Programming memristor arrays with arbitrarily high precision for analog computing.

In-memory computing represents an effective method for modeling complex physical systems that are typically challenging for conventional computing architectures but has been hindered by issues such as reading noise and writing variability that restrict scalability, accuracy, and precision in high-performance computations. We propose and demonstrate a circuit architecture and programming protocol that converts the analog computing result to digital at the last step and enables low-precision analog devices to perform high-precision computing. We use a weighted sum of multiple devices to represent one number, in which subsequently programmed devices are used to compensate for preceding programming errors. With a memristor system-on-chip, we experimentally demonstrate high-precision solutions for multiple scientific computing tasks while maintaining a substantial power efficiency advantage over conventional digital approaches.

Thousands of conductance levels in memristors integrated on CMOS.

Neural networks based on memristive devices1-3 have the ability to improve throughput and energy efficiency for machine learning4,5 and artificial intelligence6, especially in edge applications7-21. Because training a neural network model from scratch is costly in terms of hardware resources, time and energy, it is impractical to do it individually on billions of memristive neural networks distributed at the edge. A practical approach would be to download the synaptic weights obtained from the cloud training and program them directly into memristors for the commercialization of edge applications. Some post-tuning in memristor conductance could be done afterwards or during applications to adapt to specific situations. Therefore, in neural network applications, memristors require high-precision programmability to guarantee uniform and accurate performance across a large number of memristive networks22-28. This requires many distinguishable conductance levels on each memristive device, not only laboratory-made devices but also devices fabricated in factories. Analog memristors with many conductance states also benefit other applications, such as neural network training, scientific computing and even 'mortal computing'25,29,30. Here we report 2,048 conductance levels achieved with memristors in fully integrated chips with 256 × 256 memristor arrays monolithically integrated on complementary metal-oxide-semiconductor (CMOS) circuits in a commercial foundry. We have identified the underlying physics that previously limited the number of conductance levels that could be achieved in memristors and developed electrical operation protocols to avoid such limitations. These results provide insights into the fundamental understanding of the microscopic picture of memristive switching as well as approaches to enable high-precision memristors for various applications. Fig. 1 HIGH-PRECISION MEMRISTOR FOR NEUROMORPHIC COMPUTING.: a, Proposed scheme of the large-scale application of memristive neural networks for edge computing. Neural network training is performed in the cloud. The obtained weights are downloaded and accurately programmed into a massive number of memristor arrays distributed at the edge, which imposes high-precision requirements on memristive devices. b, An eight-inch wafer with memristors fabricated by a commercial semiconductor manufacturer. c, High-resolution transmission electron microscopy image of the cross-section view of a memristor. Pt and Ta serve as the bottom electrode (BE) and top electrode (TE), respectively. Scale bars, 1 µm and 100 nm (inset). d, Magnification of the memristor material stack. Scale bar, 5 nm. e, As-programmed (blue) and after-denoising (red) currents of a memristor are read by a constant voltage (0.2 V). The denoising process eliminated the large-amplitude RTN observed in the as-programmed state (see Methods). f, Magnification of three nearest-neighbour states after denoising. The current of each state was read by a constant voltage (0.2 V). No large-amplitude RTN was observed, and all of the states can be clearly distinguished. g, An individual memristor on the chip was tuned into 2,048 resistance levels by high-resolution off-chip driving circuitry, and each resistance level was read by a d.c. voltage sweeping from 0 to 0.2 V. The target resistance was set from 50 µS to 4,144 µS with a 2-µS interval between neighbouring levels. All readings at 0.2 V are less than 1 µS from the target conductance. Bottom inset, magnification of the resistance levels. Top inset, experimental results of an entire 256 × 256 array programmed by its 6-bit on-chip circuitry into 64 32 × 32 blocks, and each block is programmed into one of the 64 conductance levels. Each of the 256 × 256 memristors has been previously switched over one million cycles, demonstrating the high endurance and robustness of the devices.

Diffusive Memristors with Uniform and Tunable Relaxation Time for Spike Generation in Event-Based Pattern Recognition.

