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Memristor for parallel and analog data processing in the era of big data
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Memristor for parallel and analog data processing in the era of big data
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Content
MEMRISTOR FOR PARALLEL AND ANALOG DATA PROCESSING IN THE ERA OF BIG DATA
by
Ye Zhuo
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2023
Copyright 2023 Ye Zhuo
Dedication
To my family.
ii
Acknowledgements
I would like to express my deepest gratitude to my Ph.D. advisor, Professor Jianhua (Joshua) Yang, for
his invaluable guidance and mentorship. He not only taught me the importance of conducting research
with integrity but also fostered a collaborative and supportive environment. His extraordinary patience
has had a profound impact on my academic journey.
Throughout my pursuit of a Ph.D., I have been incredibly fortunate to come across numerous individ-
uals who have shown me tremendous kindness. I want to sincerely thank all those with whom I have had
the privilege of interacting over the past seven years. I am profoundly grateful for their acts of kindness
and unwavering support.
Lastly, I must acknowledge that my family and friends have played an indispensable role in shaping the
person I am today. Without their love and support, I would not have reached this point. I am truly grateful
for their presence in my life and would like to take this opportunity to extend my heartfelt appreciation
to each and every one of them.
iii
TableofContents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Abbreviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2: A Dynamical Compact Model of Diffusive and Drift Memristors for Neuromorphic
Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3.1 Geometries, typical electrical performance of the Pt/SiO
2
:Ag/Pt diffusive and
Ta/HfO
2
/Pt drift memristors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3.2 Schematic conduction channels of the Pt/SiO
2
:Ag/Pt diffusive and Ta/ HfO
2
/Pt
drift memristors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3.3 The static equations of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.4 The dynamic equations of the model . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.4.1 Explanation of variables and parameters in the model . . . . . . . . . . . 11
2.3.5 Experimental data and modeling results for a Pt/SiO
2
:Ag/Pt diffusive memristor . 12
2.3.6 Experimental data and modeling results for Ta/HfO
2
/Pt cross point memristor . . 15
2.3.7 Experimental data and modeling results for ’other’ memristors . . . . . . . . . . . 16
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Experimental Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Chapter 3: An artificial spiking afferent nerve based on Mott memristors for neurorobotics . . . . 20
3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3.1 Schematic of a spiking somatosensory system . . . . . . . . . . . . . . . . . . . . . 24
3.3.2 Device characteristics and modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.3 Working principle of the ASAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.4 The ASAN with an external capacitor . . . . . . . . . . . . . . . . . . . . . . . . . 31
iv
3.3.5 Power-free artificial spiking mechanoreceptor system . . . . . . . . . . . . . . . . 35
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Experimental Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Chapter 4: Early Prevention of Heart Attacks Using Memristor-Based Machine Learning and
Surface Enhanced Raman Spectroscopy with Collapsible Nanofinger . . . . . . . . . . . 40
4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Early Prevention System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.1 Biomarkers and Receptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3.2 Human Serum Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3.3 Nanofinger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.3.1 Nanofinger Fabrication and Characteristics . . . . . . . . . . . . . . . . . 46
4.3.3.2 Nanofinger Working Mechanism . . . . . . . . . . . . . . . . . . . . . . 47
4.3.3.3 Nanofinger Enhancement Ratio . . . . . . . . . . . . . . . . . . . . . . . 47
4.3.4 Raman Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3.5 Hardware Computing Acceleration with Memristor Arrays . . . . . . . . . . . . . 50
4.3.5.1 Computing Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3.6 Neural Network Classification and Prediction . . . . . . . . . . . . . . . . . . . . . 51
4.3.6.1 Principal Component Analysis (PCA) . . . . . . . . . . . . . . . . . . . . 52
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
v
ListofFigures
2.1 Geometries, typicalelectricalperformance, andschematicconductionchannels
of the Pt/SiO
2
:Ag/Pt diffusive and Ta/ HfO
2
/Pt drift memristors (a, c) Optical
microscopic images of a Pt/SiO
2
:Ag/Pt diffusive memristor (scale bar: 50 µ m) and
Ta/HfO
2
/Pt drift memristor crossbar (scale bar: 20µ m), respectively. The inset shows a
schematic illustration of the device stack. (b) A typical pulse-switching curve from a 5 by
5µ m
2
Pt/SiO
2
:Ag/Pt diffusive device revealing the dynamics of the resistive switching
behavior; (d) A typical I-V curve from a 5 by 5µ m
2
Ta/HfO
2
/Pt drift memristor cross point
showing the nonvolatile resistive switching behavior; (e, f, g) Schematics of switching
mechanisms (colors of the different layers match those of the layers in Figure ( a) and (c)
insets ), (e), conducting channel length changes under external electrical stimuli. (f), the
middle stage when the conduction channel reaches the limiting value; (g), conducting
channel shape changes under a continued external electrical stimulus. (h) Schematic of
the SPICE circuit model implementation of a drift/diffusive memristor cross point. . . . . . 7
2.2 ExperimentaldataandmodelingresultsforaPt/SiO
2
:Ag/Ptdiffusivememristor.
(a) Experimental (dashed, purple) and modeled (solid, red) pulse-switching curve. The
blue curve is the input voltage pulse. (b) A magnified view of the current range from
0 to 10µ A in Figure (a). (c) Plot of the conduction channel length (blue) and area (red)
simulated for this device over time. (d) Experimental (dashed, purple) and modeled (solid,
red) switching I-V curve with current on a log scale. (e-f) Statistical experimental result
(box plots) and simulation results (red line) of the delay time and relaxation time of this
device under different pulse amplitude (0.8-1.2V) and same 1ms pulse length. ( g-h) )
Statistical experimental result (box plots) and simulation results (red line) of the delay
time and relaxation time of this device under same pulse amplitude (1V) and different
pulse length (0.5-1.5ms). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Experimental data and modeling results for Ta/HfO
2
/Pt cross point memristor.
