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Memristor nanodevice for unconventional computing: review and applications
Abstract
A memristor is a two-terminal nanodevice. Its properties attract a wide community of re-searchers from various domains such as physics, chemistry, electronics, computer and neuro-science. The simple structure for manufacturing, small scalability, nonvolatility and potential of using in low power platforms are outstanding characteristics of this emerging technology. In this chapter, we review a brief literature of memristor from mathematic model to the physical realization and different applications. We discuss different classes of memristors based on the material used for its manufacturing. The potential applications of memristor are presented and a wide domain of applications are classified.
Introduction
Memristor has recently drawn the wide attention of scientists and researchers due to non-volatility, better alignment, and excellent scalability properties [40]. Memristor has initiated a novel research direction for the advancement of neuromorphic and neuro-inspired computing. Memristor remembers its last state after the last power plugging and has a simple physical structure, high-density integration, and low-power consumption. These features make the memristor an attractive candidate for building the next generation of memories [13]. In addition, from high-performance computing point of view, the memristor has the potential capability to conquer the memory bottleneck issue, by utilizing computational unit next to the memory [8]. Due to these unique properties and potentials of the memristor, neuroscientists and neuromorphic researchers apply it as an artificial synapse in Spiking Neural Network (SNN) architectures [12].
Memristor was predicted in 1971 by Leon Chua, a professor of electrical engineering at the Univer-sity of California, Berkeley, as the fourth fundamental device [11]. Publishing a paper in the Nature journal by Hewlett Packard (HP) [1] in May 2008, announced the first ever experimental realization of the memristor, caused an extraordinary increased interest in this passive element. Based on the symmetry of the equations that govern the resistor, capacitor, and inductor, Chua hypothesized that fourth device should exist that holds a relationship between magnetic flux and charge. After the physi-cal discovery of the memristor, several institutions have published the memristor device fabrications using a variety of different materials and device structures [1, 2, 41–43].
In 2009, Biolek et al. modeled nonlinear dopant drift memristor by SPICE [44]. One year later, Wei Lu, professor at the University of Michigan proposed a nanoscale memristor device which can mimic the synapse behavior in neuromorphic systems [45]. Later on, in 2011 a team of multidisciplinary researchers from Harvard University published an interesting paper on programmable nanowire circuits for using in nanoprocessors [46]. Until June 2016, based on the Scopus bibliographic database, 2466 papers have been published in peer-reviewed journals and ISI articles which are related to memristor fabrication or applications of the memristor in different science and technology domains.
Memristors are promising devices for a wide range of potential applications from digital memory, logic/analog circuits, and bio-inspired applications [16]. Especially because the nonvolatility property in many types of memristors,they could be a suitable candidate for making non-volatile memories with ultra large capacity [14]. In addition to non-volatility, the memristor has other attractive features such as simple physical structure, high-density, low-power, and unlimited endurance which make this device a proper choice for many applications. Different device structures are still being developed to determine which memristor device can be presented as the best choice for commercial use in memory/flash manufacturing or in neuromorphic platforms. This is based on different factors such as size, switching speed, power consumption, switching longevity, and CMOS compatibility. The rest of the chapter is organized as follows: In Section 2, a general overview of the memristor is done and the electrical properties have been investigated. Section 3 presents memristor implementation and fabrication. We investigate various types of memristors based on the different materials that have been used in the fabrication. In Section 4, potential applications of Memristor has been studied. Section 5 deals with streams of research, we have investigated a research classification from the physics level to the system design. Finally, we describe a brief summary and the future work.
Memristor device overview and properties
In this section, we discuss the memristor nanodevice which is believed to be the fourth missing fundamental circuit element, that comes in the form of a passive two-terminal device. We discuss how it can remember its state, and what is its electrical model and particular properties.
Memristor a missing electrical passive element
Memristor is a contraction of “memory & resistor,” because the basic functionality of the memristor is to remember its state history. This characteristic proposes a promising component for next generation memory. Memristor is a thin-film electrical circuit element that changes its resistance depending on the total amount of charge that flows through the device. Chua proved that memristor behavior could not be duplicated by any circuit built using only the other three basic electronic elements (Resistor,Capacitor, Inductor), that is why the memristor is truly fundamental. As it is depicted in Figure 2.1, the resistor is constant factor between the voltage and current (d v ˘ R.d i ), the capacitor is a constant factor between the charge and voltage (d q ˘ C .d v), and the inductor is a constant factor between the flux and current (d’ ˘ L.d i ). The relation between flux and charge is Obviously missing (d’ ˘ M.d q) that can be interpreted by a fourth fundamental element such as memristor [11].
