# Roadmap to neuromorphic computing with emerging technologies

Adnan Mehonic, Daniele Ielmini, Kaushik Roy, Onur Mutlu, Shahar Kvatinsky, Teresa Serrano-Gotarredona, Bernabe Linares-Barranco, Sabina Spiga, Sergey Savel'ev, Alexander G Balanov, et al.

<figure><img src="image_1.png" /></figure>

## To cite this version:

Adnan Mehonic, Daniele Ielmini, Kaushik Roy, Onur Mutlu, Shahar Kvatinsky, et al. Roadmap to neuromorphic computing with emerging technologies. APL Materials, 2024, 12 (10), 10.1063/5.0179424. [hal-04964959](https://hal.science/hal-04964959v1)

HAL Id: hal-04964959

https://hal.science/hal-04964959v1

Submitted on 25 Feb 2025

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_2.png" /></figure>
# Roadmap to neuromorphic computing with emerging technologies EP

Adnan Mehonic 🧙 ; Daniele Ielmini 🧙 ; Kaushik Roy; Onur Mutlu 🧙 ; Shahar Kvatinsky 🧙 ;

Teresa Serrano-Gotarredona; Bernabe Linares-Barranco 🧙 ; Sabina Spiga 🧙 ; Sergey Savel'ev 🧙 ;

Alexander G. Balanov 🧙 ; Nitin Chawla; Giuseppe Desoli 🧙 ; Gerardo Malavena 🧙 ;

Christian Monzio Compagnoni 🧙 ; Zhongrui Wang 🧙 ; J. Joshua Yang 🧙 ; Syed Ghazi Sarwat;

Abu Sebastian 🧙 ; Thomas Mikolajick 🧙 ; Stefan Slesazeck 🧙 ; Beatriz Noheda 🧙 ; Bernard Dieny 🧙 ;

Tuo-Hung (Alex) Hou; Akhil Varri 🧙 ; Frank Brückerhoff-Plückelmann 🧙 ; Wolfram Pernice 🧙 ;

Xixiang Zhang 🧙 ; Sebastian Pazos 🧙 ; Mario Lanza 🧙 ; Stefan Wiefels 🧙 ; Regina Dittmann 🧙 ;

Wing H. Ng 🧙 ; Mark Buckwell 🧙 ; Horatio R. J. Cox 🧙 ; Daniel J. Mannion 🧙 ; Anthony J. Kenyon 🧙 ;

Yingming Lu; Yuchao Yang 🧙 ; Damien Querlioz 🧙 ; Louis Hutin 🧙 ; Elisa Vianello;

Sayeed Shafayet Chowdhury 🧙 ; Piergiulio Mannocci 🧙 ; Yimao Cai 🧙 ; Zhong Sun 🧙 ; Giacomo Pedretti 🧙 ;

John Paul Strachan 🧙 ; Dmitri Strukov 🧙 ; Manuel Le Gallo 🧙 ; Stefano Ambrogio 🧙 ; Ilia Valov 🧙 ;

Rainer Waser 🧙 ;

<figure><img src="image_3.png" /></figure>

Check for updates

APL Mater. 12, 109201 (2024)

https://doi.org/10.1063/5.0179424

<figure><img src="image_4.png" /></figure>

View
Online

<figure><img src="image_5.png" /></figure>

Export
Citation

## Articles You May Be Interested In

### Roadmap on photonic metasurfaces

Appl. Phys. Lett. (June 2024)

### Roadmap on ferroelectric hafnia- and zirconia-based materials and devices

APL Mater. (August 2023)

### Roadmap on organic-inorganic hybrid perovskite semiconductors and devices

APL Mater. (October 2021)

<figure><img src="image_6.png" /></figure>

AIP
Publishing

APL Materials

Special Topics Open
for Submissions

Learn More

<figure><img src="image_7.png" /></figure>

AIP
Publishing
# Roadmap to neuromorphic computing
with emerging technologies EP

Cite as: APL Mater. 12, 109201 (2024); doi: 10.1063/5.0179424

Submitted: 2 October 2023 • Accepted: 20 August 2024 •

Published Online: 21 October 2024

<figure><img src="image_8.png" /></figure>

View Online

<figure><img src="image_9.png" /></figure>

Export Citation

<figure><img src="image_10.png" /></figure>

CrossMark

Adnan Mehonic,¹,⁴ ID
Daniele Ielmini,² ID
Kaushik Roy,³ Onur Mutlu,⁴ ID
Shahar Kvatinsky,⁵ ID
Teresa Serrano-Gotarredona,⁶ Bernabe Linares-Barranco,⁶ ID
Sabina Spiga,⁷ ID
Sergey Savel'ev,⁸ ID
Alexander G. Balanov,⁸ ID
Nitin Chawla,⁹ Giuseppe Desoli,¹⁰ ID
Gerardo Malavena,² ID
Christian Monzio Compagnoni,² ID
Zhongrui Wang,¹¹ ID
J. Joshua Yang,¹¹ ID
Syed Ghazi Sarwat,¹² ID
Abu Sebastian,¹² ID
Thomas Mikolajick,¹³,¹⁴ ID
Stefan Slesazeck,¹³ ID
Beatriz Noheda,¹⁵ ID
Bernard Dieny,¹⁶ ID
Tuo-Hung (Alex) Hou,¹⁷ Akhil Varri,¹⁸ ID
Frank Brückerhoff-Plückelmann,¹⁸ ID
Wolfram Pernice,¹⁸ ID
Xixiang Zhang,¹⁹ ID
Sebastian Pazos,¹⁹ ID
Mario Lanza,²⁰ ID
Stefan Wiefels,²¹ ID
Regina Dittmann,²¹ ID
Wing H. Ng,¹ ID
Mark Buckwell,¹ ID
Horatio R. J. Cox,¹ ID
Daniel J. Mannion,²² ID
Anthony J. Kenyon,¹ ID
Yingming Lu,²³ Yuchao Yang,²³ ID
Damien Querlioz,²⁴ ID
Louis Hutin,²⁵ ID
Elisa Vianello,²⁵ ID
Sayeed Shafayet Chowdhury,³ ID
Piergiulio Mannocci,² ID
Yimao Cai,²⁶ ID
Zhong Sun,²⁶ ID
Giacomo Pedretti,²⁷ ID
John Paul Strachan,²⁸,²⁹ ID
Dmitri Strukov,³⁰ ID
Manuel Le Gallo,¹² ID
Stefano Ambrogio,³¹ ID
Ilia Valov,³²,³³ ID
and Rainer Waser³²,³⁴ ID

For affiliations, please see the end of the Reference section

© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0179424

## TABLE OF CONTENTS

I. INTRODUCTION TO THE ROADMAP 2

A. Taxonomy and motivation 2

II. COMPUTING CHALLENGES 5

A. Digital computing 5

1. Status 5

2. Challenges 5

3. Potential solutions and conclusion 6

III. NEUROMORPHIC COMPUTING BASICS AND ITS EVOLUTION 6

A. What is neuromorphic computing/engineering 6

1. Neuromorphic sensing 6

2. Neuromorphic processing 7

3. Challenges and conclusion 8

B. Different neuromorphic technologies and state of the art 9

1. Status 9

2. Challenges 10

3. Potential solutions 11

4. Conclusion 11

C. Possible future computational primitives for neuromorphic computing 12

IV. MATURE TECHNOLOGIES (COMPUTING APPROACHES) 13

A. SRAM 13

1. Status 13

2. Challenges and potential solutions 14

3. Conclusions 15

B. Flash memories 16

1. Status 16

2. Challenges and potential solutions 17

a. Challenges arising from changes in the design strategy of the array. 17

b. Challenges arising from array reliability. 17

b. Challenges arising from the peripheral circuitry of the array. 17

3. Conclusion 17

V. EMERGING TECHNOLOGIES (COMPUTING APPROACHES) 18

A. Resistive switching and memristor 18

1. Status 18

2. Challenges 18

3. Potential solutions 19
<table><tbody><tr><td>4.</td><td>Conclusion</td><td>19</td></tr><tr><td>B.</td><td>Phase change materials</td><td>19</td></tr><tr><td></td><td>1. Introduction</td><td>19</td></tr><tr><td></td><td>2. Challenges</td><td>19</td></tr><tr><td></td><td>3. Potential solutions</td><td>21</td></tr><tr><td></td><td>4. Conclusion</td><td>21</td></tr><tr><td>C.</td><td>Ferroelectric materials</td><td>22</td></tr><tr><td></td><td>1. Status</td><td>22</td></tr><tr><td></td><td>2. Challenges</td><td>22</td></tr><tr><td></td><td>3. Potential solutions</td><td>23</td></tr><tr><td>D.</td><td>Spintronic materials for neuromorphic computing</td><td>24</td></tr><tr><td></td><td>1. Status</td><td>24</td></tr><tr><td></td><td>2. Challenges</td><td>25</td></tr><tr><td></td><td>3. Potential solutions</td><td>25</td></tr><tr><td></td><td>4. Concluding remarks</td><td>26</td></tr><tr><td>E.</td><td>Optoelectronic and photonic implementations</td><td>26</td></tr><tr><td></td><td>1. Status</td><td>26</td></tr><tr><td></td><td>2. Challenges</td><td>26</td></tr><tr><td></td><td>3. Potential solutions</td><td>27</td></tr><tr><td></td><td>4. Concluding remarks</td><td>27</td></tr><tr><td>F.</td><td>2D materials</td><td>28</td></tr><tr><td></td><td>1. Status</td><td>28</td></tr><tr><td></td><td>2. Challenges and potential solutions</td><td>28</td></tr><tr><td></td><td>3. Concluding remarks</td><td>29</td></tr><tr><td>VI.</td><td>MATERIALS CHALLENGES AND PERSPECTIVES</td><td>29</td></tr><tr><td>A.</td><td>Materials challenges</td><td>29</td></tr><tr><td></td><td>1. Scaling</td><td>30</td></tr><tr><td></td><td>2. Speed</td><td>30</td></tr><tr><td></td><td>3. Reliability</td><td>30</td></tr><tr><td></td><td>4. Endurance</td><td>30</td></tr><tr><td></td><td>5. Retention</td><td>31</td></tr><tr><td></td><td>6. Read disturb</td><td>31</td></tr><tr><td></td><td>7. Variability</td><td>31</td></tr><tr><td></td><td>8. Analog operation</td><td>31</td></tr><tr><td>B.</td><td>Characterization techniques</td><td>31</td></tr><tr><td></td><td>1. Status</td><td>31</td></tr><tr><td></td><td>2. Challenges and potential solutions</td><td>32</td></tr><tr><td></td><td>3. Concluding remarks</td><td>33</td></tr><tr><td>C.</td><td>Comparison between different material systems</td><td>33</td></tr><tr><td></td><td>1. Status</td><td>33</td></tr><tr><td></td><td>2. Conclusion</td><td>34</td></tr><tr><td>VII.</td><td>NOVEL COMPUTING CONCEPTS</td><td>35</td></tr><tr><td>A.</td><td>Embracing variability</td><td>35</td></tr><tr><td></td><td>1. Status</td><td>35</td></tr><tr><td></td><td>2. Challenges</td><td>36</td></tr><tr><td></td><td>3. Potential solutions</td><td>36</td></tr><tr><td></td><td>4. Concluding remarks</td><td>37</td></tr><tr><td>B.</td><td>Spiking-based computing</td><td>37</td></tr><tr><td></td><td>1. Status</td><td>37</td></tr><tr><td></td><td>2. Challenges and potential solutions</td><td>38</td></tr><tr><td></td><td>3. Conclusion</td><td>38</td></tr><tr><td>C.</td><td>Analog computing for linear algebra</td><td>39</td></tr><tr><td></td><td>1. Status</td><td>39</td></tr><tr><td></td><td>2. Challenges</td><td>40</td></tr><tr><td></td><td>3. Potential solutions</td><td>41</td></tr><tr><td></td><td>4. Conclusion</td><td>41</td></tr></tbody></table>

<table><tbody><tr><td>D.</td><td>Analog content addressable memories (CAMs) for in-memory computing</td><td>41</td></tr><tr><td></td><td>1. Status</td><td>41</td></tr><tr><td></td><td>2. Challenges</td><td>43</td></tr><tr><td></td><td>3. Potential solutions</td><td>43</td></tr><tr><td></td><td>4. Conclusion</td><td>43</td></tr><tr><td>E.</td><td>Optimization solvers</td><td>43</td></tr><tr><td></td><td>1. Status</td><td>43</td></tr><tr><td></td><td>2. Challenges</td><td>44</td></tr><tr><td></td><td>a. Challenges of mapping to hardware.</td><td>44</td></tr><tr><td></td><td>b. Scaling challenges.</td><td>44</td></tr><tr><td></td><td>c. Precision challenges.</td><td>45</td></tr><tr><td></td><td>3. Potential solutions</td><td>45</td></tr><tr><td></td><td>4. Conclusions</td><td>45</td></tr><tr><td>VIII.</td><td>TECHNOLOGICAL MATURITY</td><td>46</td></tr><tr><td>A.</td><td>Current status and next steps</td><td>46</td></tr><tr><td></td><td>1. Status</td><td>46</td></tr><tr><td></td><td>2. Challenges</td><td>46</td></tr><tr><td></td><td>3. Potential solutions</td><td>47</td></tr><tr><td></td><td>4. Conclusion</td><td>47</td></tr><tr><td>IX.</td><td>EPILOGUE AND CONCLUDING REMARKS FOR THE ROADMAP</td><td>47</td></tr><tr><td></td><td>ACKNOWLEDGMENTS</td><td>49</td></tr><tr><td></td><td>AUTHOR DECLARATIONS</td><td>49</td></tr><tr><td></td><td>Conflict of Interest</td><td>49</td></tr><tr><td></td><td>Author Contributions</td><td>49</td></tr><tr><td></td><td>DATA AVAILABILITY</td><td>50</td></tr><tr><td></td><td>REFERENCES</td><td>50</td></tr></tbody></table>

# I. INTRODUCTION TO THE ROADMAP

Adnan Mehonic, Daniele Ielmini, and Kaushik Roy

## A. Taxonomy and motivation

The growing adoption of data-driven applications, such as artificial intelligence (AI), is transforming the way we interact with technology. Currently, the deployment of AI and machine learning tools in previously uncharted domains generates considerable enthusiasm for further research, development, and utilization. These innovative applications often provide effective solutions to complex, longstanding challenges that have remained unresolved for years. By expanding the reach of AI and machine learning, we unlock new possibilities and facilitate advancements in various sectors. These include, but are not limited to, scientific research, education, transportation, smart city planning, eHealth, and the metaverse.

However, our predominant focus on performance can sometimes lead to critical oversights. For instance, our constant dependence on immediate access to information might cause us to ignore the energy consumption and environmental consequences associated with the computing systems that enable such access. Balancing performance with sustainability is crucial for the technology's continued growth.
<figure><img src="image_11.png" /><figcaption>FIG. 1. (a) Increase in computing power demands to run state-of-the-art AI models. (b) The cost associated with training AI models. Adapted and reproduced with permission from A. Mehonic and A. J. Kenyon, Nature **604**, 255 (2022). Copyright 2022 Springer Nature Limited.</figcaption></figure>
From this standpoint, the environmental impact of AI is a cause for growing concern. In addition, applications such as the Internet of Things (IoT) and autonomous robotic agents may not always rely on resource-intensive deep learning algorithms but still need to minimize energy consumption. Realizing the vision of IoT is contingent upon reducing the energy requirements of numerous connected devices. The demand for computing power is growing at a rate that far exceeds improvements achieved through Moore's law scaling. Figure 1(a) shows the computing power demands, quantified in peta-floating-point operations (petaflops, one peta = $10^{15}$) per day, as a function of time, indicating an increase of a factor 2 every two months in recent years.¹ In addition to Moore's law, significant advancements have been made through the combination of intelligent architecture and hardware-software co-design. For instance, NVIDIA graphics processing units (GPUs) performance has improved by a factor of 317 from 2012 to 2021, surpassing expectations based on Moore's law alone. Research and development efforts have demonstrated further impressive performance improvements,²⁻⁴ suggesting that more can be achieved. However, conventional computing solutions alone are unlikely to meet the demand in the long term, particularly when considering the high costs of training associated with the most complex deep learning models [Fig. 1(b)]. It is essential to explore alternative approaches to tackle these challenges and ensure the long-term sustainability of AI's rapid advancements. While global energy consumption is crucial and important, there is a relevant issue that is perhaps just as significant: the ability of low-power systems to execute complex AI algorithms without relying on cloud-based computing. It is important to keep in mind that the challenge of global AI power consumption and the ability to implement complex AI on low-power systems are two somewhat separate challenges. It might be the case that these two challenges need to be addressed with somewhat different strategies (e.g., the power consumption in data centers for the most complex, largest AI models, such as large language models, might be addressed differently than implementing mid-sized AI models, such as voice recognition, on low-power, self-contained systems that might need to run at a few milliwatts of power). The latter strategy might not be scalable for the largest models, or the optimization of the largest models might not be applicable for simpler models running on much lower power budgets. However, undeniably, for both, we need to improve the overall energy efficiency of our computing systems that are designed to execute AI workloads.

The energy efficiency and performance of computing can largely benefit from new paradigms that aim at replicating or being inspired by specific characteristics of the brain's biological mechanisms. It is important to note that biological systems might be highly specialized and heterogeneous, and therefore, different tasks are addressed by different computational schemes. However, we can still aim to take inspiration from general features when they are advantageous for specific applications. It is unlikely that a single architecture or broader approach will be best applicable for all targeted applications.

Adopting an interdisciplinary methodology, experts in materials science, device and circuit engineering, system design, and algorithm and software development are brought together to collectively contribute to the progressive field of neuromorphic engineering and computing. This collaborative approach is instrumental in fueling

innovation and promoting advancements in a domain that seeks to bridge the gap between biological systems and artificial intelligence. Coined by Mead in the late 1980s,⁵ the term “neuromorphic” originally referred to systems and devices replicating certain aspects of biological neural systems, but now, it varies across different research communities. While the term’s meaning continues to evolve, it generally refers to a system embodying brain-inspired properties, such as in-memory computing, hardware learning, spike-based processing, fine-grained parallelism, and reduced precision computing. One can also draw analogies and identify more complex phenomenological similarities between biological units (e.g., neurons) and electronic components (e.g., memristors). For example, phenomenological similarities between models of the redox-based nanoionic resistive memory cell and common neuronal models, such as the Hodgkin–Huxley conductance model and the leaky integrate-and-fire model, have been demonstrated.⁶ Even more complex biological functionalities have been demonstrated using a single third-order nanocircuit element.⁷ It should be noted that many paradigms related to the neuromorphic approach have also been independently investigated. For instance, in-memory computing,⁸ while being a cornerstone of the neuromorphic paradigm, is also examined separately. It represents one of the most promising avenues to enhance the energy efficiency of AI hardware or more general computing, offering a break from the traditional von Neumann architecture paradigm.

Neuromorphic research can be divided into three areas. First, “neuromorphic engineering” employs either complementary metal–oxide–semiconductor (CMOS) technology (e.g., transistors working in a sub-threshold regime) or cutting-edge post-CMOS technologies to reproduce the brain’s computational units and mechanisms. Second, “neuromorphic computing” explores new data processing methods, frequently drawing inspiration from biological systems and considering alternative algorithms, such as spike-based computing. Finally, the development of “neuromorphic devices” marks the third field. Taking advantage of advancements in electronic and photonic technologies, it develops innovative nano-devices that frequently emulate biological components, such as neurons and synapses, or efficiently implement desired properties, such as in-memory computing.

Furthermore, various approaches to neuromorphic research can be identified based on their primary objectives. Some systems focus on delivering efficient hardware platforms to enhance our understanding of biological nervous systems, while others employ brain-inspired principles to create innovative, efficient computing applications. This roadmap primarily focuses on the latter. While there are already outstanding roadmaps,⁹ reviews,¹⁰⁻¹² and special issues¹³ that offer comprehensive overviews of neuromorphic technologies, encompassing the integration of hardware and software solutions as well as the exploration of new learning paradigms, this particular roadmap focuses on emphasizing the significance of materials engineering in advancing cutting-edge complementary metal–oxide–semiconductor (CMOS) and post-CMOS technologies. Simultaneously, it offers a holistic perspective on the general challenges of computing systems, the reasoning behind adopting the neuromorphic approach, and concise summaries of current technologies to better contextualize the role of materials engineering within the broader neuromorphic landscape. Of course, there are other critical aspects in the development of neuromorphic tech-
nologies that need to be taken into account. For example, an excel-
lent recent review on thermal management materials, devices, and
networks is one such example.¹⁴

This roadmap is organized into several thematic sections, out-
lining current computing challenges, discussing the neuromorphic
computing approach, analyzing mature and currently utilized tech-
nologies, providing an overview of emerging technologies, address-
ing material challenges, exploring novel computing concepts, and
finally examining the maturity level of emerging technologies while
determining the next essential steps for their advancement.

