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Neuromorphic Devices for Brain-inspired Computing: Artificial Intelligence, Perception, and Robotics
Explore the cutting-edge of neuromorphic technologies with applications in Artificial Intelligence
In Neuromorphic Devices for Brain-Inspired Computing: Artificial Intelligence, Perception, and Robotics, a team of expert engineers delivers a comprehensive discussion of all aspects of neuromorphic electronics designed to assist researchers and professionals to understand and apply all manner of brain-inspired computing and perception technologies. The book covers both memristic and neuromorphic devices, including spintronic, multi-terminal, and neuromorphic perceptual applications.
Summarizing recent progress made in five distinct configurations of brain-inspired computing, the authors explore this promising technology's potential applications in two specific areas: neuromorphic computing systems and neuromorphic perceptual systems. The book also includes:
- A thorough introduction to two-terminal neuromorphic memristors, including memristive devices and resistive switching mechanisms
- Comprehensive explorations of spintronic neuromorphic devices and multi-terminal neuromorphic devices with cognitive behaviors
- Practical discussions of neuromorphic devices based on chalcogenide and organic materials
- In-depth examinations of neuromorphic computing and perceptual systems with emerging devices
Perfect for materials scientists, biochemists, and electronics engineers, Neuromorphic Devices for Brain-Inspired Computing: Artificial Intelligence, Perception, and Robotics will also earn a place in the libraries of neurochemists, neurobiologists, and neurophysiologists.
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Veröffentlichungsjahr: 2021
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Table of Contents
Cover
Title Page
Copyright
Preface
1 Two-Terminal Neuromorphic Memristors
1.1 Memristive Devices
1.2 Resistive Switching Mechanisms
1.3 Memristive Bioinspired Devices
1.4 Memristive Neural Networks
1.5 Summary and Outlook
References
2 Spintronic Neuromorphic Devices
2.1 Introduction
2.2 Magnetic Tunnel Junction for Neuromorphic Computing
2.3 Skyrmion-Based Neuromorphic Computing
2.4 Spin Torque Oscillators for Neuromorphic Computing
2.5 Conclusion and Outlook
References
3 Multiterminal Neuromorphic Devices with Cognitive Behaviors
3.1 Introduction
3.2 Multiterminal Neuromorphic Memristors
3.3 Multiterminal Neuromorphic Transistors
3.4 Neuromorphic Transistors for Perception Learning Activities
3.5 Conclusion and Outlook
Acknowledgments
References
4 Neuromorphic Devices Based on Chalcogenide Materials
4.1 Introduction
4.2 Ovonic Memory Switching (OMS) and Threshold Switching (OTS) in Chalcogenide Materials
4.3 Artificial Synapses Based on MS Behaviors
4.4 Artificial Neurons Based on TS Effects
4.5 Hardware Neural Networks
4.6 Summary and Outlook
References
5 Neuromorphic Devices Based on Organic Materials
5.1 Introduction
5.2 Two-Terminal Organic Neuromorphic Devices
5.3 Three-Terminal Organic Neuromorphic Devices
5.4 Innovative Applications of Organic Neuromorphic Devices for Bionic Perception Systems
5.5 Summary and Outlook
References
6 Neuromorphic Computing Systems with Emerging Devices
6.1 Introduction
6.2 DNNs Based on Synaptic Devices
6.3 SNNs Based on Neuromorphic Devices
6.4 Other Neuromorphic Systems
6.5 Summary and Outlook
References
7 Neuromorphic Perceptual Systems with Emerging Devices
7.1 Background
7.2 Sensation and Perception
7.3 Implementation of Artificial Perception
7.4 Challenges and Perspectives
References
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Memristive neurons.
Chapter 6
Table 6.1 Typical neuromorphic devices.
Table 6.2 Analog resistive switching device characteristics and their defini...
Table 6.3 Array demonstrations for DNNs.
Table 6.4 Chips based on memristive devices for DNNs.
Table 6.5 Hardware demonstrations of SNNs based on synaptic arrays and neuro...
Table 6.6 Hardware demonstrations for other neuromorphic computing systems.
Chapter 7
Table 7.1 The recent progresses on artificial sensory neuron.
List of Illustrations
Chapter 1
Figure 1.1 (a) Diagram of a memristive device with a capacitor-like structur...
Figure 1.2 Typical
I
–
V
characteristics for different switching behaviors in ...
Figure 1.3 Decay characteristics of volatile analog switching and threshold ...
Figure 1.4 Schematic presentation of the resistive switching processes of an...
Figure 1.5 (a) TEM image of the Ag/SiO
2
/Pt device after the forming process....
Figure 1.6 (a) Both ion mobility and redox rate are high, resulting in the f...
Figure 1.7 Schematic presentation of the switching process of a VCM device w...
Figure 1.8 (a) High-resolution TEM image of a
V
O
nanofilament in Pt/TiO
2
/Pt ...
Figure 1.9 (a) Scanning transmission X-ray microscopy (STXM) image of a TiO
2
Figure 1.10 (a, c) XPEEM images of an SrTiO
3
-based device in (a) LRS and (c)...
Figure 1.11 The interface-type resistive switching mechanism for a represent...
Figure 1.12 (a) Cross-sectional TEM image of Ti/PCMO junction. (b) Electron ...
Figure 1.13 Spectromicroscopy results using the absorption current and photo...
Figure 1.14 Biological synapses and its plasticity. (a) A biological synapse...
Figure 1.15 Short-term synaptic plasticity. (a) Paired-pulse facilitation (P...
Figure 1.16 PPF implementation in the three terminal in-plane lateral memris...
Figure 1.17 Biorealistic memristive synapses realized in diffusive memristiv...
Figure 1.18 LTP in biology. (a) Long-term potentiation (LTPot) response of t...
Figure 1.19 Biorealistic BCM learning rules obtained in second-order memrist...
Figure 1.20 Biological neurons. (a) Schematic of a biological neuron, includ...
Figure 1.21 The LIF neuron implementation in the threshold-less memristive d...
Figure 1.22 The implementation of an LIF neuron in the threshold memristive ...
Figure 1.23 LIF neuron based on a single component of threshold memristive d...
Figure 1.24 Memristive HH axon. (a) Circuit diagram of the HH axon. The chan...
Figure 1.25 HH neuron with LIF functions. (a) The cross-sectional TEM image ...
Figure 1.26 Memristive ANN computing. (a) Left: Schematic of a memristive de...
