Unveiling the Fourth Fundamental Circuit Element and Its Real-World Applications

Abstract

Memristors are a type of electronic circuit element that was first proposed in the early 1970s. Unlike traditional circuit elements such as resistors, capacitors, and inductors, memristors has last memory and can therefore be used to store information. They were initially considered a theoretical concept, but recent advances in nanotechnology have made it possible to create physical memristor devices and apply it in various aspect of life. Memristors are considered the fourth fundamental circuit element, alongside resistors, capacitors, and inductors. They have unique properties, such as the ability to store information in their resistance state, which makes them promising candidates for future computing systems. Memristors have been integrated into crossbar arrays, which allow for massively parallel computing with low power consumption. Memristor fabrication methods vary based on the materials used and the intended application. Thin-film deposition, nanoimprint lithography, and self-assembly processes are common techniques. The performance properties of the memristor, such as switching speed, endurance, and scalability, are influenced by the material selection, such as polymers or transition metal oxides. Memristors have a wide range of potential applications, including in the development of artificial intelligence and neural networks. They can also be used in memory devices, logic circuits, and sensor applications. Research is ongoing to further explore the unique properties of this lovely device and to develop various applications for it. The unique properties of memristors have also sparked interest in unconventional computing paradigms. Memristor-based systems have shown potential for implementing neural networks, cellular automata, and even analog computers, providing alternative approaches to solving complex computational problems. Memristor-based logic and arithmetic units offer advantages in terms of power efficiency and density compared to traditional transistor-based designs. This project shows the progress made in memristor technology, including the development of various memristive materials and device architectures. It explores the challenges associated with memristor fabrication, reliability, and scalability. Moreover, the paper highlights recent advancements in memristor-based applications, such as in-memory computing, deep learning accelerators, and brain-inspired computing systems. This piece provides an overview of the theory behind memristors, including their mathematical models and properties. It also discusses the different types of memristor devices that have been developed and their potential applications. Finally, it highlights some of the challenges and future directions in the field of memristor research.

1. Introduction

Memristors are electronic devices and the fourth fundamental circuit element that were first proposed by Leon Chua in 1971 and later realized experimentally in 2008. They are characterized by their ability to remember the amount of charge that has passed through them, similar to the way a resistor remembers the amount of current that has passed through it. They have various potentials in many fields such as signal processing, artificial intelligence and computer Memory [1, 2].

The conventional Chua’s diode has been suggested and implemented by several two-terminal passive electronic devices [3, 4]. Memristors are part of a group of devices known as “non-volatile” memory, meaning that they can store data which can be retrieved easily and even when power is removed from the device. The relationship between electronic charge q and the magnetic flux ($\varnothing$), generally refers to as memristor W ($\varnothing$) which has been realized physically by Stanley William’s group from HP labs as the cubic-nonlinear function can be used for theoretical, numerical and experimental studies. The smooth cubic flux-controlled memristor can be characterized by a smooth continuous cubic nonlinearity given by:

$$\left\{\begin{array}{l}q\left(\varphi \right)=\mathit{\beta \varphi }+{\mathit{\xi \varphi }}^3\\ W\left(\varphi \right)=\frac{\mathit{dq}\left(\varphi \right)}{\mathit{d\varphi }}=\beta +3{\mathit{\xi \varphi }}^2\end{array}\right..$$E1

and the current passing through the memristor is

$$i=W\left(\varphi \right)\upsilon$$E2

where $\beta$ and £ are parameters embedded in the memristive-based function, and ($\varnothing$) is the internal state variable of the smooth flux-controlled memristor. Also note that v is the input voltage, while i = f (W; v2) is the output voltage of the memristor. W($\varnothing$) is the conductivity of the memristor. The state variables correspond to voltages across each capacitor used in the designed circuit i.e. x = v1, y = v2, z = v3, w = ($\varnothing$), v = v2 and the smooth cubic flux-controlled memristive function f(w) = W($\varnothing$). It is worth noting that w is the internal state of the memristive device [2] (Figure 1).

Figure 1.

Memristor model: (a) the relationship of charge-magnetic flux; (b) the i-v characteristic.

I will be considering the theory, devices, and applications of memristors below.