This roadmap starts with a concise introduction to the current digital computing landscape, primarily characterized by Moore's law scaling and the von Neumann architecture. It then explores the challenges in sustaining Moore's law and examines the significance and potential advantages of post-CMOS technologies and architectures aiming to integrate computing and memory. Following this, this roadmap presents a historical perspective on the neuromorphic approach, emphasizing its potential benefits and applications. It provides a thorough review of cutting-edge developments in various emerging technologies, comparing them critically. The discussion addresses how these technologies can be utilized to develop computational building blocks for future computing systems. The roles of two mature technologies, static random access memory (SRAM) and flash, are also explored. The overview of emerging technologies includes resistive switching and memristors, phase change materials, ferroelectric materials, magnetic materials, spintronic materials, optoelectronic and photonic materials, and 2D devices and systems. Material challenges are discussed in detail, covering types of challenges, possible solutions, and experimental techniques to study these. Novel computing concepts are examined, focusing on embracing device and system variability, spiking-based computing systems, analog computing for linear algebra, and the use of analog content addressable memory (CAM) for in-memory computing and optimization solvers. Section VIII discusses technological maturity and potential future directions.

## II. COMPUTING CHALLENGES

Onur Mutlu and Shahar Kvatinsky

### A. Digital computing

#### 1. Status

Digital computing has a long and complex history that stretches back over a century. The earliest electronic computers were developed in the 1930s and 1940s, and they were large, expensive, and difficult to use. However, these early computers laid the foundation for the development of the modern computers that we use today and their principles are still in widespread use.

One of the key figures in the early history of digital computing was John von Neumann, a mathematician and computer scientist known for his contributions to the field of computer science. Von Neumann advocated the stored program concept and sequential instruction processing, two vital features of the von Neumann architecture¹⁵ that are still used in most computers today. Another key feature of the von Neumann architecture is the separation of the

central processing unit (CPU) and the main memory. This separation allows the CPU to access the instructions and data it needs from the main memory while executing a program, and assigns the computation and control responsibilities specifically to the CPU.

Throughout the years, the rapid scaling of semiconductor logic technology, known as Moore's law,¹⁶ has led to tremendous improvements in computer performance and energy efficiency. With the exponential increase in the number of transistors placed on a single chip provided by technology scaling, engineers have explored many ways to increase the speed and performance of computers. One way they did this was by exploiting parallelism, which is the ability of a computer to perform multiple tasks simultaneously. There are several different types of parallelism, including SISD (single instruction, single data), SIMD (single instruction, multiple data), MIMD (multiple instruction, multiple data), and MISD (multiple instruction, single data),¹⁷ all of which are exploited in modern computing systems ranging from general-purpose single-core and multi-core processors, GPUs, and specialized accelerators.

Technology scaling has also allowed for the development of more processing units, starting from duplicating the processing cores and, more recently, adding accelerators. These accelerators can off-load specific tasks, e.g., video processing, compression/decompression, vision processing, graphics, and machine learning, from the central processor, further improving performance and energy efficiency (the required energy to perform a certain task) by specializing the computation units to the task at hand. As such, modern systems are heterogeneous, with many different types of logic-based computation units integrated into the same processor die.

#### 2. Challenges

While the performance and energy of logic-based computation units have scaled very well via technology scaling, those of interconnect and memory systems have not scaled as well. As a result, communication (e.g., data movement) between computation units and memory units has emerged as a major bottleneck, partly due to the disparity in scaling and partly due to the separation and disparity between processing and memory offered in von Neumann architecture, which both have limited the ability of computers to take full advantage of the improvements in logic technology. This bottleneck is broadly referred to as the “von Neumann bottleneck” or the “memory wall,” as it can greatly limit the speed and energy at which the computer can execute instructions.

For decades, the transistor size has scaled down, while the power density has remained constant. This phenomenon, first observed in the 1970s by Dennard,¹⁸ means that as transistors become smaller and more densely packed onto a chip, the overall performance and capabilities of the chip improve. However, since the early 2000s, it has become increasingly challenging to maintain Dennard scaling as voltage (and thus frequency) scaling has greatly slowed down. The end of Dennard scaling has increased the importance of energy efficiency of different processing units and led to phenomena such as “dark silicon,”¹⁹ where large parts of the chip are powered off. The rapid move toward more specialized processing units, powered on for specific tasks, exemplifies the influence of the end of Dennard scaling.

Furthermore, in recent years, it has become increasingly challenging to maintain the pace of Moore's law due to the physical lim-
itations of transistors and the challenges of manufacturing smaller and more densely packed chips. As a result, the looming end of Moore's law has been a topic of discussion in the tech industry, as this could potentially limit the future performance improvements of computer chips. New semiconductor technologies and novel architectural solutions are required to continue computing systems' performance and energy efficiency improvements at a similar pace as in the past.

### 3. Potential solutions and conclusion

In recent years, different semiconductor and manufacturing technologies have emerged to overcome the slowdown of Moore's law. These devices include new transistor structures and materials, advanced packaging techniques, and new (e.g., non-volatile) memory devices. Some of those technologies have similar functionality as standard CMOS technology but with improved properties. Other technologies also offer radically new properties, different from CMOS. For example, memristive technologies, such as resistive RAM,²⁰ have varying resistance and provide analog data storage that also supports computation. Such novel technologies with their unique properties may serve as enablers for new architectures and computing paradigms, which could be different from and complementary to the von Neumann architecture.

The combination of Moore's law slowdown and von Neumann's bottleneck requires fresh thinking on computing paradigms. Data movement between the memory and the processing units is the primary impediment against high performance and high energy efficiency in modern computing systems.²¹⁻²⁴ In addition, this impediment only worsens with the improved processing abilities and the increased need for data. All modern computers employ a variety of methods to mitigate the memory bottleneck, all of which increase the complexity and power requirements of the system with limited (and sometimes little) success in mitigating the bottleneck. For example, modern computers have several levels of cache memories to reduce the latency and power of memory accesses by exploiting data locality. Cache memories, however, have limited capacity and are effective only when significant spatial and temporal locality exists in the program. Cache memories are not always (completely) effective due to low locality in many modern workloads, which can worsen the performance and energy efficiency of computers.²⁵,²⁶ Similarly, modern computers employ prefetching techniques across the memory hierarchy to anticipate future memory accesses and load data into caches before they are needed by the processor. While partially effective for relatively simple memory access patterns, prefetching is not effective for complicated memory access patterns and it increases system complexity and memory bandwidth consumption.²⁷ Thus, memory bottleneck remains a tough challenge and hundreds of research papers and patents are written every year to mitigate it.²⁸

Overcoming the performance and energy costs of off-chip memory accesses is an increasingly difficult task as the disparity between the efficiency of computation and the efficiency of memory access continues to grow. There is therefore a need to examine more disruptive technologies and architectures that much more tightly integrate logic and memory at a large scale, avoiding the large costs of data movement across system components.

Many efforts to move computation closer to and inside the memory units have been made,²⁹ including adding processing units

in the same package as DRAM chips,³⁰,³¹ performing digital processing using memory cells,³²,³³ and using analog computation capabilities of both DRAM and non-volatile memory (NVM) devices.³⁴⁻³⁷ One exciting novel computing paradigm to eliminate the von Neumann bottleneck is to reconsider the way computation and memory tasks are performed by getting inspiration from the brain, where, unlike von Neumann architecture, processing and storage are not separated. Many recent studies demonstrate orders of magnitude performance and energy improvements using various kinds of processing-in-memory architectures.²⁹ Processing-in-memory and, more broadly, neuromorphic (or brain-inspired) computing thus offers a promising way to overcome the major performance and energy bottleneck in modern memory systems. However, it also introduces significant challenges for adoption as it is a disruptive technology that affects all levels of the system stack, from hardware devices to software algorithms.

## III. NEUROMORPHIC COMPUTING BASICS AND ITS EVOLUTION

Teresa Serrano-Gotarredona and Bernabe Linares Barranco

### A. What is neuromorphic computing/engineering

Neuromorphic computing can be defined as the underlying computations performed by neuromorphic physical systems. Neuromorphic physical systems carry out robust and efficient neural computation using hardware implementations that operate in physical time. Typically, they are event- or data-driven and they employ low-power, massively parallel hybrid analog, digital, or mixed VLSI circuits, and they operate using similar physics of computation used by the nervous system.

Spiking neural networks (SNNs) are one very good example of a neuromorphic computing system. Computation is performed whenever a spike is transmitted and received by destination neurons. Computation can be performed at the dendritic tree, while spikes travel to their destinations, as well as at the destination neurons where they are collected to update the internal states of the neurons. Neurons collect pre-weighted and pre-filtered spikes coming from different source neurons or sensors, perform some basic computation on them, and generate an output spike whenever their internal state reaches some threshold. A neuron firing typically means that the “feature” this neuron represents has been identified in place and time. The collective computation of populations of neurons can give rise to powerful system level behaviors, such as pattern recognition, decision making, sensory fusion, and knowledge abstraction. In addition, neuromorphic computing systems can also be enabled to acquire new knowledge through both supervised and unsupervised learning, either offline or while they perform, which is typically known as online learning and which can be life-long. Neuromorphic computing covers typically from sensing to processing to learning.

#### 1. Neuromorphic sensing

Probably the most clarifying example of what neuromorphic computation is about is the paradigm of neuromorphic visual computation. Neuromorphic visual computation exploits the data
encoding provided by neuromorphic visual sensors. At present, the most widespread neuromorphic vision sensor is the Dynamic Vision Sensor (DVS).³⁸ In a DVS, each pixel sends out its (x, y) coordinate whenever its photodiode perceives a relative change of light beyond some preset thresholds $\theta^{-} > \frac{I_{n+1}}{I_n} > \theta^{+}$, with $\theta^{+}$ slightly greater than 1 and $\theta^{-}$ slightly less than 1. This is typically referred to as an “address event.” If $I_{n+1} > I_n$, then light has increased. If $I_{n+1} < I_n$, then light has decreased. To differentiate both situations, the address event can also be a signed event, by adding a sign bit “s,” (x, y, s). If events are recorded using some event-recording hardware, then a timestamp $t_n$ is added to each event ($x_n, y_n, s_n, t_n$). The full recording consists then of a list of timestamped address events. Figure 2 illustrates this. In Fig. 2(a), a DVS camera is observing a 7 kHz spiral on a classic phosphor oscilloscope (without any extra illumination source). Figure 2(b) plots in {x, y, t} space the recorded events. The camera was a 128 × 128 pixel high-contrast sensitivity DVS camera.³⁹ Therefore, x-y coordinates in Fig. 2(b) span from 0 to 127. The vertical axis is time, which spans over about 400 µs, slightly less than 100 µs per spiral turn. Each dot in Fig. 2(b) is an address event, and we can count several hundreds of them within the 400 µs. This DVS camera is capable of generating over 10 × 10⁶ events per second (about one every 100 ns). This produces a very fine timing resolution when sensing dynamic scenes.

The information (events) produced by this type of sensors can be sent directly to event-driven neuromorphic computing hardware, which would process this quasi-instantaneous dynamic visual information event by event.

DVS cameras have evolved over the past 20 years, since they first appeared.⁴⁰ They combine frames, sensitivity to color,⁴¹ and of resolutions up to 1 MP.⁴²

Other sensory modality event-driven neuromorphic devices have been reported, such as auditory cochlea,⁴³ olfactory noses,⁴⁴ or tactile sensing.¹⁵

## 2. Neuromorphic processing

Neuromorphic signal information encoding in the form of sequences of events reduces information so that only meaningful data, such as changes, are transmitted and processed. This follows the underlying principle in biological nervous systems, as information transmission (in the form of nervous spikes) and their consequent processing affect energy consumption. Thus, biological systems tend to minimize the number of spikes (events) to be transmitted and processed for a given computational task. This principle is what neuromorphic computing intends to pursue. Figure 3 shows an illustrative example of this efficient frame-free event-driven information encoding.⁴⁶ In Fig. 3(a), we see a poker card deck being browsed at a natural speed, recorded with a DVS, and played back at real-time speed with a reconstructed frame time of about 20 ms. In Fig. 3(b), the same recorded list of events is played back at 77 µs frame time. In Fig. 3(c), we show the tracked symbol input fed to a spiking convolutional neural network for object recognition, displaying the recognized output symbol. In Fig. 3(d), we show the 4-layer spiking convent structure, and in Fig. 3(e), we show the {x, y, time} representation of 20 ms input and output events occurring during a change of card so that the recognition switches from one symbol to the next in less than 2 ms. Note that here the system is composed of both, the sensor and the network executing the recognition. Both working together need less than 2 ms. This contrasts dramatically with conventional artificial systems, in which the sensor first needs to acquire two consecutive images (typically 25 ms per image) and then process both to capture the change.

Figure 3 illustrates a simple version of a neuromorphic sensing and processing system. By today, much larger neuromorphic systems, inspired in the same information encoding scheme, have been developed and demonstrated. The following are some powerful example systems:

(a)

<figure><img src="image_12.png" /><figcaption>FIG. 2. (a) 7 kHz spiral observed in a classic phosphor oscilloscope set in X/Y mode. (b) DVS output event stream when observing the oscilloscope in (a).</figcaption></figure>

(b)

<figure><img src="image_13.png" /></figure>
<figure><img src="image_14.png" /><figcaption>FIG. 3. (a) Fast speed poker deck browsing: events are collected about every 20 ms to build a frame to display on a computer screen. (b) Slow speed playback at 77 µs per reconstructed frame. (c) Poker symbol tracked and displayed on the right and recognition output on the left. (d) Event-driven CNN to classify four poker symbols. (e) {x, y, t} representation of 20 ms showing camera events together with recognition events during a change of card with a recognition switching of less than 2 ms.</figcaption></figure>

* The SpiNNaker platform<sup>47</sup> was partly developed under the Human Brain Project.<sup>48</sup> It features an 18-core Advanced RISC Machine (ARM) SpiNNaker chip. Each node on the platform comprises a printed circuit board (PCB) that holds 48 of these chips. In total, about 1200 chips are assembled into furniture-like sets that include racks. Collectively, these setups host approximately 1 million ARM cores. This system is capable of emulating $1 \times 10^9$ neurons in real time. An updated SpiNNaker chip has already been developed, performing about $10\times$ in efficiency, neuron emulation capability, and event traffic handling, while keeping similar power consumption.

* The BrainScales platform,<sup>49</sup> also developed during the Human Brain Project,<sup>47</sup> implements physical silicon neurons fabricated on full silicon 8 in. wafers, interconnecting 20 of these wafers in a cabinet, together with 48 FPGA based communication modules. It implements accelerated time computations with respect to real time (about $10\,000\times$), with spike-timing-dependent plastic synapses. Each wafer can host about 200k neurons and $44 \times 10^6$ synapses.

* The IBM TrueNorth chip<sup>50</sup> could host $1 \times 10^6$ very simple neurons, or be reconfigured to achieve a trade-off between the number of neurons and neuron model complexity. They were structured into 4096 identical cores, consuming about 63 mW each.

* Loihi from Intel is probably by today the most advanced neuromorphic chip. In its first version,<sup>51</sup> fabricated in

14 nm, it contains 128 cores, each capable of implementing 1k spiking neuronal units (compartments), and includes plastic synapses. More recently, Loihi 2 chip was introduced, with up to $1 \times 10^6$ neurons per chip, manufactured in Intel 4 technology (7 nm). Up to 768 of Loihi chips have been assembled into the Pohoiki Springs system, while operating at less than 500 W.<sup>52</sup>

### 3. Challenges and conclusion

Neuromorphic computing algorithms should be optimum when run on neuromorphic hardware, where events travel and are processed in a fully parallel manner. One of the main challenges in present day neuromorphic computing is to train and execute powerful computing systems directly on neuromorphic hardware. Traditionally, neuromorphic computing problems were mapped to more traditional deep neural networks to obtain their parameters through backpropagation based training,<sup>53</sup> which would then be mapped to their neuromorphic/spiking counterpart.<sup>46</sup> However, these transformations always resulted in a loss of performance. By today, there are many proposals of training directly in the spiking domain, combining variants of spike-timing-dependent plasticity rules, with surrogate training techniques that adapt backpropagation to spiking systems, which are tested on either fully connected or convolution based deep spiking neural networks. For an updated review, readers are referred to Ref. 54.
On the other hand, it remains to see whether novel nano-
material devices, such as memristors, can provide truly giga-scale
compact chips with billions of neurons on a single chip and
self-learning algorithms. Some initial demonstrations of single<sup>55</sup>
or multi-core systems<sup>56</sup> exploiting a nano-scale memristor com-
bined with a selector transistor as a synaptic element have been
reported, with highly promising outlooks once synapse elements
could be provided as pure nanoscale devices while stacking mul-
tiple layers of synapse fabrics together with other nano-scale neu-
rons.<sup>57</sup> In the end, the success of neuromorphic computing will rely
on the optimum combined progress in neuromorphic hardware,
most probably exploiting emerging nano-scale devices massively,
in event- and data-driven information and energy-efficient pro-
cessing methodologies, and finally in providing efficient, resilient,
and quick learning methodologies for mapping real-world applica-
tions into the available hardware and computational neuromorphic
substrates.

B. Different neuromorphic technologies and state of the art

Sabina Spiga

1. Status

The research field of neuromorphic computing has been grow-
ing significantly over the past three decades, following the pioneer-
ing research at Caltech (USA) by Mead,⁵ and it is currently attract-
ing the interest of a wide and interdisciplinary community from
devices, circuits, and systems to neuroscience, biology, computer

science, materials, and physics. Within this framework, the devel-
oped neuromorphic *hardware technologies* span from fully CMOS-
based systems<sup>58,59</sup> to solutions exploiting the use of charge-based
or resistive non-volatile memory technologies<sup>60-62</sup> and to emerg-
ing memristive device concepts and novel materials.<sup>63-66</sup> Figure 4
reports a schematic (and non-exhaustive) evolution of the main
technologies of interest. A common feature of these approaches is to
take inspiration from the brain computation, by co-locating mem-
ory and processing [in-memory computing (IMC) approach], to
overcome the von Neumann bottleneck. Hardware artificial neu-
ral networks (ANNs) can implement IMC computing and provides
an efficient physical substrate for machine learning algorithms and
artificial intelligence (AI). On the other hand, spiking neural net-
works (SNNs), encoding and processing information using spikes,
hold great promise for applications requiring always-on real-time
processing of sensory signals, for example in edge computing,
personalized medicine, and Internet of things.

In terms of the maturity of neuromorphic technologies, we can
discuss three main blocks.

(i) Current large-scale hardware neuromorphic computing systems are fully CMOS-based and exploit digital or analog/mixed-signal technologies. Examples of fabricated chips are the IBM TrueNorth, Intel Loihi, Tianjic, ODIN, and others as discussed in previous review papers.<sup>58,59</sup> In these systems, the neuron and synapse functionalities are emulated by using circuit blocks based on CMOS transistors, capacitors, and volatile SRAM memory. The scientific community is now exploiting these chips to implement novel algorithms for AI applications.