Figure 1.27 Memristive SNN computing. (a) Scanning electron micrograph of th...
Chapter 2
Figure 2.1 (a) Structure schematic of the MTJ composed of CoFeB/MgO/CoFeB th...
Figure 2.2 Structure schematic of the three-terminal SOT-MTJ device.
Figure 2.3 (a) The device structure of the spintronic memristor with the STT...
Figure 2.4 (a) Schematic topology of the proposed CMS composed of multiple (
Figure 2.5 (a) Schematic of the proposed CSS device, where the capping layer...
Figure 2.6 (a) The membrane potential of a spiking neuron with the LIF model...
Figure 2.7 The switching probability of the IMA STT-MTJ can be tuned by (a) ...
Figure 2.8 The spiking neuron can be emulated by a DW based spintronic memri...
Figure 2.9 Schematic of the ANN, where the neuron is generally characterized...
Figure 2.10 (a) SOT-MTJ as the “step” neural device with (b) two-step switch...
Figure 2.11 Proposed CSN, which can implement a multi-step transfer function...
Figure 2.12 (a) The proposed CSN circuit, which involves three operation pha...
Figure 2.13 The non-step transfer function can be implemented by connecting ...
Figure 2.14 Proposed all-spin artificial neural network with proposed CSS an...
Figure 2.15 System-level simulation results of the proposed ASANN for hand-w...
Figure 2.16 (a) Bloch skyrmion. (b) Néel skyrmion. (c) Skyrmion breathing mo...
Figure 2.17 A schematic diagram of a biological neural network describing fu...
Figure 2.18 Schematic of (a) the proposed skyrmionic synaptic device and (b)...
Figure 2.19 Analogy between the biological synapse and the electronic ternar...
Figure 2.20 (a) Schematic of the skyrmion-based artificial neuron device; (b...
Figure 2.21 Comparative concepts of (a) Conventional RC and (b) Physical RC....
Figure 2.22 (a) Schematic of the skyrmion-based RC device. (b) Resistance of...
Figure 2.23 Skyrmion reshuffler device. (a) Reshuffler operation with skyrmi...
Figure 2.24 (a) The schematic structure of the skyrmion-based TRNG: the ferr...
Figure 2.25 (a) An overview of the current challenges of skyrmion-based neur...
Figure 2.26 (a) The schematic of spin torque oscillator. (b) The balance bet...
Figure 2.27 The illustration of injection locking phenomenon.
ω
STNO
is ...
Figure 2.28 STO can be acted as a reservoir.
Figure 2.29 The flow chart for reservoir computing with STO.
Figure 2.30 Recurrent neural network based on delayed feedback of STO.
Figure 2.31 Coupled STOs act as neurons.
Figure 2.32 Coupling of two dimensional STOs through spin waves and its corr...
Chapter 3
Figure 3.1 (a) Proposed resistive switching model for bilayered HfO
2
/TiO
x
co...
Figure 3.2 Pavlovian conditioned reflex mimicked on PVA-GO hybrid memristor ...
Figure 3.3 Schematic diagram of (a) homosynaptic plasticity and (b) heterosy...
Figure 3.4 Schematic diagram of (a) electrical double-layer (EDL) mechanism ...
Figure 3.5 (a) Specific capacitance–frequency curves for the nanogranular Si...
Figure 3.6 (a) Schematic measurement layout of pH sensor based on dual-gate ...
Figure 3.7 (a) Schematic diagram of synaptic network with multiple in-plane ...
Figure 3.8 (a) Schematic diagram of a biological heterosynapse. (b) Schemati...
Figure 3.9 (a) Schematic diagram of multiplicative and additive operations. ...
Figure 3.10 Schematic diagram of human tactile afferent nerve.
Figure 3.11 (a) Schematic diagram of artificial sensory synapse based on pie...
Figure 3.12 (a) Schematic diagram of synergic effect in neurons activated by...
Figure 3.13 (a) Schematic diagram of multiterminal synaptic transistor struc...
Chapter 4
Figure 4.1 (a) Current–voltage curve of a typical memory switching device. (...
Figure 4.2 A phase map expressed by ionicity and hybridization parameters wh...
Figure 4.3 (a) Interconnection scheme of PCM synapses to reach ultrahigh den...
Figure 4.4 (a) Illustration showing the PCM device made of a selector and a ...
Figure 4.5 (a)
I
–
V
characteristics of the c-GST cell measured by DC double s...
Figure 4.6 (a) Integrate-and-fire (IF) neuron model. (b) Schematic illustrat...
Figure 4.7 (a) Equivalent circuit of the LIF neuron. (b) Oscillating outputs...
Figure 4.8 (a) The integrate-and-fire function of the OTS device-based artif...
Figure 4.9 (a) A fully connected layer with
m
input nodes and
n
output nodes...
Figure 4.10 (a) Mapping a fully connected neural network onto PCM arrays. (b...
Figure 4.11 (a) TEM image of synaptic phase change memory cell in 2T-1R conf...
Chapter 5
Figure 5.1 (a) Structural analogy between Ag/PEDOT:PSS/Ta memristor and a ty...
Figure 5.2 (a) Chemical structures of BTPA-F and EV(ClO
4
)
2
and the electroch...
Figure 5.3 (a) Schematic diagram and band structure of the e-synapse consist...
Figure 5.4 (a) Schematic diagram of the CuPc-based crossbar architecture and...
Figure 5.5 (a) Schematic illustration of the 3D bottom-gate top-contact flex...
Figure 5.6 (a) The schematic diagram of the synaptic transistors based on PE...
Figure 5.7 (a) Device structure of the ultrathin conformable organic synapti...
Figure 5.8 (a) Device structure of the light-stimulated organic synaptic tra...
Figure 5.9 (a) Schematics of the organolead halide perovskite synaptic devic...
Figure 5.10 (a) The proposed organic synaptic transistor. (b) Schematics of ...
Chapter 6
Figure 6.1 Structures of typical neural networks. (a) The structure of an FC...
Figure 6.2 Schematic of memristor-based crossbar array for neural network ha...
Figure 6.3 Synaptic behaviors based on memristive devices. (a, b) A
3 × 1
...
Figure 6.4 Illustrations of other forms of neuromorphic computing. (a) The m...
Chapter 7
Figure 7.1 The five senses of human. The people face.
Figure 7.2 The perceptual process in the sensorimotor system. The human brai...
