Hardware implementation of memristor-based artificial neural networks.

Artificial Intelligence (AI) is currently experiencing a bloom driven by deep learning (DL) techniques, which rely on networks of connected simple computing units operating in parallel. The low communication bandwidth between memory and processing units in conventional von Neumann machines does not support the requirements of emerging applications that rely extensively on large sets of data. More recent computing paradigms, such as high parallelization and near-memory computing, help alleviate the data communication bottleneck to some extent, but paradigm- shifting concepts are required. Memristors, a novel beyond-complementary metal-oxide-semiconductor (CMOS) technology, are a promising choice for memory devices due to their unique intrinsic device-level properties, enabling both storing and computing with a small, massively-parallel footprint at low power. Theoretically, this directly translates to a major boost in energy efficiency and computational throughput, but various practical challenges remain. In this work we review the latest efforts for achieving hardware-based memristive artificial neural networks (ANNs), describing with detail the working principia of each block and the different design alternatives with their own advantages and disadvantages, as well as the tools required for accurate estimation of performance metrics. Ultimately, we aim to provide a comprehensive protocol of the materials and methods involved in memristive neural networks to those aiming to start working in this field and the experts looking for a holistic approach.

Fast Fitting of the Dynamic Memdiode Model to the Conduction Characteristics of RRAM Devices Using Convolutional Neural Networks.

In this paper, the use of Artificial Neural Networks (ANNs) in the form of Convolutional Neural Networks (AlexNET) for the fast and energy-efficient fitting of the Dynamic Memdiode Model (DMM) to the conduction characteristics of bipolar-type resistive switching (RS) devices is investigated. Despite an initial computationally intensive training phase the ANNs allow obtaining a mapping between the experimental Current-Voltage (I-V) curve and the corresponding DMM parameters without incurring a costly iterative process as typically considered in error minimization-based optimization algorithms. In order to demonstrate the fitting capabilities of the proposed approach, a complete set of I-Vs obtained from Y2O3-based RRAM devices, fabricated with different oxidation conditions and measured with different current compliances, is considered. In this way, in addition to the intrinsic RS variability, extrinsic variation is achieved by means of external factors (oxygen content and damage control during the set process). We show that the reported method provides a significant reduction of the fitting time (one order of magnitude), especially in the case of large data sets. This issue is crucial when the extraction of the model parameters and their statistical characterization are required.

SPICE Implementation of the Dynamic Memdiode Model for Bipolar Resistive Switching Devices.

This paper reports the fundamentals and the SPICE implementation of the Dynamic Memdiode Model (DMM) for the conduction characteristics of bipolar-type resistive switching (RS) devices. Following Prof. Chua's memristive devices theory, the memdiode model comprises two equations, one for the electron transport based on a heuristic extension of the quantum point-contact model for filamentary conduction in thin dielectrics and a second equation for the internal memory state related to the reversible displacement of atomic species within the oxide film. The DMM represents a breakthrough with respect to the previous Quasi-static Memdiode Model (QMM) since it describes the memory state of the device as a balance equation incorporating both the snapback and snapforward effects, features of utmost importance for the accurate and realistic simulation of the RS phenomenon. The DMM allows simple setting of the initial memory condition as well as decoupled modeling of the set and reset transitions. The model equations are implemented in the LTSpice simulator using an equivalent circuital approach with behavioral components and sources. The practical details of the model implementation and its modes of use are also discussed.

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.

On the Thermal Models for Resistive Random Access Memory Circuit Simulation.

Resistive Random Access Memories (RRAMs) are based on resistive switching (RS) operation and exhibit a set of technological features that make them ideal candidates for applications related to non-volatile memories, neuromorphic computing and hardware cryptography. For the full industrial development of these devices different simulation tools and compact models are needed in order to allow computer-aided design, both at the device and circuit levels. Most of the different RRAM models presented so far in the literature deal with temperature effects since the physical mechanisms behind RS are thermally activated; therefore, an exhaustive description of these effects is essential. As far as we know, no revision papers on thermal models have been published yet; and that is why we deal with this issue here. Using the heat equation as the starting point, we describe the details of its numerical solution for a conventional RRAM structure and, later on, present models of different complexity to integrate thermal effects in complete compact models that account for the kinetics of the chemical reactions behind resistive switching and the current calculation. In particular, we have accounted for different conductive filament geometries, operation regimes, filament lateral heat losses, the use of several temperatures to characterize each conductive filament, among other issues. A 3D numerical solution of the heat equation within a complete RRAM simulator was also taken into account. A general memristor model is also formulated accounting for temperature as one of the state variables to describe electron device operation. In addition, to widen the view from different perspectives, we deal with a thermal model contextualized within the quantum point contact formalism. In this manner, the temperature can be accounted for the description of quantum effects in the RRAM charge transport mechanisms. Finally, the thermometry of conducting filaments and the corresponding models considering different dielectric materials are tackled in depth.

