Fundamental Circuit Element Research Articles

Stochasticity Modeling in Memristors

Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on nondeterministic memristor logic.

Bio-hybrid interfaces to study neuromorphic functionalities: New multidisciplinary evidences of cell viability on poly(anyline) (PANI), a semiconductor polymer with memristive properties

The interfacing of artificial devices with biological systems is a challenging field that crosses several disciplines ranging from fundamental research (biophysical chemistry, neurobiology, material and surface science) to frontier technological application (nanotechnology, bioelectronics). The memristor is the fourth fundamental circuit element, whose electrical properties favor applications in signal processing, neural networks, and brain–computer interactions and it represents a new frontier for technological applications in many fields including the nanotechnologies, bioelectronics and the biosensors. Using multidisciplinary approaches, covering surface science, cell biology and electrophysiology, we successfully implemented a living bio-hybrid system constituted by cells adhering to films of poly(aniline) (PANI), a semiconductor polymer having memristive properties assembled with polyelectrolytes. Here we tested whether the PANI devices could support survivor, adhesion and differentiation of several cell lines, including the neuron-like SHSY5Y cells. Moreover, we performed electrophysiology on these cells showing that the biophysical properties are retained with differences occurring in the recorded ion currents. Taken together, the cell viability here reported is the key requirement to design and develop a reliable functional memristor-based bio-hybrid able to mimic neuronal activity and plasticity.

A Physics-based Memristor Model Based on Chalcogenide Alloy

Memristor, as the fourth fundamental circuit element, has recently attracted considerable attention due to its widespread applications from programmable logic to neural networks. Today, the most representative memristor consists of a thin film of titanium oxide sandwiched by two electrodes. However, such a memristor gives rise to a relatively low switching speed, discouraging it from receiving more research enthusiasm. To overcome the disadvantages of the already established memristors (e.g. low switching speed and poor endurance) and thus to optimize the memristor performance, we proposed a novel memristor concept using chalcogenide alloy that has been widely used for nonvolatile memory storage. According to the developed electro-thermal model, the designed memristor using chalcogenide alloy clearly shows a variation of resistance along with the history of current as well as a fast switching speed and ultra-low energy consumption. Keywords: Cycle, chalcogenide, Ge2Sb2Te5, memristor, model.

A novel memristor based physically unclonable function

Memristor is an exciting new addition to the repertoire of fundamental circuit elements. Alternatives to many security protocols originally employing traditional mathematical cryptography involve novel hardware security primitives, such as Physically Unclonable Functions (PUFs). In this paper, we first introduce a novel hybrid memristor–CMOS XOR/XNOR logic circuit that offers several advantages such as combinational circuit behavior, simpler operation and lower hardware overhead than existing solutions. Then, we use this XOR circuit as a component to design a hybrid memristor–CMOS PUF circuit and demonstrate its effectiveness through extensive simulations of environmental and process variation effects. The proposed PUF circuit has substantially lesser hardware overhead than previously proposed memristor-based PUF circuits, while being resistant against machine learning based modelling attacks. The proposed PUF can be conveniently used in many security applications and protocols based on hardware-intrinsic security.

Toward the complete relational graph of fundamental circuit elements**Project supported by the National Natural Science Foundation of China (Grant Nos. 11227405, 11374347, 11274363, and 11474335) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB07030200).

A complete and harmonized fundamental circuit relational graph with four linear and four memory elements is constructed based on some newly defined elements, which provides a guide to developing novel circuit functionalities in the future. In addition to resistors, capacitors, and inductors, which are defined in terms of a linear relationship between charge q, current i, voltage v, and magnetic flux φ, Chua proposed in 1971 a fourth linear circuit element to directly relate φ and q. A nonlinear resistive device defined in memory i–v relation and dubbed memristor, was later attributed to such an element and has been realized in various material structures. Here we clarify that the memristor is not the true fourth fundamental circuit element but the memory extension to the concept of resistor, in analogy to the extension of memcapacitor to capacitor and meminductor to inductor. Instead, a two-terminal device employing the linear ME effects, termed transtor, directly relates φ and q and should be recognized as the fourth linear element. Moreover, its memory extension, termed memtranstor, is proposed and analyzed here.