Figure 7.3 The temporal and spatial processing of (a) normal sensor and (b) ...
Figure 7.4 The simplification of the sensory neuron for the design of recent...
Figure 7.5 The evolution of the artificial sensory neuron. The square, trian...
Figure 7.6 A summary of the artificial sensory neuron (or memory) with diffe...
Figure 7.7 The power consumption for several kinds of artificial sensory neu...
Figure 7.8 Information flow in an artificial perceptual system for pattern r...
Figure 7.9 A roadmap for neuromorphic perceptual system. The human brain, ha...
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
Begin Reading
Index
End User License Agreement
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Neuromorphic Devices for Brain-Inspired Computing
Artificial Intelligence, Perception, and Robotics
Edited by Qing Wan and Yi Shi
Editors
Professor Qing WanNanjing UniversityElectronic Science & EngineeringNo. 163, Xianlin AvenueQixia District210093 NanjingChina
Professor Yi ShiNanjing UniversitySchool of Electronic Science and EngineeringNo. 163, Xianlin Da DaoQixia District210023 NanjingChina
Cover Image: © vs148/Shutterstock
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Print ISBN: 978-3-527-34979-1ePDF ISBN: 978-3-527-83529-4ePub ISBN: 978-3-527-83530-0oBook ISBN: 978-3-527-83531-7
Preface
Neuromorphic Devices for Brain-inspired Computing provides an overview of the development on neuromorphic electronics, which aimed at building a neuromorphic computing system from the bottom up. Neuromorphic computing, also called brain-like computing, is one promising computing paradigm in the post-Moore's Law era. The models, approaches, and hardware for neuromorphic computing are designed by replicating the neural network structures and information processing principles of the human brain. Just as the metal–oxide–semiconductor field-effect transistors (MOSFETs) to the integrated circuits, the fundamental neuromorphic device is the key element for building a neuromorphic computing system. Hence, it is urgent and meaningful to provide a comprehensive view on these neuromorphic devices and to look into the possibility of this new wave. Thus, we invited some experts from each neuromorphic electronics related sub-topic to fulfill the aforementioned target together. We have listed their names and affiliations in the list of contributors.
Chapter 1 introduces the device structure, materials, and switching behaviors of memristive devices, as well as the state-of-the-art memristive synapses, neurons, and neural networks.
Chapter 2 is focused on the spintronic device-based neuromorphic emulation and computing. Spintronic devices have unique properties such as low power, nearly infinite endurance, good scalability, and grate compatibility with the complementary metal–oxide–semiconductor (CMOS) technology and are recently recognized as promising candidates for neuromorphic devices.
Chapter 3 introduces multi-terminal devices, which are mainly transistors. Interesting dendritic integration functions and dendritic algorithms based on this type of devices are also discussed and briefly introduced.
Chapter 4 is devoted to neuromorphic devices based on chalcogenide materials that show the intriguing memory switch and threshold switch behaviors to emulate synaptic plasticity and neural firing functions.
Chapter 5 is devoted to neuromorphic devices based on organic materials. Organic neuromorphic devices are involved in both two-terminal devices and three-terminal devices, and they are notable for building bionic systems.
Chapter 6 is mainly about the neuromorphic computing implemented by emerging devices. The neuromorphic devices facilitate energy-efficient computing in deep neural networks (DNNs), spiking neural networks (SNNs), and other intelligent systems.
Chapter 7 describes another promising direction for neuromorphic electronics: the building of neuromorphic perceptual systems by emerging devices. This direction is aimed to endow intelligence to the bionic systems.
With more than one year of preparation, this book has finally been published. We all hope you will find our labors useful. Your comments and corrections will be highly appreciated.
1Two-Terminal Neuromorphic Memristors
Hui-Kai He, He-Ming Huang, and Rui Yang
Huazhong University of Science and Technology, School of Materials Science and Engineering, Wuhan 430074, P. R. China
1.1 Memristive Devices
A memristive device is a resistive device with an inherent memory; its theory was creatively conceived by Prof. Chua in 1971 [1] and was connected to the physical devices in 2008 by HP [2]. Since then, memristive devices have been extensively studied over the past decade due to their prominent advantages, such as simple structure, high operation speed, and low power consumption in applications of data storage, logic operation, and neuromorphic computation [3]. In this section, we will introduce traditional two-terminal memristive devices, mainly focusing on device structure and memristive materials.
1.1.1 Memristive Device Structure and Materials
1.1.1.1 Memristive Device Structure
Typically, a memristive device has a metal/insulator/metal (MIM) structure, composed of a switching layer sandwiched between two metal electrodes (possibly different), as shown in Figure 1.1a. Because of its simple structure, highly scalable cross-point and multilevel stacking memory structures have been proposed (Figure 1.1b), which is promising for the construction of huge neural networks and neuromorphic computing systems [3]. It is well known that electrodes play a crucial role in the resistive switching behavior of memristive devices. To date, in addition to metals (such as Ag [5], Cu [6], Pt [7], Au [8], Al [9], and W [10]), a variety of conductive materials have been explored as electrodes for memristors, including nitrides such as TiN [11], carbon materials such as graphene [12] and carbon nanotubes [13], conductive oxides such as ITO [14] and SrRuO3 (SRO) [15], p- and n-type Si [16], and so on. Among these metals, Ag and Cu are the most popular ones due to their ability to dissolve in thin film electrolyte at low electric field and their high ionic mobility [17]. In addition to the electrodes, the switching layer where the resistive switching takes place is the key layer in memristive devices and has a great impact on the device performance. Typically, the switching layer is an insulator or a semiconductor. Also, it is normally in the form of thin film, which is compatible to large-scale integration in the semiconductor industry. Recently, other forms of the switching layer are also intensively investigated, including nanoparticles [18], nanowires [19], two-dimensional (2D) materials [20], three-dimensional nanoarrays, etc. Note that we mainly discuss memristors in the form of thin film in all below sections.
Figure 1.1 (a) Diagram of a memristive device with a capacitor-like structure in which a switching layer is sandwiched between two metal electrodes. (b) Diagram of a cross-point memory structure. Word and bit lines are used for selecting a memristive device and writing/reading data, respectively.
Source: Sawa [4].
