Decision trees within a molecular memristor.

Profuse dendritic-synaptic interconnections among neurons in the neocortex embed intricate logic structures enabling sophisticated decision-making that vastly outperforms any artificial electronic analogues1-3. The physical complexity is far beyond existing circuit fabrication technologies: moreover, the network in a brain is dynamically reconfigurable, which provides flexibility and adaptability to changing environments4-6. In contrast, state-of-the-art semiconductor logic circuits are based on threshold switches that are hard-wired to perform predefined logic functions. To advance the performance of logic circuits, we are re-imagining fundamental electronic circuit elements by expressing complex logic in nanometre-scale material properties. Here we use voltage-driven conditional logic interconnectivity among five distinct molecular redox states of a metal-organic complex to embed a 'thicket' of decision trees (composed of multiple if-then-else conditional statements) having 71 nodes within a single memristor. The resultant current-voltage characteristic of this molecular memristor (a 'memory resistor', a globally passive resistive-switch circuit element that axiomatically complements the set of capacitor, inductor and resistor) exhibits eight recurrent and history-dependent non-volatile switching transitions between two conductance levels in a single sweep cycle. The identity of each molecular redox state was determined with in situ Raman spectroscopy and confirmed by quantum chemical calculations, revealing the electron transport mechanism. Using simple circuits of only these elements, we experimentally demonstrate dynamically reconfigurable, commutative and non-commutative stateful logic in multivariable decision trees that execute in a single time step and can, for example, be applied as local intelligence in edge computing7-9.

Third-order nanocircuit elements for neuromorphic engineering.

Current hardware approaches to biomimetic or neuromorphic artificial intelligence rely on elaborate transistor circuits to simulate biological functions. However, these can instead be more faithfully emulated by higher-order circuit elements that naturally express neuromorphic nonlinear dynamics1-4. Generating neuromorphic action potentials in a circuit element theoretically requires a minimum of third-order complexity (for example, three dynamical electrophysical processes)5, but there have been few examples of second-order neuromorphic elements, and no previous demonstration of any isolated third-order element6-8. Using both experiments and modelling, here we show how multiple electrophysical processes-including Mott transition dynamics-form a nanoscale third-order circuit element. We demonstrate simple transistorless networks of third-order elements that perform Boolean operations and find analogue solutions to a computationally hard graph-partitioning problem. This work paves a way towards very compact and densely functional neuromorphic computing primitives, and energy-efficient validation of neuroscientific models.

Potential and challenges of computing with molecular materials.

We are at an inflection point in computing where traditional technologies are incapable of keeping up with the demands of exploding data collection and artificial intelligence. This challenge demands a leap to a new platform as transformative as the digital silicon revolution. Over the past 30 years molecular materials for computing have generated great excitement but continually fallen short of performance and reliability requirements. However, recent reports indicate that those historical limitations may have been resolved. Here we assess the current state of computing with molecular-based materials, especially using transition metal complexes of redox active ligands, in the context of neuromorphic computing. We describe two complementary research paths necessary to determine whether molecular materials can be the basis of a new computing technology: continued exploration of the molecular electronic properties that enable computation and, equally important, the process development for on-chip integration of molecular materials.

Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing.

At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal-insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator and observe a tunable range of periodic and chaotic self-oscillations. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such memristors into the hardware of a Hopfield computing network can greatly improve the efficiency and accuracy of converging to a solution for computationally difficult problems.

Fast Spiking of a Mott VO2-Carbon Nanotube Composite Device.

The recent surge of interest in brain-inspired computing and power-efficient electronics has dramatically bolstered development of computation and communication using neuron-like spiking signals. Devices that can produce rapid and energy-efficient spiking could significantly advance these applications. Here we demonstrate direct current or voltage-driven periodic spiking with sub-20 ns pulse widths from a single device composed of a thin VO2 film with a metallic carbon nanotube as a nanoscale heater, without using an external capacitor. Compared with VO2-only devices, adding the nanotube heater dramatically decreases the transient duration and pulse energy, and increases the spiking frequency, by up to 3 orders of magnitude. This is caused by heating and cooling of the VO2 across its insulator-metal transition being localized to a nanoscale conduction channel in an otherwise bulk medium. This result provides an important component of energy-efficient neuromorphic computing systems and a lithography-free technique for energy-scaling of electronic devices that operate via bulk mechanisms.

Summary of the Faraday Discussion on New memory paradigms: memristive phenomena and neuromorphic applications.