<figure><img src="image_15.png" /><figcaption>FIG. 4. Schematic evolution of the main hardware technologies of interest for neuromorphic computing (the decades represent only a time frame). Triangular symbols mark the reference period for early stage studies or starting interest in the technology development. From bottom to top of the figure, the listed technologies are today at higher maturity level and more advanced at system integration level.</figcaption></figure>
(ii) *Non-volatile memory technologies.* In the past decade, resistive non-volatile memory (NVM) technologies, such as Resistive Random Access Memory (RRAM), phase change memory (PCM), ferroelectric memory (FeRAM) and ferroelectric transistor (FeFET), and magnetoresistive random access memory (MRAM), have been proposed as possible compact, low power, and dynamical elements to implement in hardware the synaptic nodes, replacing SRAMs, or as a key element of neuronal blocks.⁶⁰,⁶¹,⁶⁷ While these NVMs have been developed over the past twenty years mainly for data storage applications, and introduced in the market, they can be considered emerging technologies in the field of neuromorphic computing and their great potential is still not fully exploited. Over the past 10 years, novel concepts for computing, based on hybrid CMOS/non-volatile resistive memory circuits and chips,⁵⁶ have been proposed in the literature. In parallel, also more conventional charge-based non-volatile memories, such as flash and NRAM, are currently being investigated for IMC since they are mature technologies. Finally, it is worth mentioning the emerging memory technologies that are attracting increasing interest in the field of IMC and neuromorphic computing, namely the ferroelectric tunnel junction (FTJ)⁶⁸ and the 3-terminal electrochemical random access memory (ECRAM).⁶⁹

(iii) *Advanced memristive materials, devices, and novel computation concepts* that are currently investigated include 2D materials, organic materials, perovskites, nanotubes, self-assembled nano-objects and nanowire networks, advanced

device concepts in the field of spintronics (domain wall, race-trace memory, and skyrmions), devices based on metal-insulator transition (for instance, VO₂-based devices), and volatile memristors.⁶⁵,⁶⁶,⁷⁰⁻⁷² These technologies are currently proofs of concept at a single device level and circuit blocks connecting a reduced number of devices. The computing system is sometimes demonstrated with a mixed hardware/software approach, where the measured device characteristics are used to simulate large systems. Finally, it is worth mentioning the increasing interest in architectures that can exploit photonic components for computing, toward the building of neuromorphic photonic processors taking advantage of the silicon photonic platforms and co-integration with novel optical memory devices and advanced materials, such as phase-change materials.⁷³,⁷⁴

Figure 5 schematically shows examples of the material systems currently most investigated in various approaches and technologies for neuromorphic computing.

## 2. Challenges

The current and future challenges can be considered at various levels.

(i) For large-scale neuromorphic processors, the progress of CMOS-based technologies and their scaling still provide room to advance the research field. The main challenges are at the architecture and algorithm level. On the other hand,

<figure><img src="image_16.png" /><figcaption>FIG. 5. Examples of materials systems currently employed in memristive technologies. The list of materials is not exhaustive and includes only some of the most used ones. For the NVM devices (top line), the main active material is indicated, but each device includes also various types of material electrodes depending on the technology.</figcaption></figure>
most NVM memories (RRAM, PCM, FeRAM, FeFET, and MRAM) have been already integrated with CMOS at scaled technological nodes and large integration density and hold interesting properties (depending on the specific technology), such as small size, scalability, possible easy integration also in 3D array stacking, low programming energy, and multilevel programming capability. Therefore, it is expected that NVM technologies will play an increasing role in future IMC chips or neuromorphic processors, by enabling energy-efficient computation. Prototype IMC chips have been reported in the literature,⁵⁶,⁷⁵ as well as innovative circuits for SNNs implementing advanced learning rules to compute with dynamics.⁷⁶,⁷⁷

On the other hand, it is worth mentioning that the NVM tech-
nologies exhibit several device-level non-idealities, as discussed in
more detail in Sec. V of this roadmap. As examples and a non-
exhaustive list, we can mention nonlinearity and stochasticity in
conductance update vs a number of pulses at a fixed voltage (PCM,
RRAM, and FeRAM), asymmetry (RRAM) in the bidirectional tun-
ing of conductance, conductance drift (PCM) or broadening of
the resistance distribution (RRAM) after programming, device-to-
device and cycle-to-cycle variability of the programmed states, low
resolution due to the limited number of programmable levels (up to
8 or 16 are demonstrated for RRAM and PCM at the array level),
restricted memory window (MRAM) or limited endurance (general
issue except for MRAM), and relatively high conduction also in the
OFF state. All these aspects can impact the neural network accu-
racy and reliability, although proper algorithms/architectures can
take advantage from stochasticity or asymmetry of conductance tun-
ing.⁷⁸ Therefore, a careful co-design of hardware and algorithms is
required together with an improvement of circuit design and/or pro-
gramming device strategies to fully exploit NVMs in combination
with CMOS and in large systems. The specific challenges and possi-
ble specific applications of the listed technologies will be discussed
further in Secs. V A-V D of this roadmap, while a more deep view
on application scenario is reported in Sec. VII.

(ii) Regarding the plethora of *emerging materialsdevices and novel concepts* proposed for neuromorphic computing (beyond the ones discussed in the previous point, see some examples in Secs. V D-V F of this roadmap), the main challenge is that they are mostly demonstrated at the single device level or in early stage proofs of concept in small arrays/large device sizes, which are implemented in ANNs or SNNs only at the simulation level. To leverage these concepts at higher technology readiness level (TRL), it is necessary to prove that the device characteristics are reproducible and scalable, the working principle well understood, and to provide more advanced characterizations on several down-scaled devices, and finally to close the current gap between laboratory exploration of single materialsdevices and integration in arrays or circuits. Another challenge is to address in more detail how to exploit nanodevices’ peculiarities, such as dynamic or stochastic behavior, to implement in hardware more complex bio-inspired functionalities or even to perform radically new computation paradigms. Indeed, while the more standard technologies (CMOS, flash, and SRAM) can also be used in hardware

neural networks to implement complex functions, this is
possible only at the high cost of increased circuit complex-
ity. To give an example, the required dynamic to reproduce
the synaptic or neuronal functionality in SNNs is imple-
mented at the circuit level and/or using large area capacitors,
which are not easily scalable in view of large systems. One
possible approach is to exploit the emerging memristive tech-
nologies and their properties (variability, stochasticity, and
non-idealities) to implement complex functions with more
compact and low-power devices. One example is the use of
resistivity drift in PCM (usually an unwanted characteris-
tic for IMC or storage applications) to implement advanced
learning rules in hardware SNNs.⁷⁹ Another example (disc-
cussed in Sec. VII A) is to use the inherent variability and
stochasticity of some nanodevices to build efficient ran-
dom number generators (for data security applications) and
stochastic computing models. Overall, this scenario points
out a long-term development research, likely up to ten years
or more, to close the gap between these novel concepts and
real industrial applications.

3. Potential solutions

To pursue advances in the development of neuromorphic hard-
ware chips, it is necessary to develop a common framework to
compare and benchmark different approaches, also in view of some
metrics, such as computing density, energy efficiency, computing
accuracy, learning algorithms, theoretical framework, and target
possible killer applications that might significantly benefit from
neuro-inspired chips. Within this framework, materials strategies
can still be relevant to address some of the outlined challenges
for NVMs, but materials need to be co-developed together with a
demonstration of a device at the scaled node and array level. An
important strategy for the future is also the possibility to substi-
tute current mainstream materials with green materials or to identify
fabrication processes more sustainable in terms of cost and environ-
mental impact, without compromising the hardware functionality.
Moreover, other important aspects include the development of hard-
ware architecture that can lead to the integration of several devices
and exploiting a large connectivity among them; the implementation
of efficient algorithms supporting online learning, also on different
time scales as in biological systems; and addressing the low power
analysis of large amount of data also for Internet of things and edge
devices. Overall, it is a necessary and holistic view that includes
the materials/devices/architectures/algorithms co-design to develop
a large-scaled neuromorphic chip.

4. Conclusion

The development of advanced neuromorphic hardware that
can efficiently support AI applications is becoming more and more
important. Despite the several prototypes and results presented in
the literature, neuro-inspired chips are still only at an early stage of
development and there is plenty of room for further development.
Many mature NVM devices are definitely candidates to become a
future mainstream technology for large scale neuromorphic pro-
cessors that can outperform the current platform based only on
CMOS circuits. In the long term, it is also necessary to close the gap
between emerging materials and concepts, currently demonstrated
only by proofs of concept, and their possible integration in func-
tional systems. Materials research and an understanding of physical
principles enabling novel functionalities are important parts for this
scenario.

C. Possible future computational primitives
for neuromorphic computing

Sergey Savel'ev and Alexander Balanov

The core idea of neuromorphic computing to develop and
design computational systems mimicking electrochemical activ-
ities in brain cortex is currently booming, embracing areas of
deep physical neural networks,⁸⁰ classical and quantum reser-
voir computing,⁸¹,⁸² oscillator-based computing,⁸³ and spiking
networks,⁸⁴ among many other concepts.⁸⁵ These computational
paradigms imply new ways for information processing and stor-
age different from conventional computing and, therefore, require
elementary base and primitives that often involve unusual novel
physical principles.⁸⁶

At present, memristors—electronic switchers with memory—
and their circuits demonstrate great potential for application in the
primitives for future neuromorphic computing systems. In partic-
ular, different types of volatile and non-volatile memristors can
serve as artificial neurons and synapses, respectively, which facil-
itate the transfer, storage, and processing of information.⁸⁷ For
example, volatile Mott memristors⁸⁸ can work as an electric oscil-
lator with either regular or chaotic dynamics,⁷ while memristors
with filament-formation⁸⁹ demonstrate tunable stochasticity,⁹⁰,⁹¹
and allow designing neuromorphic circuits with different degrees of
plasticity, chaoticity, and stochasticity to address diverse computa-
tional aims in mimicking dynamics of different neuron populations.
Furthermore, a crossbar of non-volatile memristors (servicing to
memorize training) attached to volatile memristors (working as
readouts) enables the design of AI hardware with unsupervised
learning capability.⁹² Thus, combining memristive circuits with dif-
ferent functionalities paves the way for building a wide range of
in-memory computational blocks for a broad spectrum of artificial
neural networks (ANNs) starting from deep learning accelerators to
spiking neuron networks.⁹³

A rapidly developing class of volatile memristive elements⁹⁴ has
been shown to demonstrate a rich spectrum of versatile dynami-
cal patterns,⁷,⁹,⁵,⁹⁶ which makes them suitable for the realization of
a range of neuroscience-motivated AI concepts.⁹⁷⁻⁹⁹ For instance,
the ANNs based on volatile memristors can go well beyond usual
oscillator-based computing⁸³ or spiking neural networks.⁸⁴ They
rely on manipulating information by utilizing complexity in dynam-
ical regimes that offer a novel computational framework⁷,⁹⁸ with
cognitive abilities closer to biological brains. There is a specific
emphasis on using dynamical behaviors of memristors, instead of
only static behaviors.¹⁰⁰

Remarkably, memristive elements can be realized not only in
electronic devices but also within spintronic or photonic frame-
works, which have their own advantages compared to electron-
ics. Therefore, hybridized design promises great benefits in the

further development of neuromorphic primitives. For example,
a combination of memristive chipsets with spintronic and/or
photonic components can potentially create AI hardware with
enhanced parallelism offered by optical devices operating simul-
taneously at many frequencies (e.g., optical cavity eigenfrequen-
cies),¹⁰¹ energy-efficient magnetic non-volatile memories, and flex-
ible memristive spiking network architectures. An important step
in the realization of this approach is the development of inter-
face technologies for bringing electronic, photonic, and spin-
tronic technologies together. A possible example is the spintronic
memristor,⁶⁵,¹⁰²,¹⁰³ where the transformation of magnetic structure
influences the resistance of the system.¹⁰⁴ An interface between neu-
romorphic optical and electronic subsystems of a hybrid device
could be realized using optically controlled electronic memristive
systems,¹⁰⁵ thus paving a path for neuromorphic optoelectronic
systems.¹⁰⁶

The conventional ANNs with a large number of connections
require training to be efficient in the task requiring frequent retrain-
ing for “moving target” problems, for example in the recognition of
characteristics changing in time. A potential solution for such tasks
is to implement filtering or pre-processing data by a “reservoir,”⁸¹
usually consisting of neuron units connected by fixed weights. The
reservoir is assisted by a small readout ANN, which requires much
less data for training, thus removing significant retraining burden.
Recently, an important evolution has taken place in the development
of reservoir computing systems, where the function of the reser-
voir is realized by photon, phonon, and/or magnon mode mixing in
spintronic¹⁰⁷,¹⁰⁸ and photonic¹⁰⁹ devices. Substitution of the interac-
tion of many artificial neurons by wave processes resembles neural
wave computation in the visual cortex⁹⁸ and promotes miniaturiza-
tion, robustness, and energy efficiency of the reservoirs (neuromor-
phic accelerators), which in the future could become an additional
class of primitive, especially in neuromorphic computational sys-
tems dealing with temporal or sequential data processing.¹¹⁰ In AI
training, it has also been shown that memristive matrix multipli-
cation hardware can enable noisy local learning algorithms, which
perform training at the edge with significant energy efficiencies
compared to graphics processing units.¹¹¹

Finally, we briefly outline another exciting perspective consti-
tuted by a combination of quantum and neuromorphic technolo-
gies.¹¹² Currently, quantum AI¹¹³ attracts significant attention by
increasingly competing with more traditional quantum computing.
One of the most promising quantum AI paradigms is quantum
reservoir computing,¹¹⁴ which offers not only much larger state
space than classical reservoir computing but also essentially non-
classical quantum feedback on the reservoir via measurements. A
quantum reservoir built from quantum memristors¹¹⁵,¹¹⁶ could sig-
nificantly gain quantum AI efficiency as it can readily be integrated
with existing quantum and classical AI devices and also lead to an
“exponential growth”¹¹⁷ in the performance of “reservoirs” with the
possibility of relaxing requirements on decoherence compared to
traditional quantum computing.

The above trends and directions in the development of the
primitives for neuromorphic computing are obviously only a slice
of exciting future AI hardware technology. Even though we rec-
ognize that our choice is subjective, we hope that the outlined
systems should provide a flavor of future computational hardware,
which should be based on reconfigurable life-mimicking devices
utilizing different physical principles in combination with novel
mathematical cognitive paradigms.<sup>118-121</sup>

# IV. MATURE TECHNOLOGIES (COMPUTING APPROACHES)

## A. SRAM

Nitin Chawla and Giuseppe Desoli

### 1. Status

SRAM-based computing in memory (CIM) or in-memory computing is seen as a mature and widely available technology for accelerating matrix and vector calculations in deep learning applications, yet many technology driven optimizations are still possible. To make CIM more compatible, researchers have been exploring ways to improve the design of the bitcell (Fig. 6), which is the basic unit of memory. This has led to the development of high-end SRAM chips with large capacities, such as 107, 128, and 256 Mb SRAM chips at 10, 7, 5, and 4 nm.<sup>122-125</sup> These large SRAM capacities help reduce the need for off-chip DRAM access. However, in more cost-sensitive applications, such as embedded systems and consumer products, modifying the bitcell design can be too costly and may limit the ability to easily transfer the technology to different manufacturing nodes.

A key difference exists between analog and digital SRAM CIM. Analog CIM has been heavily studied using capacitive or resistive sharing techniques to maximize row parallelism,<sup>126</sup> but this comes at the cost of inaccuracies and loss of resolution due to variations in devices across process, voltage, and temperature (PVT) and the limitations of signal-to-noise ratio (SNR) and dynamic range in analog-to-digital converter (ADC)/readout circuits. The impacts of device variations for different kinds of devices are listed below.

* Resistive devices, such as PCM or RRAM, experience a variation in the resistive values across the nominal behavior, which can vary based on the process, and for a case of ±10%–20% change in resistance value, there will be a corresponding change of current values, which are then input to the readout circuits, and hence, this will impact the quantization step of readout circuits, hence impacting the

<figure><img src="image_17.png" /><figcaption>FIG. 6. Standard SRAM bitcells are usually designed with six or eight transistors.</figcaption></figure>

SNR, which will then need a higher dynamic range to compensate for the same. The temperature behavior for resistors also needs to be taken care in the noise margin.

* MOS devices: These devices can vary in their performance (threshold voltage) due to the following:

1. Global lot positioning, such as slow, typical, and fast, can vary around ±20%, which can be less or more based on technology and voltage of operation. This is a deterministic shift.

2. Local variation: within the same lot, there are device to device variations, which are random in nature and need statistical analysis based on capacity in use to analyze the impact of variations. These impact the SNR and quantization as in the case of resistive devices and will need a higher dynamic range to compensate for the loss in accuracy.

Analog SRAM CIM solutions often use large logic bitcells and an aggressive reduction in ADC/readout bit width, resulting in low memory density and computing inaccuracies, making it difficult to use in situations where functional safety, low-cost testing, and system scalability are required. On the other hand, digital CIM offers a fast path for the next generation of neural processing systems due to its deterministic behavior and compatibility with technology scaling rules.

Researchers have improved the SRAM-based CIM's performance by modifying the SRAM bitcell structure and developing auxiliary peripheral circuits. They proposed read-write isolation cells to prevent storage damage and transposable cells to overcome storage arrangement limitations. Peripheral circuits, such as digital-to-analog converters (DACs), redundant reference columns, and multiplexed ADCs, were proposed to convert between analog and digital signals. The memory cell takes up most of the SRAM area in the core module of a standard SRAM cut. However, the complexity of the additional operations performed in the memory unit poses additional problems to utilize the memory cells to their full potential. Researchers have explored various trade-offs to implement the necessary computational functionality while preserving density and power and, last but not least, minimizing the additional cost associated with bitcell modifications required for requalification when deployed in standard design flows. Most system-on-chips (SoCs) use standard 6T structures due to their high robustness and access speed and to minimize area overhead. The 6T storage cell is made up of two P-channel Metal-Oxide-Semiconductor (PMOSs) and four N-channel Metal-Oxide-Semiconductor (NMOSs) to store data stably. To perform CIM using the conventional 6T SRAM cell, operands are represented by the word line (WL) voltage and storage node data, and processing results are reflected by the voltage difference between bit line (BL) and bit line bar (BLB).

Figure 6 shows the conventional 6T and 8T bitcells that form the basic building block of the SRAM design. The 8T bitcell is made out of a conventional 6T bitcell and a read port that allows read and write in parallel. These bitcells were never designed for parallel access across rows, and this poses one of the main challenges for enabling analog SRAM CIM.

Dual-split 6T cells with double separation have been proposed,<sup>127,128</sup> allowing for more sophisticated functions due to
the separated WL and GND, which can use different voltages to represent various types of information. Dong *et al.*¹²⁹ proposed a 4 + 2T SRAM cell to decouple data from the read path. The read is akin to that of the standard 6T SRAM, writes instead, and use the N-well as the Word-Line Write (WWL) and two PMOS sources as the Write-Bit Line (WBL) and Write Bit Line Bar (WBLB). In computational mode, different voltages on the WL and storage node encode the operands.

In general, CIM adopting the 6T bitcell structure is unable to efficiently perform computing operations and may not fully meet the requirements of future CIM architectures. Hence, many studies on CIM have modified the 6T structure because using the 6T standard cell directly poses a reliability challenge as the contents of the bitcells get effectively shorted if accessed in parallel on the same bit line. This means that special handling on the word line voltage is required, which adds lot of complexity and limits the dynamic range. Furthermore, the variability and linearity of devices become very difficult to control when limiting the device operation to reduced voltage levels due to these reliability constraints, impacting the overall energy efficiency of the solution.¹³⁰,¹³¹

For practical applications, and specifically for AI ones, it is important to evaluate the end to end algorithmic accuracy vs the key metrics. To this end, recent research¹³²⁻¹³⁶ has suggested various analytical models to examine the balance between the costs (accuracy) and benefits (primarily, energy efficiency and performance) of digital vs analog SRAM CIM. This is based on the idea that many machine and deep learning algorithms can tolerate some degree of computational errors and that there are methods such as retraining and fine-tuning as well as hardware-aware training to address these errors.

The implementation of neural processing units incorporating CIM components for large-scale deep neural networks (DNNs) presents significant difficulties, CIM macros can incur substantial column current magnitudes, which can result in power delivery difficulties and sensing malfunctions. Furthermore, the utilization of analog domain operations necessitates the incorporation of ADCs and DACs, which consume a significant amount of area and energy resources. Further to this, the pitch matching of ADCs with SRAM bitcells also poses a big challenge for arrays and ADC interfaces. It is clear that the realization of the full potential of SRAM-CIM necessitates development of innovative and sophisticated techniques.