(a) Experimental (dashed, purple) and modeled (solid, red) pulse-switching curve. The
blue curve is the input voltage pulse. (b)A magnified view of the current range from 0 300
µ A in Figure (a). (c) Plot displays the simulated conduction channel length (blue) and
area (red) in this device over time. (d)Experimental (dashed, purple) and modeled (solid,
red) switching I-V curves on a log current plot, showing very good agreement. . . . . . . . 14
vi
2.4 Experimentaldataandmodelingresultsfor’other’memristors (a) The measured
and simulated (Equation 2.5 and 2.6) multi-channel switching I-V curves (b) The measured
and simulated unipolar switching of Pd/TiO2/Pd (n = 8,m = 2 in Equation 2.3 and 2.4)
(c) Plot of the conductance (weight) change of the drift memristor with difference in time,
showing the spike-timing-dependent plasticity of an electronic synapse, which emulates
the timing-dependent response of biological synapses. . . . . . . . . . . . . . . . . . . . . . 17
3.1 Biological afferent nerve vs. artificial afferent nerve. (a) Schematic of the afferent
nerve of a biological somatosensory system. Action potentials are generated in the skin
and transported to the brain for processing. Spiking frequency increases with increasing
stimuli intensity and decreases under strong stimuli due to protective inhibition. (b) The
artificial spiking somatosensory system consists of a mechanical sensor and an artificial
spiking afferent nerve (ASAN) made of a resistor and a NbO
x
memristor. The spiking
frequency shows a similar trend to that seen in its biological counterpart, which is then
transmitted to the spiking neural processing unit for further processing to complete a
complex task. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 NbO
x
device analysis. (a) Scanning electron micrograph cross-sectional image of the
NbO
x
device. (b-f) The elemental mapping of the materials in the system for Si, O, Nb,
N, and Ti, respectively. (g,h) Zoom-in views of the channel locations. (i) The diffraction
pattern extracted by Fourier transform of h. (j) Energy dispersive spectra (EDS) of line
scans of the channel. (k) Two switching cycles under triangular waves with a 2.5 V/100
µ s ramp rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Characteristicsoftheartificialspikingafferentnerve(ASAN). (a) Schematic of the
ASAN. A resistor R
c
(75 kΩ ) and a NbO
x
memristor with parallel parasitic capacitance
are combined together (R
HRS
≫ R
c
≫ R
LRS
). In real applications, the voltage on the
NbO
x
top electrode serves as the output spiking signal. The parasitic capacitor (C
parasitic
)
is tested to be about 20 pF. (b) The oscillation behavior of the ASAN. For the sake of
simplicity, the current flowing through the memristor is measured as the response. The
charging time from V
H
to V
TH
is defined as the integration time and the discharging time
from V
TH
to V
H
as the relaxation time. (c) ASAN response under different input voltages.
(d) Extracted mean value of spiking frequency vs. voltage inc. (e) Frequency response of
the ASAN with triangular stimuli pulses. (f) The quasi-linear frequency–voltage curve
extracted frome. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 artificial spiking afferent nerve (ASAN) with an external capacitor (a) Schematic
of the ASAN with an external parallel capacitor (4.7 nF). (b) Frequency response with
different input voltages. ( c) The frequency–voltage curve with two stages: the excitatory
spiking stage under low input voltages and the protective inhibition stage under high
voltages. (d-f) The frequency response with a sinusoidal signal as input. (d,f) The input
signals only with a positive voltage, protective inhibition can be observed inf which has
a higher amplitude. (e) An input sinusoidal signal without bias, where the oscillation
behavior can be obtained upon applications of both positive and negative voltage. . . . . 31
vii
3.5 Illustrationoftheartificialspikingmechanoreceptorsystem(ASMS) (a) Schematic
of the ASMS. A piezoelectric device is used as the tactile sensor and connected with the
artificial spiking afferent nerve. The voltage generated by the piezoelectric device serves
as the input signal. (b) The experimental data of the ASMS. (c-f) A closer view of b, the
protective inhibition behavior can be observed in c. (g) The frequency response of the
ASMS under different pressure intensities. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1 Schematic of the proposed Early Prevention System, which is comprised of Nanofinger
Platform, Memristor Crossbar identification, and Early Intervention . . . . . . . . . . . . . 44
4.2 Left: A transmission electron microscopy (TEM) image and scanning electron microscopy
(SEM) image of the nanogap after the nanofinger collapsed. Right: The numerical
simulation of the electric-field enhancement of a collapsed nanofinger. . . . . . . . . . . . 46
4.3 Raman signals of serum from healthy and patient individuals were collected using the
nanofinger platform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4 Scanning Electron Microscope of the 1T1R device inside a crossbar array (Scale Bar 20µ m) 50
4.5 Photograph of a probe card in contact with an operational 128 × 64 1T1R array (scale bar
500µ m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.6 The Comprehensive Architecture of the 1T1R Measurement System for Neural Network
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.7 Accuracy Evolution of the Memristor Neural Network during Training. The accuracy
gradually increases over the course of training, showcasing the network’s learning
capabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
viii
ListofAbbreviations
1S1M one-selector-one-memristor
1T1R One Transistor One Memristor
ALD atomic layer deposition
AMI acute myocardial infarction
ASAN artificial spiking afferent nerve
ASMS artificial spiking mechanoreceptor system
BNP brain natriuretic peptide
CMOS complementary metal-oxide semiconductor
EDS Energy dispersive spectra
HRS high resistance state
LRS low resistance state
MIM Metal-Insulator-Metal
NDR negative differential resistance
ix
NIL nanoimprint lithography
NVM nonvolatile memory
ORO organic ring oscillator
PCA Principal Component Analysis
SEM scanning electron microscopy
SERS surface-enhanced Raman spectroscopy
SNN spiking neural network
SPICE Simulation Program with Integrated Circuit Emphasis
STDP Spike-Timing-Dependent Plasticity
TEM transmission electron microscopy
WGFMU waveform generator/fast measurement unit
x
Abstract
This thesis comprises three works that utilize emerging semiconductor devices, specifically memris-
tors, to address three key challenges in the era of big data. These advancements have the potential to
accelerate data processing and other applications.