Obviously, in memristive devices, the nonlinear resistance can be changed and memorized by controlling the flow of the electrical charge or the magnetic flux. This control any two-terminal black box is called a memristor if, and only if, it exhibits a pinched hysteresis loop for all bipolar periodic input current signaling is interesting for the computation capability of a device similar to the controlling of the states of a transistor. For instance in an analog domain, one can control the state of a transistor to stay in an active area for amplification. Nevertheless, in the digital domain to stay in Off (cut-off ) state for logic ’0’ and in On (saturated) state for logic ’1’ one can perform with controlling the gate voltage. The output current in MOSFET (Metal-Oxide semiconductor Field Effect Transistor) is managed by changing the gate voltage as well as in BJT (Bipolar Junction Transistor) the input current (base current) can control the output current (collector-emitter current). The main difference between the memristor and transistor for managing the states is that in transistor there is a third terminal to control the states however, in contrast a memristor is a two-terminal device and there is no extra terminal to control the device state. The challenge of using memristor as a computational component
Figure 2.1: Relations between the passive devices and the anticipating the place of the fourth funda-mental element based on the relations between charge (q) and flux (’) (from [1]).
instead of transistor lies in the ability to control the working states as accurate as possible. Indeed, in a memristor both potentials for analog and digital computing have been presented. Consequently, using memristor in digital computing to make gate library or crossbar architecture as well as using memristor in analog domain (neuro-inspired or traditional) for computation are introduced in several work [8, 19–21, 47]. In next sections, we discuss different possibilities and our contributions to apply memristor in both digital and analog platforms.
Memristive device functionality
When you turn off the voltage, the memristor remembers its most recent resistance until the next time you turn it on, whether that happens a day later or a year later. It is worth mentioning that the duration to store the data in resistive form is dependent of the nano-device material. In other words, the volatility is different depending on the device materials in fabrication.
To understand the functionality of a memristor, let us imagine a resistor as a pipe which water flows through it. The water simulates the electric charge. The resistor obstruction of the flow of charge is comparable to the diameter of the pipe: the narrower the pipe, the greater the resistance. For the history of circuit design, resistors have had a fixed pipe diameter. But a memristor is a pipe that its diameter changes with the amount and direction of the water flows through it. If water flows through this pipe in one direction, it expands the pipe diameter (more conductive). But if the water flows in the opposite direction and the pipe shrinks (less conductive). Furthermore, let us imagine while we turn off the flow, the diameter of the pipe freezes until the water is turned back on. It mimics the memristor characteristic to remember last state. This freezing property suits memristors brilliantly for the new generation of memory. The ability to indefinitely store resistance values means that a memristor can be used as a nonvolatile memory.
Chua demonstrated mathematically that his hypothetical device would provide a relationship between flux and charge similar to what a resistor provides between voltage and current. There was no obvious physical interaction between charge and the integral over the voltage before HP discovery. Stanley Williams in [48] explained how they found the missing memristor and what is the relation between what they found and Chua mathematic model. In Figure 2.2, the oxygen deficiencies in the TiO2¡x manifest as bubbles of oxygen vacancies scattered throughout the upper layer. A positive voltage on the switch repels the (positive) oxygen deficiencies in the metallic upper TiO2¡x layer, sending them into the insulating TiO2 layer below. That causes the boundary between the two materials to move down, increasing the percentage of conducting TiO2¡x and thus the conductivity of the entire switch.
Therefore, the more positive voltage causes the more conductivity in the cube. A negative voltage on the switch attracts the positively charged oxygen bubbles, pulling them out of the TiO2. The amount of insulating of resistive TiO2 increases, thereby making the switch more resistive. The more negative voltage causes the less conductivity in the cube. What makes this switch a special device? When the voltage across the device is turned off–positive or negative–the oxygen bubbles do not migrate. They will freeze where they have been before, which means that the boundary between the two titanium dioxide layers is frozen. That is how the Memristor “remembers” the last state of conductivity as well as it proves the plasticity properties in memristor to be applied as a synapse in an artificial neural network architecture and neuromorphic platform.