## 2. Challenges and potential solutions

In deep learning, convolutional kernels and other types of kernels rely heavily on matrix/vector and matrix/matrix multiplication (MVM). These operations are computationally expensive and involve dot product operations between activation and kernel values. In-memory multiplication in CIM macro devices can be classified into three primary categories: current-based, charge-sharing-based for analog computation, and one for all-digital. All-digital CIM exhibits the same level of precision as purely digital Application-Specific Integrated Circuit (ASIC) implementations. Various implementation topologies ranging from bit-serial to all parallel arithmetic implementations have been proposed for digital CIM solutions. Digital CIM, as in a previous study,¹³⁷ represents a modified logic bitcell to support element-wise multiplication followed by a digital accumulation tree sandwiched within

<figure><img src="image_18.png" /><figcaption>FIG. 7. Digital CIM memory macro with 8T bitcells and embedded digital logic.</figcaption></figure>

the SRAM array. The solution improves on energy efficiency by reducing data movement alongside the efficiency benefits of a custom-built Multiply Accumulate (MAC) pipeline with improved levels of parallelism over traditional digital Neural Processing Units (NPUs), for example, as in Fig. 7.¹³⁸ The digital CIM implementations also have a wide voltage and frequency dynamic range allowing runtime reconfigurability between the competing Tera Operations Per Second Per Watt (TOPS/W) and TOPS/mm² performance criteria. The operating range and mission profiles of these architectures can also be extended by leveraging read-and-write assist schemes as is commonly done for ultra-low voltage SRAM design. The digital CIM solution's energy efficiency depends on the operand precision, and due to the deterministic precision and bit true computation nature, it begins to decline as we increase the operand precision.

Current-based CIM, as represented in one of the early research works,¹³⁹ implements a WL DAC driving a multi-level feature input with multiple rows active in parallel. The results of the element-wise multiplications of all the parallel rows are accumulated as current on the bit lines of the CIM macro that terminates in a current-based readout/ADC. The current accumulation on the bit line essentially implements a reduction operation limited by the SNR of the readout circuit. Current-based CIM, as presented in this work, suffers from significant degradation in accuracy due to bitcell variabilities and nonlinearities of the WL DAC, while the throughput is limited by the readout circuits. Kang *et al*.¹⁴⁰ implemented a variation with CIM using a 6T-derived bitcell with a Pulse Width Modulation (PWM) WL modulation and focused on storing and computing multi-bit weights per column. The modulation scheme uses binary weighted
pulse duration based on the index of the bitcell in the column effec-
tively encoding the multi-bit weight in the column to impact the
value of the global bit line. The multiplication is effectively done
in the periphery of this CIM using a switched capacitor circuit.
Bitcell variations and nonlinearities as in the previous case signif-
icantly limit the accuracy of this implementation, thus restricting
the industrialization potential of these current-based CIM solutions.
The work in Ref. 141 tries to address the limitations of the above
analog CIM techniques and implements charge-based CIM by using
a modified SRAM logic bitcell that performs element-wise binary
multiplication (XNOR) and transfers the results to a small capaci-
tor. Multiple rows operating in parallel is key to the energy efficiency
of these CIM topologies. In this work, the element-wise multiplica-
tion result is transferred as a charge to the global bit line followed
by a voltage-based readout. The inherent implementation benefits
from the fact that capacitors suffer less from process variability
and present fairly linear transfer characteristics. This architecture,
however, like other analog CIM is impacted by dynamic range com-
pression due to the limited SNR regime of the readout at the end of
the column. Jia et al.¹⁴² extended this approach to support multi-
bit implementations using a bit-sliced architecture. The multi-bit
weights are mapped to different columns, while the feature data are
essentially transferred as 1-bit serial data on parallel word lines and
each column performs a binary multiplication followed by accu-
mulation on the respective bit lines. The near-memory all-digital
recombination unit in this approach performs the shift and scale
operations based on the column index to recreate the results of the
multi-bit MAC operation. The approach is flexible to support asym-
metric features and weight precision and can be made reconfigurable
to support different features and weight precisions on the fly. This,
however, still suffers from the same SNR constraints as each col-
umn operation is compressing the dynamic range and is limited by
the peak dynamic range of the readout ADC. The ADC in most
of these schemes is mostly shared across multiple columns, thus
making it a critical design component in determining the through-
put of such CIM architectures. The specific bit-sliced approach has
impressive TOPS/W numbers for the lower weights and activation
precision regime but starts to taper off due to the quadratic increase
in the computation energy with increasing weight and activation
precision The work in Ref. 143 instantiates multiple of these CIM
macros to demonstrate a system-level approach connecting these
CIM macros with a flexible interconnect and adding digital SIMD
and scalar arithmetic units to support real-world neural network
execution. This specific work due to the limited readout speed of
the CIM macros and the overhead of the other digital units suf-
fers from a moderate TOPS/mm² number for the full solution but
presents impressive TOPS/W numbers, especially at the lower pre-
cision regime. The work in Ref. 144 represents another effort with
a system-level solution of a hybrid NPU comprising analog CIM
units and traditional digital accelerator blocks. The work leverages
a low-precision (2-bit) analog CIM macro coupled with a traditional
8-bit digital MAC accelerator. The two orders of magnitude differ-
ence in energy efficiency between the 8-bit digital MAC engine and
the 2-bit analog CIM macro can be leveraged by mapping differ-
ent layers to the appropriate computation engine but needs careful
articulation of mapping algorithms with the precision constraints of
the analog CIM while keeping the overhead of the write refresh and

other digital vector/scalar operators low. This, to some extent, is a
trade-off between a very specialized use case and a general-purpose
NN accelerator.

3. Conclusions

Analog CIM solutions based on charge-based CIM display a
lower degree of variability when compared to current-based CIM,
due to variability in the technologies employed for capacitors and
threshold voltage effects. In addition, charge-based CIM solutions
are able to activate a greater number of word lines per cycle and thus
achieve higher amounts of row parallelism. However, both current-
based and charge-based CIM are limited in terms of accuracy and the
equivalent bit precision of the dynamic range of the accumulation.
Selecting an appropriate ADC bit-precision and MVM parallelism
is a challenging task that requires balancing accuracy and power
consumption. Measurements and empirical evidence suggest that
an increase in the accumulation values is correlated with a higher
degree of variability. However, it is important to note that such
high values are relatively rare in practical neural network models, as
shown by the statistical distribution of activation data and resultant
accumulation outcomes. This characteristic along with noise-aware
training can be leveraged to optimize the precision and throughput
demands of the analog-to-digital converter, thereby improving the
figure of merit (FOM) of these analog CIM techniques. The research
on noise-aware training in the state of the art is limited to aca-
demic works on relatively small neural networks and datasets. This
for an industrial deployment still needs to mature and demonstrate
scalability to larger models and datasets.

All-digital CIM provides a deterministic and scalable path to
intercept the implementation of NPUs by bringing an order or more
of gain vs traditional all-digital NPUs. Digital CIM solutions pro-
vide excellent scaling for area and energy efficiency as we move
toward more advanced CMOS nodes with a wide operating volt-
age and frequency range tunability while still maintaining a general
purpose and application-agnostic view of embedded neural network
acceleration at the edge.

On the other hand, for applications that can handle approx-
imate computing, analog SRAM CIM-based solutions provide a
much-increased level of computation parallelism and energy effi-
ciency while still operating in an SNR-limited regime. The impacts
of dynamic range compression and readout throughput are key
algorithmic and design trade-offs while designing an analog CIM
solution, which tries to operate in a much more restricted voltage
and frequency regime as opposed to a digital CIM solution. That the
application choices are more vertically defined as opposed to gen-
eral purpose is also a deciding factor in choosing an analog SRAM
CIM-based solution as opposed to digital CIM solutions. In con-
clusion, due to the rapid industrialization potential of SRAM-based
CIM solutions and the opportunity of exploiting the duality of these
CIM instances to serve as SRAM capacity to support the system in
other operating modes, there are enough reasons to remain invested
in SRAM CIM. The scope to improve both digital and analog SRAM
CIM remains very high, both at the design and at the technology
level, to exploit the best gains out of these two solutions, which in
the future can also be combined to form a hybrid solution serving
multiple modalities of neural network execution at the edge.
## B. Flash memories

Gerardo Malavena and Christian Monzio Compagnoni

### 1. Status

Thanks to a relentless expansion in all the application fields of electronics since their conception in the 1980s, flash memories became ubiquitous non-volatile storage media in everyday life and a source of market revenues exceeding $60B in 2021. The origin of this success can be traced back to their capability to solve the trade-off against cost, performance, and reliability in data storage much better than any other technology. Multiple solutions to that trade-off, in addition, were devised through different design strategies that, in the end, allowed flash memories to target a great variety of applications in the best possible way. Among these different design strategies, the two leading to the so-called NOR flash memories¹⁴⁵ and NAND flash memories¹⁴⁶ became by far the most important.

As in all flash memory designs, NOR and NAND flash memories store information in memory transistors arranged in an array whose operation relies on an initialization, or erase, step performed in a flash on a large number of devices simultaneously. In particular, the erase step moves the threshold-voltage ($V_T$) of all the memory transistors in a block/sector of the array to a low value. From that initial condition, data are stored through program steps performed in parallel on a much smaller subset of memory transistors, raising their $V_T$ to one or more predefined levels. This working scheme of the array allows us to minimize the number of service elements needed for information storage and, in the end, is on the basis of the high integration density, high performance, and high reliability of flash memories. Starting from it, the structure of the memory transistors, the architectural connections among them to form the memory array, the array segmentation in the memory chip, the physical processes exploited for the erase and program steps, and many other aspects are markedly different in NOR and NAND flash memories.

NOR flash memories follow a design strategy targeting the minimization of the random access time to the stored data, reaching latencies as short as a few tens of nanoseconds. A strong array segmentation is then adopted to reduce the delay time of the word-lines (WLs) and bit-lines (BLs) driving the memory transistors. As depicted in Fig. 8(a), moreover, the memory transistors are independently connected to the WLs, BLs, and source lines (SLs) of the array to simplify and speed up the sequence of steps needed to randomly access the stored data and to allow device operation at relatively high currents (currents in the microampere scale are typical to sense the data stored in the memory transistors). Fast random access is also achieved through a very robust raw array reliability, with no or limited adoption of error correction codes (ECCs). This design strategy, on the other hand, does not make NOR flash memories the most convenient solution from the standpoint of the area and, hence, the cost of the memory chip and limit the chip storage capacity to low or medium sizes (up to a few Gbits).

NAND flash memories rely on a design strategy pointing to the minimization of the data storage cost. Therefore, limited array segmentation is adopted and the memory transistors are in series

<figure><img src="image_19.png" /><figcaption>FIG. 8. Schematic for the connection of the memory transistors in (a) a NOR flash memory array (a common ground architecture of stacked-gate memory transistors has been assumed); (b-1) a planar and (b-2) a vertical (3D) NAND flash memory array.</figcaption></figure>

connection along strings to reduce the area occupancy of the memory chip. Figures 8(b-1) and 8(b-2) schematically show the arrangement of the memory transistors in a planar and in a vertical (or, 3D) NAND flash array, respectively. At present, 3D arrays represent the mainstream solution for NAND flash memories, capable of pushing their bit storage density up to 15 Gbits/mm²,¹⁴⁷ a level unreachable by any other storage technology. Such an achievement was made possible also by the use of multi-bit storage per memory transistor and resulted in memory chips with capacity as high as 1 Tbit.¹⁴⁷ The NAND flash memory design strategy, on the other hand, makes the random access time to the stored data relatively long (typically, a few tens of microseconds). That is the outcome of time delays of the long WLs and BLs in the microsecond timescale, low sensing currents (tens of nanoampere) during data retrieval due to series resistance limitations in the strings, and the need of multi-bit detection per memory transistor. In addition, array reliability relies on powerful ECCs.

Given the successful achievements of flash memories as non-volatile storage media for digital data, exploiting them in the emerging neuromorphic-computing landscape appears as a natural expansion of their application fields and is attracting widespread interests. In this landscape, flash memories may work not only as storage elements for the parameters of artificial neural networks (ANNs) but also as active computing elements to overcome the von Neumann
bottleneck of conventional computing platforms. The latter may represent, of course, the most innovative and disruptive application of flash memories in the years to come. At the same time, the use of flash memories as active computing elements may boost the performance, enhance the power-efficiency, and reduce the cost of ANNs, making their bright future even brighter. In this context, relevant research has been focusing on employing flash memory arrays as artificial synaptic arrays in hardware ANNs and as hardware accelerators for the vector-by-matrix multiplication (VMM), representing the most common operation in ANNs. Quite promising results have already been reported in the field, through either NOR<sup>148,149</sup> or NAND<sup>150-155</sup> flash memories. In these proofs of concept, different encoding schemes for the inputs (e.g., voltage amplitude or pulse width modulation, with signals on the BLs or WLs of the memory array) and different working regimes of the memory transistors have been successfully explored. Interested readers may go through the references provided in this section for a detailed description of the most relevant schemes proposed so far to operate a flash array as a computing element.

## 2. Challenges and potential solutions

Despite the encouraging proofs of concept already reported, the path leading to flash memory-based ANNs still appears long and full of challenges. The latter can be classified into the following categories:

a. *Challenges arising from changes in the design strategy of the array.* As previously mentioned, the success of flash memories as non-volatile storage media for digital data arises from precise design strategies. Modifying those strategies to meet the requests of ANNs may deeply impact the figures of merit of the technology and should be carefully done. For instance, ANN topologies requiring to decrease the segmentation of NOR flash arrays may worsen their performance in terms of working speed. Increasing the segmentation of NAND flash arrays to meet possible ANN topology constraints or to enhance their working speed may significantly worsen their cost per memory transistor.

The cost per memory transistor of flash memories, in addition, is strictly related to the array capacity. Modifying the latter or not exploiting it all through the ANN topology may reduce the cost-effectiveness of the technology. In this regard, the very different capacities of NOR and NAND flash arrays make the former suitable for small/medium size ANNs (less than 1 giga parameters) and the latter suitable for large size ANNs (more than 1 giga parameters). The organization of the memory transistors into strings in NAND flash arrays represents an additional degree of complexity for the exploitation of their full capacity in ANNs. In fact, the number of memory transistors per string is the outcome of technology limitations and cost minimization and, therefore, cannot be freely modified. Exploiting all the memory transistors per string, then, necessarily sets some constraints on the ANN topology (the number of hidden layers, the number of neurons, etc.), which, of course, should be compatible with the required ANN performance.

Another important aspect to consider is that the accurate calibration of the $V_T$ of the memory transistors needed by high-performance and reliable ANNs may not be compatible with the block/sector erase scheme representing a cornerstone of all the design strategies of flash memories. Solutions to carry out the erase

step on single memory transistors are then to be devised. These solutions may require a change of the array design as in Refs. 148 and 149 or new physical processes and biasing schemes of the array lines to accomplish the erase step as in Refs. 156-158. All of these approaches, however, necessarily impact relevant aspects of the technology, affecting its cost, performance, or reliability, and should be carefully evaluated.

The change of the typical working current of the memory transistors when exploiting flash memories for ANN applications is another critical point to address. In fact, reducing the working current of the memory transistors may make it more affected by noise and time instabilities. Increasing it too much, on the other hand, may raise issues related to the parasitic resistances of the BLs and SLs, and, in the case of NAND flash arrays, of the unselected cells in the strings.

b. *Challenges arising from array reliability.* Flash memories are highly reliable non-volatile storage media for digital data. That, however, does not assure that they can satisfactorily meet the reliability requirements needed to operate as computing elements for ANN applications. Especially in the case of NAND flash memories, in fact, array reliability in digital applications is achieved through massive use of ECCs and a variety of smart system-level stratagems to take under control issues, such as electrostatic interference between neighboring memory transistors, lateral migration of the stored charge along the charge-trap storage layer of the strings, and degradation of memory transistors after program/erase cycles. All of that can hardly be exploited to assure the reliable operation of flash arrays as computing elements. In addition, the requirements on the accuracy of the placement and the stability over time of the $V_T$ of the memory transistors when using flash arrays as computing elements may be more severe than in the case of digital data storage. The possibility to satisfy those requirements in the presence of the well-known constraints to the reliability of all flash memory designs<sup>146,159,160</sup> is yet to be fully demonstrated. In this context, periodic recalibration of the $V_T$ of the memory transistors and on-chip learning<sup>155</sup> may mitigate the array reliability issues.

c. *Challenges arising from the peripheral circuitry of the array.* As in the case of flash memory chips for non-volatile storage of digital data, the peripheral circuitry of flash memory arrays used as computing elements for ANNs should not introduce severe burdens on the chip area, cost, power efficiency, and reliability. In the latter case, this aspect is particularly critical due to the need to integrate on the chip not only the circuitry to address the memory transistors in the array and to carry out operations on them, but also, for instance, the circuitry to switch between the digital and the analog domain in VMM accelerators or to implement artificial neurons in hardware ANNs. Along with effective design solutions at the circuit level,<sup>150</sup> process solutions, such as CMOS-under-array integration<sup>147</sup> or heterogeneous integration schemes,<sup>152</sup> should be exploited for successful technology development.

## 3. Conclusion

Flash memories may play a key role in the neuromorphic-computing landscape. Expanding their fields of application, they can be the elective storage media for ANN parameters. However, they can also be active computing media for high-performance, power-efficient, and cost-effective ANNs. To achieve this intriguing goal,
relevant challenges must be faced from the standpoint of the array
design, reliability, and peripheral circuitry. Winning those chal-
lenges will be a matter of engineering and scientific breakthroughs
and will pave the way for years of unprecedented prosperity for both
flash memories and ANNs.

V. EMERGING TECHNOLOGIES (COMPUTING APPROACHES)

Zhongrui Wang and J. Joshua Yang

A. Resistive switching and memristor

1. Status

Resistive switches (often called memristors when device non-
linear dynamics are emphasized) are electrically tunable resistors, of
a simple metal–insulator–metal structure. Typically, their resistance
changes as a result of redox reactions and ion migrations, driven by
electric fields, chemical potentials, and temperature.⁶⁴ There are two
types of resistive switches according to the mobile ion species. In
many dielectrics, especially transition metal oxides and perovskites,
anions such as oxygen ions (or equivalently oxygen vacancies) are
relatively mobile and can form a conduction percolation path, lead-
ing to the so-called valence change switching. For example, a conical
pillar-shaped nanocrystalline filament of the Ti₄O₇ Magnéli phase
was visualized using a transmission electron microscope (TEM) in
a Pt/TiO₂/Pt resistive switch.¹⁶¹ On the other hand, the conduction
channels can also be created by the redox reaction and migration of
cations, which involves the oxidation of an electrochemically active
metal, such as Ag and Cu, followed by the drift of mobile cations
in the solid electrolyte and the nucleation of cations to establish a
conducting channel upon reduction. The dynamic switching pro-
cess of a planar Au/SiOₓ:Ag/Au diffusive resistive memory cell was
captured by in situ TEM.⁸⁹

Resistive switches provide a hardware solution to address
both the von Neumann bottleneck and the slowdown of Moore's
law faced by conventional digital computers. When these resistive
switches are grouped into a crossbar array, they can naturally per-
form vector-matrix multiplication, one of the most expensive and
frequent operations in machine learning. The matrix is stored as
the conductance of the resistive memory array, where Ohm's law
and Kirchhoff's current law physically govern the multiplication and
summation, respectively.⁶⁴ As a result, the data are both stored and
processed in the same location. This in-memory computing con-
cept can largely obviate the energy and time overheads incurred by
expensive off-chip memory access on conventional digital hardware.
In addition, the resistive memory cells are of simple capacitor-like
structures, equipping them with excellent scalability and 3D stack-
ability. So far, resistive in-memory computing has been used for
hardware implementation of deep learning models to handle both
unstructured (e.g., general graphs, images, audios, and texts) and
structured data, as discussed in the following.