In Chapter 2, we focus on modeling various types of memristors. Our objective is to facilitate the sim-
ulation of memristor applications without the need for physical fabrication. We investigate the underlying
mechanisms of several memristors and propose a set of formulas that can accurately emulate three typical
types of memristors. Additionally, we demonstrate the application of this model in the construction of a
circuit capable of emulating Spike-Timing-Dependent Plasticity (STDP) learning.
Chapter 3 presents the design and proposal of an artificial receptor based on a NbO
2
memristor. This
receptor serves as an interface, analogous to an afferent nerve in biology, that converts analog signals
from sensors into spikes within spiking neural networks. The spiking frequency of the afferent nerve
is proportional to the stimulus intensity until it encounters noxiously high stimuli, at which point the
spiking frequency begins to decrease at an inflection point. Leveraging this afferent nerve, we further
develop a power-free spiking mechanoreceptor system that utilizes a passive piezoelectric device as a
tactile sensor. Experimental results indicate the promising potential of our afferent nerve in constructing
self-aware neurorobotics in the future.
In Chapter 4, we propose a novel approach to early detection and prevention of heart attacks, em-
ploying memristor-based machine learning and plasmon-enhanced Raman spectroscopy with collapsible
xi
nanofingers. Our system offers a simple, low-cost, and rapid detection time of only 10 seconds, providing
accurate warnings of silent heart-attack attempts prior to actual attacks. By utilizing a memristor-based
array for classification, we can leverage the unique properties of memristors, such as improved speed and
energy efficiency, to achieve high precision and accuracy above 90%, potentially even in portable devices.
Our demonstrations suggest that memristor-based machine learning has the potential to revolutionize
heart attack detection and prevention, opening up a promising new avenue for improving patient out-
comes.
xii
Chapter1
Introduction
Big data is characterized by three fundamental concepts: variety, velocity, and volume. These concepts
also represent the critical challenges that must be addressed when constructing large-scale AI systems in
the era of big data: variety, velocity, and volume.
In the big data era, data manifests in diverse types and formats, including temporal and spatial infor-
mation, videos, images, and text. Efficient processing of such data necessitates appropriate hardware, such
as memristor devices, within the circuit. When developing a large-scale AI system based on memristors,
it is essential to consider the variety of memristors employed for data processing. For instance, temporal
data can be processed using dynamical volatile memristors as neurons, while images require non-volatile
devices as synapses to store weights during the training process. To address this, we propose a dynami-
cal compact model capable of simulating various memristors employed in large-scale circuit design. The
compact model is well-suited for designing extensive circuits, and notably, it accurately reproduces the
dynamic behavior of memristors, which poses a challenge for most existing models. Refer to Chapter 2 for
detailed information. This work was submitted to Advanced Electronic Materials[122].
In the real world, different types of sensors are deployed to detect and respond to a wide range of
inputs from the physical environment. The output data from these sensors is expected to be generated
endlessly and rapidly. However, traditional architectures store sensing data in one location and process it
1
at another, resulting in a slowdown in the real-time processing of sensor-generated data. Consequently,
the prompt processing of real-time sensor data presents a challenge for current computer architectures.
To address this, we propose a self-powered artificial spiking mechanoreceptor system that integrates a
sensor with a dynamical memristor processor. This seamless integration operates in the analog domain,
converting analog signals into spike frequencies. As a result, the system becomes compact and efficient in
processing data. In essence, this system serves as an interface between the environment and the spiking
neural network within a large-scale AI system, facilitating accelerated processing of real-time data. Further
details can be found in Chapter 3. This work was submitted to Nature communications [119]
The exponential growth of data volume demands suitable systems for processing such large amounts
of data. A large memristor array, capable of parallel and analog data processing, emerges as an appropriate
solution. Particularly, the utilization of a One Transistor One Memristor (1T1R) array enables parallel and
analog data processing, thereby reducing data access waiting time. In Chapter 4, we present a heart attack
early prevention system based on a memristor 1T1R array with nano-fingers. For more comprehensive
information, please refer to that chapter.
2
Chapter2
ADynamicalCompactModelofDiffusiveandDriftMemristorsfor
NeuromorphicComputing
2.1 Abstract
Different from non-volatile memory applications, neuromorphic computing applications utilize not
only the static conductance states but also the switching dynamics for computing, which calls for compact
dynamical models of memristive devices. In this work, we present a generalized model to simulate diffusive
and drift memristors with the same set of equations, which have been used to reproduce experimental
results faithfully. We chose the diffusive memristor as the basis for our generalized model because it
possesses complex dynamical properties that are difficult to model efficiently. A data set from statistical
measurements onSiO
2
:Ag diffusive memristors was collected to verify the validity of the general model.
As an application example, spike-timing-dependent plasticity was demonstrated with an artificial synapse
consisting of a diffusive memristor and a drift memristor, both modeled with this comprehensive compact
model.
3
2.2 Introduction
Memristors [11][104] are considered a promising candidate for the next-generation nonvolatile mem-
ory (NVM) and hold much potential for bio-inspired computing [29][42][118][54][55][15], machine learn-
ing [91][88][66][107], and other applications [95][27][109][98][87]. Different types of memristors have
been fabricated using a variety of materials[96][28][18][92][8], and their properties vary significantly.
Complicated neuromorphic architectures have been constructed by combining different kinds of memris-
tors. Drift memristors as memory devices to store information have been widely demonstrated and can be
used as computing elements for vector-matrix-multiplications in high-density[91][88][66] and large-scale
arrays[107][41][94][44][3].