1.1.1.2 Memristive Materials
As mentioned above, the materials involved in memristors include switching materials and electrode materials. Here, we mainly focus on switching materials, which is also termed as memristive materials. Up to now, a great number of memristive materials have been explored for memristive devices used in neuromorphic computing. In this chapter, the memristive materials are subdivided into inorganic and organic materials. Generally speaking, inorganic materials have significant advantages over organic ones in switching stability and manufacturing technology, while organic ones stand out in terms of high-mechanical flexibility and low cost.
Inorganic materials for memristors can be loosely divided into binary oxides (e.g. TiOx[21], TaOx[22], HfOx[23], WOx[24], and ZnO [14]), perovskite oxides (e.g. SrTiO3[25] and BiFeO3[26]), and 2D materials (e.g. graphene [27], hexagonal boron nitride (h-BN) [28], and molybdenum disulfide (MoS2) [20]). Among these inorganic materials, binary oxides have been intensively studied since they are the most abundant and show superior switching characteristics including ultrahigh ON/OFF ratio, sub-ns operation speed, and extreme endurance. In addition, their simple composition enables them to be easily fabricated by various film deposition technologies, mainly including magnetron sputtering [14, 24], atomic layer deposition (ALD) [29], thermal oxidation [30], and plasma oxidation [11]. Magnetron sputtering is a high-rate, high-efficient film deposition technology and is becoming increasingly popular owing its high-yield and low-cost production of uniform films over large areas. Recently, ALD has also attracted increasing attention for the deposition of binary oxides due to its ability to accurately control the thickness and uniformity of the films. Furthermore, binary oxides have good compatibility with conventional complementary metal oxide semiconductor (CMOS) process and good thermal stability. Thus, binary oxides have been the focus of both academic and industrial communities over the past decade. In particular, research interest in HfOx and TaOx has been extremely high in the past few years since they exhibit both sub-ns operation speed and extreme endurance of >1010 cycles and may be the most promising memristive materials for practical applications in the near future.
In addition to binary oxide, perovskite oxides such as SrTiO3, SmNiO3, BiFeO3, and SrRuO3 have also been researched for memristors over the past few years. Among these perovskite oxides, SrTiO3 receives the most attention for the implementation of memristive synapses because of its superior memristive properties and rich switching dynamics [25, 31, 32]. It has been found that perovskite oxides have advantages of excellent localized accumulation of oxygen ions and can be easily converted into a defective structure. However, it should be mentioned that they are generally obtained through pulsed laser deposition (PLD) under high temperature. Although this is an advanced deposition method that can obtain high-quality thin films with accurate stoichiometry, it is not widely used in the semiconductor industry due to its high-cost and the small uniform area of the deposited film, greatly hindering the development and application of perovskite oxides in memristors.
In recent years, 2D materials have become a new focus in memristors for the realization of artificial synapses and neurons due to their superior physical, chemical, and mechanical properties, including graphene, MoS2, and h-BN. Graphene is one of the highly desirable materials for memristive bioinspired devices owing to its excellent properties of low cost, tunability, nontoxicity, flexibility, and biocompatibility [33, 34]. However, graphene is inherently a semimetallic material and needs to be oxidized or doped when it is used as a switching layer. In contrast to graphene, transition metal chalcogenides (TMDs), such as MoS2 and tungsten selenide (WSe2), are semiconductors with proper bandgaps from 1 to 2 eV [35]. Therefore, TMDs are considered as ideal substitutes for graphene. MoS2, the common member of the TMDs family, has been intensively investigated and shows superior performance including ultrahigh ON/OFF ratio [36], ultralow operating voltage [37], and excellent thermal stability [38]. Reliable production of 2D materials with uniform properties is essential for translating their new electronic and optical properties into applications. Until now, various fabrication methods including mechanical exfoliation [39], liquid-phase exfoliation [40], and chemical vapor deposition (CVD)[41] have been employed to obtain atomically thin flakes of 2D materials. First discovered by Novoselov et al. in 2004, ultrathin 2D materials are peeled from their parent bulk crystals by mechanical exfoliation using adhesive tape. This method produces single-crystal flakes of high purity and cleanliness that are suitable for fundamental characterization. Liquid-phase exfoliation method is also a feasible way to prepare atomically thin 2D material. It can produce gram quantities of submicrometer-sized monolayers, but the resulting exfoliated material differs structurally and electronically from the bulk material [42]. To obtain large-area and uniform layers, CVD method is very promising. Such methods give reasonably good-quality material with typical flake sizes of hundreds of nanometers to a few centimeters, although the flake thickness is not conclusively shown to be monolayers.
Compared with inorganic materials, organic materials have the advantages of low cost, ease of fabrication, and, especially, high-mechanical flexibility. In addition, it is easy to modulate the electrical performance of organic materials by a designed molecular synthesis [43]. Accordingly, organic materials are attracting more and more attention that enable them to be promising for future flexible electronics, although most switching characteristics of organic materials are still not comparable with those of inorganic materials. It is well known that organic materials consist of large molecules with long chains of repeating monomer units. Hence, solution processes, for example, spin coating, are normally adopted to prepare organic films [44, 45]. Note that organic materials still suffer from some problems like poor thermal stability and bad compatibility with CMOS process [46].
1.1.2 Resistive Switching Behavior
The intrinsic physical phenomenon behind memristive devices is resistive switching (RS), which means the resistance can be reversely changed between low resistive state (LRS) and high resistive state (HRS) under external electric stimuli, resulting in a pinched hysteresis current–voltage (I–V) loop. If the resistance state of the memristive device changes from HRS to LRS, it is called an SET operation and is also considered as a “write” process. In contrast, if the resistance state is converted from LRS to HRS, it is called RESET operation and means an “erase” process (Figure 1.2).
Actually, the switching behavior can be classified into different types on the basis of I–V characteristics according to different criteria. Based on the polarity of the external electric field, the switching behaviors can be classified into two types: unipolar and bipolar resistive switching. The unipolar switching operates independently of the voltage polarity, which is also named nonpolar switching sometimes. Meanwhile, the bipolar switching shows a directional resistive switching, depending on the polarity of the applied voltage. On the basis of the switching dynamics, the switching behavior can be classified into digital and analog types. Generally, the digital resistive switching shows abrupt current jumping in the I–V curves, while the analog switching has continuous current curve during voltage sweeping. Digital resistive switching is preferable in the information storage because of its high ON/OFF ratio and fast switching speed [48, 49]. In contrast, the analog resistive switching is particularly concerned for artificial synaptic devices, since the gradual change of the resistance well resembles the potentiation/inhabitation of the synaptic weight in the adaptive learning process of a synapse [50]. The switching behaviors in Figure 1.2b,d are generally nonvolatile and widely used in the application of data storage. Notably, the analog switching shown in Figure 1.2c is usually nonvolatile but sometimes is volatile with current decay effect. The volatile analog switching with versatile time constants is desirable for simulating short-term and long-term synaptic plasticity. The unipolar digital switching shown in Figure 1.2a is volatile and is usually named as threshold switching, in which the device switches to LRS upon the application of a certain threshold voltage and then spontaneously decays back to HRS after the removal of the external voltage. This threshold switching is promising for implementing the threshold firing process of the neuron. Below, we mainly focus on the volatile and nonvolatile resistive switching.