2. Theory

Leon Chua created the theory of memristors in 1971 after investigating other basic circuit components outside the resistor, capacitor, and inductor. Chua proposed the memristor, which has a unique characteristic known as memristance, as the fourth essential circuit component. A combination of the word’s “memory” and “resistor,” “memristor” emphasizes the device’s capacity to store a recollection of the charge that has passed through it.

Memristors are identified by their uniqueness, known as the ability to store data, which is called “Memory”. When a voltage is supplied across a memristor, the resistance of the device gets adjusted, and this change is sustained even when the voltage is removed. This property is referred to as “memristance,” which is a combination of the word “memory” and “resistance.” Memristors can be modeled using a mathematical equation such as a nonlinear dynamics system [5], which is similar to the equation that describes the behavior of capacitors, inductors, and resistors. This equation can be used to design and analyze memristor circuits.

At its core, the theory of memristors revolves around the relationship between charge (q), current (i), and flux (Φ). In traditional circuit elements, such as resistors, capacitors, and inductors, these variables are linearly related. However, the memristor introduces a non-linear relationship between them, allowing for the storage of information in the form of resistance.

The fundamental equation that defines the behavior of a memristor is:

$$\mathrm{v}=\mathrm{M}\left(\mathrm{q}\right)\ast \mathrm{I}$$E3

where v represents the voltage across the memristor, q is the charge that has passed through it, i is the current flowing through it, and M(q) is the memristance function.

The memristor’s resistance is determined by the quantity of charge that has flowed through it and is described by the memristance function, M(q). The memristor’s resistance may alter over time if the function has a temporal component. This characteristic is referred to as “dynamic memristance.”

The term “flux linkage,” shown by, describes the connection between charge and memristance. The integral of the voltage across the memristor with respect to time is represented by flux linkage:

$$\mathrm{\Phi }=\int \mathrm{v}\mathrm{dt}$$E4

The memristance is determined by the derivative of the flux linkage with regard to charge:

$$\mathrm{M}\left(\mathrm{q}\right)=\mathrm{d\Phi }/$$E5

This derivative determines how the memristor’s resistance changes as charge passes through it. If the memristance increases as the charge increases, the memristor is said to have “positive memristance.” Conversely, if the memristance decreases with increasing charge, it is referred to as “negative memristance.”

Memristors have the remarkable ability to maintain resistance levels even in the absence of power, making them non-volatile memory components. This feature results from the fact that total charge flow through the memristor, rather than momentary voltage or current, determines its state.

Pinched hysteresis loops shown in the current-voltage (I-V) characteristics provide as another illustration of the behavior of memristors. When a voltage is applied across a memristor, the current on the I-V graph follows a path that resembles a compressed figure-eight. The charge-dependent resistance leads to these squeezed hysteresis loops, which are a distinguishing characteristic of memristive behavior.

One of the key properties of memristors is their ability to retain their resistance state even when power is turned off, making them non-volatile memory elements. This arises from the fact that the memristor’s state is determined by the total charge that has flowed through it rather than the instantaneous voltage or current. The memristor “remembers” its resistance state because it retains the accumulated charge.

The behavior of memristors can be further characterized by their “pinched hysteresis loops.” When a voltage is applied across a memristor, the current flowing through it traces a loop-like path on the current-voltage (I-V) graph. This loop shape resembles a pinched figure-eight, hence the term “pinched hysteresis loop.” The pinched hysteresis loop is a distinctive signature of memristive behavior and is a result of the charge-dependent resistance [6].

The theory of memristors has led to extensive research in both understanding their fundamental properties and developing practical applications. Memristors have the potential to revolutionize memory technologies, neuromorphic computing, analog circuitry, and more. As researchers delve deeper into the theory and fabrication of memristors, their applications are expected to expand, further unlocking their transformative capabilities in various fields of electronics and computing [7].

3. Devices

Memristors have been fabricated and proposed using a variety of materials such as resistive random-access memory (RRAM), including oxides, polymers, and nanowires. One of the most promising applications of memristors is in the development of “neuromorphic” computing systems, which a replica of the structure and function of the human brain Memristors can also be used in non-volatile memory devices, such as flash memory and solid-state drives, where they offer advantages over traditional memory technologies in terms of speed, space, power consumption, and durability [3, 4, 5, 6, 8].