General graph: Graph-type data consist of a set of nodes
together with a set of edges. The theoretical formulation has
been made for graph learning using resistive memory on datasets

such as WikiVote.<sup>162,163</sup> Experimentally, a resistive memory-
based echo state graph neural network has been used to clas-
sify graphs in MUTAG and COLLAB datasets as well as nodes
in the CORA dataset,<sup>164</sup> including few-shot learning of the
latter.<sup>165</sup>

Images: Images are special graph-type data. Both supervised and unsupervised learning of ordinary images have been experimentally implemented on resistive memory. For supervised learning, offline trained resistive memory, where optimal conductance of memory cells is calculated by digital computers and transferred to resistive memory, is used to classify simple patterns,<sup>166,167</sup> MNIST handwritten digits,<sup>168–171</sup> CIFAR-10/100 datasets,<sup>172–174</sup> ImageNet,<sup>175</sup> and Omniglot one-shot learning dataset.<sup>176</sup> In addition to offline training, online training adjusts the conductance of resistive memory in the course of learning, which is more resilient to hardware nonidealities in classifying simple patterns,<sup>37,166</sup> Yale Face and MNIST datasets,<sup>177,178</sup> CIFAR-10 dataset,<sup>179</sup> and meta-learning of Omniglot dataset.<sup>180</sup> Besides supervised learning, unsupervised offline learning with resistive memory is used for sparse coding of images<sup>181</sup> and MNIST image restoration.<sup>182</sup>

Audios and texts: Learning sequence data, such as audios and texts, have been implemented on resistive memory. Supervised online learning using recurrent nodes has been done on the Johann Sebastian Bach chorales dataset.<sup>183</sup> In addition, delayed-feedback systems based on dynamic switching of resistive memory are used for temporal sequence learning, such as spoken number recognition and chaotic series prediction.<sup>66,184,185</sup> For offline learning, resistive memory is used for modeling the Penn Treebank dataset;<sup>186</sup> Wortschatz Corpora language dataset and Reuters-21578 news dataset;<sup>187</sup> and Bonn epilepsy electroencephalogram dataset and NIST TI-46 spoken digit dataset.<sup>188,189</sup>

Structured data: Despite unstructured data, structured data, such as those of a tabular format, have been tackled by resistive memory, including supervised classification of the Boston housing dataset on an extreme learning machine;<sup>190</sup> K-means clustering of IRIS dataset and principal component analysis of the breast cancer Wisconsin (diagnostic) dataset;<sup>191,192</sup> and correlation detection of quality controlled local climatological database.<sup>193</sup>

2. Challenges

Major challenges can be categorized at different levels.

Device level: The ionic nature of resistive switching, although benefits data retention, imposes challenges on programming precision, energy, and speed. The programming precision limits the representation capability of the resistive switch, or equivalently how many bits a device can encode. In addition, the programming energy and speed impact online learning performance. In addition, the degradation of the representation capability is further intensified by the read noise, manifestation by the current fluctuation under a constant voltage bias.

Circuit level: Analog resistive memory arrays are mostly inter-
faced with up- and downstream digital modules in a computing
pipeline. As such, there is inevitable signal acquisition and conver-
sion cost, which leads to the question of how to achieve trade-off
between signal acquisition rate, precision, and power consumption.
In addition, the parasitic resistance and capacitance, like the non-
zero wire resistance, incur the so-called IR drop in the resistive
memory crossbar array.

Algorithm level: So far, many applications of resistive memory suffer from significant performance loss in the presence of resistive memory nonlinearities (e.g., noises), thus defeating their efficiency advantage over alternative digital hardware.

### 3. Potential solutions

Device level: Various approaches are used to address the programming stochasticity, such as the local confinement of conducting filament.¹⁹⁴ A denoising protocol using sub-threshold voltages has recently been developed to suppress the fluctuation of the device state and achieve up to 2048 conductance levels.¹⁹⁵ In addition, homogeneous switching may suppress stochasticity at the cost of larger program energy and time overheads.⁶⁴ In terms of programming energy, small redox barriers and large ion mobilities may reduce switching energy and accelerate switching speed, at the expense of retention and thermal stability though.

Circuit level: Typically, resistive in-memory computing relies on Ohm's law and Kirchoff's current law, resulting in current summation. However, there is a recent surge of interest in replacing current summation by voltage summation, which lowers down the static power consumption by eliminating current summation incurred Joule heating. In addition, fully analog neural networks have been proposed to get rid of the frequent analog-to-digital and digital-to-analog conversions.¹⁹⁶ To combat with the parasitic wire resistance, a simple solution is to increase device resistance in both ON and OFF states, such as that demonstrated in a 256 × 256 in-memory computing macros.¹⁹⁵

Algorithm level: A recent trend is hardware-software co-design to leverage resistive memory nonlinearities and turn them into advantages. For example, the programming stochasticity can be exploited by neural networks of random features (e.g., echo state networks¹⁶⁴,¹⁶⁵ and extreme learning machines¹⁹⁰) and Bayesian inference using Markov Chain Monte Carlo (MCMC), such as Metropolis-Hastings algorithm.¹⁹⁷ In addition, such programming noise is a natural regularization to suppress overfitting in online learning.¹⁹⁸ Moreover, hyperdimensional computing¹⁸⁷ and mixed-precision design, such as high-precision iterative refinement algorithm paired with low-precision conjugate gradient,¹⁹⁹ can withstand resistive memory programming noise. The reading noise can also be exploited for solving combinatorial optimization problems using simulated annealing, serving as a natural noise source to prevent the system from falling into the local minimum.²⁰⁰,²⁰¹

### 4. Conclusion

The advent of resistive switch-based in-memory computing in the past decade has demonstrated a wide spectrum of applications in machine learning and neuromorphic computing, reflected by its handling of different types of data.

However, there is still plenty of room, at device, circuit, and algorithm levels, to improve, which will help fully unleash the power of in-memory computing with resistive switches and potentially yield a transformative impact on future computing.

## B. Phase change materials

Abu Sebastian and Ghazi Sarwat Syed

### 1. Introduction

Phase-change memory (PCM) is arguably the most advanced memristive technology. Similar to conventional metal-oxide based memristive devices, information is stored in terms of changes in atomic configurations in a nanometric volume of material and the resulting change in resistance of the device.²⁰² However, unlike the vast majority of memristive devices, PCM exhibits volumetric switching as opposed to filamentary switching. The volumetric switching is facilitated by certain material compositions along the GeTe-Sb₂Te₃ pseudo-binary tie line, such as Ge₂Sb₂Te₅, that can be switched reversibly between amorphous and crystalline phases of different electrical resistivities.²⁰³ Both transitions are Joule-heating assisted. The crystalline to amorphous phase transition relies on a melt-quench process, whereas the reverse transition relies mostly on crystal growth (Fig. 9).

There are essentially two key properties that make PCM devices particularly well suited for neuromorphic computing²⁰⁴ (see Fig. 10). Interestingly, this was pointed out by Stanford Ovshinsky, a pioneer of PCM technology, way back in 2003 when PCM was being considered just for memory applications.²⁰⁵ The first property is that PCM devices can store a range of conductance values by modulating the size of the amorphous region typically achieved by partial RESET pulses that melt and quench a certain volume of the PCM material. This analog storage capability, combined with a crossbar topology, allows for matrix-vector multiplication (MVM) operations to be carried out in O(1) time complexity by leveraging Kirchoff's circuit laws. This makes it possible to realize an artificial neural network on crossbar arrays of PCM devices, with each synaptic layer of the DNN mapped to one or more of the crossbar arrays.⁶⁷,²⁰⁶ The second property referred to as accumulative property results from the progressive crystallization of the PCM material upon application of an increasing number of partial SET pulses. It is used for implementing DNN training;²⁰⁷ temporal correlation detection;¹⁹³ continual learning;²⁰⁸ local learning rules, such as spike-timing-dependent plasticity;²⁰⁹,²¹⁰ and neuronal dynamics.²¹¹

PCM is at a very high maturity level of development and has been commercialized as both stand-alone memory²¹² and embedded memory.²¹³ This fact, together with the ease of embedding PCM on logic platforms (embedded PCM),²⁰⁶ makes this technology of unique interest for neuromorphic computing.

### 2. Challenges

PCM devices offer write operations in the tens of nanosecond timescale, which is sufficient for most neuromorphic applications, in particular those targetting deep learning inference. The cycling endurance could also exceed a billion cycles (dependent on the device geometry), which is several orders of magnitudes higher than commercial flash memory.²¹⁴ This is sufficient for deep learning inference applications. The cycling endurance for partial SET pulses is much higher than that for full SET-RESET cycling and hence is widely considered sufficient for other neuromorphic applications as
<figure><img src="image_20.png" /><figcaption>**FIG. 9.** Summary of emerging memories, such as memristors, and their capabilities in processing various data types, such as images, audios, texts, 3D points, graphs, and events. Image samples are taken from the ImageNet dataset. The audio waveform visualizes a sample from the TIDIGITS dataset. 3D points visualize a sample from the ModelNet10 dataset. The graph sample is from the CORA dataset.</figcaption></figure>

well. The read endurance is almost infinite for PCM when suffi-
ciently low read bias is applied. Another key attribute is retention,
which is typically tuned through material choice.²¹⁵ However, the
use of analog conductance states in neuromorphic computing makes
the retention time of intermediate phase configurations even more
important, which could be substantially lower than that of fully
RESET states.

One of the primary challenges for PCM is integration den-
sity. For example, for DNN inference, it is desirable to have at least
10–100 × 10⁶ on-chip weight capacity. The crossbar array for neu-
romorphic computing comprises metal lines intersected by synaptic
elements, which are composed of one or more PCM devices and

selector devices. Access devices, such as bipolar junction transistors or metal oxide-semiconductor field effect transistors, are preferred for accurate programming, while two-terminal polysilicon diodes offer scalability. To achieve high memory density, stacking multiple crossbar layers vertically is beneficial. Back-end of-line (BEOL) selectors, such as ovonic threshold switches, show promise but face challenges in achieving precise current control. Edge effects and thermal crosstalk between neighboring cells become significant at smaller feature sizes.²⁴⁷⁻²⁴⁹

Compute precision is a crucial aspect especially for DNN
inference applications. The key challenges are 1/f read noise
and conductance drift²¹⁶ (see Fig. 11). Drift is attributed to the
<figure><img src="image_21.png" /><figcaption>FIG. 10. Operational regimes of a phase change device when used for neuromorphic computing. On the right plot, the direct overwrite regime utilizing melt-quench dynamics is illustrated. The programming curves display the achievable conductance values in response to partial RESET pulses of varying amplitudes. As the RESET pulse is increased in amplitude, a larger amorphous volume is created mostly independent of the phase configuration prior to the application of the pulse. On the left plot, the characteristic accumulative property is demonstrated. It shows the evolution of conductance values over successive applications of a SET pulse with a constant amplitude. As the amorphous region reduces in size due to crystallization dynamics, the device conductance progressively increases. Multiple experimental traces are overlaid in both plots.</figcaption></figure>

structural relaxation of the melt-quenched amorphous phase and
exhibits a log time dependence. Conductance variations arising from
temperature variations could also impact the compute precision.²¹⁷
Another potential source of imprecision is voltage polarity depen-
dence.²¹⁸ The intrinsic stochasticity associated with the accumula-
tive behavior could also be a challenge for applications such as online
learning.²¹⁹

For applications that exploit the accumulative behavior, there
is a significant incentive to minimize the programming current.
In fact, reducing the programming currents could also help with
achieving better integration density by minimizing the require-
ments on the access devices. The primary way to achieve lower
programming current is via scaling down the volume of switching
material. PCM devices have decreased in programming energies by a
factor of 1000 since the first memory chip was reported. Some device
structures now exhibit programming energies in the tens of femto-
joules (i.e., on par with the most efficient charge-based memories)
via extreme volume scaling.²²⁰⁻²²³ However, analog capability is typ-
ically compromised, and extreme scaling also leads to fabrication
challenges.

### 3. Potential solutions

Two main approaches have been taken to improve PCM
devices: material engineering and device engineering. Material engi-
neering involves exploration of new phase-change material compo-
sitions as well as alloying of phase-change materials with elements
such as germanium, silicon, carbon etc.²¹⁵ Yet another approach
is the use of superlattice heterostructures.²²⁴,²²⁵ They utilize alter-
nating layers of two different phase change materials that are

only a few atoms thick, which create an electro-thermal confine-
ment effect that enhances write efficiency.²²⁶,²²⁷ This approach also
improves the write endurance and reduces the resistance drift and
noise.²²⁸ However, additional research is necessary to fully com-
prehended the mechanisms and examine the impact of device
geometries and the randomness that accompanies crystal growth
and amorphization.²²⁹⁻²³²

Device engineering involves creating devices such as pro-
jected phase-change memory, which have a noninsulating projection
segment that is placed in parallel to the phase-change material
segment.²³³,²³⁴ Another fascinating approach is that of relying on
nanoscale confinement of simple materials such as antimony to
design better PCM devices.²³⁵ Besides improving the PCM devices
themselves, one could also conceive innovative synaptic units with
more than one PCM device to enhance the conductance window
and to improve the compute precision.²³⁶ There is also potential to
enhance the compute precision by programming approaches such
as gradient-descent programming that relies on minimizing the
MVM error as opposed to minimizing the programming error per
device.²³⁷

Phase-change materials have functional properties in the opti-
cal domain that enable neuromorphic computing on photonic inte-
grated circuits using photonic phase-change memory devices.²³⁸
By integrating these materials onto silicon waveguides,²³⁹,²⁴⁰ ana-
log multiplication of incoming optical signals becomes feasible.
Additionally, spike aggregation and convolution operations can be
conducted in a single time step using wavelength division multiplex-
ing.²⁴¹,²⁴² The accumulative behavior of phase-change materials also
allows for more intricate operations such as correlation detection
with high efficiency.²⁴³ This opens opportunities for the develop-
ment of novel phase-change materials engineered specifically for
photonic applications.

There are also reports of PCM device non-idealities being exploited for computational purposes. For example, the stochasticity associated with the accumulative behavior can create biorealistic randomly spiking neurons,²¹¹ and structural relaxation can be used to implement eligibility traces for reinforcement learning.²⁴⁴ The conductance fluctuations in PCM have also been exploited in an in-memory factorizer to disentangle visual attributes.²⁴⁵ Finally, the ability to induce field effect modulation in PCM devices combined with the analog storage capability can be exploited to realize mixed synaptic plasticities for solving optimization and sequential learning problems.²⁴⁶

### 4. Conclusion

With well-understood device physics models, established man-
ufacturability, and proven integration capability with state-of-the-
art CMOS logic platforms using BEOL processing, PCM becomes
arguably the most advanced memristive technology. More recently
PCM has been extensively researched for neuromorphic comput-
ing by exploiting its analog storage capability and accumulative
behavior. However, commercialization of such technology requires
improvements in achievable compute precision, integration density,
all within the purview of BEOL compatible materials and processing.
Moreover, as with commercialization of any emerging technology, a
key deciding factor would be the manufacturing cost. The expec-
tation is that the manufacturing cost barrier when PCM is used
for computing applications is not as limiting as for storage-class
<figure><img src="image_22.png" /><figcaption>FIG. 11. PCM non-idealities. (a) Device data after programming show variability, reflected in broad distributions of analog conductance values due to programming inaccuracies, read noise, and drift variability (the top panel). Temperature increase raises state conductivity due to thermal carrier excitation and accelerates structural relaxation. (b) The conductance fluctuations manifest as synaptic weight noise, here shown as additive noise in terms of the percentage of the maximum synaptic weight. Using two PCM devices per synapse reduces this error. (c) The accumulative behavior exhibits significant stochasticity mostly attributed to variations in the crystallization kinetics.</figcaption></figure>

memory applications. Most likely, neural processing units for DNN inference based on embedded PCM for analog in-memory computing would be commercialized first. Depending on the level of commercial acceptance of this technology, full-edged PCM-based accelerators could be developed to serve high-end edge applications or even cloud-based applications.

## C. Ferroelectric materials

Thomas Mikolajick, Stefan Slesazeck, and Beatriz Noheda

### 1. Status

Ferroelectric materials are, in theory, ideally suited for information storage tasks since their switching is purely field-driven, holding the promise of extremely low write energy, and non-volatile at the same time. Moreover, unlike competing concepts, such as resistive switching or magnetic switching, ferroelectric materials offer three different readout possibilities giving a lot of flexibility in device design.²⁵⁰ In detail, the following readout schemes can be applied (see also the middle part of Fig. 12):

* Direct sensing of the switched charge during polarization reversal, as used in the ferroelectric RAM (FeRAM) concept, results in a cell design similar to a dynamic random-access memory (DRAM).²⁵¹

* Coupling of the ferroelectric to the gate of a field effect transistor and readout of the resulting drain current, as used in the ferroelectric field effect transistor (FeFET). This results in a cell that is similar to classical transistor-based charge storage (floating gate or charge trapping) memory cell, which is most prominently used in flash memories.²⁵²

* Modulation of the tunneling barrier in a ferroelectric tunneling junction (FTJ). As a result, we can realize a two-terminal

device, which is essentially a special version of a resistive switching memory cell (see Sec. V A).²⁵³

Each of the mentioned readout schemes has advantages and disadvantages, and therefore, the flexibility to use one of the three is a plus, especially in applications that go beyond pure memories, such as neuromorphic computing.

However, traditionally, ferroelectricity was only experienced in chemically complex materials, such as lead-zirconium titanate (PZT), strontium bismuth tantalate (SBT), or bismuth ferrite (BFO), which all are very difficult to incorporate into the processing flow for integrated electronic circuits, due to their limited stability in reducing environments. Another pervasive issue for the integration of ferroelectrics is their tendency to depolarize upon downscaling, an issue that is accentuated by their high permittivity. Organic ferroelectrics, the most prominent example being polyvinylidene difluoride (PVDF), can mitigate this problem, as their low permittivities reduce the depolarization fields, while a rather high coercive field increases the stability of the polarization state. Such materials are ideally suited for lab scale demonstrations of new device concepts, due to their simple fabrication using a solution-based process, and are highly preferred for flexible and biocompatible electronics.²⁵⁴ However, their limited thermal stability has taken them out of the game for devices in integrated circuits. Therefore, although the technology in the form of FeRAM²⁵⁵ is on the market for more than 25 years, it has lacked the ability to scale in a similar manner as conventional memory elements and, therefore, it is still limited to niche applications that require a high rewrite frequency together with non-volatility as in data logging applications.

### 2. Challenges

With the discovery of ferroelectricity in hafnia (HfO₂) and zirconia (ZrO₂), the biggest obstacle of the limited compatibility with integrated circuit fabrication could be solved.²⁵⁶ HfO₂ and
ZrO₂ are stable both in reducing ambient and in contact with sili-
con, and their fabrication using established atomic layer deposition
processes is standard in modern semiconductor process lines. How-
ever, new difficulties, especially with respect to reliability,²⁵⁷ need
to be solved. Challenges in this direction are aggravated by the
metastable nature of the ferroelectric phase, which appears mostly
at the nanoscale, making a full understanding of the polar phase
quite demanding. While their high coercive field makes them very
stable with respect to classical retention, the ferroelectric phase typ-
ically exists together with other non-polar phases, which prevents
them from reaching the predicted polarization values (of the order
of 50 µC/cm²).²⁵⁸ Moreover, the most serious problem of any non-
volatile ferroelectric device, the imprint, becomes very complex to
manage in hafnia/zirconia-based ferroelectrics. The imprint is a shift
of the hysteresis loops due to an internal bias. While this effect leads
to a classical retention of the stored state that may look perfect,
after switching, retention will be degraded and fixing the so-called
opposite-state retention loss needs to be carefully done by material
and interface engineering. Moreover, the high coercive field in this
material class becomes a problem as HfO₂ and ZrO₂ often show
a pronounced wake-up and fatigue behavior and the field-cycling
endurance is in many cases limited by the dielectric breakdown of
the material.

While the issues mentioned so far are valid for any non-volatile
device application, in neuromorphic systems, additional challenges
arise, including the linearity of the switching behavior and tuning

of the retention to achieve both short-term and long-term plastic-
ity, as well as specific effects to mimic neurons, such as accumulative
switching,²⁵⁰,²⁵⁹ which need to be explored using material and device
design measures. Finally, large-scale neuromorphic systems will
require a high integration density that demands three-dimensional
integration schemes, realized either by the punch-and-plug technol-
ogy well-known from NAND flash or by integrating devices into the
back-end of the line.

3. Potential solutions

Since the original report on ferroelectricity in hafnium oxide,²⁵⁶ the boundary conditions for stabilizing the ferroelectric phase have been much better understood, although there are still a number of open questions. The goal is to achieve a high fraction of the ferroelectric phase without dead layers of non-ferroelectric phases at the interface to the electrodes or in the bulk of the film. This needs to be done under the boundary conditions of a realistic fabrication process, which means that sophisticated methods to control the crystal structure based on epitaxial growth are not possible. Epitaxial growth can help clarify scientific questions, but the achieved results need to be transferred to chemical vapor deposition (CVD), including most prominently atomic layer deposition (ALD), or physical vapor deposition (PVD) processes using electrodes such as TiN or TaN that can be integrated into electronic processes.