While drift memristors have been extensively used as synaptic devices to mimic synapses, the dynam-
ical plasticity of biological synapses cannot be faithfully realized by drift memristors alone. In contrast
to non-volatile drift memristors, purely diffusive memristors exhibit volatile threshold switching with dif-
fusion dynamics that emulate biological systems[29][92][56][106]. Such dynamics in combination with a
drift memristor yield a more faithful emulation of synaptic plasticity observed in synapses[92][105][65].
Because of the increasing complexity of computational tasks and applications, a single type of mem-
ristor is usually not capable of meeting all the requirements for neuromorphic circuit design; hence using
a combination of drift and diffusive memristor is a more desirable way to meet the demands[92]. In the
implementation of such applications, reliable, efficient and accurate compact models are needed for sim-
ulation and design of large circuits[37][4][112][121][1][76]. Different modeling techniques and different
materials could lead to different memristor models, even for the nominally same device structure. While
many aspects of memristor modeling have been widely studied[4][112][76][111][120][78][116][32], the
execution time of complete physics models for understanding detailed mechanisms is much too long to be
useful for circuit simulation. In addition, using specific models for different memristor types significantly
complicates simulation.
4
In this paper, a comprehensive compact model based on the device physics for both drift and diffu-
sive memristors is presented and quantitatively verified by comparison to experimental data. This model
possesses the nonvolatile memory of a drift memristor and faithfully emulates the long and short-term
dynamics of a diffusive memristor, utilizing different parameters for the materials used in these two device
types. By tuning the parameters, this model can also be used to reproduce the behaviors of unipolar and
multi-conduction channel bipolar switching devices. Spike-Timing-Dependent Plasticity (STDP) observed
in biological synapses was emulated and experimentally demonstrated by combining a drift and a diffu-
sive memristor in a one-selector-one-memristor (1S1M) configuration. A good agreement between the
simulation and the experimental data for STDP was achieved.
2.3 Results
2.3.1 Geometries, typical electrical performance of the Pt/SiO
2
:Ag/Pt diffusive and
Ta/HfO
2
/Ptdriftmemristors
Figure 2.1(a) shows an optical microscopic image of a diffusive memristor considered in this paper, and
the inset illustrates the material stack of a 5 by 5µ m
2
device, which consists of a 15 nm thick Ag doped
SiO
2
switching layer with Pt bottom and top electrodes (See Experimental Section for details). Switching
driven by voltage pulses for a Pt/SiO
2
:Ag/Pt diffusive memristor is shown in Figure 2.1(b). The dynamical
properties of diffusive memristors were studied by applying a square voltage pulse and measuring the cor-
responding current output. As the voltage was increased from 0 to 1V with a current compliance of 60µ A
(a transistor was connected in series with the diffusive), an abrupt increase in current was observed after
a characteristic delay time. The current jumped abruptly by several orders of magnitude at the beginning
5
of the switching process and then slowly increased further while under bias as the conduction channel di-
ameter grew. After the magnitude of the voltage pulse decreased to 0.08V(Reading Voltage), the resistance
gradually relaxed back to its initial high state after a characteristic relaxation time.
An optical microscope image of a Ta/HfO
2
/Pt drift memristor with 5 by 5 µ m
2
cross point area is
shown in Figure 2.1(c). The Metal-Insulator-Metal (MIM) structure is schematically illustrated in Figure
2.1(c). (See Experimental Section for more details). Figure 2.1(d) presents typical SET and RESET data. The
as-prepared MIM junctions were initially in their high resistance state (HRS) or OFF-state. The resistance
of the as-prepared device was about 10
10
ohms at 0.1 V. The device was initially electro-formed at 3.5 V
and a 1µ A compliance current to make it electrically switchable. The current through the device increased
abruptly but then returned to the HRS while sweeping the voltage back to zero (FIRST RESET). The device
switched ON at a much lower voltage (0.7 V) in the next positive sweep (FIRST SET) after the electro-
forming process. The IV curve displays an abrupt SET transition for a positive sweep and a gradual RESET
transition for a negative sweep.
2.3.2 Schematic conduction channels of the Pt/SiO
2
:Ag/Pt diffusive and Ta/ HfO
2
/Pt
driftmemristors
Figure 2.1(e-g) schematically shows a typical pictorial illustration[32][112] of conductance switching
in a drift memristor, during which a nanoscale current channel develops. This acts as the framework for
several drift memristor models. Oxygen vacancies accumulate near the Ta electrode under a positive bias,
as shown in Figure 2.1(e). The accumulation is a stochastic process, hence the channel could always grow
into some irregular shapes. For the sake of simplicity of simulation, we chose a cylindrical shape of con-
ducting channel instead of other shapes, e.g. conical channel. Such simplification does not really affect the
accuracy of the model as the gap between the tip of the filament and the electrode dominates the electron
transport instead of the shape of the filament itself. The conduction channel is modeled as a cylinder with
6
0 2 4 6 8 10
Time[ms]
0.2
0.4
0.6
0.8
1.0
Voltage[V]
0
10 µ
20 µ
30 µ
40 µ
50 µ
Current[A]
Voltage
Current
(b)
BE
TE
15 nm Pt
15 nm SiO2:Ag
20 nm Pt
(a)
S0
(f)
S0
h
hmax
(e)
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
Voltage[V]
10
−8
10
−7
10
−6
10
−5
10
−4
10
−3
Current[A]
(d)
BE
BE
TE TE
20 nm Pt
5 nm HfO2
50 nm Ta (c)
S0
S
(g)
Gh
I =dh/dt Ch
h
GS
I =dS/dt CS
S
TE
BE
(h)
Figure 2.1: Geometries, typical electrical performance, and schematic conduction channels of
thePt/SiO
2
:Ag/PtdiffusiveandTa/ HfO
2
/Ptdriftmemristors (a,c) Optical microscopic images of a
Pt/SiO
2
:Ag/Pt diffusive memristor (scale bar: 50 µ m) and Ta/HfO
2
/Pt drift memristor crossbar (scale bar:
20 µ m), respectively. The inset shows a schematic illustration of the device stack. (b) A typical pulse-
switching curve from a 5 by 5µ m
2
Pt/SiO
2
:Ag/Pt diffusive device revealing the dynamics of the resistive
switching behavior; (d) A typical I-V curve from a 5 by 5 µ m
2
Ta/HfO
2
/Pt drift memristor cross point
showing the nonvolatile resistive switching behavior; (e,f,g) Schematics of switching mechanisms (colors
of the different layers match those of the layers in Figure ( a) and (c) insets ), (e), conducting channel length
changes under external electrical stimuli. (f), the middle stage when the conduction channel reaches the
limiting value; (g), conducting channel shape changes under a continued external electrical stimulus. (h)
Schematic of the SPICE circuit model implementation of a drift/diffusive memristor cross point.
