Memristive systems were proposed in 1976 by Leon Chua and Sung Mo Kang as a model for 2-terminal passive nonlinear dynamical systems which exhibit memory effects. Such systems were originally shown to be relevant to the modeling of action potentials in neurons in regards to the Hodgkin-Huxley model and, more recently, to the modeling of thin film materials such as TiO2-x proposed for non-volatile resistive memory. However, over the past 50 years a variety of 3-terminal non-passive dynamical devices have also been shown to exhibit memory effects similar to that predicted by the memristive system model. This article extends the original memristive systems framework to incorporate 3-terminal, non-passive devices and explains the applicability of such dynamic systems models to 1) the Widrow-Hoff memistor, 2) floating gate memory cells, and 3) nano-ionic FETs.
Keywords-memristive systems, memistor, transconductance, synaptic transistor, non-linear dynamic systems
In this manuscript we demonstrate experimentally that a thin film of MoS2 monolayers formed by drop-casting on a gold interdigitated electrode on Si/SiO2 behaves like a complementary memristive device, which is a key device of future crossbar memories. The hysteretic behavior of this device is modulated by light in a spectral range expanding from UV up to IR. In contrast to previous complementary memristive devices based on complicated oxides heterostructures, this device has a simple fabrication procedure and can be controlled by light, in addition to electrical signals.
Continued progress in high speed computing depends on breakthroughs in both materials synthesis and device architectures. The performance of logic and memory can be enhanced significantly by introducing a memristor, a two terminal device with internal resistance that depends on the history of the external bias voltage. State of the art memristors, based on metal insulator metal (MIM) structures with insulating oxides, such as TiO2, are limited by a lack of control over the filament formation and external control of the switching voltage. Here, we report a class of memristors based on grain bou…
Flexible and biocompatible memristive devices are particularly attractive for bioelectronic systems due to the interest in improving computing capabilities and the motivation to interface electronics with biological systems including drug delivery, neural interfaces and biosensors. Structures made of more unorthodox, organic material can address different issues due to their characteristics: flexibility, conformability, biocompatibility and simple and low-cost fabrication. It has been observed that gating graphene/ionic liquid (IL) devices leads to the formation of an electrical double layer (…
We report on resistive switching of memristive electrochemical metallization devices using 3D kinetic Monte Carlo simulations describing the transport of ions through a solid state electrolyte of an Ag/TiO$_{\text{x}}$/Pt thin layer system. The ion transport model is consistently coupled with solvers for the electric field and thermal diffusion. We show that the model is able to describe not only the formation of conducting filaments but also its dissolution. Furthermore, we calculate realistic current-voltage characteristics and resistive switching kinetics. Finally, we discuss in detail the …
The advent of reliable, nanoscale memristive components is promising for next generation compute-in-memory paradigms, however, the intrinsic variability in these devices has prevented widespread adoption. Here we show coherent electron wave functions play a pivotal role in the nanoscale transport properties of these emerging, non-volatile memories. By characterizing both filamentary and non-filamentary memristive devices as disordered Anderson systems, the switching characteristics and intrinsic variability arise directly from the universality of electron transport in disordered media. Our fra…
We suggest a novel methodology to obtain a digital representation of analog signals and to perform its back-conversion using memristive devices. In the proposed converters, the same memristive systems are used for two purposes: as elements performing conversion and elements storing the code. This approach to conversion is particularly relevant for interfacing analog signals with memristive digital logic/computing circuits.
This short note clarifies that the "pinched hysteresis loop" fingerprint of a memristor, or a memristive device, must hold for all amplitudes, for all frequencies, and for all initial conditions, of any periodic testing waveform, such as sinusoidal or triangular signals, which assumes both positive and negative values over each period of the waveform. We proved that the systems presented in [1] are not memristive devices because their hysteresis loops are not pinched at the origin for all amplitudes, and for all initial conditions.