A diffusive memristor is a promising building block for brain-inspired computing hardware. However, the randomness in the device relaxation dynamics limits the wide-range adoption of diffusive memristors in large arrays. In this work, the device stack is engineered to achieve a much-improved uniformity in the relaxation time (standard deviation σ reduced from ≈12 to ≈0.32 ms). The memristor is further connected with a resistor or a capacitor and the relaxation time is tuned between 1.13 µs and 1.25 ms, ranging from three orders of magnitude. The hierarchy of time surfaces (HOTS) algorithm, to utilize the tunable and uniform relaxation behavior for spike generation, is implemented. An accuracy of 77.3% is achieved in recognizing moving objects in the neuromorphic MNIST (N-MNIST) dataset. The work paves the way for building emerging neuromorphic computing hardware systems with ultralow power consumption.

Memristive Field-Programmable Analog Arrays for Analog Computing.

The increasing interests in analog computing nowadays call for multipurpose analog computing platforms with reconfigurability. The advancement of analog computing, enabled by novel electronic elements like memristors, has shown its potential to sustain the exponential growth of computing demand in the new era of analog data deluge. Here, a platform of a memristive field-programmable analog array (memFPAA) is experimentally demonstrated with memristive devices serving as a variety of core analog elements and CMOS components as peripheral circuits. The memFPAA is reconfigured to implement a first-order band pass filter, an audio equalizer, and an acoustic mixed frequency classifier, as application examples. The memFPAA, featured with programmable analog memristors, memristive routing networks, and memristive vector-matrix multipliers, opens opportunities for fast prototyping analog designs as well as efficient analog applications in signal processing and neuromorphic computing.

A fully hardware-based memristive multilayer neural network.

Memristive crossbar arrays promise substantial improvements in computing throughput and power efficiency through in-memory analog computing. Previous machine learning demonstrations with memristive arrays, however, relied on software or digital processors to implement some critical functionalities, leading to frequent analog/digital conversions and more complicated hardware that compromises the energy efficiency and computing parallelism. Here, we show that, by implementing the activation function of a neural network in analog hardware, analog signals can be transmitted to the next layer without unnecessary digital conversion, communication, and processing. We have designed and built compact rectified linear units, with which we constructed a two-layer perceptron using memristive crossbar arrays, and demonstrated a recognition accuracy of 93.63% for the Modified National Institute of Standard and Technology (MNIST) handwritten digits dataset. The fully hardware-based neural network reduces both the data shuttling and conversion, capable of delivering much higher computing throughput and power efficiency.

Standards for the Characterization of Endurance in Resistive Switching Devices.

Resistive switching (RS) devices are emerging electronic components that could have applications in multiple types of integrated circuits, including electronic memories, true random number generators, radiofrequency switches, neuromorphic vision sensors, and artificial neural networks. The main factor hindering the massive employment of RS devices in commercial circuits is related to variability and reliability issues, which are usually evaluated through switching endurance tests. However, we note that most studies that claimed high endurances >106 cycles were based on resistance versus cycle plots that contain very few data points (in many cases even <20), and which are collected in only one device. We recommend not to use such a characterization method because it is highly inaccurate and unreliable (i.e., it cannot reliably demonstrate that the device effectively switches in every cycle and it ignores cycle-to-cycle and device-to-device variability). This has created a blurry vision of the real performance of RS devices and in many cases has exaggerated their potential. This article proposes and describes a method for the correct characterization of switching endurance in RS devices; this method aims to construct endurance plots showing one data point per cycle and resistive state and combine data from multiple devices. Adopting this recommended method should result in more reliable literature in the field of RS technologies, which should accelerate their integration in commercial products.

Roadmap on emerging hardware and technology for machine learning.

Recent progress in artificial intelligence is largely attributed to the rapid development of machine learning, especially in the algorithm and neural network models. However, it is the performance of the hardware, in particular the energy efficiency of a computing system that sets the fundamental limit of the capability of machine learning. Data-centric computing requires a revolution in hardware systems, since traditional digital computers based on transistors and the von Neumann architecture were not purposely designed for neuromorphic computing. A hardware platform based on emerging devices and new architecture is the hope for future computing with dramatically improved throughput and energy efficiency. Building such a system, nevertheless, faces a number of challenges, ranging from materials selection, device optimization, circuit fabrication and system integration, to name a few. The aim of this Roadmap is to present a snapshot of emerging hardware technologies that are potentially beneficial for machine learning, providing the Nanotechnology readers with a perspective of challenges and opportunities in this burgeoning field.

An artificial spiking afferent nerve based on Mott memristors for neurorobotics.