7
a height h between 0 and h
max
, determined by the distance between the electrodes, and cross-sectional
areaS with an initial valueS
0
. Following channel nucleation, h increases rapidly at constantS
0
until it
reachesh
max
, as illustrated in Figure 2.1(f). Under continued bias, oxygen vacancies keep accumulating on
the channel, which broadens more rapidly near the Pt electrode, as illustrated in Figure 2.1(g). The RESET
process starts when a negative bias is applied to the drift memristor. The conduction channel area shrinks
back toS
0
, followed by channel rupture and decrease ofh to return to the configuration of Figure 2.1(e).
Figure 2.1(e-g) can also be used to illustrate the evolution of the conduction channel for a diffusive mem-
ristor, which is important because it enables a common framework for two switching mechanisms. One of
the major differences is that the SET process is based on a conduction channel formed from Ag instead of
oxygen vacancies, which have a slow drift velocity that is the rate-limiting step for channel formation in
drift memristors. In contrast, the fast drift velocity of Ag
+
insideSiO
2
ensures that Ag rapidly accumulates
on the negative electrode and the conduction channel nucleates there. For the "RESET" process, diffusion
of Ag driven by Ag/SiO
2
interfacial energy minimization causes the conduction channel to rupture after
the power is turned off, which results in a volatile switching mechanism called the relaxation process of
the diffusive memristor.
2.3.3 Thestaticequationsofthemodel
The mathematical formulation of a generic memristor compact model begins with a generalized state-
dependent Ohm’s Law, e.g.
V =R(h, S)× I (2.1)
in which R(h, S) is a function of the state variables h and S. The model considers two different resistors
in series, the channel with metallic conductivity and the other representing an insulating gap between
8
the channel and the uncontacted electrode. As a result, the resistance of the device can be expressed by
Equation 2.2:
R(h, S)=R
on
× h
h
max
r
S
0
S
+R
off
×
exp(
h
max
− h
λ )− 1
/
exp(
h
max
λ )− 1
(2.2)
whereh
max
,λ andS
0
are constants for a particular device across all states and cycling history, and depend
on the device’s properties, especially the switching materials. In practice, these constants can be treated
as fitting parameters independent of state variables h and S. The first term represents the ohmic resistance
of the conducting channel, where R
on
is the resistance of the device when it is fully switched ON. The
second term describes the tunneling resistance through the gap between the tip of the conduction channel
and the uncontacted electrode. In the second term, R
off
is the resistance of the fully OFF state of our
device, which is essentially electron tunneling and λ is a fitting parameter characterizing a tunneling
length. Hence, h=h
max
indicates fully ohmic conduction and h=0 represents fully tunneling-dominated
conduction. The metallic resistance depends on the resistivity and the morphology of the conduction
channel. For the sake of simplifying the definition of memristance and representing the basic properties
of the resistance of memristors, we focused on investigating the properties of the switching layer and the
ions/oxygen vacancies here. As a future research direction, the influence that comes from electrodes, such
as the current-rectify effect, will also be considered to better represent the voltage-current relationship.
2.3.4 Thedynamicequationsofthemodel
The time derivatives of the state variables (h and S) depend on the transport rate of oxygen vacancies or
ions. They are heavily influenced by the electric field, temperature, materials, etc. In this model, the electric
field, Joule heating, and the minimum interfacial energy influence the operation of the device and are
implicitly incorporated within the model. A future research direction will be to refine the thermal behavior
of the model, and any other non-dominant voltage effect[85] which also contributes to the acceleration
9
or inhibition of the dissolution process, for which additional experiments are needed[100]. Although the
minimization of interfacial energy is not usually considered a significant factor in drift-type memristors,
we include it here in the dynamical equations to simulate long-time state retention. The dynamic equations
for the channel length h and area S are, respectively:
dh
dt
=αV
n
N(µ +
, σ 2
+
)− βh N(µ − , σ 2
− ) (2.3)
dS
dt
=γV
m
exp(− S)− θS (2.4)
whereα is an electric field pre-factor, n is the power of the electric field fitting factor and β is the diffusion
fitting coefficient for h; γ is the electric field fitting pre-factor, m is the power of the electric field fitting
factor and θ is the diffusion fitting coefficient for S; and N(µ, σ 2
) is the normalized Gaussian function
withµ +
,µ − ,σ +
,σ − as the fitting parameters.
Equation 2.3 describes the dynamics of state variable h. The first term represents the influence of the
drift force on the mobile ion distribution. In order to represent decay and/or dissipation of the channel
height, which comes from thermal diffusion of the oxygen vacancies and the minimization of interfacial
energy, the second term,βh N(µ − , σ 2
− ), was included in Equation 2.3, whereβ is the diffusion pre-fitting
parameter. The two terms compete against each other and determine the conduction channel evolution
during the SET and RESET processes.