We demonstrate that memristive devices can be fabricated by tip-induced oxidation of thin metallic films using atomic force microscope. Electrical measurements of such prepared Ti/TiOx/Ti test structures confirmed their memristive behavior and inferred diffusion of oxygen vacancies in the TiOx barrier. Consequent Kelvin probe force microscopy studies provided evidence for the diffusion, as well as for expected oxygen vacancy drift. Time evolution of the space distribution of the vacancies due to the diffusion process revealed minute-scale (at least) retention times of the devices. The work pre…
Although memristive devices with threshold voltages are the norm rather than the exception in experimentally realizable systems, their SPICE programming is not yet common. Here, we show how to implement such systems in the SPICE environment. Specifically, we present SPICE models of a popular voltage-controlled memristive system specified by five different parameters for PSPICE and NGSPICE circuit simulators. We expect this implementation to find widespread use in circuits design and testing.
Frequency generators are widely used in electronics. Here, we report the design and experimental realization of a memristive frequency generator employing a unique combination of only digital logic gates, a single-supply voltage and a realistic threshold-type memristive device. In our circuit, the oscillator frequency and duty cycle are defined by the switching characteristics of the memristive device and external resistors. We demonstrate the circuit operation both experimentally, using a memristor emulator, and theoretically, using a model memristive device with threshold. Importantly, nanos…
In this work we report on kinetic Monte-Carlo calculations of resistive switching and the underlying growth dynamics of filaments in an electrochemical metallization device consisting of an Ag/TiO2/Pt sandwich-like thin film system. The developed model is not limited to i) fast time scale dynamics and ii) only one growth and dissolution cycle of metallic filaments. In particular, we present results from the simulation of consecutive cycles. We find that the numerical results are in excellent agreement with experimentally obtained data. Additionally, we observe an unexpected filament growth mod…
Comprehensive understanding of the world's most energy efficient powerful computer, the human brain, is an elusive scientific issue. Still, already gained knowledge indicates memristors can be used as a building block to model the brain. At the same time, brain cortex is folded allowing trillions of neurons to be integrated in a compact volume. Therefore, we report flexible aluminium oxide based memristive devices fabricated and then derived from widely used bulk mono-crystalline silicon (100). We use complementary metal oxide semiconductor based processes to layout the foundation for ultra la…
Usually, resistive switching (RS) devices show digital RS memory (sharp SET and RESET process), which is most suitable for digital data storage applications. Some RS devices also manifest ideal memristive behavior or analog memory characteristics (gradual change in resistance states). The analog RS properties of memristive devices widen their application domain to a much broader field of neuromorphic computing. The tunability of memristive devices to digital or analog memory applications greatly depends upon the switching medium. In this work, we report a comparative study on RS properties of …
Memristive switching devices, candidates for resistive random access memory technology, have been shown to switch off through a progression of states with quantized conductance and subsequent non-integer conductance (in terms of conductance quantum $G_0$). We have performed calculations based on density functional theory to model the switching process for a Pt-HfO$_2$-Pt structure, involving the movement of one or two oxygen atoms. Oxygen atoms moving within a conductive oxygen vacancy filament act as tunneling barriers, and partition the filament into weakly coupled quantum wells. We show tha…
Single-molecule magnets weakly coupled to two ferromagnetic leads act as memory devices in electronic circuits---their response depends on history, not just on the instantaneous applied voltage. We show that magnetic anisotropy introduces a wide separation of timescales between fast and slow relaxation processes in the system, which leads to a pronounced memory dependence in a wide intermediate time regime. We study the response to a harmonically varying bias voltage from slow to rapid driving within a master-equation approach. The system is not purely memristive but shows a partially capaciti…