A Novel Memristor-Based Hardware Security Primitive

Memristor is an exciting new addition to the repertoire of fundamental circuit elements. Alternatives to many security protocols originally employing traditional mathematical cryptography involve novel hardware security primitives, such as Physically Unclonable Functions (PUFs). In this article, we propose a novel hybrid memristor-CMOS PUF circuit and demonstrate its suitability through extensive simulations of environmental and process variation effects. The proposed PUF circuit has substantially less hardware overhead than previously proposed memristor-based PUF circuits while being inherently resistant to machine learning-based modeling attacks because of challenge-dependent delays of the memristor stages. The proposed PUF can be conveniently used in many security applications and protocols based on hardware-intrinsic security.

What are Memristor, Memcapacitor, and Meminductor?

Memristor, memcapacitor, and meminductor are new fundamental circuit elements, whose properties depend on the history of devices. This paper presents the physical analysis of these memory devices. Three simple examples are given for the memristor, memcapacitor, and meminductor, and are then generalized to reveal their general physical origin. It is found that the memristance, memcapacitance, and meminductance are caused by different combinations of nonlinear electric responses. The mathematical expressions for the currents through any voltage-driven memristor, memcapacitor, and meminductor are given, and the corresponding expressions for the memristance, memcapacitance, and meminductance are derived. Moreover, a method to determine the charge-flux relationship of a memristor is proposed.

Adaptive Synchronization of Memristor - based Chaotic Neural Systems

Adaptive Synchronization of Memristor - based Chaotic Neural Systems

Overview of emerging memristor families from resistive memristor to spintronic memristor

AbstractMemristor is a fundamental circuit element in addition to resistor, capacitor, and inductor. As it can remember its resistance state even encountering a power off, memristor has recently received widespread applications from non-volatile memory to neural networks. The current memristor family mainly comprises resistive memristor, polymeric memristor, ferroelectric memristor, manganite memristor, resonant-tunneling diode memristor, and spintronic memristor in terms of the materials the device is made of. In order to help researcher better understand the physical principles of the memristor, and thus to provide a promising prospect for memristor devices, this paper presents an overview of memristor materials properties, switching mechanisms, and potential applications. The performance comparison among different memristor members is also given.

Modelling of nanostructured TiO2-based memristors

The fourth fundamental circuit element memristor completes the missing link between charge and magnetic flux. It consists of the function of the resistor as well as memory in nonlinear fashion. The property of the memristor depends on the magnitude and direction of applied potential. This unique property makes it the primitive building block for many applications such as resistive memories, soft computing, neuromorphic systems and chaotic circuits etc. In this paper we report TiO2-based nanostructured memristor modelling. The present memristor model is constructed in MATLAB environment with consideration of the linear drift model of memristor. The result obtained from the linear drift model is well matched with earlier reported results by other research groups.

Memristor Based van der Pol Oscillation Circuit

The memristor is referred to as the fourth fundamental passive circuit element of which inherent nonlinear properties offer to construct the chaos circuits. In this paper, a flux-controlled memristor circuit is developed, and then a van der Pol oscillator is implemented based on this new memristor circuit. The stability of the circuit, the occurring conditions of Hopf bifurcation and limit circle of the self-excited oscillation are analyzed; meanwhile, under the condition of the circuit with an external exciting source, the circuit exhibits a complicated nonlinear dynamic behavior, and chaos occurs within a certain parameter set. The memristor based van der Pol oscillator, furthermore, has been created by an analog circuit utilizing active elements, and there is a good agreement between the circuit responses and numerical simulations of the van der Pol equation. In the consequence, a new approach has been proposed to generate chaos within a nonautonomous circuit system.

TiO2-based memristors and ReRAM: materials, mechanisms and models (a review)

The memristor is the fundamental nonlinear circuit element, with uses in computing and computer memory. Resistive Random Access Memory (ReRAM) is a resistive switching memory proposed as a non-volatile memory. In this review we shall summarize the state of the art for these closely-related fields, concentrating on titanium dioxide, the well-utilized and archetypal material for both. We shall cover material properties, switching mechanisms and models to demonstrate what ReRAM and memristor scientists can learn from each other and examine the outlook for these technologies.