Table of contents :
1 Introduction
1.1 Introduction
1.2 Part I:Motivation, state-of-the-art and application of using emerging nanodevices for unconventional computing
1.3 Part II:Our contribution in spiking neural network architecture: Simulator, New synapse box, Parameter exploration and Spiking deep learning
1.4 Manuscript outline
I Motivation, state-of-the-art and application of using emerging nanodevices for unconventional computing
2 Memristor nanodevice for unconventional computing: review and applications
2.1 Introduction
2.2 Memristor device overview and properties
2.2.1 Memristor a missing electrical passive element
2.2.2 Memristive device functionality
2.2.3 Electricalmodel
2.3 Memristor classification based on different materials and applications
2.3.1 ResistiveMemristor
2.3.2 SpintronicMemristor
2.3.3 Organic (Polymeric)Memristor
2.3.4 FerroelectricMemristor
2.3.5 Evaluation ofMemristor with differentmaterials
2.4 Potential applications of memristors
2.4.1 Memristor-based nonvolatile memory
2.4.2 Digital computing
2.4.3 Analog domain applications
2.5 Streams of research
2.6 Conclusions and summary
3 Unconventional digital computing approach: memristive nanodevice platform
3.1 Introduction
3.2 Stateful implication logic
3.2.1 Functionally complete Boolean operations
3.3 Crossbar architecture
3.3.1 Memristive switches in crossbar architectures
3.3.2 Configurable crossbar array logic gates
3.4 Evaluation
3.5 Conclusions
4 Neuromorphic computing in Spiking Neural Network architecture
4.1 Introduction
4.2 Spiking Neural Networks
4.2.1 Spike information coding
4.2.2 Network topology
4.3 Spiking neuron model
4.3.1 Biological, artificial and spiking neuron
4.4 Synapse and learning
4.4.1 Synaptic learning and plasticity
4.5 Hardware spiking neural network systems
4.6 Discussion
4.7 Conclusion
II Our contribution in spiking neural network architecture: Simulator, Newsynapse box, Parameter exploration and Spiking deep learning
5 N2S3, an Open-Source Scalable Spiking Neuromorphic Hardware Simulator
5.1 Introduction
5.2 Event-Driven Simulation Architecture
5.2.1 Event-Driven vs Clock-Driven Simulation
5.2.2 Technological Choices: Scala and Akka
5.2.3 Software Architecture
5.3 Neuron, Synapse, NetworkModeling
5.3.1 NeuronModeling
5.3.2 Synapse modeling and learning
5.3.3 Network Topologies
5.4 N2S3 Features
5.4.1 Input Processing
5.4.2 Visualization tools
5.4.3 Experiment Specification Language
5.4.4 Software Engineering Practices
5.4.5 Standard experiments
5.5 Conclusion
6 Combining a Volatile and Nonvolatile Memristor in Artificial Synapse to Improve Learning in Spiking Neural Networks
6.1 Introduction
6.2 Circuit Design of Neuron and Synapse in RBM Network
6.2.1 Leaky Integrate-and-Fire neurons
6.2.2 New artificial synapse using memristors
6.2.3 New plasticity learning method
6.2.4 Combining a volatile and nonvolatile memristor to make a new artificial synapse
6.2.5 Network topology and learning
6.3 Experimental Validation
6.3.1 MNIST recognition improvement
6.4 Conclusion
7 Evaluation methodology and parameter exploration to improve performance of memristor based spiking neural network architecture
7.1 Introduction
7.2 Experimental evaluation of the influence of four parameters on the classification of handwritten digits
7.2.1 Effect of spike distribution
7.2.2 Effect of STDP window duration
7.2.3 Effect of neuron threshold
7.2.4 Effect of synapse ¯ parameter
7.2.5 Discussion
7.3 Conclusions
8 Deep learning in spiking neural network
8.1 Introduction
8.2 Restricted BoltzmannMachine and Contrastive Divergence
8.3 Deep learning in artificial neural networks versus spiking neural networks
8.4 Developing and Training Deep Belief Network with Siegert Units
8.5 Evaluating the model
8.6 Conclusion and future works
9 Conclusion
Bibliography