For the conducting channel area evolution, Equation 2.4, for the sake of simplifying, changes only
when the conducting channel connects the top and bottom electrodes. It also combines two terms, one
for drift and the other for diffusion. When the conducting channel length reached the maximum length
h
max
, the mobile ions will keep agglomerating together to grow as a thicker conduction channel under
the application of the same polarity of the voltage. Meanwhile, the conduction channel tends to minimize
the interfacial surface energy, so the second term, θS , was used to depict the effect of dissipation. The
10
cross-sectional area S has a minimum areaS
0
, which is related to the area of an atom. When the supplied
bias is removed or not strong enough, the area of conducting channel will shrink back toS
0
, followed by
the conduction channel rupture.
2.3.4.1 Explanationofvariablesandparametersinthemodel
The Gaussian functionN(µ, σ 2
) =
1
σ √
2π exp
− 1
2
h− µ σ
2
is used to describe the motion of the
drift front of the growing or retreating conduction channel and the broadening of the front caused by
diffusion. The analytical solution to the one-dimensional drift/diffusion equation is the Error function,
which provides a value for the state variable h as a function of time. The dynamical equation is determined
from the time derivative of h, which yields the Gaussian function used in Equation 2.3[51]. In addition,
oxygen vacancies reduce the oxide-metal interfacial energy[92], i.e., the Gibbs Thomson effect, for which
the dynamics can also be approximated by a Gaussian function. Different µ values were assigned to the
drift and diffusion processes for the evolution of the conduction channel height, which determine the SET
delay and the RESET relaxation times. For instance, for theSiO
2
:Ag diffusive memristor, µ +
, andµ − were
related to the threshold voltage and hold voltage, respectively. The variables σ +
and σ − are associated
with the latency of the conduction channel change.
The values of m and n indicate the non-linear response to voltage for the drift and diffusion, which also
determine what type of memristor the model represents, i.e., drift or diffusive. Even powers of n denote a
higher-order power dependence, while odd powers of n signify thermal assisted drift. Even values of m and
n are used to model symmetric diffusive memristor devices and unipolar drift memristors[77]. However,
m and n need to be odd for the bipolar drift memristor. Since the model is fairly compact, it is suitable to
be implemented in SPICE utilizing the schematic circuit shown in Figure 2.1(h). For conduction channel
length h, a capacitor integrates the current coming from a voltage-dependent current source, representing
the rate change of a state variable, and the voltage on the capacitor expresses the value of the state variable.
11
0.5 0.8 1.0 1.2 1.5
Pulse length[ms]
0
2
4
6
8
Time[ms]
Relax time vs. Pulse length
Experimental
Simulation
(h)
0.8 1.0 1.2
Pulse amplitude[V]
0
2
4
6
8
Time[ms]
Relax time vs. Pulse amplitude
Experimental
Simulation
(f)
0.5 0.8 1.0 1.2 1.5
Pulse length[ms]
0.1
0.2
0.3
0.4
0.5
0.6
Time[ms]
Delay time vs. Pulse length
Experimental
Simulation
(g)
0.8 1.0 1.2
Pulse amplitude[V]
0.2
0.4
0.6
0.8
1.0
Time[ms]
Delay time vs. Pulse amplitude
Experimental
Simulation
(e)
−0.2 0.0 0.2 0.4 0.6
Voltage[V]
10
−14
10
−12
10
−10
10
−8
10
−6
10
−4
Current[A]
Simulation
Experimental
(d)
0 2 4 6
Time[ms]
0
2 µ
4 µ
6 µ
8 µ
10 µ
Current[A]
Simulation Current
Experimental Current
(b)
0.0 2.5 5.0 7.5 10.0
Time[ms]
0
2 n
5 n
8 n
10 n
13 n
15 n
Channel Length [m]
100.00 a
100.02 a
100.04 a
100.06 a
Area [ ] m
2
Channel Length
Channel Area
(c)
0 2 4 6 8 10
Time[ms]
0.0
0.2
0.4
0.6
0.8
1.0
Voltage[V]
0
10 µ
20 µ
30 µ
Current[A]
Voltage
Simulation Current
Experimental Current
(a)
Figure 2.2: Experimental data and modeling results for a Pt/SiO
2
:Ag/Pt diffusive memristor. (a)
Experimental (dashed, purple) and modeled (solid, red) pulse-switching curve. The blue curve is the input
voltage pulse. (b) A magnified view of the current range from 0 to 10 µ A in Figure (a). (c) Plot of the
conduction channel length (blue) and area (red) simulated for this device over time. (d) Experimental
(dashed, purple) and modeled (solid, red) switching I-V curve with current on a log scale. (e-f) Statistical
experimental result (box plots) and simulation results (red line) of the delay time and relaxation time
of this device under different pulse amplitude (0.8-1.2V) and same 1ms pulse length. ( g-h) ) Statistical
experimental result (box plots) and simulation results (red line) of the delay time and relaxation time of
this device under same pulse amplitude (1V) and different pulse length (0.5-1.5ms).
The governing equation of the memristor is expressed by Equation 2.2 and implemented by an element
called the arbitrary behavioral source in the circuit.
2.3.5 ExperimentaldataandmodelingresultsforaPt/SiO
2
:Ag/Ptdiffusivememristor
To verify the model, we fabricated Pt/SiO
2
:Ag/Pt diffusive memristors and selected n = 2,m = 2 in
Equations 2.3 and 2.4 for performing the model simulations. The simulation results show a good agree-
ment with the measured data in Figure 2.2. We performed electrical pulse measurements for characterizing
the switching dynamics of these devices, which exhibit a delay time for SET in Figure 2.2 (a) after a one
volt pulse is applied. A low voltage (0.1V) is used to monitor the resistance state of the device both before
and after the switching pulse. The regions where the state of the memristor is read have been magnified
and are shown in Figure 2.2(b), and the calculated pulse-switching characteristic using the model matched
the experimental results reasonably well. The internal dynamics of switching can be estimated from the
12
evolution of the state variables h and S, as shown in Figure 2.2(c) (More details can be found in the Supple-
mentary Information of [122]). The conduction channel height h increased abruptly after the delay time,
in concert with the current. After reaching its maximum height, the conduction channel area increased.