The Faraday Discussion on New memory paradigms: memristive phenomena and neuromorphic systems was held from October 15-17 on the campus of the Rheinisch-Westfälische Technische Hochschule Aachen University, or RWTH Aachen University, under the auspices of the Royal Society of Chemistry. The Discussion brought together over 100 experts and students from over 20 different countries to present, question, and debate the latest breakthroughs in a field that is exhibiting dramatic growth. There were a large number of excellent oral presentations and posters covering the topics of the Discussion, and the conversations among the participants were lively and informative. The first day and a half encompassed the experimental characterization and analysis of memristors for which the primary resistive switching mechanisms involved electrochemical metallization, chemical valence transformation, or thermodynamic phase change, which illustrated the diversity of the physical properties that can be harnessed for building memristive systems. The final half-day of the Discussion was devoted to synaptic and neuromorphic functions of memristors, which have been growing explosively in the past few years and demonstrate that resistive switching is important for much more than a non-volatile memory, but can also be utilized for learning and computation. The high quality of the presentations and discussions in this section demonstrated that this new research area has been solidly launched and we can expect significant advancements and real applications within a few years as new discoveries from biology are incorporated into neuromorphic hardware. I will not attempt to recapitulate the content of all of the sessions here, since the papers collected for this Faraday Discussions volume speak more eloquently for themselves than I can affect. What I hope to accomplish is to point out a few general concepts that arose when considering multiple papers together, especially during the discussions, and point out a particularly novel concept that deserves special attention.

Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing.

The accumulation and extrusion of Ca2+ in the pre- and postsynaptic compartments play a critical role in initiating plastic changes in biological synapses. To emulate this fundamental process in electronic devices, we developed diffusive Ag-in-oxide memristors with a temporal response during and after stimulation similar to that of the synaptic Ca2+ dynamics. In situ high-resolution transmission electron microscopy and nanoparticle dynamics simulations both demonstrate that Ag atoms disperse under electrical bias and regroup spontaneously under zero bias because of interfacial energy minimization, closely resembling synaptic influx and extrusion of Ca2+, respectively. The diffusive memristor and its dynamics enable a direct emulation of both short- and long-term plasticity of biological synapses, representing an advance in hardware implementation of neuromorphic functionalities.

Low-Power, Self-Rectifying, and Forming-Free Memristor with an Asymmetric Programing Voltage for a High-Density Crossbar Application.

A Pt/NbOx/TiOy/NbOx/TiN stack integrated on a 30 nm contact via shows a programming current as low as 10 nA and 1 pA for the set and reset switching, respectively, and a self-rectifying ratio as high as ∼105, which are suitable characteristics for low-power memristor applications. It also shows a forming-free characteristic. A charge-trap-associated switching model is proposed to account for this self-rectifying memrisive behavior. In addition, an asymmetric voltage scheme (AVS) to decrease the write power consumption by utilizing this self-rectifying memristor is also described. When the device is used in a 1000 × 1000 crossbar array with the AVS, the programming power can be decreased to 8.0% of the power consumption of a conventional biasing scheme. If the AVS is combined with a nonlinear selector, a power consumption reduction to 0.31% of the reference value is possible.

Repeatable, accurate, and high speed multi-level programming of memristor 1T1R arrays for power efficient analog computing applications.

Beyond use as high density non-volatile memories, memristors have potential as synaptic components of neuromorphic systems. We investigated the suitability of tantalum oxide (TaOx) transistor-memristor (1T1R) arrays for such applications, particularly the ability to accurately, repeatedly, and rapidly reach arbitrary conductance states. Programming is performed by applying an adaptive pulsed algorithm that utilizes the transistor gate voltage to control the SET switching operation and increase programming speed of the 1T1R cells. We show the capability of programming 64 conductance levels with <0.5% average accuracy using 100 ns pulses and studied the trade-offs between programming speed and programming error. The algorithm is also utilized to program 16 conductance levels on a population of cells in the 1T1R array showing robustness to cell-to-cell variability. In general, the proposed algorithm results in approximately 10× improvement in programming speed over standard algorithms that do not use the transistor gate to control memristor switching. In addition, after only two programming pulses (an initialization pulse followed by a programming pulse), the resulting conductance values are within 12% of the target values in all cases. Finally, endurance of more than 10(6) cycles is shown through open-loop (single pulses) programming across multiple conductance levels using the optimized gate voltage of the transistor. These results are relevant for applications that require high speed, accurate, and repeatable programming of the cells such as in neural networks and analog data processing.

'Memristive' switches enable 'stateful' logic operations via material implication.

The authors of the International Technology Roadmap for Semiconductors-the industry consensus set of goals established for advancing silicon integrated circuit technology-have challenged the computing research community to find new physical state variables (other than charge or voltage), new devices, and new architectures that offer memory and logic functions beyond those available with standard transistors. Recently, ultra-dense resistive memory arrays built from various two-terminal semiconductor or insulator thin film devices have been demonstrated. Among these, bipolar voltage-actuated switches have been identified as physical realizations of 'memristors' or memristive devices, combining the electrical properties of a memory element and a resistor. Such devices were first hypothesized by Chua in 1971 (ref. 15), and are characterized by one or more state variables that define the resistance of the switch depending upon its voltage history. Here we show that this family of nonlinear dynamical memory devices can also be used for logic operations: we demonstrate that they can execute material implication (IMP), which is a fundamental Boolean logic operation on two variables p and q such that pIMPq is equivalent to (NOTp)ORq. Incorporated within an appropriate circuit, memristive switches can thus perform 'stateful' logic operations for which the same devices serve simultaneously as gates (logic) and latches (memory) that use resistance instead of voltage or charge as the physical state variable.