Figure 1.2 Typical I–V characteristics for different switching behaviors in memristive devices. (a) Unipolar threshold switching. (b) Unipolar digital switching with nonvolatility. (c) Bipolar analog switching with tunable volatility. (d) Bipolar digital switching with nonvolatility.
Source: Yang et al. [47].
1.1.2.1 Volatile Resistive Switching
The current of the memristive device showing spontaneously decay after the removal of the external electric field is termed as volatile resistive switching, including volatile analog switching and threshold switching. Both of them can be utilized in the construction of artificial synapses and neurons.
To date, volatile analog switching has been observed in a variety of materials, such as WOx[24], Pr0.7Ca0.3MnO3 (PCMO) [51], and Nb-SrTiO3[11]. Moreover, it has been found that this switching is generally based on interface-type resistive switching, which will be discussed later. Note that the decay characteristics are essential in the emulation of both short- and long-term plasticity of biological synapses. Thus, we next give a brief introduction to the dynamic process of volatile analog switching using the Pd/WOx/W memristor as an example [30]. After the stimulation of write pulses, current decay process of the device is carefully monitored by small read pulses, as shown in Figure 1.3a. The stimulation drives the current higher; however after the stimulation is removed, the current decreases with time. One can see that the decay appears to occur at two different time scales: right after stimulation, the current shows a very fast decay, and the decay becomes much slower after several seconds. Then, the decay can be well fitted by the sum of two stretched exponential functions with two time constants: a short-term effect with time constant ≈52.5 ms and a long-term time constant ≈92.5 seconds:
where τs (τ1), I0s (I01), and βs (β1) are the characteristic relaxation time, prefactor, and stretch index for the short-term (long-term term) process, respectively. Borrowing terms used in neuroscience, the first stage with time constant ≈52.5 ms is considered short-term, and the second stage with time constant ≈92.5 seconds is considered long-term. These two time constants differ by more than 3 orders of magnitude, which enable the memristor to emulate important rate- and timing-dependent behaviors at both short term and long term.
In addition to volatile analog switching, threshold switching is also volatile, and the current will decay over time once the applied voltage or pulse is removed. Recently, threshold switching was demonstrated by Wang et al. in two-terminal diffusive memristors based on Ag-doped SiOxNy[52]. Also, the decay process was attributed to the spontaneous rupture of the Ag filament driven by minimization of the interfacial energy between Ag and the dielectric after removing the external electric field. Figure 1.3b displays decay characteristics of the SiOxNy:Ag diffusive memristor showing variation of current (open circle) with applied voltage pulses (solid line). Under an applied pulse, the device exhibits threshold switching to an LRS after an incubation period (delay time). This delay time is related to the growth and clustering of silver nanoparticles to eventually form conduction channels. Following channel formation, the current jumps abruptly by several orders of magnitude and then slowly increases further under bias as the channel thickens. Once the voltage pulse is removed, the device relaxes back to its original HRS over a characteristic time (relaxation time). More importantly, the relaxation time is on the same order as the response of bio-synapses, that is, tens of milliseconds. Furthermore, it has been demonstrated that the relaxation time is related to the temperature, the voltage pulse parameters, operation history, Ag concentration, host lattice, device geometry, and humidity, which alone or in combination can be used to tune the desired dynamics for neuromorphic systems.
Figure 1.3 Decay characteristics of volatile analog switching and threshold switching devices. (a) Current decay of the Pd/WOx/W device after the removal of the applied voltage pulses. The experimental data (black squares) can be fitted by the sum of two stretched exponential functions with distinct relaxation time constants. (b) Decay characteristics of the SiOxNy:Ag diffusive device showing variation of current (open circles) with applied voltage pulses.
Source: Du et al. [30].
Source: Wang et al. [52].
1.1.2.2 Nonvolatile Resistive Switching
Unlike volatile resistive switching, nonvolatile resistive switching, including bipolar digital switching and nonvolatile analog switching, means that the conductance is maintained after the removal of the external electric field. For bipolar digital switching, the device abruptly changes to LRS upon the application of a positive (negative) threshold voltage and then returns to HRS upon the application of a negative (positive) threshold voltage. Such switching is preferable in data storage due to its high ON/OFF ratio, fast switching speed, and long retention. Recently, thanks to high scalability and large dynamic range, this switching has also been used in memristors for the construction of artificial synapses [53, 54]. However, one disadvantage of this switching is the limited number of conductance states and low conductance update linearity, highly hindering its application and development in neuromorphic computing.
In contrast, nonvolatile analog switching, with multilevel conductance states and high conductance update linearity, has recently attracted increasing attention in the construction of neural network accelerators and neuromorphic systems. On the basis of the nonvolatile analog switching, vector–matrix multiplication (VMM) or weighted summation operation can be physically implemented in a cross-bar array of memristive devices based on Ohm and Kirchhoff laws [55, 56]. In this case, the VMM operation can be accelerated in a parallel, in-memory, and analog manner in the memristor crossbar, which could largely benefit data-centric and VMM-intensive algorithms, including a large majority of artificial neural network (ANN) algorithms and many other arithmetic calculations. This part will be introduced in detail in Section 1.5.
1.2 Resistive Switching Mechanisms
In the past few years, the switching mechanisms of memristors have been vigorously investigated to predict and manipulate the switching profiles to achieve superior switching performance [49, 57]. Especially for artificial synapses and neurons, the required characteristics are broadened to work sensitively to the input stimulus and generate controllable conductance change [58]. To closely mimic biological synapses and neurons, regulating the conductance change of the memristive device under electric stimuli becomes extremely important. Therefore, it is necessary for us to have a deep understanding of the switching mechanisms of memristors. Here, the common switching mechanisms are classified into two types including filamentary-type resistive switching and interface-type resistive switching according to the position where the resistive switching occurs.