A solid-state electrical component with memristive behavior is known as a memristor device. It is based on the idea of a memristor, a passive, two-terminal electronic component whose resistance can vary depending on the amount of charge that has flowed through it. Due to their distinctive qualities, including non-volatility, great scalability, and prospective uses in memory, computation, and neuromorphic systems, memristor devices have drawn a lot of attention. A thin film of a memristive material is often deposited between two electrodes using thin-film deposition processes, such as sputtering or atomic layer deposition. The application requirements and desired performance dictate the choice of memristive material. Titanium dioxide (TiO2), hafnium oxide (HfO2), or tantalum oxide (Ta2O5) are examples of transition metal oxides or delete data in a non-volatile way.

Memristor technology has a number of benefits over conventional memory technologies. Their non-volatile nature, which enables them to maintain their resistance states even when the power is switched off, is one important advantage. Due to this property, they are suitable for in-memory computing and storage-class memory systems, which require quick and high-density non-volatile memory. Scalability, endurance, and low-power operation are all advantages of memristor-based memory devices like conductive-bridging random-access memory (CBRAM) and resistive random-access memory (RRAM).

Memristor technology also has a lot of potential for neuromorphic computing. Building artificial neural networks is attracted to them due to their capacity to imitate certain synaptic behaviors, including as long-term potentiation and spike-timing-dependent plasticity. Neuromorphic systems based on memristors have the potential to be parallel and energy-efficient [7, 9].

Pattern recognition, machine learning, and cognitive computing can be made possible by computing, through the use of memristor.

Memristor device research is advancing quickly, with continual efforts to enhance its functionality, dependability, and compatibility with current semiconductor technology. Future developments in memristor technology may result in innovations in memory, computation, and brain-inspired systems, influencing the design of electronic devices and systems in the future [10, 11].

The working principle of a memristor device is based on resistive switching, which refers to the ability to change the device’s resistance by applying an electric field. Memristors can exist in two or more resistance states, typically referred to as high resistance (HRS) and low resistance (LRS). The transition between these states is non-volatile, meaning that it persists even when the power is turned off. The resistance of a memristor can be controlled by applying voltage pulses of different magnitudes and durations, allowing for precise manipulation of its electrical properties [9]. Memristor technology has also shown promise in analog and mixed-signal circuits. They can be used to build chaotic circuits, nonlinear dynamical systems, and analog signal processing operations. Memristors’ capacity to store and retrieve analog states creates opportunities for the creation of novel circuit topologies, such as adaptable filters and reconfigurable analog circuits [12].

4. Applications

Memristors have various potential applications in a variety of fields, including computing sensing, neuromorphic computing, signal processing, artificial intelligence and energy storage. In Signal Processing, memristors have been used to realize non-linear-signal signal processing functions such as neural thresholding and spike base computation. In computing, memristors can be used to develop more efficient and powerful computer architectures, such as neural networks and deep learning algorithms. In sensing, memristors can be used to detect changes in electrical signals, which has applications in areas such as biosensing and environmental monitoring. In energy storage, memristors can be used to store energy, which has potential applications in areas such as renewable energy systems and electric vehicles [3, 8, 13, 14, 15, 16].

With its distinctive electrical characteristics, memristor devices have created intriguing new opportunities for a variety of applications in electronics and computing. This study gives a thorough description of the various uses of memristors, emphasizing their potential to transform analog circuitry, neuromorphic computing, memory technology, and other fields. The study explores the particular applications, going into detail about their importance and possible impact. In addition, pertinent citations are included to back up the topic and offer further directions for investigation.

Few of the applications of memristors are listed below:

1. Non-volatile memory technologies: Memristors hold great promise as alternatives to conventional flash memory. This section discusses resistive random-access memory (RRAM) and crossbar arrays as examples of memristor-based memory technologies. The advantages of memristor-based memories, such as high-density storage, low power consumption, and compatibility with existing fabrication processes, are discussed in detail. Relevant citations showcase the research advancements and potential future developments in this field.

2. Neuromorphic computing: Memristors exhibit properties similar to synapses in biological neurons, making them ideal for implementing neuromorphic computing systems. This section explores the utilization of memristors in artificial neural networks and discusses their potential for energy-efficient, parallel computing. The concept of synaptic plasticity and spike-timing-dependent plasticity is explained, emphasizing the role of memristors in emulating these behaviors. Citations highlight notable research in neuromorphic computing using memristors and provide insights into future directions.