Review of Nanostructured Resistive Switching Memristor and Its Applications

Resistive switching memristor, predicted as the fourth fundamental passive circuit element (in addition to resistor, capacitor, and inductor) in the world by Leon Chua in 1971 and demonstrated by Hewlett Packard laboratory in 2008, has attracted extensive research attention for its high scalability and versatility. In this paper, we reviewed the working mechanisms and mathematical models of nanostructured resistive switching memristors, and examined various emerging applications of the memristors, including memory, analog, logic and neuromorphic applications.

Dithienopyrrole-/Benzodithiophene-Based Donor-Acceptor Polymers for Memristor

Invited for this month’s cover is the group of Prof. Dr. Yu Chen from East China University of Science and Technology, P. R. China. The cover picture shows fundamental passive circuit elements of resistor, capacitor, inductor and memristor and the correlations between the circuit variables. Read the full text of the article at 10.1002/cplu.201402133

Study of Memristive Elements Networks

The existence of the fourth fundamental circuit element, the memristor, was first postulated over 30 years ago by Leon Chua. The implementation of the first modern memristor prototype by Hewlett Packard Laboratories in 2008 initiated a great scientific interest for these unique nanoelectronic devices and currently, there is a growing variety of systems that exhibit memristive behavior. However, most of the research has focused on the properties of the single devices, therefore very little is known about their response when these devices are organized into networks. In this work, the composite characteristics of memristive elements connected in network configurations are studied and the relationships among the single devices are investigated. We finally show how the threshold-dependent nonlinear memristive behavior could be elaborated to make possible the development of novel and sophisticated digital/analog memristive nanosystems.

Research on a chaotic circuit based on an active TiO 2 memristor

The memristor is the fourth fundamental circuit element besides the resistor, inductor and capacitor. As a two-terminal nonlinear resistor, the memristor has a broad application prospect. In this paper, a negative memconductance expression of a flux-controlled memristor is derived from the relationship between voltage and current for the Hewlett-Packard memristor. By replacing Chua's diode with the active flux-controlled TiO 2 memristor, a chaotic circuit is obtained. By means of the conventional dynamic analysis method, dynamic behaviors of the chaotic circuit are investigated. Software simulation and theoretical analysis all indicate that this active memristor-based chaotic circuit has more complex behaviors. Furthermore, the integrated circuit experiment on the digital signal processor chip of this circuit was also realized.

Memristive chaotic circuit based on modified SC-CNNs

Memristor, as a fundamental nonlinear circuit element, is very suitable for realizing new nonlinear circuits that are able to exhibit complex dynamical behaviors. A modified state-controlled cellular nonlinear network (SC-CNN) cell containing memristors, the output nonlinear function of which is implemented with the intrinsic nonlinearity of memristor, is presented in this paper. By using appropriate connection of four modified SC-CNN cells, a SC-CNN based memristive chaotic circuit is developed. In particular, an imitative memristive circuit is developed to experimentally investigate its dynamical behaviors. The resemblance of experimental results with those of numerical simulations shows that the memristive chaotic circuit can be efficiently implemented in terms of SC-CNN scheme.

Two types of nanoscale nonlinear memristor models and their series-parallel circuits

The memristor is a novel kind of electronic device with dynamic variable resistance that is dependent on the past history of the input current or voltage. As the fourth fundamental circuit element, the memristor captures a number of unique properties that have been found to possess attractive potentials in some promising fields such as nonvolatile memory, nonlinear circuit and system, and neuromorphic system. Additionally, compared with a circuit of single memristor, series-parallel circuit of memristors possesses more abundant device characteristics which arouses increasingly extensive interest from numerous researchers. In this paper, the mathematical closed-form charge-governed and flux-governed HP memristor nonlinear models are presented with constructive procedures. In particular, these models are more realistic by taking into account the nonlinear dopant drift effect nearby the terminals and the boundary conditions, and by adding a simple and effective window function. Furthermore, based on the internal parameters and threshold of the memristor respectively, the theoretical derivation and numerical analysis of the memristor-based series-parallel connection circuits have been made comprehensively. For obtaining the characteristics of the memristor-based combinational circuits intuitively, a graphical user interface is designed based on Matlab software, which is beneficial to displaying the properties of the memristive system clearly. The results in the present paper may provide theoretical reference and reliable experimental basis for the further development of the memristor-based combinational circuits.