1.2.1 Filamentary-Type Resistive Switching
In a memristive device base on the filamentary-type resistive switching, a forming process is usually required to obtain stable resistive switching behavior, during which conductive filaments (CFs) form and the memristive device reaches a LRS. Subsequently, local rupture and re-formation of the CFs occur during the reset and set processes, respectively, resulting in the alternation between HRS and LRS. Accordingly, the resistance value of LRS exhibits no or weak dependence on the device size in filamentary-type memristive devices [49]. Generally, the growth and rupture of CFs results from ion migration. Based on the polarities of the charges, there are two types of ions: cations and anions in nature, and they migrate in opposite directions under an external electric field. Thus, the filamentary-type resistive switching can be subdivided into cation migration-related filaments and anion migration-related filaments, and growth and rupture processes of the CFs based on each of these are discussed separately as follows.
1.2.1.1 Cation Migration-Related Filaments
The cation migration-based memristive devices typically have an electrochemically active electrode (AE), such as Ag or Cu; an electrochemically inert counter electrode (CE), such as Pt, Au, or W; and a thin film of a solid electrolyte, such as Ag+ or Cu+ ion conductor, sandwiched between both electrodes [59]. The CFs are formed via electrochemical dissolution and then redeposition of the active metal atoms. Therefore, such memristive devices are often called electrochemical metallization cells (ECM) and are also referred to programmable metallization cells (PMCs) or atomic switches in some literatures [60–62]. The first observation of a metal filament in ECM was achieved by Hirose in 1976. [63]. They demonstrated nonvolatile resistive switching behavior in the Ag/Ag–As2S3/Mo sandwich device. To clarify the switching mechanism, a planar Ag/Ag–As2S3/Au device was fabricated at the same time, and the growth of Ag filaments from the CE (Au electrode) to the AE (Ag electrode) was confirmed by optical microscopy.
The resistive switching process of an ECM device with Cu as the AE and Pt as the CE is schematically shown in Figure 1.4. The overall switching process consists of the following steps: (a) Upon applying a high enough positive voltage to Cu, metallic Cu is oxidized to Cu+ ions in accordance with the reaction, Cu → Cu+ + e−. (b) Cu+ ions migrate along fast diffusion channels toward the CE driven by external electric field, and Cu+ ions are reduced back to metallic Cu according to the reaction, Cu+ + e− → Cu. (c) The Cu filament continues to grow, and two electrodes become connected. As a result, the ECM device switches from HRS to LRS. (d) Under negative voltage, the Cu filaments can be electrochemically dissolved with the help of Joule heating, thereby resetting the ECM device back to the HRS.
Although there is no doubt about the presence of metal filaments in cation migration-based memristors, the direct observation of metal filaments, especially their dynamic growth and rupture processes, has attracted great interest in academia. Originally, only ex situ observations of metal filaments in planar microscale ECM cells were reported. In recent years, thanks to advances in fabrication and characterization of nanomaterials, both ex situ and in situ observations of metal filaments in vertical nanoscale ECM cells have been extensively explored. In 2012, Yang et al. reported the formation/rupture of nanoscale Ag filaments in Ag/SiO2/Pt device by transmission electron microscopy (TEM) technique [65]. After application of a positive voltage bias to the Ag electrode, the as-fabricated device was switched to the LRS with an abrupt increase in current, as shown in Figure 1.5c. The electrical resistance change was found to accompany changes in the electrode and the switching material (Figure 1.5a), where Ag was injected into the insulating SiO2 layer and the two electrodes were connected by the Ag filaments. Upon voltage bias of opposite polarity, the device switched back to the HRS (Figure 1.5d), corresponding to the rupture of the Ag filaments (Figure 1.5b). These observations unambiguously reveal the physical nature of the resistive switching process, where the physically displaced Ag atoms lead to the dramatic changes to the device's electrical properties. Besides direct observation of the metal filaments during resistive switching by ex situ TEM, in situ TEM technique provides important information concerning the microscopic dynamic ionic processes during filament growth. In Yang's work, the filament growth was further demonstrated in vertical Ag/a–Si/W ECM device via in situ TEM observation, as shown in Figure 1.5e. One can identify the real-time structural evolution of the ECM device since the filament growth is directly related to the electric measurements. The systematic in situ TEM analyses offers a complete picture of the different dynamic processes that occur in the ECM device, e.g. filament growth direction, position, and morphology [66].
Figure 1.4 Schematic presentation of the resistive switching processes of an ECM device with Cu as the AE and Pt as the CE. (a) forming process, (b) SET process, (c) ON state, (d) RESET process.
Source: Zidan et al. [64].
Figure 1.5 (a) TEM image of the Ag/SiO2/Pt device after the forming process. Scale bar: 200 nm. (b) TEM image of the same device after erasing. Scale bar: 200 nm. (c) Corresponding I–t curve during the forming process that led to the image in (a). The applied voltage was 8 V. (d) Corresponding I–t curve during the erasing process that led to the image in (b). The applied voltage was −10 V. (e) Real-time structural evolutions of an Ag/a-Si/W-based device obtained through in situ TEM observation, showing the dynamic filament growth process that initiates from the reactive electrode.
Source: Yang et al. [65].
Notably, the filament growth/dissolution dynamics can be affected by the ionic mobility and the redox reaction rate. Therefore, the filament dynamics can be classified into four categories (Figure 1.6). (i) In the case of high ion mobility and high redox rate, the ions can reach the inert electrode without agglomerating, thus avoiding nucleation within the insulating film so filament growth initiates from the inert electrode, and the large amount of ion supply due to high redox rate leads to the formation of cone-shaped filaments with its base at the inert electrode interface as shown in Figure 1.6a. Such case can be found in ECM devices with traditional solid electrolytes such as GeTe [67] that are known to be good ionic conductors. (ii) In the case of low ion mobility and low redox rate (Figure 1.6b), the ions can pile and reach the critical nucleation conditions inside the dielectric, and further filament growth is fulfilled by cluster displacement via the repeated splitting–merging processes. An experimental example is the filament growth in amorphous Si, where the filament is initiated from the active electrode and grows toward the inert electrode as discrete nanoclusters [68]. (iii) In the case of low ion mobility and high redox rate, nucleation can occur inside the dielectric while large amounts of atoms can be deposited onto the cathode sides of the nuclei, leading to the gap filling shown in Figure 1.6c. (iv) In the case of high ion mobility and low redox rate (Figure 1.6d), nucleation only occurs at the inert electrode, but the limited ion supply means that the reduction predominately occurs at the edges with high field strengths, thus leading to the branched filament growth toward the active electrode.