3. Analog and mixed-signal circuits: Memristors offer exciting opportunities in the field of analog and mixed-signal circuits. This section explores their potential applications in non-linear dynamical systems, chaotic circuits, and analog signal processing. The ability of memristors to store and recall analog states opens up new avenues for developing novel circuit architectures. Relevant citations illustrate the potential of memristors in these applications and showcase the progress made in implementing memristor-based analog circuits.

4. Beyond electronics and computing: This section discusses potential applications of memristors beyond traditional electronics and computing. It explores interdisciplinary areas where memristors can make a significant impact, such as bioelectronics, neuromorphic robotics, and brain-computer interfaces. Citations provide insights into the ongoing research in these interdisciplinary fields and highlight the potential future impact of memristors.

5. Conclusion

In conclusion, memristor technology is a tremendous advancement in computers and electronics with a wide range of revolutionary uses. Unlocking the full potential of memristor technology and advancing analog circuitry, computing systems, memory technologies, and multidisciplinary fields depend on ongoing research and development in this field. Memristors are expected to play a significant role in determining the direction of electronics and computing as the industry develops by providing novel solutions and pushing the envelope of what is practical.

Memristors are a promising area of research for the development of future computing technology. They offer unique properties that make them well-suited for a variety of applications, including neuromorphic computing, non-volatile memory, sensing, and energy storage. As researchers continue to explore the potential of memristors, we will likely see more applications of these devices soon (Table 1).

	Previous	Current
Theory	The earlier memristor theory, proposed by Leon Chua in 1971, introduced the concept of a fourth building block of a passive circuit alongside resistors, capacitors and inductors. Chua theorized that a memristor, short for “memory resistance,” would possess a unique property called memristance. According to this theory, memristance represents memory-like behavior in resistive devices, where their resistance can be changed and “stored” depending on the magnitude and direction of the applied voltage. In other words, the memristor would have a different resistance depending on the amount of charge that previously flowed through it.	Memristors continue to be an active area of research and development, with ongoing efforts to understand their behavior, optimize their properties, and explore their applications in various fields
Devices	First Practical Memristor: After several decades, in 2008, researchers at Hewlett-Packard (HP) Labs led by Stan Williams successfully created the first practical memristor device. They used a thin film of titanium dioxide as the active material, sandwiched between two metal electrodes. The resistance of the device could be adjusted by applying voltage across it.	There are Improved Materials and Variations, which researchers continued to explore different materials and structures to improve the performance of memristors. Various oxides, such as hafnium oxide, tantalum oxide, and niobium oxide, were tested as potential active materials. These advancements led to improved device characteristics, such as faster switching speed, lower power consumption, and higher endurance.
Application	Here are some previous applications of memristor as stated below: Non-Volatile Memory: One of the primary applications of memristors is in non-volatile memory technology. Memristors can retain their resistance state even when power is turned off, making them suitable for use in high-density and energy-efficient memory devices.; Neuromorphic Computing: Memristors have gained significant attention in the field of neuromorphic computing, which aims to build brain-inspired computing systems Reconfigurable Circuits: Memristors can be utilized in reconfigurable circuits, enabling the creation of programmable analog and digital circuits. By adjusting the resistance of memristors, the behavior and functionality of the circuits can be modified dynamically, allowing for adaptive and flexible circuit designs.; Sensor and IoT Applications: Memristors can be integrated into sensing devices to enable novel functionalities.	Memristors are still in the early stages of commercialization, and their widespread adoption is growing rapidly in all areas such as: Artificial Intelligence (AI) Hardware Acceleration: Memristors hold potential for accelerating AI computations by providing efficient and scalable hardware solutions. Their ability to perform analog computations and emulate synaptic behavior can enhance the efficiency of neural network training and inference tasks, leading to improved AI performance.; Bio-Inspired Systems: Memristors are being investigated for their potential in bio-inspired systems, such as brain-machine interfaces and neuro prosthetics. The ability to emulate synaptic behavior and process analog signals makes memristors suitable for building interfaces between electronic systems and biological organisms.; It’s important to note that the field of memristor research is still evolving, and new applications and advancements continue to emerge. Researchers and industry experts are actively exploring the potential of memristors and working towards their integration into practical applications across various spheres.

Table 1.

Simple bench mark table showing previous and current work on memristor: Theory, device and application.