Neuromorphic computing based on spikes offers great potential in highly efficient computing paradigms. Recently, several hardware implementations of spiking neural networks based on traditional complementary metal-oxide semiconductor technology or memristors have been developed. However, an interface (called an afferent nerve in biology) with the environment, which converts the analog signal from sensors into spikes in spiking neural networks, is yet to be demonstrated. Here we propose and experimentally demonstrate an artificial spiking afferent nerve based on highly reliable NbOx Mott memristors for the first time. The spiking frequency of the afferent nerve is proportional to the stimuli intensity before encountering noxiously high stimuli, and then starts to reduce the spiking frequency at an inflection point. Using this afferent nerve, we further build a power-free spiking mechanoreceptor system with a passive piezoelectric device as the tactile sensor. The experimental results indicate that our afferent nerve is promising for constructing self-aware neurorobotics in the future.

A Low-Current and Analog Memristor with Ru as Mobile Species.

The switching parameters and device performance of memristors are predominately determined by their mobile species and matrix materials. Devices with oxygen or oxygen vacancies as the mobile species usually exhibit a great retention but also need a relatively high switching current (e.g., >30 µA), while devices with Ag or Cu as cation mobile species do not require a high switching current but usually show a poor retention. Here, Ru is studied as a new type of mobile species for memristors to achieve low switching current, fast speed, good reliability, scalability, and analog switching property simultaneously. An electrochemical metallization-like memristor with a stack of Pt/Ta2 O5 /Ru is developed. Migration of Ru ions is revealed by energy-dispersive X-ray spectroscopy mapping and in situ transmission electron microscopy within a sub-10 nm active device area before and after switching. The results open up a new avenue to engineer memristors for desired properties.

Understanding memristive switching via in situ characterization and device modeling.

Owing to their attractive application potentials in both non-volatile memory and unconventional computing, memristive devices have drawn substantial research attention in the last decade. However, major roadblocks still remain in device performance, especially concerning relatively large parameter variability and limited cycling endurance. The response of the active region in the device within and between switching cycles plays the dominating role, yet the microscopic details remain elusive. This Review summarizes recent progress in scientific understanding of the physical origins of the non-idealities and propose a synergistic approach based on in situ characterization and device modeling to investigate switching mechanism. At last, the Review offers an outlook for commercialization viability of memristive technology.

Publisher Correction: Memristive crossbar arrays for brain-inspired computing.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Memristive crossbar arrays for brain-inspired computing.

With their working mechanisms based on ion migration, the switching dynamics and electrical behaviour of memristive devices resemble those of synapses and neurons, making these devices promising candidates for brain-inspired computing. Built into large-scale crossbar arrays to form neural networks, they perform efficient in-memory computing with massive parallelism by directly using physical laws. The dynamical interactions between artificial synapses and neurons equip the networks with both supervised and unsupervised learning capabilities. Moreover, their ability to interface with analogue signals from sensors without analogue/digital conversions reduces the processing time and energy overhead. Although numerous simulations have indicated the potential of these networks for brain-inspired computing, experimental implementation of large-scale memristive arrays is still in its infancy. This Review looks at the progress, challenges and possible solutions for efficient brain-inspired computation with memristive implementations, both as accelerators for deep learning and as building blocks for spiking neural networks.

Memristor crossbar arrays with 6-nm half-pitch and 2-nm critical dimension.

The memristor1,2 is a promising building block for next-generation non-volatile memory3, artificial neural networks4-7 and bio-inspired computing systems8,9. Organizing small memristors into high-density crossbar arrays is critical to meet the ever-growing demands in high-capacity and low-energy consumption, but this is challenging because of difficulties in making highly ordered conductive nanoelectrodes. Carbon nanotubes, graphene nanoribbons and dopant nanowires have potential as electrodes for discrete nanodevices10-14, but unfortunately these are difficult to pack into ordered arrays. Transfer printing, on the other hand, is effective in generating dense electrode arrays15 but has yet to prove suitable for making fully random accessible crossbars. All the aforementioned electrodes have dramatically increased resistance at the nanoscale16-18, imposing a significant barrier to their adoption in operational circuits. Here we demonstrate memristor crossbar arrays with a 2-nm feature size and a single-layer density up to 4.5 terabits per square inch, comparable to the information density achieved using three-dimensional stacking in state-of-the-art 64-layer and multilevel 3D-NAND flash memory19. Memristors in the arrays switch with tens of nanoamperes electric current with nonlinear behaviour. The densely packed crossbar arrays of individually accessible, extremely small functional memristors provide a power-efficient solution for information storage and processing.

