 V). Doping the thin film of TiO₂ with metal–non-metal had a significant effect on the switching properties and conduction mechanism as it directly affected the energy bandgap by lowering it from 3.2 eV to 2.76 eV. Doping enhanced the mobility of charge carriers and eased the process of filament formation by suppressing its randomness between electrodes under the applied electric field. Furthermore, metal–non-metal-doped TiO₂ thin film exhibited less switching current and improved non-linearity by controlling the surface defects.

Learning by mistakes in memristor networks

Recent results revived the interest in the implementation of analog devices able to perform brainlike operations. Here we introduce a training algorithm for a memristor network which is inspired by previous work on biological learning. Robust results are obtained from computer simulations of a network of voltage-controlled memristive devices. Its implementation in hardware is straightforward, being scalable and requiring very little peripheral computation overhead.

Global minimization via classical tunneling assisted by collective force field formation

Simple elements interacting in networks can give rise to intricate emergent behaviors. Examples such as synchronization and phase transitions often apply in many contexts, as many different systems may reduce to the same effective model. Here, we demonstrate such a behavior in a model inspired by memristors. When weakly driven, the system is described by movement in an effective potential, but when strongly driven, instabilities cause escapes from local minima, which can be interpreted as an unstable tunneling mechanism. We dub this collective and nonperturbative effect a “Lyapunov force,” which steers the system toward the global minimum of the potential function, even if the full system has a constellation of equilibrium points growing exponentially with the system size. This mechanism is appealing for its physical relevance in nanoscale physics and for its possible applications in optimization, Monte Carlo schemes, and machine learning.

On the degeneracy of spin ice graphs, and its estimate via the Bethe permanent

The concept of spin ice can be extended to a general graph. We study the degeneracy of spin ice graph on arbitrary interaction structures via graph theory. We map spin ice graphs to the Ising model on a graph and clarify whether the inverse mapping is possible via a modified Krausz construction. From the gauge freedom of frustrated Ising systems, we derive exact, general results about frustration and degeneracy. We demonstrate for the first time that every spin ice graph, with the exception of the one-dimensional Ising model, is degenerate. We then study how degeneracy scales in size, using the mapping between Eulerian trails and spin ice manifolds, and a permanental identity for the number of Eulerian orientations. We show that the Bethe permanent technique provides both an estimate and a lower bound to the frustration of spin ices on arbitrary graphs of even degree. While such a technique can also be used to obtain an upper bound, we find that in all finite degree examples we studied, another upper bound based on Schrijver inequality is tighter.

Avalanches and edge-of-chaos learning in neuromorphic nanowire networks

The brain's efficient information processing is enabled by the interplay between its neuro-synaptic elements and complex network structure. This work reports on the neuromorphic dynamics of nanowire networks (NWNs), a unique brain-inspired system with synapse-like memristive junctions embedded within a recurrent neural network-like structure. Simulation and experiment elucidate how collective memristive switching gives rise to long-range transport pathways, drastically altering the network's global state via a discontinuous phase transition. The spatio-temporal properties of switching dynamics are found to be consistent with avalanches displaying power-law size and life-time distributions, with exponents obeying the crackling noise relationship, thus satisfying criteria for criticality, as observed in cortical neuronal cultures. Furthermore, NWNs adaptively respond to time varying stimuli, exhibiting diverse dynamics tunable from order to chaos. Dynamical states at the edge-of-chaos are found to optimise information processing for increasingly complex learning tasks. Overall, these results reveal a rich repertoire of emergent, collective neural-like dynamics in NWNs, thus demonstrating the potential for a neuromorphic advantage in information processing.

Study of Quantized Hardware Deep Neural Networks Based on Resistive Switching Devices, Conventional versus Convolutional Approaches

A comprehensive analysis of two types of artificial neural networks (ANN) is performed to assess the influence of quantization on the synaptic weights. Conventional multilayer-perceptron (MLP) and convolutional neural networks (CNN) have been considered by changing their features in the training and inference contexts, such as number of levels in the quantization process, the number of hidden layers on the network topology, the number of neurons per hidden layer, the image databases, the number of convolutional layers, etc. A reference technology based on 1T1R structures with bipolar memristors including HfO2 dielectrics was employed, accounting for different multilevel schemes and the corresponding conductance quantization algorithms. The accuracy of the image recognition processes was studied in depth. This type of studies are essential prior to hardware implementation of neural networks. The obtained results support the use of CNNs for image domains. This is linked to the role played by convolutional layers at extracting image features and reducing the data complexity. In this case, the number of synaptic weights can be reduced in comparison to MLPs.

Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System

In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four-dimensional (4D) Euler equation. The generalized Hamiltonian energy function has been given, and it is composed of conservative and non-conservative parts of the Hamiltonian. The Hamiltonian of the Euler equation remains constant, while the three-terminal memristor’s Hamiltonian is mutative, causing non-conservation in energy. Through proof, only centers or saddles equilibria exist, which meets the definition of the conservative system. A non-Hamiltonian conservative chaotic system is proposed. The Hamiltonian of the conservative part determines whether the system can produce chaos or not. The non-conservative part affects the dynamic of the system based on the conservative part. The chaotic and quasiperiodic orbits are generated when the system has different Hamiltonian levels. Lyapunov exponent (LE), Poincaré map, bifurcation and Hamiltonian diagrams are used to analyze the dynamical behavior of the non-Hamiltonian conservative chaotic system. The frequency and initial values of the system have an extensive variable range. Through the mechanism adjustment, instead of trial-and-error, the maximum LE of the system can even reach an incredible value of 963. An analog circuit is implemented to verify the existence of the non-Hamiltonian conservative chaotic system, which overcomes the challenge that a little bias will lead to the disappearance of conservative chaos.

Quantum Memristors in Frequency-Entangled Optical Fields

A quantum memristor is a passive resistive circuit element with memory, engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system-bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequency-entangled optical fields and a frequency mixer that, working similarly to a beam splitter, produces state superpositions. We show that the characteristic hysteretic behavior of memristors can be reproduced when analyzing the response of the system with respect to the control, for different experimentally attainable states. Since memory effects in memristors can be exploited for classical and neuromorphic computation, the results presented in this work could be a building block for constructing quantum neural networks in quantum photonics, when scaling up.

Compensating Circuit to Reduce the Impact of Wire Resistance in a Memristor Crossbar-Based Perceptron Neural Network

Wire resistance in metal wire is one of the factors that degrade the performance of memristor crossbar circuits. In this paper, an analysis of the impact of wire resistance in a memristor crossbar is performed and a compensating circuit is proposed to reduce the impact of wire resistance in a memristor crossbar-based perceptron neural network. The goal of the analysis is to figure out how wire resistance influences the output voltage of a memristor crossbar. It emerges that the wire resistance on horizontal lines causes the neuron’s output voltage to vary more than the wire resistance on vertical lines. More interesting, the voltage variation caused by wire resistance on horizontal lines increases proportionally to the length of metal wire. The first column has small voltage variation whereas the last column has large voltage variation. In addition, two adjacent columns have almost the same amount of voltage variation. Under these observations, a memristor crossbar-based perceptron neural network with compensating circuit is proposed. The neuron’s outputs of two columns are put into a subtractor circuit to eliminate the voltage variation caused by the wire resistance. The proposed memristor crossbar-based perceptron neural network is trained to recognize the 26 characters. The proposed memristor crossbar shows better recognition rate compared to the previous work when wire resistance is taken into account. The proposed memristor crossbar circuit can maintain the recognition rate as high as 100% when wire resistance is as high as 2.5 Ω. By contrast, the recognition rate of the memristor crossbar without the compensating circuit decreases by 1%, 5%, and 19% when wire resistance is set to be 1.5, 2.0, and 2.5 Ω, respectively.

Asymptotic Behavior of Memristive Circuits

The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics, and a strong dependence on the circuit topology. We provide evidence that also purely memristive circuits can be employed for computational purposes. In the present paper we show that a polynomial Lyapunov function in the memory parameters exists for the case of DC controlled memristors. Such a Lyapunov function can be asymptotically approximated with binary variables, and mapped to quadratic combinatorial optimization problems. This also shows a direct parallel between memristive circuits and the Hopfield-Little model. In the case of Erdos-Renyi random circuits, we show numerically that the distribution of the matrix elements of the projectors can be roughly approximated with a Gaussian distribution, and that it scales with the inverse square root of the number of elements. This provides an approximated but direct connection with the physics of disordered system and, in particular, of mean field spin glasses. Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit. We estimate the number of stationary points of the approximate Lyapunov function and provide a scaling formula as an upper bound in terms of the circuit topology only.

Memristor in a Reservoir System-Experimental Evidence for High-Level Computing and Neuromorphic Behavior of PbI2

Lead halides in an asymmetric layered structure form memristive devices which are controlled by the electronic structure of the PbX₂|metal interface. In this paper, we explain the mechanism that stands behind the I- V pinched hysteresis loop of the device and shortly present its synaptic-like plasticity (spike-timing-dependent plasticity and spike-rate-dependent plasticity) and nonvolatile memory effects. This memristive element was incorporated into a reservoir system, in particular, the echo-state network with delayed feedback, which exhibits brain-like recurrent behavior and demonstrates metaplasticity as one of the available learning mechanisms. It can serve as a classification system that classifies input signals according to their amplitude.