Memristors for Neuromorphic Circuits and Artificial Intelligence Applications.

Artificial Intelligence has found many applications in the last decade due to increased computing power. Artificial Neural Networks are inspired in the brain structure and consist in the interconnection of artificial neurons through artificial synapses in the so-called Deep Neural Networks (DNNs). Training these systems requires huge amounts of data and, after the network is trained, it can recognize unforeseen data and provide useful information. As far as the training is concerned, we can distinguish between supervised and unsupervised learning. The former requires labelled data and is based on the iterative minimization of the output error using the stochastic gradient descent method followed by the recalculation of the strength of the synaptic connections (weights) with the backpropagation algorithm. On the other hand, unsupervised learning does not require data labeling and it is not based on explicit output error minimization. Conventional ANNs can function with supervised learning algorithms (perceptrons, multi-layer perceptrons, convolutional networks, etc.) but also with unsupervised learning rules (Kohonen networks, self-organizing maps, etc.). Besides, another type of neural networks are the so-called Spiking Neural Networks (SNNs) in which learning takes place through the superposition of voltage spikes launched by the neurons. Their behavior is much closer to the brain functioning mechanisms they can be used with supervised and unsupervised learning rules. Since learning and inference is based on short voltage spikes, energy efficiency improves substantially. Up to this moment, all these ANNs (spiking and conventional) have been implemented as software tools running on conventional computing units based on the von Neumann architecture. However, this approach reaches important limits due to the required computing power, physical size and energy consumption. This is particularly true for applications at the edge of the internet. Thus, there is an increasing interest in developing AI tools directly implemented in hardware for this type of applications. The first hardware demonstrations have been based on Complementary Metal-Oxide-Semiconductor (CMOS) circuits and specific communication protocols. However, to further increase training speed andenergy efficiency while reducing the system size, the combination of CMOS neuron circuits with memristor synapses is now being explored. It has also been pointed out that the short time non-volatility of some memristors may even allow fabricating purely memristive ANNs. The memristor is a new device (first demonstrated in solid-state in 2008) which behaves as a resistor with memory and which has been shown to have potentiation and depression properties similar to those of biological synapses. In this Special Issue, we explore the state of the art of neuromorphic circuits implementing neural networks with memristors for AI applications.

Multi-terminal Transistor-like Devices Based on Strongly Correlated Metallic Oxides for Neuromorphic Applications.

Memristive devices are attracting a great attention for memory, logic, neural networks, and sensing applications due to their simple structure, high density integration, low-power consumption, and fast operation. In particular, multi-terminal structures controlled by active gates, able to process and manipulate information in parallel, would certainly provide novel concepts for neuromorphic systems. In this way, transistor-based synaptic devices may be designed, where the synaptic weight in the postsynaptic membrane is encoded in a source-drain channel and modified by presynaptic terminals (gates). In this work, we show the potential of reversible field-induced metal-insulator transition (MIT) in strongly correlated metallic oxides for the design of robust and flexible multi-terminal memristive transistor-like devices. We have studied different structures patterned on YBa2Cu3O7-δ films, which are able to display gate modulable non-volatile volume MIT, driven by field-induced oxygen diffusion within the system. The key advantage of these materials is the possibility to homogeneously tune the oxygen diffusion not only in a confined filament or interface, as observed in widely explored binary and complex oxides, but also in the whole material volume. Another important advantage of correlated oxides with respect to devices based on conducting filaments is the significant reduction of cycle-to-cycle and device-to-device variations. In this work, we show several device configurations in which the lateral conduction between a drain-source channel (synaptic weight) is effectively controlled by active gate-tunable volume resistance changes, thus providing the basis for the design of robust and flexible transistor-based artificial synapses.

On the Application of a Diffusive Memristor Compact Model to Neuromorphic Circuits.