A methodology for memristance calculation

A memristor is a newly found fundamental circuit element whose behavior can be predicted using either the charge-dependent function called memristance or the flux-dependent function called memductance. Therefore, it is important to find the memristance or memductance function of a memristor. To the best of our knowledge, there is no methodology describing how to obtain the memristance function or memristor characteristic in the literature for this purpose as of yet. In this work, a methodology is suggested to find the memristance or memductance functions. The methodology suggests first doing several experiments with a memristor using a square-wave signal to acquire data and then using an algorithm inspired by the experience on ionic memristors reported in the literature to obtain its memristance and memductance functions. The methodology is applied to calculate the memristance function and memristor characteristic of a memristor emulator. Justifications for this method are also given.

Interview

Hiroya Tanaka from Toyota Central Research and Development Laboratories in Japan talks about the work behind the paper ‘Memristance enhancement by external voltage source’ on page 1446. Hiroya Tanaka I was engaged in the research of mobile antennas and radio wave propagation analysis during my Ph.D. Afterwards, I joined Toyota Central Research and Development Laboratories, Inc.. A lot of electric and electrical components are used in recent vehicles for energy management and advanced control. My current interests are nano-structured electromagnetic devices, nonlinear circuit elements and electromagnetic compatibility management for automotive applications. The result reported in the Electronics Letters paper is an output from the current research activity. An amazing finding has been reported by Professor M. Di Ventra's group. They have indicated that memristance is enhanced by white noise due to the nonlinear phenomenon of stochastic resonance. In our Letter, an alternative approach for the enhancement is proposed. The proposed circuit uses an external voltage source instead of white noise. The external voltage source has higher amplitude and frequency than the original signal. The numerical analysis reveals the increase of the memristance. Moreover, the current-voltage characteristic of the original signal is modulated by the external voltage source and then the hysteresis characteristic is enlarged. In our approach, the memristance is enhanced by the external voltage source instead of the white noise. The white noise level is tuned by temperature variation. On the other hand, the amplitude and frequency of external voltage source can be arbitrarily and easily tuned. Therefore, the proposed system is suitable for circuit implementation. The results in our Letter indicate that the memristance enhancement and hysteresis loop can be engineered by modulating memristance. In the past two decades, the role of fluctuation in system enhancement has been discussed in the context of nonlinear physics. One of the famous phenomena is ‘stochastic resonance’, which is induced by noise. The other example is ‘vibrational resonance.’ In this scheme, the noise is replaced by a periodic signal. The proposed system is included in the scheme of the vibrational resonance. The nonlinear physics based on the fluctuation has been applied to the field of signal processing. Various applications have been theoretically investigated, such as signal detection, imaging and wireless communication. The memristors are among interesting nonlinear circuit elements. Therefore, we have explored the possibility of memristors. Adequate parameters of the external voltage source – the amplitude, frequency and relative phase – should be set to maximise the memristance enhancement. In our Letter, the optimum parameters are determined numerically. Optimum condition of the external voltage source is strongly desired for maximising the circuit performance in the viewpoint of design. In the next step, I will derive the framework of designing the effective external voltage source. I am currently analysing the time response of memristance in the circuit using the external voltage source. The optimum condition of memristance enhancement circuit using external voltage source will be discussed in a later publication. The scheme of stochastic and vibrational resonance has often been discussed theoretically. And then the great enhancement of signal processing performance has been reported. However, to the best of our knowledge, there has been no successful example in practical applications. This is because the applied fluctuation should be controlled adaptively following the environment to maximise the signal processing performance. In addition, the memristive devices giving the maximum enhancement of the system performance should be developed. We have a big challenge in applying the interesting nonlinear physics to the real-world applications. Various schemes of memristive devices have been investigated theoretically and experimentally. Those include not only memristors but also memcapacitors and meminductors. Combinations of memristive systems with fundamental circuit elements will bring novel functions and advantages into the current analogue and digital circuit. Various applications of memristive devices have been investigated, such as digital memory, logic, neuromorphic circuits, learning circuit and programmable circuits. The memristive devices will be put into these practical applications in the near future.