In this work we report on the role of ion transport for the dynamic behavior of a double barrier quantum mechanical Al/Al$_2$O$_3$/Nb$_{\text{x}}$O$_{\text{y}}$/Au memristive device based on numerical simulations in conjunction with experimental measurements. The device consists of an ultra-thin Nb$_{\text{x}}$O$_{\text{y}}$ solid state electrolyte between an Al$_2$O$_3$ tunnel barrier and a semiconductor metal interface at an Au electrode. It is shown that the device provides a number of interesting features for potential applications such as an intrinsic current compliance, a relatively long…
Traditional studies of memristive devices have mainly focused on their applications in non-volatile information storage and information processing. Here, we demonstrate that the third fundamental component of information technologies { the transfer of information { can also be employed with memristive devices. For this purpose, we introduce a metastable memristive circuit. Combining metastable memristive circuits into a line, one obtains an architecture capable of transferring a signal edge from one space location to another. We emphasize that the suggested transmission lines employ only resis…
Ferroelectric memristors are intensively studied due to their potential implementation in data storage and processing devices. In this work we show that the memristive behavior of metal/ferroelectric oxide/metal devices relies on the competition of two effects: the modulation of metal/ferroelectric interface barriers by the switchable ferroelectric polarization and the electromigration of oxygen vacancies, with the depolarizing field playing a fundamental role in the latter. We simulate our experimental results with a phenomenological model that includes both effects and we reproduce several n…
While the size of functional elements in memristors becomes of the orders of nano-meters or even smaller, the quantum effects in their dynamics can significantly influence their transport properties, consistent with recent experimental observations of conductance quantisation in memristors. This requires the development of experimentally realizable procedures to detect quantumness of memristors. Here we developed an experimental protocol allowing us to find evidence that the memristor can be in a superposition of states with different memristivities. We simulate the nonlinearity induced in the…
Redox-based memristive devices are among the alternatives for the next generation of non volatile memories, but also candidates to emulate the behavior of synapses in neuromorphic computing devices. It is nowadays well established that the motion of oxygen vacancies (OV) at the nanoscale is the key mechanism to reversibly switch metal/insulator/metal structures from insulating to conducting, i.e. to accomplish the resistive switching effect. The control of OV dynamics has a direct effect on the resistance changes, and therefore on different figures of memristive devices, such as switching spee…
The development of novel devices for neuromorphic computing and non-traditional logic operations largely relies on the fabrication of well controlled memristive systems with functionalities beyond standard bipolar behavior and digital ON-OFF states. In the present work we demonstrate for Ta$_2$O$_5$-based devices that it is possible to selectively activate/deactivate two series memristive interfaces in order to obtain clockwise or counter-clockwise multilevel squared remanent resistance loops, just by controlling the (a)symmetry of the applied stimuli and independently of the nature of the use…
Nanoscale metal oxide memristors have potential in the development of brain-inspired computing systems that are scalable and efficient1-3. In such systems, memristors represent the native electronic analogues of the biological synapses. However, the characteristics of the existing memristors do not fully support the key requirements of synaptic connections: high density, adjustable weight, and low energy operation. Here we show a bilayer memristor that is forming-free, low-voltage (~|0.8V|), energy-efficient (full On/Off switching at ~2pJ), and reliable. Furthermore, pulse measurements reveal …
Flexible solution processed memristors show different behaviour dependent on the choice of electrode material. Use of gold for both electrodes leads to switchable WORM (Write Once Read Many times) resistive devices. Use of aluminium for both electrodes increases the richness of behaviour allowing both curved and triangular memristive switching resistance memories. A comparison device with an aluminium bottom electrode and gold top electrode only exhibited significant memristive resistance switching when the aluminium electrode was the cathode, suggesting that the electrode is acting as a sourc…