Memristive devices have found application in both random access memory and neuromorphic circuits. In particular, it is known that their behavior resembles that of neuronal synapses. However, it is not simple to come by samples of memristors and adjusting their parameters to change their response requires a laborious fabrication process. Moreover, sample to sample variability makes experimentation with memristor-based synapses even harder. The usual alternatives are to either simulate or emulate the memristive systems under study. Both methodologies require the use of accurate modeling equations. In this paper, we present a diffusive compact model of memristive behavior that has already been experimentally validated. Furthermore, we implement an emulation architecture that enables us to freely explore the synapse-like characteristics of memristors. The main advantage of emulation over simulation is that the former allows us to work with real-world circuits. Our results can give some insight into the desirable characteristics of the memristors for neuromorphic applications.

Electrochemical Tuning of Metal Insulator Transition and Nonvolatile Resistive Switching in Superconducting Films.

Modulation of carrier concentration in strongly correlated oxides offers the unique opportunity to induce different phases in the same material, which dramatically change their physical properties, providing novel concepts in oxide electronic devices with engineered functionalities. This work reports on the electric manipulation of the superconducting to insulator phase transition in YBa2Cu3O7-δ thin films by electrochemical oxygen doping. Both normal state resistance and the superconducting critical temperature can be reversibly manipulated in confined active volumes of the film by gate-tunable oxygen diffusion. Vertical and lateral oxygen mobility may be finely modulated, at the micro- and nano-scale, by tuning the applied bias voltage and operating temperature thus providing the basis for the design of homogeneous and flexible transistor-like devices with loss-less superconducting drain-source channels. We analyze the experimental results in light of a theoretical model, which incorporates thermally activated and electrically driven volume oxygen diffusion.

Investigation on the Conductive Filament Growth Dynamics in Resistive Switching Memory via a Universal Monte Carlo Simulator.

In resistive random access memories, modeling conductive filament growing dynamics is important to understand the switching mechanism and variability. In this paper, a universal Monte Carlo simulator is developed based on a cell switching model and a tunneling-based transport model. Driven by external electric field, the growing process of the nanoscale filament occurring in the gap region is actually dominated by cells' conductive/insulating switching, modeled through a phenomenological physics-based probability function. The electric transport through the partially formed CF is considered as current tunneling in the framework of the Quantum Point Contact model, and the potential barrier is modulated during cells' evolution. To demonstrate the validity and universality of our simulator, various operation schemes are simulated, with the simulated I - V characteristics well explaining experimental observations. Furthermore, the statistical analyses of simulation results in terms of Weibull distribution and conductance evolution also nicely track previous experimental results. Representing a simulation scale that links atomic-scale simulations to compact modeling, our simulator has the advantage of being much faster comparing with other atomic-scale models. Meanwhile, our simulator shows good universality since it can be applied to various operation signals, and also to different electrodes and dielectric layers dominated by different switching mechanisms.

Analysis on the Filament Structure Evolution in Reset Transition of Cu/HfO2/Pt RRAM Device.

The resistive switching (RS) process of resistive random access memory (RRAM) is dynamically correlated with the evolution process of conductive path or conductive filament (CF) during its breakdown (rupture) and recovery (reformation). In this study, a statistical evaluation method is developed to analyze the filament structure evolution process in the reset operation of Cu/HfO2/Pt RRAM device. This method is based on a specific functional relationship between the Weibull slopes of reset parameters' distributions and the CF resistance (R on). The CF of the Cu/HfO2/Pt device is demonstrated to be ruptured abruptly, and the CF structure of the device has completely degraded in the reset point. Since no intermediate states are generated in the abrupt reset process, it is quite favorable for the reliable and stable one-bit operation in RRAM device. Finally, on the basis of the cell-based analytical thermal dissolution model, a Monte Carlo (MC) simulation is implemented to further verify the experimental results. This work provides inspiration for RRAM reliability and performance design to put RRAM into practical application.

Conductance Quantization in Resistive Random Access Memory.