Figure 1.6 (a) Both ion mobility and redox rate are high, resulting in the filament growth from the inert electrode and an inverted cone shape. (b) Both ion mobility and redox rate are low, resulting in the filament growth from the active electrode with discrete nanoclusters and a forward cone shape. (c) Ion mobility is low, but redox rate is high, resulting in the filament nucleation inside the dielectric and reconnection with the source. (d) Ion mobility is high, but redox rate is low, resulting in the filament growth from the inert electrode and a branched structure.
Source: Yang et al. [66].
Ion mobility and redox rate can be tuned by the careful selection of the electrode material and the switching materials, as well as the operating conditions since both can be strongly affected by the applied electric field and temperature. Hence, it is possible to adjust the filament dynamics by selecting proper electrode material, switching materials, and operating conditions. The behavior and characteristics of filament are important for artificial synapses and neurons because the filament dynamics is closely related to the synaptic plasticity.
1.2.1.2 Anion Migration-Related Filaments
Besides metal ions, the redox and migration processes of anions, mostly oxygen ions, are involved in the memristive devices based on transition metal oxides without electrochemical active electrodes. The migration of oxygen ions usually induces a redox reaction expressed by a valence change of the cation sublattice and leads to a stoichiometry change of the oxides. Therefore, anion migration-related filament mechanism is typically named as valence change mechanism (VCM). In a VCM device, resistive switching generally relies on the creation and annihilation of oxygen-deficient (or oxygen vacancies, ) CFs based on oxygen migration. In contrast to ECM devices, VCM devices generally consist of inert electrodes and the switching materials. The switching layer is normally a transition metal oxide such as binary metal oxides and ternary perovskite oxide.
The switching process of a VCM device with inert electrodes and a transition metal oxide is schematically shown in Figure 1.7. are randomly distributed at the initial state (Figure 1.7a). When the top electrode (TE) is positively biased, migrate toward the bottom electrode (BE) and accumulate in the oxide/BE interface (Figure 1.7b). Afterward, continue to accumulate under the positive voltage bias. Once the CFs form and connect the TE and BE, the device switches into the LRS (Figure 1.7c). With the growth mode from the BE to the TE, the thinnest part of the formed CF should be located near the TE. When the TE is negatively biased, Joule heat is mainly concentrated on the thinnest part of the CF, and in this region migrate toward the TE and then is replaced by the oxygen ions. As a result, the concentration of in the thinnest part of the CF will be significantly decreased, leading to the rupture of the CF at that location (Figure 1.7d).
Figure 1.7 Schematic presentation of the switching process of a VCM device with inert electrodes and a transition metal oxide. (a) The initial state with randomly distributed . (b) The nucleation and subsequent growth from cathode to anode of filament during forming process. (c) The LRS with a complete filament whose thinnest region is near the anode. (d) The HRS with a partially ruptured filament at its thinnest region.
Source: Pan et al. [48].
Figure 1.8 (a) High-resolution TEM image of a VO nanofilament in Pt/TiO2/Pt device after the set operation. (b) High-resolution TEM image of an incomplete filament in the same device after the reset operation.
Source: Kwon et al. [68].
Similar to ECM devices, a host of material characterization techniques such as TEM and spectroscopic analysis have recently been employed to reveal the microscopic origin of resistive switching behaviors in VCM devices. Figure 1.8 shows high-resolution TEM (HRTEM) image of the same location in a Pt/TiO2/Pt device after applying negative (set) and positive (reset) voltages, respectively [68]. Clear contrast differences in the HRTEM images can be observed, indicating changes in the composition of the film at different resistance states. In the set sample (Figure 1.8a), a connected VO filament in the conical shape (marked by a gray line) was found between top electrode and bottom electrode. After the reset operation (Figure 1.8b), the connected filament ruptured and an incomplete filament was present near the top electrode, verifying the role of VO migration during the resistive switching process of VCM devices.
It is generally more challenging to directly observe the VO migration process and filament evolution in VCM devices since the filaments consist of native defects, i.e. rather than foreign metallic species. Careful spectroscopic analysis is typically required to confirm the composition changes. Various state-of-the-art techniques such as X-ray absorption spectroscopy (XAS) [69, 70] and photoemission electron microscopy (PEEM) [71, 72] have recently been employed to comprehensively characterize the changes in film microstructure, composition, and chemical states accompanying the resistive switching process in VCM devices.
XAS Analysis Spatially resolved XAS using scanning transmission X-ray microscope (STXM) was performed to nondestructively investigate the chemical and structural changes during resistive switching. Figure 1.9a,b shows the presence of three distinct states of the TiO2 within the junction area taken at an X-ray energy of 460.0 eV in the Ti L3-edge in a Pt/TiO2/Pt device after electroforming and set/reset cycling [69]. Region is outside of the junction area and is most similar to the as-deposited TiO2, which is known from X-ray diffraction (XRD) to be an amorphous phase. Within the junction (region ii), the spectrum strongly matches the known XAS for anatase, one of the crystalline polymorphs of TiO2. The altered absorption spectrum in region iii matches that of reduced titanium oxide, in which the valence state of the Ti ions is reduced from +4 to +3. Furthermore, electron diffraction measurement revealed that the region iii is composed of the Ti4O7 phase with metallic conductivity, which proves the formation of localized conductive filament due to the migration of . Thermally driven radial migration of was also demonstrated by in operando X-ray absorption spectromicroscopy in a Ta2O5-based device (Figure 1.9c,d) [70]. After 105 cycles, a ring-like feature with a bright inner core and a dark perimeter was observed as shown in Figure 1.9c. In addition to field driven drift of in the vertical direction, temperature gradients due to Joule heating near the localized conduction channels produce thermophoretic forces that cause lateral migration of . As a result, lateral segregation of oxygen-deficient and oxygen-rich regions occurs, corresponding to the bright and dark regions in Figure 1.9c.