In the past years, it became obvious that oxygen vacancies are,
on the one hand, required to stabilize the ferroelectric phase²⁶⁰ and,

<figure><img src="image_23.png" /><figcaption>FIG. 12. Ferroelectric materials (center) enable three different basic memory cells (middle ring). These can be used in various ways in neuromorphic circuits (for examples, see the outer part of the figure). The rich switching dynamics of ferroelectrics allow us to tailor new devices mimicking neurons and synapses in a much more flexible and area efficient way as compared to their pure CMOS counterparts.</figcaption></figure>
on the other hand, detrimental to both the imprint and the field cycling behavior.²⁶¹ Therefore, many proposals to integrate the ferroelectric layer with additional thin layers in the film stack have been made, and currently, a lot of work is going in that direction. Moreover, it is clear that the interface to the electrodes needs careful consideration. In this direction,²⁶² facilitating the transport of oxygen, not only in the ferroelectric layer but also across the electrode interfaces, by minimizing the strain effects, may be key to improving device performance.²⁶³ When it comes to structures that are in direct contact with silicon, a recent observation of a quasi-epitaxial growth of extremely thin hafnium-zirconium oxide films on silicon could be an interesting direction.²⁶⁴ For concrete neuromorphic applications, the rich switching dynamics can be very helpful (see Fig. 12).²⁶⁵ While in large devices, a continuous switching between different polarization states is possible, devices scaled in the 10 nm regime show abrupt and accumulative switching.²⁵⁹ The former can be used for mimicking synaptic functions, while the latter is helpful to mimic neurons. In classical non-volatile memories, the depolarization fields created by non-ferroelectric layers or portions of the layer in series to the ferroelectric are a concern for the retention of the device. However, when creating short and long-term plasticity in synaptic devices, this can be turned into an advantage such that the device retention can be tailored.

# D. Spintronic materials for neuromorphic computing

## Bernard Dieny and Tuo-Hung (Alex) Hou

### 1. Status

Spintronics is a merging of magnetism and electronics in which the spin of electrons is used to reveal new phenomena, which are implemented in devices with improved performances and/or new functionalities. Spintronics has already found many applications in magnetic field sensors, in particular in hard disk drives and, more recently, as non-volatile memory (MRAM) in replacement of e-FLASH and last-level cache memory. Spintronics can also bring very valuable solutions in the field of neuromorphic computing both as artificial synapses and as neurons.

Artificial synapses are devices supposed to store the potential weight of the bounds linking two neurons. Various types of spintronic synapses have been proposed and demonstrated.⁶⁵ They are magnetoresistive non-volatile memory cells working either as binary memory, as multilevel memory, or even in an analog fashion. Their resistance depends on the history of the current that has flown through the device (memristor). Most of these devices are based on magnetic tunnel junctions (MTJs), which basically consist of two magnetic layers separated by a tunnel barrier. One of the magnetic layers has a fixed magnetization (the reference layer), whereas the magnetization of the other (the storage layer) can be changed by either a pulse of magnetic field or current using phenomena such as spin transfer torque (STT) or spin-orbit torque (SOT).²⁶⁶ The resistance of the device depends on the amplitude and orientation of the magnetic moment of the storage layer relative to that of the reference layer (tunnel magnetoresistance effect—TMR). For a binary memory as in STT-MRAM or SOT-MRAM, only the parallel and antiparallel magnetic configurations are used.²⁶⁷ For multilevel or

analog memory, several options are possible as illustrated in Fig. 13. One consists of varying the proportion of the storage layer area that is in parallel or antiparallel magnetic alignment with the reference layer magnetization. This can be achieved by step-by-step propagation of a domain wall within the storage layer using the STT produced by successive current pulses [Fig. 13(a)],²⁶⁸ or by gradually switching the magnetization of the storage layer exchange coupled to an antiferromagnet using the SOT produced by the pulsed current flow in the antiferromagnet [Fig. 13(c)],²⁶⁹ or by gradually switching the grains of a granular storage medium similar to the ones used in hard disk drives [Fig. 13(d)],²⁷⁰ or by nucleating a controlled number of magnetic spin nanotextures in the storage layer, such as skyrmions [Fig. 13(e)].²⁷¹ Alternatively, the memristor resistance can also be varied by changing the relative angle between the magnetization of the reference and storage layers using all intermediate angles between 0° and 180° instead of only parallel and antiparallel configurations [Fig. 13(b)].¹⁰⁵ Chains of binary magnetic tunnel junctions can also be used to achieve spintronic memristors but at the expense of a larger footprint.²⁷²

Concerning artificial neurons, the conventional CMOS neuron circuit is limited by its large area because a large number of transistors and a large-area membrane capacitor are required for implementing Integrate-and-Fire (I&F) functions.²⁷³ Recently, several spintronic neuron devices have been reported to generate spike signals by leveraging nonlinear and stochastic magnetic dynamics without the need for additional capacitors and complex peripheral circuitry. Spintronic neurons potentially show a great advantage for compact neuron implementation.²⁷⁴

Assembly of interacting spin-torque nano-oscillators (STNOs) based on the structure of magnetic tunnel junctions (MTJs) was proposed to achieve neuron functionality. An unstable conductance oscillation that mimics spike generation is induced at hundreds of MHz to several tens of GHz by flowing a current through the device. The frequency and amplitude of oscillation vary with the applied current and magnetic field. Torrejon et al. demonstrated spoken-digit or vowel recognition using such an array of nanoscale oscillators.²⁷⁵

Superparamagnetic tunnel junctions can also be used to mimic stochastic neurons. They have much lower thermal stability compared to the MTJ used for memory, so they stochastically switch between antiparallel (AP) and parallel (P) states due to thermal fluctuations, which is referred to as telegraphic switching.²⁷⁶ This switching mode can be used to generate Poisson spike trains in spiking neural networks (SNNs) as well as for probabilistic computing.²⁷⁷ A MTJ device with high thermal stability, which can implement not only synapses but also neurons in an all-spin neural network, was proposed by Wu et al.²⁷⁸ The reduction in the thermal stability factor is induced by self-heating at a high bias voltage for neuron operations.²⁷⁹ At a low bias, it stably stores weight information as synapses.

Many other new spintronic materials and mechanisms were also investigated for the feasibility of neuron devices, in particular based on magnetoelectric effects. For instance, by playing with magneto-ionic effects influencing the anisotropy at magnetic metal/oxide interfaces, the density of skyrmions²⁸⁰ and even their chirality could be controlled electrically.²⁸¹ Jaiswal et al. designed a magnetoelectric neuron device for SNNs.²⁸² Zahedinejad et al. demonstrated that electrically manipulated spintronic mem-
<figure><img src="image_24.png" /><figcaption>FIG. 13. Various realizations of spintronic memristors: (a) based on domain wall propagation in the storage layer; (b) based on variation of angle between storage layer and reference layer magnetization; (c) based on SOT in ferromagnetic storage layer exchange coupled to an antiferromagnetic SOT line; (d) implementing a storage layer made of a granular layer similar to the one used in recording technology; and (e) based on a controlled number of skyrmions nucleated in the storage layer.</figcaption></figure>

ristors can be used to control the synchronization of spin Hall nano-oscillators for neuromorphic computing.²⁸³

## 2. Challenges

Building useful fully functional neuronal circuits requires large-scale integration of layers of artificial neurons interconnected with spintronic synapses. Crossbar architectures can achieve cumulate and multiply functions very efficiently in an analog manner. An advantage of magnetic tunnel junctions over other technologies based on materials such as resistive oxides or phase change is their write endurance associated with the fact that their resistance change does not involve ionic migration. However, they exhibit a lower $R_{OFF}/R_{ON}$ ratio (~4 for MRAM vs 10–100 for RRAM or PCM) and also narrower cell-to-cell distribution of resistance in $R_{OFF}$ and $R_{ON}$ states. In crossbar architectures, MTJs should have high resistance to minimize power consumption. Therefore, efforts should be pursued to further increase the TMR amplitude of MgO-based MTJs and bring it closer to the expected theoretical values of several 1000%.²⁸⁴ In high-resistance MTJs, other approaches, such as SOT or voltage control of anisotropy (VCMA), could be used to change the MTJ resistance. In all cases, the control of the resistance change induced by current or voltage pulses must be improved. The operating temperature has often also a significant impact on magnetic properties, which imposes challenges on system design.

Concerning artificial neurons, the DC power required to trigger the magnetization dynamics of STNO neurons is still relatively high (mW range).²⁸⁵ Ways must be found to reduce it by using different materials or new designs. The switching speed

and endurance in superparamagnetic tunnel junctions and self-heating-assisted MTJ neurons could be further enhanced to improve processing speed and system reliability.²⁸⁶,²⁸⁷ How to continue improving variability across millions of synapses and thousands of neurons to ensure high accuracy in future neuromorphic systems remains an actively research topic. Interconnecting all these devices is also a challenge, and innovative approaches beyond classical interconnects must be found notably by taking advantage of 3D integration.

## 3. Potential solutions

STT-MRAM entered volume production in 2019 at major microelectronic companies.²⁸⁸ This marked the adoption of this hybrid CMOS/magnetic technology by the microelectronic industry. Thanks to the combined efforts of the chip industry, equipment suppliers, and academic laboratories, spintronics is progressing very fast. Materials research is very important to increase magnetoresistance amplitude, switching currents, STT and SOT efficiency, and VCMA efficiency; reduce dependence on operating temperature; reduce current to trigger oscillations in STNOs; and reduce disturbance due to parasitic field. Investigations are in progress involving antiferromagnetic materials for reduced sensitivity to the field and access to THz frequency operation;²⁸⁹ half-metallic materials, such as Heusler alloys, for enhanced TMR amplitude and reduced write current;¹⁰⁴ and topological insulators for very efficient spin/charge current interconversion possibly combined with ferroelectric materials.²⁹⁰

Concerning interconnects, fortunately, magnetic materials are grown in backend technology and can be stacked but at the expense of complexity and cost. Long-range information transmission can
be carried out via spin-current or magnons or by propagating mag-
netic textures, such as domain walls²⁹¹ or skyrmions.²⁹² Light could
also be used to transmit information in conjunction with recent
developments related to all-optical switching of magnetization.²⁹³ In
addition, a great advantage of spintronic stacks is that they can be
grown on almost any kind of substrates, provided that the rough-
ness of the substrate is low enough compared to the thickness of
the layers comprised in the stack. This enables the use of the third
dimension by stacking several spintronic structures, thereby gaining
in interconnectivity.²⁹⁴

4. Concluding remarks

Spintronics can offer valuable solutions for neuromorphic
computing. Considering that STT-MRAM is already in commercial
production, it is very likely that the first generation of spintronic
neuromorphic circuits will integrate this technology. Next, crossbar
arrays implementing analog MTJs may be developed as well as neu-
ronal circuits based on the dynamic properties of interacting STNOs
for learning and inference. Still, many challenges are on the way
toward practical applications, including speed, reliability, scalabil-
ity, and variation tolerance, which need to be addressed in future
research.

E. Optoelectronic and photonic implementations

Akhil Varri, Frank Brückerhoff-Plückelmann, and
Wolfram Pernice

1. Status

Computing using light offers significant advantages in highly
parallel operation exploiting concepts such as wavelength and
time multiplexing. Moreover, optical data transfer enables low
power consumption, better interconnectivity, and ultra-low latency.
Already in the 1980s, first prototypes were developed; however, the
bulky tabletop experiments could not keep pace with the flourishing
CMOS industry. At present, novel fabrication processes and mate-
rials enable the (mass) production of photonic integrated circuits,
allowing photonic systems to compete with their electronic counter-
parts. Especially in the area of data-heavy neuromorphic computing,
the key advantages of photonic computing can be exploited.

Scientific efforts in neuromorphic photonic computing can be
segregated in two major directions: (i) one approach is building
hardware accelerators that excel at specific tasks, e.g., computing
matrix-vector multiplications, by partially mimicking the working
principles of the human brain, and (ii) the other is creating designs
that aim to emulate the functionality of biological neural networks.
Such devices are able to replicate the behavior of a neuron, a synapse,
and learning mechanisms and to ultimately implement a spiking
neural network.

There has been considerable progress in the (i) direction since
2017 when Shen et al.²⁹⁵ demonstrated vowel recognition where
every node of the artificial neural network is physically repre-
sented in the hardware using a cascaded array of interferometers.
This scheme has also been scaled to implement a three-layer deep
neural network with in situ training capability.²⁹⁶ In addition,

Feldmann et al.²⁹⁷ have demonstrated neurosynaptic networks on-chip and used them to perform image recognition. The photonic circuit deploys a non-volatile phase change material (PCM) to emulate the synapses and exploits the switching dynamics as a nonlinear activation function. As highlighted in Sec. V B, the integration of PCMs also leads to in-memory computing functionality owing to their non-volatile nature.

For the (ii) direction, significant work has been done on a
device level to mimic individual components of the brain. Excitable
lasers combining different material platforms, such as III-V com-
pounds, and graphene have been shown to demonstrate leaky
integrate and fire-type characteristics of a neuron.⁷³ In addition,
neurons based on optoelectronic modulators have been shown in
the literature. For synapses, photonic devices combined with PCMs,
amorphous oxide semiconductors, and 2D materials have been used
to demonstrate synaptic behaviors, such as spike-time-dependent
plasticity and memory.⁷³,298,299 Furthermore, key synaptic functions
have also been demonstrated using optically controlled reversible
tuning in amorphous oxide memristors.³⁰⁰,⁵⁰¹ Optical control of
the conductance levels in memristors, such as those described in
Sec. V A, enables low-power switching dynamics important to
neuromorphic computing efforts.

In the following, we break down the challenge of building neu-
romorphic photonic hardware to various subtopics, ranging from
increasing the fabrication tolerance of the photonic circuit to co-
packaging the optics and electronics. Then, we review the current
advances in those areas and provide an outlook on the future
development of neuromorphic photonic hardware.

## 2. Challenges

A major challenge is combining the various building blocks
shown in Fig. 14. Silicon on insulator is the platform of choice for
building large circuits owing to the matured CMOS process flow and
the high refractive index contrast between the silicon waveguide and
oxide cladding. However, silicon has no second-order nonlinear-
ity as it is centrosymmetric. Furthermore, silicon being an indirect
bandgap material cannot emit light. This strongly limits the options
for implementing nonlinear functions and spiking dynamics crucial
for an all-optical neural network. Therefore, most of the research
on mimicking neurons is focused on novel material platforms that
support gain. A key challenge is integrating those different material
platforms. For example, a circuit may deploy neurons based on III-V
semiconductor heterojunctions and synapses built with PCMs on
silicon. Therefore, compact and fabrication error-tolerant optical
interconnects are crucial for the performance of the whole system.

Apart from packaging various optical components, the electro-
optic interface imposes an additional challenge. Typically, the input
data are provided by digital electrical signals, whereas optical data
processing is analog. This requires analog-to-digital converters
(ADCs) and digital-to-analog converters (DACs) for digital systems
to interface with the chip as shown in Fig. 14. For large circuits, co-
packaging electronics and photonics increases the footprint and cost
significantly. This negatively affects the throughput.

In addition to the above, fabrication imperfections will also
impact the performance of a photonic circuit. Components such
as ring resonators, cavities, and interferometers employed in many
photonic circuits are designed to operate at a certain wavelength.
<figure><img src="image_25.png" /><figcaption>**FIG. 14.** An illustration of an optoelectronic system capable of performing computing operations. The electro-optic modulator (EOM) encodes the input data from the memory or a real-time sensor into the light fields. The encoded light fields are then coupled to a photonic processor that emulates the neurosynaptic behavior. The results from the processor are passed on to detectors that transform the signals back into the electronic domain and are finally stored in a memory.</figcaption></figure>

However, due to factors such as etching rate, sidewall angle, and surface roughness, the wavelength of operation many times does not match with the design. Hence, in many cases, active methods such as thermo-optic phase shifters are employed to post-fabricate trim the wavelength. This results in unnecessarily increased electronic circuitry adversely affecting the scalability of the system.

Finally, a challenge that may be critical in the future is the electro-optic modulator (EOM) efficiencies that depend on the material properties and configurations. An important figure of merit for EOM efficiency is VpiL. This merit shows the voltage that needs to be applied and the length of the modulator required to obtain a pi phase shift to the input. A smaller merit figure suggests increased power efficiency and a compact footprint. As photonic neuromorphic circuits are supposed to scale up in the future, the power budget and space available on-chip will play an essential role in influencing the designs.

### 3. Potential solutions

Solutions addressing the challenges mentioned above lie on multiple fronts. First, we discuss how the scalability can be improved from a device-level perspective. The compact footprint, power efficiency, and cascadability of the neurons are essential characteristics for improving the scalability. In this regard, modulator-based neurons can be improved by integrating with materials such as electro-optic polymers. These materials have an order of magnitude

higher r33 electro-optic coefficient compared to bulk lithium niobate, which has been conventionally the material of choice for modulators. As a result, electro-optic polymers integrated with silicon waveguides show very low VpiL among fast modulators.302 In addition, novel materials, such as epsilon-near-zero (ENZ), which are promising for optical nonlinearity, can also be explored.303 Nevertheless, for the widespread use of these devices, a better understanding of the material properties and engineering efforts to integrate them into the existing manufacturing process flow is required.

Particularly, integration techniques, such as micro-transfer printing, flip-chip bonding, and photonic wire bonding, will play a key role. To solve the problem of packaging with electronics, strategies such as monolithic fabrication, where the photonics and electronics are on the same die, need to be investigated. Foundries are now offering multi-project wafer runs with these state-of-the-art packaging techniques.

For improving the scalability of spike-based processing systems, another class of neurons that is very promising is the vertical cavity surface emitting lasers (VCSELs). VCSELs can integrate 100 picosecond-long pulses and fire an excitable spike when the sum crosses a certain threshold, emulating biological neurons. Recently, it has been shown that the output of one layer of VCSEL neurons combined with a software-implemented spiking neural network can perform 4-bit image recognition.304 In order to build the entire system on hardware and perform larger experiments, 2D VCSEL arrays flip-chip bonded on a silicon die can be examined.

Finally, to address the challenge of fabrication imperfections, passive tuning approaches can be of interest, which need no additional circuitry and are non-volatile. One direction could be the use of phase change materials, such as GaS and Sb<sub>2</sub>S<sub>3</sub>, to correct for the variability in photonic circuits.305 These materials are very interesting since their real part of the refractive index can be tuned while keeping low absorption at telecom wavelengths. Another approach for post-fabrication passive trimming could be to use an electron beam or ion beam to change the material properties of the waveguide. This method is also scalable as these tools are widely used in the semiconductor industry.

### 4. Concluding remarks

Applications such as neuromorphic computing are particularly promising for optics where their unique advantages (i.e., high throughput, low latency, and high power efficiency) can be utilized. At present, there have been instances in the literature where different devices have been proposed to emulate the individual characteristics of a neurosynaptic model. However, there is a lot of scope for research in materials science to pave the way for more compact, cascadable, and fabrication-friendly implementations. Furthermore, large-scale networks are expected to scale in the near future by integrating state-of-the-art packaging techniques that are now available to research groups and startups.

To summarize, the growth of integrated photonics has led to a resurgence of optical computing not only as a research direction but also commercially. It is exciting to see how the field of neuromorphic photonics will shape as advancements in science and technology continue to happen.
## F. 2D materials

### Mario Lanza, Xixiang Zhang, and Sebastian Pazos

#### 1. Status

Multiple studies have claimed the observation of resistive switching (RS) in two-dimensional layered materials (2D-LMs), but very few of them reported excellent performance (i.e., high endurance and retention plus low switching energy, time, and voltage) in a reliable and trustable manner and in a device small enough to be attractive for high-integration-density applications (e.g., memory and computation).