Capacitive neural network with neuro-transistors.

Experimental demonstration of resistive neural networks has been the recent focus of hardware implementation of neuromorphic computing. Capacitive neural networks, which call for novel building blocks, provide an alternative physical embodiment of neural networks featuring a lower static power and a better emulation of neural functionalities. Here, we develop neuro-transistors by integrating dynamic pseudo-memcapacitors as the gates of transistors to produce electronic analogs of the soma and axon of a neuron, with "leaky integrate-and-fire" dynamics augmented by a signal gain on the output. Paired with non-volatile pseudo-memcapacitive synapses, a Hebbian-like learning mechanism is implemented in a capacitive switching network, leading to the observed associative learning. A prototypical fully integrated capacitive neural network is built and used to classify inputs of signals.

Silicon Oxide (SiOx ): A Promising Material for Resistance Switching?

Interest in resistance switching is currently growing apace. The promise of novel high-density, low-power, high-speed nonvolatile memory devices is appealing enough, but beyond that there are exciting future possibilities for applications in hardware acceleration for machine learning and artificial intelligence, and for neuromorphic computing. A very wide range of material systems exhibit resistance switching, a number of which-primarily transition metal oxides-are currently being investigated as complementary metal-oxide-semiconductor (CMOS)-compatible technologies. Here, the case is made for silicon oxide, perhaps the most CMOS-compatible dielectric, yet one that has had comparatively little attention as a resistance-switching material. Herein, a taxonomy of switching mechanisms in silicon oxide is presented, and the current state of the art in modeling, understanding fundamental switching mechanisms, and exciting device applications is summarized. In conclusion, silicon oxide is an excellent choice for resistance-switching technologies, offering a number of compelling advantages over competing material systems.

Efficient and self-adaptive in-situ learning in multilayer memristor neural networks.

Memristors with tunable resistance states are emerging building blocks of artificial neural networks. However, in situ learning on a large-scale multiple-layer memristor network has yet to be demonstrated because of challenges in device property engineering and circuit integration. Here we monolithically integrate hafnium oxide-based memristors with a foundry-made transistor array into a multiple-layer neural network. We experimentally demonstrate in situ learning capability and achieve competitive classification accuracy on a standard machine learning dataset, which further confirms that the training algorithm allows the network to adapt to hardware imperfections. Our simulation using the experimental parameters suggests that a larger network would further increase the classification accuracy. The memristor neural network is a promising hardware platform for artificial intelligence with high speed-energy efficiency.

An artificial nociceptor based on a diffusive memristor.

A nociceptor is a critical and special receptor of a sensory neuron that is able to detect noxious stimulus and provide a rapid warning to the central nervous system to start the motor response in the human body and humanoid robotics. It differs from other common sensory receptors with its key features and functions, including the "no adaptation" and "sensitization" phenomena. In this study, we propose and experimentally demonstrate an artificial nociceptor based on a diffusive memristor with critical dynamics for the first time. Using this artificial nociceptor, we further built an artificial sensory alarm system to experimentally demonstrate the feasibility and simplicity of integrating such novel artificial nociceptor devices in artificial intelligence systems, such as humanoid robots.

Memristor-Based Analog Computation and Neural Network Classification with a Dot Product Engine.

Using memristor crossbar arrays to accelerate computations is a promising approach to efficiently implement algorithms in deep neural networks. Early demonstrations, however, are limited to simulations or small-scale problems primarily due to materials and device challenges that limit the size of the memristor crossbar arrays that can be reliably programmed to stable and analog values, which is the focus of the current work. High-precision analog tuning and control of memristor cells across a 128 × 64 array is demonstrated, and the resulting vector matrix multiplication (VMM) computing precision is evaluated. Single-layer neural network inference is performed in these arrays, and the performance compared to a digital approach is assessed. Memristor computing system used here reaches a VMM accuracy equivalent of 6 bits, and an 89.9% recognition accuracy is achieved for the 10k MNIST handwritten digit test set. Forecasts show that with integrated (on chip) and scaled memristors, a computational efficiency greater than 100 trillion operations per second per Watt is possible.