This study presents a comprehensive examination of the development of TiN/SiO$_\mathrm{x}$/Cu/SiO$_\mathrm{x}$/TiN memristive devices, engineered for neuromorphic applications using a wedge-type deposition technique and Monte Carlo simulations. Identifying critical parameters for the desired device characteristics can be challenging with conventional trial-and-error approaches, which often obscure the effects of varying layer compositions. By employing an \textit{off-center} thermal evaporation method, we created a thickness gradient of SiO$_\mathrm{x}$ and Cu on a 4-inch wafer, facilitating d…
Tuning the memristive response of TaO$_x$-based devices with Ag Nanoparticles
Centro Atómico Bariloche, Instituto Balseiro (UNCuyo), CONICET（巴里洛切原子中心，巴尔塞罗研究所）；Zernike Institute for Advanced Materials, University of Groningen（格罗宁根大学泽尔尼克先进材料研究所）；CogniGron Center, University of Groningen（格罗宁根大学认知格罗宁根中心）；Instituto de Nanociencia y Materiales de Aragón (INMA-Unizar)（阿拉贡纳米科学与材料研究所）；Departamento de Física de la Materia Condensada, UNIZAR（萨拉戈萨大学凝聚态物理系）；Laboratorio de Microscopías Avanzadas, UNIZAR-CSIC（萨拉戈萨大学-西班牙国家研究委员会先进显微镜实验室）；Laboratorio de Ablación Láser (INN-CONICET-CNEA), Centro Atómico Constituyentes（constituent 原子中心激光烧蚀实验室）
It is crucial that magnetic memory devices formed from magnetic heterostructures possess sizable spin-orbit torque (SOT) efficiency and high thermal stability to realize both efficient SOT control and robust storage of such memory devices. However, most previous studies on various types of magnetic heterostructures have focused on only their SOT efficiencies, whereas the thermal stabilities therein have been largely ignored. In this work, we study the temperature-dependent SOT and stability properties of two types of W-based heterostructures, namely W/CoFeB/MgO (standard) and CoFeB/W/CoFeB/MgO…
There are three theoretical models which purport to relate experimentally-measurable or fabrication-controllable device properties to the memristor's operation: 1. Strukov et al's phenomenological model; 2. Georgiou et al's Bernoulli rewrite of that phenomenological model; 3. Gale's memory-conservation model. They differ in their prediction of the effect on memristance of changing the electrode size and factors that affect the hysteresis. Using a batch of TiO$_2$ sol-gel memristors fabricated with different top electrode widths we test and compare these three theories. It was found that, contr…
A common approach to model memristive systems is to include empirical window functions to describe edge effects and non-linearities in the change of the memristance. We demonstrate that under quite general conditions, each window function can be associated with a sigmoidal curve relating the normalised time-dependent memristance to the time integral of the input. Conversely, this explicit relation allows us to derive window functions suitable for the mesoscopic modelling of memristive systems from a variety of well-known sigmoidals. Such sigmoidal curves are defined in terms of measured variab…
Due to their memristive properties nanowire networks are very promising for neuromorphic computing applications. Indeed, the resistance of such systems can evolve with the input voltage or current as it confers a synaptic behaviour to the device. Here, we propose a network of silver nanowires (Ag-NWs) which are grown in a nanopourous membrane with interconnected nanopores by electrodeposition. This bottom-up approach fabrication method gives a conducting network with a 3D architecture and a high density of Ag-NWs. The resulting 3D interconnected Ag-NW network exhibits a high initial resistance…
Memristive systems are generalisations of memristors, which are resistors with memory. In this paper, we present a quantum description of memristive systems. Using this model we propose and experimentally demonstrate a simple and practical scheme for realising memristive systems with quantum dots. The approach harnesses a phenomenon that is commonly seen as a bane of nanoelectronics, i.e. switching of a trapped charge in the vicinity of the device. We show that quantum-dot memristive systems have hysteresis current-voltage characteristics and quantum jump induced stochastic behaviour. Realisin…
In this study, direct-current reactive sputtered ZnO and ZnO1-x based thin film (30 nm and 300 nm in thickness) memristor devices were produced and the effects of oxygen vacancies and thickness on the memristive characteristics were investigated. The oxygen deficiency of the ZnO1-x structure was confirmed by SIMS analyses. The memristive characteristics of both the ZnO and ZnO1-x devices were determined by time dependent current-voltage (I-V-t) measurements. The distinctive pinched hysteresis I-V loops of memristors were observed in all the fabricated devices. The typical homogeneous interface…