The best RS performance observed in 2D-LMs is based on out-of-plane ionic movements. In such types of devices, the presence and quality of the RS phenomenon mainly depend on three factors: the density of native defects, the type of electrode used, and the volume of the dielectric (thickness and area). In general, 2D-LMs with excellent crystallographic structure (i.e., without native defects, such as those produced by mechanical exfoliation) do not exhibit stable resistive switching. Reference 306 reported that mechanically exfoliated multilayer MoS₂ does not show RS; only after oxidizing it (i.e., introducing defects), it shows RS based on the migration of oxygen ions. Along these lines, Ref. 307 showed that mechanically exfoliated multilayer hexagonal boron nitride (h-BN) does not exhibit RS; instead, the application of voltage produces a violent dielectric breakdown (DB) followed by material removal. The more violent DB phenomenon in h-BN compared to MoS₂ is related to the higher energy for intrinsic vacancies formation: >10 eV for boron vacancies in h-BN vs <3 eV for sulfur vacancies in MoS₂. Some articles claimed RS in mechanically exfoliated 2D-LMs, but very few cycles and poor performance were demonstrated; those observations are more typical of unstable DB than stable RS. Reference 308 reported good RS in a crossbar array of Au/h-BN/graphene/h-BN/Ag cells produced by mechanical exfoliation, but in that study, the graphene film shows an amorphous structure in the cross-sectional transmission electron microscope images. Hence, stable and high-quality RS based on ionic movement has never been demonstrated in as-prepared mechanically exfoliated 2D-LMs. This is something expected because ionic-movement-based RS is only observed in materials with high density of defects (e.g., high-k materials and sputtered SiO₂) but not in materials with low density of defects (e.g., thermal SiO₂), as the higher energy-to-breakdown forms an irreversible DB event.

On the contrary, 2D-LMs prepared by chemical vapor deposition (CVD) and liquid phase exfoliation (LPE) have exhibited stable RS in two-terminal memristors³⁰⁹ and three-terminal (memristors) configurations,³¹⁰ although in the latter, the switching mechanism is largely different. In two-terminal devices, RS is enabled by the migration of ions across the 2D-LM. In transition metal dichalcogenides (TMDs), the movement of chalcogenide ions can be enough to leave behind a metallic path (often referred to as conductive nanofilament or CNF) that produces switching (similar to oxygen movement in metal-oxides).³⁰⁶ However, in h-BN, metal penetration from the adjacent electrodes is needed, as this material contains no metallic atoms.³⁰⁷ In 2D-LMs prepared by

CVD and LPE methods, ionic movement takes place at lower energies (than in mechanically exfoliated ones) due to the presence of native defects (mainly lattice distortions and impurities). The best performance so far has been observed in CVD-grown ~6 nm-thick h-BN, as it is the only material with enough insulation and thickness to keep low the current in the high resistive state.⁷² This includes the coexistence of bipolar and threshold regimes (the second one with highly controllable potentiation and relaxation), bipolar RS with endurances >5 × 10⁶ cycles (similar to commercial RRAM memories and phase-change memories),³¹¹ and ultra-low switching energies of ~8.8 zJ in the threshold regime.³¹² Moreover, a high yield (~98%) and low variability have been demonstrated.³¹² In 2D-LMs produced by LPE or other solution-processing methods,³¹³ the junctions between the flakes and their size play a very important role, and while there is evidence of potentially good endurance, synaptic behavior, and variability, sub-µm downscaling still has not shown equivalent performance.³¹⁴

Apart from ionic movement, 2D-LMs can also exhibit RS based on ferroelectric effect.²⁵⁰ A remarkable example is In₂Se₃, which has electrically switchable out-of-plane and in-plane electric dipoles. Recent works have demonstrated that RS in ferroelectric In₂Se₃ is ensured by three independent variables (polarization, initial Schottky barrier, and barrier change) and that it delivers multidirectional switching and photon storage.³¹⁵ However, the endurance and retention time are still limited to hundreds of cycles, and stable ferroelectric RS at the single-layer limit remains unexplored. Finally, tunable optoelectronic properties and unique electronic structure attainable through 2D-LM heterostructures present enormous potential for near-/in-sensor computing in neuromorphic systems. The responsiveness to physical variables (light, humidity, temperature, pressure, and torsion) of 2D-LM memristor and mem-transistor devices allows us to mimic biological neurosynaptic cells (visual cortex and tactile receptors).³¹⁶

#### 2. Challenges and potential solutions

The main challenge of RS devices (of any type) is to exhibit high endurance in small devices. Many studies have reported RS in large devices with sizes >10 µm² and claimed that their devices are "promising" for memory and computing applications. This is a huge and unreasonable exaggeration; these two applications require high integration density, as commercial devices for those applications have sizes down to tens or hundreds of nanometers. It should be noted that in ionic-movement-based RS devices, the CNF always forms at the weakest location of the sample; when the device size is reduced, the density and size of defects are (statistically) reduced, which produces an increase in the forming voltage.³¹⁷ Hence, the CNF of smaller devices is wider due to the larger amount of energy delivered during the forming. This has a huge effect on state resistances, switching voltages, time, and energy, as well as endurance, retention time, and device-to-device variability. In other words, the fact that a large device (>10 µm²) exhibits good RS does not mean that a small device (<1 µm²) made with the same materials will also exhibit it; hence, RS "promising for memory and computation" is only the one that is observed in devices with sizes of tens/hundreds of square nanometers.

Taking this into account, the main challenge in 2D-LM based devices is to observe RS in small devices, and the most difficult figure-of-merit to obtain is (by far) the endurance. Reference 318
demonstrated good RS in 5 × 5 µm² Au/h-BN/Au devices, in which h-BN was ~6 nm-thick and grown by the CVD method; however, when the size of the devices was reduced to 320 × 420 nm², the yield and the number of devices observed were very limited. The main issue was the current overshoot during the switching, which takes place randomly and produced irreversible DB in most devices. Similarly, solution-processed Pt/MoS₂/Ti devices³¹⁹ showed excellent performance across all figures-of-merit observed in 25 µm² devices, but such performance has not been reported for 500 × 500 nm² devices patterned via electron beam lithography. In this case, the large size of the nanoflakes (slightly below 1 µm minimum) may be imposing an intrinsic scaling limitation. Meanwhile, the scaling and overshoot problem was solved in Ref. 72 integrating CVD-grown h-BN right on top (via the wet-transfer method) of a silicon complementary metal-oxide-semiconductor (CMOS) transistor, which acted as an instantaneous current limitation. Moreover, this approach brings the advantage of a very small device size (in Ref. 72, it was only 0.053 µm², as the bottom electrode of the RS device is from one of the metallization levels). The heterogeneous integration of the 2D-LMs at the back-end-of-line (BEOL) wiring of silicon microchips could be a good way of testing materials for RS applications and directly integrating selector devices with each memristor (into one transistor–one memristor (1T1M) cells), which is fundamental for the realization of large memristive synapse arrays—all state-of-the-art demonstrations of memristive neural accelerators based on mature memristor devices use 1T1M cells or differential implementations of such cells (2T2M and 4T4M). So far, these CMOS testing vehicles for RS materials have mainly been employed by the industry; in the future, spreading this type of testing vehicles among academics working in the field of RS could improve the quality of the knowledge generated. In addition, these devices may benefit from common practices in the field of silicon microchip manufacturing, such as surface planarization, plug deposition, and high-quality thick interconnect techniques.

Next steps in the field of 2D-LMs for RS applications consist in improving the materials quality to achieve better reproducibility of the experiments (from one batch to another) and adjust the thickness and density of defects to achieve better figures-of-merit in nanosized RS devices while growing 2D-LM at the wafer-scale.³²⁰ Recent studies successfully synthesized large-area single-crystal 2D-LMs via CVD,³²¹ although in most cases, it is only monolayer. However, monolayer 2D-LMs are less than 1-nm-thick, and when they are exposed to an out-of-plane electrical field, a very high leakage current is generated even if no defects are present, which increases a lot the current in the high-resistance state (HRS) and the energy consumption of the device. Reference 322 presented the synthesis of single-crystal multilayer h-BN using scalable methods, but controlling the number of layers is still difficult. Electrical studies in such types of single-crystal multilayer samples should be conducted. Improving manipulating methods to prevent the formation of cracks during transfer is also necessary, although it is worth mentioning that multilayer h-BN materials are more mechanically stable than monolayers.

Recent demonstration of vector-matrix multiplication using MoS₂ memtransistors²²³ is a promising advance in terms of a higher-level functional demonstration, although the fundamental phenomenon exploited is the well-known floating gate memory

effect, not unique to 2D-LM themselves. Meanwhile, understanding the role of flake size in the functionality of solution-processed 2D-LM two-terminal synaptic devices is critical to address the true scaling limitations of such an approach, a key aspect to define potential realistic applications in neuromorphic systems. On the other hand, sensing capabilities emerge with great potential for biological synaptic mimicking. The full potential of different 2D-LM material heterostructures and memtransistors opens a huge design-space worth of exploration. In that sense, the complex physical characteristics offered by different 2D-LMs hold the potential not only for basic neuromorphic functionality but also for higher-order complexity. This could be exploited to achieve high-complexity neural and synaptic functions,¹⁰⁰ more closely mimicking actual biological systems. However, in parallel to elucidating the physical properties and capabilities of these material systems, efforts should be put into strengthening the quality of the reported results, focusing on proper characterization methods, reliable practices, and statistical validation.

### 3. Concluding remarks

Leading companies, such as TSMC, Samsung, IBM, and Imec, have started to work with 2D-LMs, but mainly for sensors and transistors. In the field of 2D-LM based neuromorphic devices, most work is being carried out by academics. In this regard, unfortunately, many studies make a simple proof-of-concept using a novel nanomaterial without measuring essential figures-of-merit, such as endurance, retention, and switching time. What is even worse, in many cases, the studies employ unsuitable characterization protocols that heavily overestimate the performance (the most popular case is the erroneous measurement of endurance³²⁴), withholding information regarding the failure mechanisms that lead to certain performance metrics not being achieved on some devices. This working style often result in articles with striking numbers (i.e., performance), but those are unreliable, and it is really bad for the field because it creates a hype of expectations and disillusion among investors and companies. The most important is that the scientists working in this field follow a few considerations: (i) always aim to show high performance in small (<1 µm²) devices fabricated using scalable methods (even better if they are integrated on a functional CMOS microchip, not on an unfunctional SiO₂ substrate); (ii) measure all the figures-of-merit of several (>100) memristive devices for the targeted application (this may vary depending on the application);²¹⁴ (iii) clearly define the yield-pass criteria and the yield achieved, as well as the device-to-device variability observed; and (iv) whenever a failure mode is observed preventing reaching a desired figure-of-merit, clearly convey it to maximize the probabilities of finding a solution.

## VI. MATERIALS CHALLENGES AND PERSPECTIVES

### Stefan Wiefels and Regina Dittmann

#### A. Materials challenges

For the neuromorphic computing approaches addressed in Sec. III, the use of emerging memories based on novel materials will
<figure><img src="image_26.png" /><figcaption>FIG. 15. Materials challenges for neuromorphic computing. Novel NVMs need to be scalable, fast, and reliable and allow for analog operation.</figcaption></figure>

be key in order to improve their performance and energy-efficiency. This chapter discusses the most relevant properties and challenges for different use cases and how they relate to the respective materials properties. However, it is important to note that a dedicated co-development of materials with the readout and write algorithms and circuitry will be required in order to advance the field (Fig. 15).

## 1. Scaling

One main driving force to use emerging materials and devices is to gain space and energy efficiency by the fabrication of highly dense crossbar arrays. For STT-MRAM, scaling down to 11 nm cells has been demonstrated, as well as the realization of 2 Mb embedded MRAM in 14 nm FinFET CMOS.³²⁵ However, due to the small resistance ratio of 2–3, the readout of magnetic tunnel junctions (MTJs) is more complex than for other technologies. Nevertheless, a 64 × 64 MTJ array, integrated into 28 nm CMOS, has recently been realized.⁷⁵ Advancements from the material side will be needed in order to increase the resistance ratio of MTJs in the future.

For ferroelectric HfO₂-based devices, the main challenge with respect to scaling is to decrease the thickness reliably in order to enable 3D capacitors with 10 nm node and to obtain a uniform polarization at the nanoscale of a material that currently still contains a mixture of different phases. Therefore, ultrathin films with the pure ferroelectric orthorhombic phase and without any dead-layers at the interfaces will be key to approach the sub-20 nm regime of hafnia-based ferroelectric devices.⁹

PCM devices can be fabricated on the sub-10 nm scale.³²⁶ The limiting factor for CMOS integrated PCM devices is the high RESET current, which is required to implement larger access transistors.²⁰² Commercially available ReRAM cells with conventional geometries have been co-integrated on 28 nm CMOS technology. By employing a sidewall technique and nanofin Pt electrodes, small arrays with 1 × 3 nm² HfO₂²⁰² cells and 3 × 3 arrays of Pt/HfO₂/TiOx/Pt cells with a 2 nm feature size and a 6 nm half-pitch have been fabricated, respectively.³²⁷

With respect to ultimate scaling, the loss of oxygen to the environment might pose limitations to the retention times for ReRAM devices scaled in the sub-10 nm regime.³²⁸ However, filaments in the size of 1–2 nm can be stable if they are stabilized by structural defects, such as grain boundaries or dislocations. Therefore, finding

materials solution for confining oxygen vacancies to the nanoscale might retain the required retention for devices in the few nm scale.

## 2. Speed

Although the extensive parallelism leads to high demands for scaling, it is considered an advantage as it makes the race for ever increasing clock frequencies obsolete.³²⁹ In contrast, the operation speed is closely linked to the respective application, i.e., the timing is based on real physical time.³²⁹ As signals processed by humans are typically on a time scale of milliseconds or longer, the expected speed benchmark is well below the reported speed limits of emerging NVMs. Nevertheless, it is reasonable to understand the ultimate speed limits of NVM concepts in order to estimate maximum learning rates, to explore the impact of short spiking stimulation. Furthermore, novel computing concepts, as discussed in Sec. VII, might still benefit from higher clock frequencies. For MRAM, reliable 250 ps switching has been demonstrated by using double spin-torque MTJs, which consist of two reference layers, a tunnel barrier, and a non-magnetic spacer.³³⁰ FeRAM arrays have successfully been switched with 14 ns at 2.5 V. Ferroelectric field effect transistors (FeFETs) have been shown to switch with <50 ns pulses in 1 Mbit memory arrays.⁹ PCM devices can be switched with pulses <10 ns.³²⁶ In general, their speed is limited by the crystallization time of the material. It has been shown exemplarily on GeₓSnᵧTe samples that this time can be tuned in a broad range of 25 ns up to 10 ms by adjusting the material composition.³³¹ Thus, it has a high potential to match the operation time of an NC system to the respective application. For VCM ReRAM, SET and RESET switching with 50 and 400 ps have been demonstrated.³³² Both are so far limited by extrinsic effects and device failure modes rather than by intrinsic physical rate limiting steps.

## 3. Reliability

Independent of the application, the reliability of the memory technology has to be taken into account. In the case of implementing NVMs as artificial synapses, the requirements of learning and inference phases have to be distinguished. Whereas the endurance is more relevant for learning schemes, the stability of the programmed state, i.e., the retention and robustness against read disturb, has to be sufficient for reliable inference operations.

## 4. Endurance

While MRAM has, in principle, unlimited endurance, all memristive devices that are based on the motion or displacement of atoms, such as ReRAM, PCM, and ferroelectric systems, have limited endurance. For silicon-based FeFETs, the endurance is typically on the order of 10⁵, which is mainly limited by a dielectric breakdown in the SiO₂ at the Si–HfO₂ interface.⁹ Regarding the endurance of VCM ReRAM, it has been demonstrated with convincing statistics that > 10⁶ cycles are realistic. Some reports suggest maximum cycle numbers of more than 10¹⁰.³²⁴ Depending on the material system, various failure mechanisms for endurance are discussed. The microstructure of the switching material might degrade or be irreversibly penetrated by metallic atoms.⁹ In VCM ReRAM, an excessive generation of oxygen vacancies was discussed as an endurance limiting factor.³³³ Novel material solutions, which confine ions to the intended radius of action, might be a pathway to increase the endurance of
ReRAM devices. For PCM, it was suggested to implement multi-PCM synapses. Arbitration over multiple memory elements might circumvent endurance and variability issues.⁹

A typical limitation with respect to a reliable operation of ferroelectric memories is the so-called wake-up effect, which causes an increasing polarization after a few cycles and the fatigue resulting in a decrease in the polarization for high cycle numbers. Both are induced by the motion of defects such as oxygen vacancies and will have to be tackled in the future by intense materials research in this field.

## 5. Retention

After training, the state of the non-volatile memory synapse is required to be stable for 10 years at an operating temperature of 85 °C. However, for many applications in the field of neuromorphic applications, the requirement is much more relaxed in particular for the training phase. From a thermodynamical point of view, the states in ferroelectric or ferromagnetic memories might both be stable. In contrast, ReRAM and PCM devices store information in the configuration of atoms where both low-resistance state (LRS) and HRS are metastable states and the retention is determined by material parameters, such as the diffusion coefficient of the respective species.⁹ Here, the degradation is not a digital flipping of states but a gradual process. For PCM, the drift of the resistance state is caused by the structural relaxation of the melt-quenched amorphous phase.²⁰² Apart from a drifting of the state, a broadening of the programmed state distribution (e.g., resistance) is typically observed for ReRAM.³³⁴ Furthermore, since analog or multi-level programming is highly relevant for NC, it should be considered that intermediate resistance states might have a reduced retention compared to the edge cases of high and low resistive states as demonstrated for PCM devices.⁹

## 6. Read disturb

During inference, frequent reading of the memory elements is required, which should not change the learned state. For a bipolar ReRAM memory, a read disturb in the HRS/LRS occurs mainly when reading with a SET/RESET polarity since the read-disturb can be considered as an extrapolation of the SET/RESET kinetics to lower voltages. Nevertheless, the HRS state in bipolar filamentary VCM has been demonstrated by extrapolation to be stable for years at read voltages up to 350 mV.³³⁵

## 7. Variability

Variability is most pronounced for systems that rely on the stochastic motion and redistribution of atoms, such as ReRAM and PCM. Here, the variability from device to device (D2D), from cycle to cycle (C2C), and even from one read to the next (R2R) has to be distinguished. By optimizing fabrication processes, the D2D variability can be kept comparatively low. In contrast, the C2C variability for filamentary resistive ReRAM and PCM can be significant due to the randomness of filament³³⁵ or crystal²⁰² growth, respectively. However, using smart programming algorithms, the C2C variability can be very well reduced to a minimum.³³⁵ By contrast, R2R variations remain in the form of read noise in filamentary VCM. It is typically attributed to the activation and deactivation of traps or the random redistribution of defects³³⁵ and strongly depends on the material.³³⁶ For PCM, R2R variations are caused by 1/f noise and

temperature induced resistance variations. One approach to address these issues as well as the drift is to use the so-called projected phase change memory with a non-insulating projection segment in parallel to the PCM segment.

Although the variability is a challenge for storage applications, it might be possible to design neuromorphic systems to exploit it.³²⁹ In the end, a thorough understanding of the intrinsic variability might enable to match neuromorphic applications and materials.³³⁶

## 8. Analog operation

For most computing concepts described in Sec. III, their operation with binary memory devices is strongly limited and the possibility to adjust multiple states is of crucial importance. For devices with thermodynamically stable states, such as ferroelectric or magnetic memory, intermediate states rely on the presence of domains. As a result, the performance strongly depends on the specific domain structure and scaling might be limited by the size of the domains. Nevertheless, multilevel switching has been demonstrated by fine-tuning of programming voltages for both FTJ and FeRAM.³³⁷

For ReRAM and PCM, the metastable intermediate states have to be programmed in a reliable manner. Since these states are kinetically stabilized during programming, the success depends strongly on the switching kinetics of the specific system, the operation regime, and the intrinsic R2R variability of the material. For PCM devices, intermediate states can be addressed by partial reset pulses, which result in partial amorphization. As a result of the crystallization kinetics, a gradual crystallization can be obtained by consecutive pulses.