The intrinsic scaling-down ability, simple metal-insulator-metal (MIM) sandwich structure, excellent performances, and complementary metal-oxide-semiconductor (CMOS) technology-compatible fabrication processes make resistive random access memory (RRAM) one of the most promising candidates for the next-generation memory. The RRAM device also exhibits rich electrical, thermal, magnetic, and optical effects, in close correlation with the abundant resistive switching (RS) materials, metal-oxide interface, and multiple RS mechanisms including the formation/rupture of nanoscale to atomic-sized conductive filament (CF) incorporated in RS layer. Conductance quantization effect has been observed in the atomic-sized CF in RRAM, which provides a good opportunity to deeply investigate the RS mechanism in mesoscopic dimension. In this review paper, the operating principles of RRAM are introduced first, followed by the summarization of the basic conductance quantization phenomenon in RRAM and the related RS mechanisms, device structures, and material system. Then, we discuss the theory and modeling of quantum transport in RRAM. Finally, we present the opportunities and challenges in quantized RRAM devices and our views on the future prospects.

Engineering of the chemical reactivity of the Ti/HfO2 interface for RRAM: experiment and theory.

The Ti/HfO2 interface plays a major role for resistance switching performances. However, clear interface engineering strategies to achieve reliable and reproducible switching have been poorly investigated. For this purpose, we present a comprehensive study of the Ti/HfO2 interface by a combined experimental-theoretical approach. Based on the use of oxygen-isotope marked Hf*O2, the oxygen scavenging capability of the Ti layer is clearly proven. More importantly, in line with ab initio theory, the combined HAXPES-Tof-SIMS study of the thin films deposited by MBE clearly establishes a strong impact of the HfO2 thin film morphology on the Ti/HfO2 interface reactivity. Low-temperature deposition is thus seen as a RRAM processing compatible way to establish the critical amount of oxygen vacancies to achieve reproducible and reliable resistance switching performances.

Statistical characteristics of reset switching in Cu/HfO2/Pt resistive switching memory.

A major challenge of resistive switching memory (resistive random access memory (RRAM)) for future application is how to reduce the fluctuation of the resistive switching parameters. In this letter, with a statistical methodology, we have systematically analyzed the reset statistics of the conductive bridge random access memory (CBRAM) with a Cu/HfO2/Pt structure which displays bipolar switching property. The experimental observations show that the distributions of the reset voltage (V reset) and reset current (I reset) are greatly influenced by the initial on-state resistance (R on) which is closely related to the size of the conductive filament (CF) before the reset process. The reset voltage increases and the current decreases with the on-state resistance, respectively, according to the scatter plots of the experimental data. Using resistance screening method, the statistical data of the reset voltage and current are decomposed into several ranges and the distributions of them in each range are analyzed by the Weibull model. Both the Weibull slopes of the reset voltage and current are demonstrated to be independent of the on-state resistance which indicates that no CF dissolution occurs before the reset point. The scale factor of the reset voltage increases with on-state resistance while that of the reset current decreases with it. These behaviors are fully in consistency with the thermal dissolution model, which gives an insight on the physical mechanism of the reset switching. Our work has provided an inspiration on effectively reducing the variation of the switching parameters of RRAM devices.

Voltage and power-controlled regimes in the progressive unipolar RESET transition of HfO2-based RRAM.

Resistive switching (RS) based on the formation and rupture of conductive filament (CF) is promising in novel memory and logic device applications. Understanding the physics of RS and the nature of CF is of utmost importance to control the performance, variability and reliability of resistive switching memory (RRAM). Here, the RESET switching of HfO2-based RRAM was statistically investigated in terms of the CF conductance evolution. The RESET usually combines an abrupt conductance drop with a progressive phase ending with the complete CF rupture. RESET1 and RESET2 events, corresponding to the initial and final phase of RESET, are found to be controlled by the voltage and power in the CF, respectively. A Monte Carlo simulator based on the thermal dissolution model of unipolar RESET reproduces all of the experimental observations. The results contribute to an improved physics-based understanding on the switching mechanisms and provide additional support to the thermal dissolution model.

Modeling transport in ultrathin Si nanowires: charged versus neutral impurities.

At room temperature dopants in semiconducting nanowires are ionized. We show that the long-range electrostatic potential due to charged dopants has a dramatic impact on the transport properties in ultrathin wires and can virtually block minority carriers. Our quantitative estimates of this effect are obtained by computing the electronic transmission through wires with either charged or neutral P and B dopants. The dopant potential is obtained from density functional theory (DFT) calculations. Contrary to the neutral case, the transmission through charged dopants cannot be converged within a supercell-based DFT scheme, because the system size implied by the long-ranged electrostatic potential becomes computationally unmanagable. We overcome this problem by modifying the DFT potential with finite element calculations. We find that the minority scattering is increased by a factor of 1,000, while majority transmission is within 50% of the neutral dopant results.