After the applied voltage returned to 0.1V, the conduction channel area shrank back to its original area,
followed by the decrease of the height over the relaxation time.
A characteristic I-V hysteresis plot for a Pt/SiO
2
:Ag/Pt diffusive memristor is shown in Figure 2.2(d). As
the voltage was swept from 0 to 1V with a current compliance of 100µ A, an abrupt increase in current was
observed at about 0.2 V, called threshold voltage (V
th
). During the reverse sweep from 1 to 0V, the device
switched to its OFF state very close to 0.1 V, which is called hold voltage (V
hold
). The diffusive memristor
(Figure 2.2(d)) does not require electro-forming to precondition the device before normal operations[92].
We collected statistical data in order to further understand the dynamics of these devices. For each test-
ing set, 100 repeated pulse patterns were applied, and the resulting delay/relaxation times were extracted
and plotted in Figure 2.2(e-h). The delay and relaxation times under different conditions were accurately
reproduced by our model, and the comparison between the simulation and experimental data is also shown
in the same figures. The delay time depends on the magnitude of the applied pulse. The relationship is
roughly inversely proportional, which can be observed in Figure 2.2(e). Varying the pulse width leads to
a less clear trend, as shown in Figure 2.2(g). These devices also need a certain amount of time to tran-
sition back to their High Resistance States once switched to their Low Resistance State. This duration is
referred to as relaxation or OFF switching time. Relaxation time approximately depends linearly on both
the pulse width and amplitude, as shown in Figure 2.2(f, h) (Original Experimental results can be found in
Supplementary Information of [122]).
13
0.2 0.4 0.6 0.8 1.0 1.2
Time[ms]
50 µ
100 µ
150 µ
200 µ
250 µ
300 µ
Current[A]
Simulation current
Experimental Current
0.0 0.5 1.0
Time[ms]
0
2 n
5 n
8 n
10 n
13 n
15 n
Channel Length [m]
100.00 a
100.02 a
100.04 a
100.06 a
100.08 a
100.10 a
Area [ ] m
2
Channel Length
Channel Area
−2 −1 0 1 2
Voltage[V]
10
−10
10
−8
10
−6
10
−4
Current[A]
Simulation
Experimental
0.00 0.25 0.50 0.75 1.00 1.25
Time[ms]
−2
−1
0
1
2
Voltage[V]
−4 m
−2 m
0
2 m
4 m
Current[A]
Voltage
Simulation current
Experimental Current
(a) (b)
(d) (c)
Figure 2.3: Experimental data and modeling results for Ta/HfO
2
/Pt cross point memristor. (a)
Experimental (dashed, purple) and modeled (solid, red) pulse-switching curve. The blue curve is the input
voltage pulse. (b)A magnified view of the current range from 0 300 µ A in Figure (a). (c) Plot displays
the simulated conduction channel length (blue) and area (red) in this device over time. (d)Experimental
(dashed, purple) and modeled (solid, red) switching I-V curves on a log current plot, showing very good
agreement.
14
2.3.6 ExperimentaldataandmodelingresultsforTa/HfO
2
/Ptcrosspointmemristor
Different switching layer materials(e.g. HfO2, SiO2) absorb moisture/protons in different ways, hence,
even for the same type of memristor, the bipolar drift model parameters need to be adjusted to match
different materials stacks. To better demonstrate the relevance and applicability of our model, we choose
HfO2 as a representative and commercial drift memristor to simulate and compare with our experimental
results. We fabricated Ta/HfO
2
/Pt cross points and choosen=3,m=5 in Eqs. 2.3 and 2.4 for simulations,
since a drift memristor is characterized by bipolar switching. Different polarities of voltage bias are needed
for SET and RESET processes.
As shown in Figure 2.3(a), pulse measurements were performed on these drift devices. The device
was SET with a 2V, 50µ s pulse and RESET using a -2V, 50µ s pulse repeatedly for several cycles. A short
and low voltage pulse was applied to monitor the resistance state of the device both before and after the
switching pulses. The regions where the state of the device was monitored were magnified and shown in
Figure 2.3(b). The calculated pulse-switching characteristics during this process using the model matched
the experimental results. The dynamics of the switching can be studied by examining the simulated time
dependence of the state variables h and S, as shown in Figure 2.3(c) (More details can be found in Sup-
plementary Information of [122]). The conduction channel height h increased as the current increased
immediately after the SET pulse was applied. After h reached its maximum value, the conduction channel
area S increased. After the switching voltage pulse turned off, h and S maintained their values until a RE-
SET pulse was applied; firstly S shrunk back to S
0
, and then h decreased to zero, indicating the conclusion
of the RESET process. The characteristic I-V plot for a cross point memristor is shown in Figure 2.3 (d). The
device current increased abruptly but then returned to the HRS while sweeping the voltage back to zero
(FIRST RESET). The device switched ON at a much lower voltage in the following positive sweep (FIRST
SET) (0.7 V). The simulation result (dashed, purple) shows good agreement with the measured data (solid,
red).