Figure 1.9 (a) Scanning transmission X-ray microscopy (STXM) image of a TiO2-based device after electrical cycling, showing structural changes and the formation of a localized channel. (b) Corresponding Ti L-edge X-ray absorption spectra from the three regions in panel (a). (c) O K-edge transmission intensity map of a Ta2O5-based device cycled to 120 000 cycles imaged at an energy of 531.2 eV. (d) 3D color intensity plot of the ring seen in (c), displaying the profile of the ring.
Source: (a, b) Strachan et al. [69].
Source: (c, d) Kumar et al. [70].
X-ray PEEM analysis In operando X-ray PEEM (XPEEM) analysis is a desirable technique to nondestructively reveal the changes in film microstructure, composition, and chemical states during the resistive switching process with high spatial resolution and interface or surface sensitivity. Recently, quantitative redox reactions were demonstrated via in operando XPEEM analysis in a SrTiO3-based device with a graphene top electrode that offers excellent electrical conductivity and photoelectron transparency to allow electrical programming and spectromicroscopy measurements [71]. Noticeable changes were observed in the normalized intensity of O K-edge when the device alternated between the HRS and LRS, indicating the formation and dissolution of the filament (Figure 1.10). Furthermore, quantitative information on the charge-carrier density differences between different resistance states is available since XPEEM is a highly surface-sensitive technique.
1.2.2 Interface-Type Resistive Switching
In contrast to the filamentary-type resistive switching, interface-type resistive switching generally originates from the variation of the Schottky barrier caused by migration of [73]. In this case, the resistance in the LRS is inversely proportional to the electrode area, suggesting the entire electrode area is involved in the switching behavior. Furthermore, the interface-type switching normally does not require a forming process and can easily obtain a multilevel storage because it changes the resistance value by a uniform interface effect. Overcoming the forming randomness of memristors, devices could achieve excellent reproducibility and cell-to-cell uniformity [74].
Figure 1.10 (a, c) XPEEM images of an SrTiO3-based device in (a) LRS and (c) HRS, showing a localized filament with changes of the O concentration. Scale bars: 1 μm. (b, d) O K-edge spectra obtained from the filament region [light curve for LRS in panel (b) and dark gray for HRS in panel (d)] and the surrounding region (black curves).
Source: Modified from Baeumer et al. [71].
The interface-type resistive switching mechanism was first reported by Sawa in 2008 [4]. According to the article, the I–V curves of the Ti/PCMO, Au/Nb:STO, and SRO/Nb:STO interfaces show rectifying I–V behavior, thus revealing the presence of Schottky contacts. In addition to the rectification, I–V curves for these interfaces exhibit hysteretic behavior indicative of resistive switching. Furthermore, they found the migration of at the interface plays a key role in the resistive switching. Up to now, different devices with interface-type switching have been explored, including Pt/WO3−x/Pt [75], Pt/ZnO nanorod/FTO [76], Pt/Nb:STO/Al [77], ZrO2:Y/PCMO [78], InGaZnO (IGZO)/a-IGZO[79], and so on.
The resistive switching process in the interface-type switching is schematically illustrated in Figure 1.11, using n-type semiconductor as an example [74, 80]. n-Type semiconductor forms a Schottky barrier when in contact with a metal with a large work function (such as Pt or SRO) and forms an Ohmic contact when associated with a low work function metal (such as Ti). In the conventional Schottky model, the capacitance is given by , where Wd is the width of the depletion layer, ɛ0 is the relative dielectric constant of a vacuum, ɛs is the semiconductor relative dielectric constant, and S is the cell area. This equation indicates that LRS is achieved by tunneling through the Schottky barrier with a narrow Wd, while HRS is created by inhibited tunneling at the Schottky barrier with a wide Wd. With the application of a negative bias (Figure 1.11a), positively charged oxygen vacancies are attracted to the electrode narrowing the barrier, and the device switches to the LRS. A positive bias will result in the repulsion of the oxygen vacancies and in the restoration of the barrier width, and the device switches back to HRS (Figure 1.11b).
The current lack of full understanding of the underlying switching mechanisms remains a major challenge for interface-type memristive devices and a significant obstacle to their widespread applications. For this reason, in the past few years, a variety of materials characterization techniques have been employed to clarify the switching mechanisms in interface-type memristive devices, including the combination of TEM and electron energy-loss spectra (EELS) [81], spectromicroscopy studies [82], and so on.
Figure 1.11 The interface-type resistive switching mechanism for a representative n-type semiconductor. (a) In the LRS, accumulate at the interface, reducing the depletion width. (b) In the HRS, there are less at the interface, increasing the depletion width.
Figure 1.12 (a) Cross-sectional TEM image of Ti/PCMO junction. (b) Electron energy-loss spectra of Mn L-edge at several positions in Ti/PCMO junction indicated in (a).
Source: (b) Asanuma et al. [81]. Copyright 2009, American Physical Society.
Combination of TEM and EELS As an example, the migration of in the Ti/PCMO interface was demonstrated by the combination of cross-sectional TEM and the EELS spectra, as shown in Figure 1.12. An amorphous TiOy layer between the Ti electrode and the PCMO layer was clearly observed in the cross-sectional TEM (Figure 1.12a). Furthermore, the EELS of the Mn L-edge obtained at different positions in the PCMO layer was carried out to confirm the diffusion of oxygen ions at the interface. As seen in Figure 1.12b, the peak intensity ratio of Mn-L3 and Mn-L2, I(L3)/I(L2), decreased with increasing distance from the boundary between the TiOy and the PCMO layers, indicating the valence of the Mn ion in the vicinity of the interface was smaller than that far from the interface. The above results suggest that the number of oxygen vacancies in the vicinity of the interface was increased due to the migration of oxygen ions from the PCMO layer to the Ti electrode.
Spectromicroscopy Studies Figure 1.13 shows spectromicroscopy results using the absorption current and photoemission electrons of the Au/Al/PCMO/CMO/PCMO/Pt device in the LRS and HRS, respectively. There are three different regions in Figure 1.13a, b: Au/Al/PCMO, Au/PCMO, and PCMO. Au/PCMO and PCMO, respectively, are the most (light) and least (dark gray) conductive in both resistive states. A significant change in current occurred in the Au/Al/PCMO region, with high (light gray) and low (dark gray) current intensity in the LRS and HRS, respectively, indicating the Al top electrode plays a key role in the resistive switching. Furthermore, from Al 2p photoelectron peaks and spectromicroscopy spectra (Figure 1.13