Filamentary ReRAM devices usually undergo an abrupt SET, which is caused by the self-accelerating, thermally driven filament formation. However, it is possible to obtain intermediate states with good control of the SET current, by precisely controlling the timing of the SET voltage pulses, or by slowing down the switching kinetics. This is the case for non-filamentary systems, which show a very pronounced gradual behavior for both SET and RESET.³²⁷

Furthermore, resistive switching devices with purely electronic switching mechanisms, such as trapping and de-trapping of electrons at defect states, might be promising for analog operation.³³⁸

# B. Characterization techniques

Adnan Mehonic, Wing H. Ng, Mark Buckwell, Horatio R. J. Cox, Daniel J. Mannion, and Anthony J. Kenyon

## 1. Status

Memristive devices pose challenges to the experimentalist both in investigating the physics underpinning the device behavior and in optimizing functionality. The wide range of physical phenomena involved in memristance—from metal diffusion in dielectrics to Mott metal–insulator transitions, phase changes, and the formation of oxygen vacancy filaments—requires comprehensive physical, electrical, and chemical characterization and even the development
of novel analytical techniques.³³⁹ Here, rather than an exhaustive literature survey, we provide examples to illustrate the recent progress in characterization of memristive materials and devices. While we concentrate on oxide-based RRAM materials and devices for reasons of space, most techniques reviewed here are applicable to other memristor types (PCM, MRAM, and FeRAM), which require similar characterization of structural, chemical, and electrical changes occurring in devices as a result of operation. The challenges presented to the experimentalist, particularly when it comes to structural and chemical analyses, are largely similar across all memristive devices.

## 2. Challenges and potential solutions

Looking first at resistance switching materials and devices, we see that early work from the 1960s on dielectric breakdown suggested the formation of conductive filaments in electrically biased oxide³⁴⁰ and, while experimental techniques at the time were unable to image them, the authors correctly surmised their existence. The small sizes of these filaments, which can be of the order of a few nanometers in diameter, make studying their formation and disruption difficult. This is particularly true for oxygen vacancy filaments in oxides; the minimal contrast between the oxide matrix and the oxygen-deficient filament when imaged using electron beam techniques, such as TEM-EELS, means that there are few direct observations of such filaments. This contrasts with several published TEM studies of metal filaments in oxides, including the seminal work by Yang *et al.*,³⁴¹ which demonstrated field-driven movement of silver ions through $SiO_2$, $Al_2O_3$, and amorphous silicon to form dendritic conductive filaments. The large contrast between metal ions and oxide matrix makes it a more tractable problem to image individual conductive filaments. Subsequent work demonstrated different filament growth modes that depend on the relative magnitudes of metal ion mobility and the applied field.³⁴² The work by Waser *et al.*³⁴³ details earlier TEM work on electrical and physical characterization of resistive switching dielectrics, including observations dating from as early as 1976 of silver dendrites formed in AgS under the application of an external field. Here again, the contrast between the silver filaments and the surrounding matrix provides a significant advantage. It is worth noting that the use of TEM measurements to characterize phase change memory (PCM) materials and devices is rather easier than in the case of oxide-based RRAM as the contrast between amorphous and crystalline phases of PCM materials is easier to detect, although *in situ* and in operando measurements can pose significant challenges, thanks to the fast switching speeds of PCM devices.³⁴⁴

The difficulty of imaging oxygen vacancy filaments using electron beam techniques can be overcome using conductive atomic force microscopy (CAFM) tomography ("scalpel AFM"), a review of which can be found in Ref. 345. In this technique, sequential CAFM scans of a sample surface imaged using a conductive diamond tip contacting the sample with sufficient force to scrape away the surface provide layer-by-layer conductivity maps that, when stacked, provide three-dimensional images of conductive regions within the oxide. Such studies reveal that electroforming generates large-scale changes beneath device top electrodes, modifying the conductivity of large volumes of material, while one or more highly localized conductive filaments bridge the inter-electrode gap. The technique

also reveals details of the internal microstructure of the oxide, showing, for example, the columnar structure of sputter-deposited oxides, as the edges of columns are more conductive than their cores.³⁴⁶ It should be noted that this technique only maps conductive regions that are connected to the bottom electrode, so they may be better thought of as a measure of *connectivity* rather than of regions of high conductivity.

The need to apply multiple analysis techniques to probe the movement of oxygen within, and emission of oxygen from, oxides under electrical stress was demonstrated by Mehonic *et al.*³⁴⁷ TEM, EELS, CAFM, XPS, and mass spectrometry measurements of oxygen emission from samples under electrical stress combine with atomistic modeling to give a fuller picture of the dynamics of oxygen movement and its role in resistance switching. It is clear from such measurements that electrically biasing oxides—particularly those with some structural inhomogeneities—can drive large-scale changes in stoichiometry, reinforcing the CAFM tomography results referred to above. It has been known for some time that this can cause surface distortions and localized bubbling of both electrode and oxide surfaces.³⁴⁰,³⁴⁸ While the work reported in Ref. 347 examines such features using AFM and TEM, the question of how mobile oxygen interacts with electrode materials is partly addressed in a recent work by Cox *et al.*³⁴⁹ Oxide-based RRAM devices rely on the repeated reduction and oxidation of the switching oxide. To compete with high density flash, at least $10^4$ cycles are required, and for many applications, more than $10^7$ are needed. For such high numbers of cycles, oxygen should not be lost from the switching region around the conductive filament, implying the need for an oxygen reservoir that can both accommodate and release oxygen under appropriate electrical biases. This may be within the oxide, at an oxide/electrode interface, or within one or the other electrode. The need to measure oxygen movement is critical. Cox *et al.*³⁴⁹ demonstrated that both the electrode material and the microstructure of the oxide layer influence the reversibility of oxygen movement. In the case of electrode metals with high oxygen affinities, oxygen moves easily from the oxide into the electrode, but its movement back again varies significantly between metals. Molybdenum, for example, both accepts and releases oxygen readily when the bias polarity is reversed, while titanium is easily oxidized when positively biased (and when neutral) but does not release oxygen back again when negatively biased. Platinum, having a very low electron affinity, does not accept or release oxygen.

Oxide porosity and sensitivity to moisture are important factors in resistance switching both by metal diffusion (extrinsic switching) and oxygen vacancy formation (intrinsic switching).³⁵⁰ The presence of moisture in the switching oxide can lead to a highly variable resistance switching behavior. While the origin of such effects remains somewhat unclear, electrical measurements must be interpreted with care in the presence of moisture. The difficulty in measuring hydrogen content in materials and devices reliably and quantitatively is a particular challenge, not only for RRAM but also for other memristive devices. Hydrogen, even in relatively low concentrations, can affect the electrical properties of oxides and electrode stacks, as has been recognized for decades in the CMOS community. However, there have been very few studies on the role of hydrogen in memristive devices. At the same time, there is considerable interest in reducing variability and increasing stability in memristors. One cannot help but suppose that detailed
studies of hydrogen, and control of its presence, could help these efforts.

Electrical characterization of memristive devices poses other challenges. A critical issue in RRAM is electroforming conductive filaments. While some materials and devices are forming-free, the majority require an initial conditioning step in which a voltage higher than the normal programming (SET or RESET) voltages is applied to form a conductive filament that will subsequently be partially oxidized (RESET) and reduced (SET) by a sequence of voltage sweeps or pulses. Electroforming causes an abrupt drop in oxide resistance, which can span several orders of magnitude, over a timescale of nanoseconds or shorter. Without an appropriate limit on delivered current, this can destroy the device by irreversible oxide breakdown due to Joule heating. It is, therefore, essential to implement fast current limiting during electroforming. Response times of standard characterization instruments are generally too long, so current overshoots can over-stress the oxide, leading to breakdown or to conductive filaments too large (hence, too strong) to reset. Consequently, full electrical characterization of devices requires integrated current limiting devices, such as transistors or series resistors. Care must be taken to avoid parasitic capacitances or inductances, so the most reliable methods involve on-chip series resistors or transistors in the 1R1R or 1T1R configurations, where the first R or T label refers to the integrated current limiter (resistor or transistor) and the second R refers to the resistance switching element.

On the other hand, electrical characterization of RRAM devices can reveal important clues to the physical mechanisms responsible for resistance switching. Careful analysis of current/voltage curves can indicate a range of electron transport mechanisms, including various forms of tunneling (direct, trap-assisted, and Fowler-Nordheim), thermally assisted transport (Poole-Frenkel), and Ohmic conduction. These, in turn, provide evidence for microscopic processes, such as charge trapping/detrapping, formation of Schottky barriers, or various interface-related electronic states. However, more than one transport mechanism may contribute as, for example, currents may flow in parallel both through a conductive filament and through a highly defective surrounding oxide.³⁵¹ In the case of nanoscale filament formation, the thinnest point of the filament can behave as a quantum constriction, allowing only currents that are multiples of the conductance quantum, G₀, to flow. Such effects can be seen easily at room temperature.³⁵¹ Reviews of electrical characterization techniques for resistance switching devices can be found in Refs. 324 and 352.

### 3. Concluding remarks

The inherently interdisciplinary approach that is needed to fully characterize memristive devices poses challenges to the experimentalist. A wide range of techniques are required, which is often beyond the capabilities of a single laboratory, and in some cases, these techniques are operating close to their limits. While there have been significant advances in characterization (CAFM tomography, for example), more work is needed, for instance, to better characterize the role of hydrogen in resistance switching. Where characterization has been most successful has been when there is close collaboration, not only between experts in different experimental techniques but also with theorists who provide models to interpret experimental results.

## C. Comparison between different material systems

Yuchao Yang and Yingming Lu

### 1. Status

Various types of memristors can be realized based on the abundant resistive switching mechanisms in different materials. Each type of memristor has certain characteristics (such as power consumption and switching speed) that are suited for specific applications, while different materials also have their own shortcomings and limitations. A clear understanding of the respective advantages and shortcomings of each material is key to its development and application.

Among various types of resistive switching materials, transition metal oxides (TMOs) are the most widely used due to their rich resistive switching mechanisms and characteristics. The retention time of TMO-based memristive devices, which indicates how long the resistive state can be maintained after electrical stimulation, is distributed in a wide range from µs to years. According to the retention time, TMOs can be generally divided into non-volatile TMOs and Mott TMOs.

The resistive switching of non-volatile TMOs, such as HfOₓ and TaOₓ, originates from the migration and redox reactions of oxygen ions or vacancies driven by an external electric field or thermal effects, which in turn create or destroy conductive filaments between the electrodes. The filaments can exist stably for a long time, and the continuous electrical modulation of geometric characteristics of the filaments, such as their lengths or diameters, results in multi-level resistive states. Therefore, the non-volatile TMO can be used to imitate the long-term plasticity (LTP) of biological synapses¹⁶⁹ and can accelerate the computationally intensive matrix-vector multiplication (MVM) in artificial neural networks. Furthermore, due to the mature and CMOS-compatible manufacturing process, a variety of in-memory computing chips based on non-volatile TMOs have been demonstrated.⁵⁶ One of the challenges of non-volatile TMO in circuit applications is the existence of the forming process, which requires a high voltage to initialize the TMO layer and subsequently increases the requirements for the voltage and robustness of peripheral circuits. In addition, due to the switching mechanism of non-volatile TMOs, the conductance change during the programming process usually shows nonlinear characteristics, along with obvious variations and noises, which increases the difficulty of programming, for example by necessitating closed-loop write-and-verify programming.

There are many other similar TMO systems, such as WOₓ and TiOₓ. Depending on the robustness of the formed filaments, the retention time can be gradually reduced as a result of filament dissolution, and the conductance of volatile TMOs can undergo a continuous decay process. This can effectively map information in time series into high-dimensional vectors, which is widely used in reservoir¹⁸⁴ for image classification or time series prediction.

Mott TMOs, mainly including VO₂ and NbO₂, show high resistance in body-centered tetragonal (BCT) or monoclinic (M) phases at low temperatures. Once the temperature of Mott TMOs exceeds a threshold, the reversible Mott transition occurs and results in
structural transition into the rutile (R) phase, accompanied by a sig-
nificant resistance drop. Based on threshold switching, Mott TMOs
are widely used in artificial neurons for constructing neuromor-
phic computing or sensory systems.³⁵³ Meanwhile, the nonlinear
transport mechanism of NbO₂ shows high-order complexity dur-
ing current sweeps, which can effectively realize the rich dynamics of
biological neural systems.⁷ However, as the Mott transition is closely
related to temperature, the operation of Mott TMOs can be affected
by ambient temperature. On the other hand, this could serve as
the physical foundation for temperature sensing. Furthermore, the
metallic domains produced by previous switching events have been
found to remain in VO₂ for a long time, which will affect the switch-
ing threshold voltage of the devices³⁵⁴ subsequently. The transition
temperatures of VO₂ and NbO₂ are around 70 and 800 °C, respec-
tively, which are too low and too high from the perspective of circuit
applications. A Mott TMO with ideal transition temperature is yet
to be developed.

Phase change materials mainly refer to chalcogenide glass materials with reversible phase transition processes. Phase change materials show high resistance in the amorphous state and relatively low resistance in the crystalline state. The phase change memory (PCM) constructed by these materials shows multilevel non-volatile conductance states, and hence, PCM can also be exploited to accelerate MVM combined with a crossbar.<sup>355</sup> Traditional phase change materials are the ternary GeSbTe compounds along the pseudo-binary tie lines of GeTe–Sb<sub>2</sub>Te<sub>3</sub>, Ge–Sb<sub>2</sub>Te<sub>3</sub>, and GeTe–Sb.<sup>356</sup> By adjusting the proportions of the three elements in the compound or by incorporating other elements into the compound, these phase change materials can exhibit advantages in various aspects, such as ON/OFF ratio, switching speed, and retention. Among these materials, Ge<sub>2</sub>Sb<sub>2</sub>Te<sub>5</sub>, with its outstanding recyclability, is currently widely used and has been applied in commercial products. In addition to compound-type phase change materials, monatomic Sb exhibits completely different resistances in the crystalline and amorphous states, making it also suitable as a phase change material.<sup>357</sup> This type of simplest material can effectively avoid the problem of stoichiometry deviation during the phase change process, which is important for further reducing the size of PCM devices. One of the challenges faced by PCM comes from its conductance drift, caused by the spontaneous structural relaxation in unstable amorphous materials, which leads to a gradual conductance decay over time and seriously affects computing accuracy and reliability. Therefore, a compensation circuit or strategy for conductance drift is desired. Another challenge originates from the long heating time required for the crystallization of PCM, which not only affects the programming speed<sup>358</sup> but also results in higher energy consumption during programming.

In addition, magnetic material-based magnetic random access
memory (MRAM) is also widely used in neuromorphic computing,
which has relatively mature technology, high endurance, etc. The
typical structure of MRAM is a magnetic tunnel junction (MTJ),
which is composed of two layers (pinned and free) of a magnetic
material and an insulator (usually MgO) sandwiched in between.
There are two types of magnetic materials mainly used in MTJs.<sup>359</sup>
The first one is the multilayers formed by transition metals (e.g.,
Co and Fe) and noble metals (e.g., Pt and Pd), such as (Co/Pd)<sub>n</sub>
and (Co/Pt)<sub>n</sub>. These materials have advantages in terms of ther-
mal stability and scalability. Another important magnetic material

is CoFeB, which shows extremely low programming currents and
good matching with the lattice of the MgO barrier layer. By tuning
the magnetization orientations of the free magnetic layer to parallel
(P) or antiparallel (AP) orientation with the pinned layer, MTJs can
exhibit low or high resistance, respectively. Because only the mag-
netization orientation of the material is changed without large-scale
atomic migration or rearrangement, MRAM has low device varia-
tion and high reliability. However, the main shortcoming of MRAM
is reflected in its relatively low resistance even in the high resistance
state,⁷⁵ which will increase the power consumption for MVM com-
puting. Moreover, it has a small ON/OFF ratio, which supports only
two states, indicated P and AP, and limits its applications in analog
computing.

Similar to MTJs, ferroelectric tunneling junctions (FTJs) also
change their resistance by adjusting the polarization orientations
of the ferroelectric material sandwiched between two metal elec-
trodes. The commonly used ferroelectric material systems include
perovskite oxides, fluorite ferroelectric materials, and wurtzite fer-
roelectric materials. Perovskite oxides are the most widely used
ferroelectric materials with advantages of scalability and switch-
ing speed.³⁶⁰ Among these materials, Pb[ZrₓTi₁₋ₓO₃] (PZT) and
Sr₂Bi₂TaO₉ (SBT) have more mature technology and have been
applied in commercial memory devices. The fluorite ferroelectric
materials, such as HfZrO₂, are also widely utilized and studied due
to their CMOS-compatible fabrication process and good scalabil-
ity.³⁶¹ The wurtzite materials, such as Al₁₋ₓScₓN, belong to a new
type of ferroelectric material system, characterized by their high
ON/OFF ratio, thermal stability, and retention.³⁶² Since the polariza-
tion orientations of the ferroelectric layer can be tuned by the electric
field with a very low tunneling current, the programming of FTJs
consumes low power. Meanwhile, the FTJ shows multilevel conduc-
tance³⁶³ for MVM acceleration in the edge AI platforms. However,
ferroelectric materials can have retention degradation caused by
intrinsic depolarization fields in the ferroelectric layer, while recent
Hafnium Zirconium Oxide (HZO) based ferroelectric materials
exhibit relatively high coercive voltages and low endurance.

Ion-gated transistors (IGTs) are a type of three-terminal device,
where the electric field from the gate drives small ions (such as H⁺
and Li⁺) in electrolytes into the device channels to continuously tune
the conductance of the channel.<sup>364</sup> Among the reported material sys-
tems for IGTs, the most chosen material for channel is TMOs, which
shows the potential for mass production and environmental stabil-
ity. For the material consideration of electrolyte, the phosphosilicate
glass shows clear advantages over previously used Li-ions elec-
trolyte, which is more mature and compatible in the COMS process
platform. Owing to the low gate leakage current and separated pro-
gramming and reading terminals, the IGT shows significantly lower
power consumption during programming compared with most two-
terminal devices. Furthermore, the weight modulation of IGTs can
be much more linear, which can greatly reduce the overhead for
weight programming compared with devices based on other mate-
rials. However, the IGT devices shown to date usually have lower
compatibility with standard fabrication processes and have difficulty
in the fabrication of large-scale arrays.

## 2. Conclusion

In conclusion, memristors based on resistive switching mate-
rials with different mechanisms have demonstrated a variety of
encouraging characteristics, such as low power consumption, high scaling potential, fast switching speed, long retention, multilevel conductance, and high-order complexity. The MVM engines, artificial neurons, artificial synapses, and sensory systems constructed using memristive devices have shown great potential in highly efficient and functional neuromorphic computing. However, depending on the specific resistive switching mechanism, technological maturity, and manufacturing cost, there are still technical challenges related to the above material systems. It is important to compensate and correct the adverse effects existing in the application of the materials through the improvement from materials, systems, and even algorithms, such as reducing the impact of conductance drift and programming noise on the accuracy of PCM based convolutional neural networks (CNNs) by improving the training algorithms.¹⁷⁵ On the other hand, we can also design systems and algorithms to exploit the non-ideal effects in various memristors as resources for improving computational efficiency, such as utilizing the variations and noise in memristor arrays for accelerating the convergence of Hopfield neural networks.²⁰⁰ Once the physical attributes of the memristive devices are properly utilized, they can play important roles in efficient neuromorphic computing.

# VII. NOVEL COMPUTING CONCEPTS

## A. Embracing variability

Damien Querlioz, Louis Hutin, and Elisa Vianello

### 1. Status

Emerging nanoelectronic components, such as memristors and spintronic devices, offer exceptional features. However, these devices also exhibit a high degree of variability in their behavior due to their atomic-level features and reliance on sophisticated, sometimes incompletely understood, physics. This variability has made it necessary to model these devices using statistical tools, effectively treating them as random variables. Interestingly, multiple applications, particularly in machine learning and security, require random variables, which are expensive to generate using the traditional CMOS technology. Therefore, exploiting the inherent variability of these nanodevices presents a unique opportunity to develop efficient random number generators and stochastic computing models (see Fig. 16).

<figure><img src="image_27.png" /><figcaption>FIG. 16. Illustration of some leading approaches exploiting the variability of nanodevices for computing. Top: measurements of the programming variability of hafnium-oxide filamentary memristors. The statistical rule that this variability naturally implements can be used to perform Markov chain Monte Carlo training. Bottom: measurement of stochastic magnetic tunnel junctions, naturally implementing p-bits, used, for example, in Ising machines. Both devices can also be used for random number generation.</figcaption></figure>