A scalable neuristor built with Mott memristors.

The Hodgkin-Huxley model for action potential generation in biological axons is central for understanding the computational capability of the nervous system and emulating its functionality. Owing to the historical success of silicon complementary metal-oxide-semiconductors, spike-based computing is primarily confined to software simulations and specialized analogue metal-oxide-semiconductor field-effect transistor circuits. However, there is interest in constructing physical systems that emulate biological functionality more directly, with the goal of improving efficiency and scale. The neuristor was proposed as an electronic device with properties similar to the Hodgkin-Huxley axon, but previous implementations were not scalable. Here we demonstrate a neuristor built using two nanoscale Mott memristors, dynamical devices that exhibit transient memory and negative differential resistance arising from an insulating-to-conducting phase transition driven by Joule heating. This neuristor exhibits the important neural functions of all-or-nothing spiking with signal gain and diverse periodic spiking, using materials and structures that are amenable to extremely high-density integration with or without silicon transistors.

The missing memristor found.

Anyone who ever took an electronics laboratory class will be familiar with the fundamental passive circuit elements: the resistor, the capacitor and the inductor. However, in 1971 Leon Chua reasoned from symmetry arguments that there should be a fourth fundamental element, which he called a memristor (short for memory resistor). Although he showed that such an element has many interesting and valuable circuit properties, until now no one has presented either a useful physical model or an example of a memristor. Here we show, using a simple analytical example, that memristance arises naturally in nanoscale systems in which solid-state electronic and ionic transport are coupled under an external bias voltage. These results serve as the foundation for understanding a wide range of hysteretic current-voltage behaviour observed in many nanoscale electronic devices that involve the motion of charged atomic or molecular species, in particular certain titanium dioxide cross-point switches.

Electrical performance and scalability of Pt dispersed SiO2 nanometallic resistance switch.

Highly reproducible bipolar resistance switching was recently demonstrated in a composite material of Pt nanoparticles dispersed in silicon dioxide. Here, we examine the electrical performance and scalability of this system and demonstrate devices with ultrafast (<100 ps) switching, long state retention (no measurable relaxation after 6 months), and high endurance (>3 × 10(7) cycles). A possible switching mechanism based on ion motion in the film is discussed based on these observations.

True random number generation using the spin crossover in LaCoO3.

While digital computers rely on software-generated pseudo-random number generators, hardware-based true random number generators (TRNGs), which employ the natural physics of the underlying hardware, provide true stochasticity, and power and area efficiency. Research into TRNGs has extensively relied on the unpredictability in phase transitions, but such phase transitions are difficult to control given their often abrupt and narrow parameter ranges (e.g., occurring in a small temperature window). Here we demonstrate a TRNG based on self-oscillations in LaCoO3 that is electrically biased within its spin crossover regime. The LaCoO3 TRNG passes all standard tests of true stochasticity and uses only half the number of components compared to prior TRNGs. Assisted by phase field modeling, we show how spin crossovers are fundamentally better in producing true stochasticity compared to traditional phase transitions. As a validation, by probabilistically solving the NP-hard max-cut problem in a memristor crossbar array using our TRNG as a source of the required stochasticity, we demonstrate solution quality exceeding that using software-generated randomness.

Memristors with Tunable Volatility for Reconfigurable Neuromorphic Computing.

Neuromorphic computing promises an energy-efficient alternative to traditional digital processors in handling data-heavy tasks, primarily driven by the development of both volatile (neuronal) and nonvolatile (synaptic) resistive switches or memristors. However, despite their energy efficiency, memristor-based technologies presently lack functional tunability, thus limiting their competitiveness with arbitrarily programmable (general purpose) digital computers. This work introduces a two-terminal bilayer memristor, which can be tuned among neuronal, synaptic, and hybrid behaviors. The varying behaviors are accessed via facile control over the filament formed within the memristor, enabled by the interplay between the two active ionic species (oxygen vacancies and metal cations). This solution is unlike single-species ion migration employed in most other memristors, which makes their behavior difficult to control. By reconfiguring a single crossbar array of hybrid memristors, two different applications that usually require distinct types of devices are demonstrated - reprogrammable heterogeneous reservoir computing and arbitrary non-Euclidean graph networks. Thus, this work outlines a potential path toward functionally reconfigurable postdigital computers.