15
2.3.7 Experimentaldataandmodelingresultsfor’other’memristors
A single conduction channel is usually formed and ruptures if the switching layer was deposited uni-
formly. Although the Ta/HfO
2
/Pt bipolar memristor usually has a low device to device variation and
negligible cycle to cycle variation[28], occasionally a device will have imperfections, which can result in
the formation of multiple conduction channels[112][17] (dashed, purple) as shown in Figure 2.4(a). As the
voltage was swept from 0 to 2V, an abrupt increase in current was first observed near 1.0 V, indicating the
formation of a conduction channel. A second abrupt increase in current was observed at 1.26 V, indicating
that a second conduction channel had formed before it reached the current compliance. When the voltage
was swept from 0 to -2V, the device switched from the LRS to HRS. As discussed above,µ is related to the
switching threshold voltage, andσ is associated with the latency of the conduction channel change. For
multiple conduction channels, there exists several switching threshold voltages and characteristic times;
hence multiple dynamical equations need to be combined, as follows:
dh
dt
=
j
X
i=1
α i
V
n
i
N(µ i+
, σ 2
i+
)− β i
hN(µ i− , σ 2
i− )
(2.5)
dS
dt
=
j
X
i=1
[γ i
V
m
i
exp(− S)− θ i
S] (2.6)
where j is the number of conduction channels involved. By choosing different parameters for different
channels, we can control the forming voltages and speed in the model, which was used to simulate the
device of Figure 2.4 (a) (solid, red).
There are two types of non-volatile memristors: bipolar and unipolar (or nonpolar). Unlike the Ta/HfO
2
/Pt
bipolar memristor in Figure 2.3, a unipolar device does not require opposite polarity voltages for SET and
RESET switching[18][77][64]. Since the values of m and n in Equations 2.3 and 2.4 are related to conduc-
tion channel evolution, we investigated the potential of our model to simulate a unipolar switching device,
16
−10 −5 0 5 10
Δ t [ms]
−100
−50
0
50
Δ W (%)
Simulation
Experimental
(c)
−0.5 0.0 0.5 1.0 1.5 2.0 2.5
Voltage[V]
10
−8
10
−6
10
−4
Current[A]
Simulation
Experimental
(b)
−2 −1 0 1 2
Voltage[V]
10
−7
10
−5
10
−3
Current[A]
Simulation
Measurement
(a)
Figure 2.4: Experimental data and modeling results for ’other’ memristors (a) The measured and
simulated (Equation 2.5 and 2.6) multi-channel switching I-V curves (b) The measured and simulated unipo-
lar switching of Pd/TiO2/Pd (n = 8,m = 2 in Equation 2.3 and 2.4) (c) Plot of the conductance (weight)
change of the drift memristor with difference in time, showing the spike-timing-dependent plasticity of
an electronic synapse, which emulates the timing-dependent response of biological synapses.
Pd/TiO
2
/Pd, which was fabricated and measured. To verify the model, we choosen = 8,m = 2 in Eqs.
2.3 and 2.4 for the model simulation. A characteristic I-V plot for unipolar devices is shown in Figure 2.4(b),
along with the calculated switching results. Under a current compliance, the SET was performed using a
DC voltage sweep, while no current compliance was needed for RESET. An ON/OFF conductance ratio of
1000 at 0.1 V was observed in this device. The device switched ON at 1.5V, while a lower voltage ( 0.7V)
was used for the RESET process. A good agreement between the experimental results and the simulated
results was found and shown in Figure 2.4(b).
Finally, we combined the drift and diffusive memristor models to create a synapse emulator that can
capture the diffusion dynamics for a demonstration of Spike-Timing-Dependent Plasticity (STDP). We also
experimentally connected a SiO
2
:Ag diffusive memristor in series with a Ta/ HfO
2
/Pt drift memristor to
form an artificial synapse for electrical testing, as previously demonstrated in reference[92]. Figure 2.4(c)
presents the conductance change as a function of the time difference ∆ t between pre-synaptic and post-
synaptic spikes, and the calculated results match well with the experimental data.
2.4 Conclusion
We demonstrated a dynamical model that can reproduce the long-term memory of drift memristors
and the short-term plasticity of diffusive memristors. We showed that the model captures the quasi-static
17
and dynamic characteristics of these devices. A decent agreement has been observed between simulation
results and the experimental data based on a HfO
2
drift memristor and a SiO
2
:Ag diffusive memristor
that we fabricated to verify the model. Furthermore, we utilized the same model with different fitting
parameters to reproduce the switching behavior of multi-channel bipolar and unipolar switching. The
spike-timing-dependent plasticity of a synapse was emulated in both experiment and simulation, which
showcased the applicability of our model to bio-inspired computing. Moreover, the model is compact and
suitable for SPICE simulations of complex neuromorphic circuits without compatibility issues between
models of different memristor types.
2.5 ExperimentalSection
Memristor Device Fabrication: The drift memristor devices were grown on a p-type (100) Si wafer
with 100 nm thermally grownSiO
2
. The bottom electrodes were defined by ultraviolet photolithography,
and the liftoff process. 2 nm Ti/20 nm Pt was deposited by e-beam evaporator, followed by a liftoff process
in acetone, to form the bottom electrode. After that, a 5 nmHfO
2
blanket layer was deposited by atomic
layer deposition (ALD) using water and tetrakis(dimethylamido) hafnium as precursors at 250 C. The 50
nm thick Ta top electrodes were defined by a second photolithography step and metallization using DC
sputtering and liftoff. The diffusive memristor devices used the same substrates and bottom electrodes as
the drift memristor devices. The switching layer was grown by cosputteringSiO
2
and Ag for a thickness
of 15 nm in an ambient of mixed Ar andO
2
followed by photolithography. Top electrodes were deposited
by evaporating Pt(20 nm) and the liftoff process.
Electrical Characterization: A B1500A semiconductor parameter analyzer (Keysight) was used for
the DC measurements, and the pulse measurements were performed using B1530A waveform genera-
tor/fast measurement unit (WGFMU) (Keysight). For all the electrical measurements, the bottom electrodes
were grounded while the top electrodes were biased. We performed the STDP experiments with the drift
18
memristor in series with aSiO
2
:Ag diffusive memristor. The B1530A WGFMU was used for applying the
pre- and spike-postsynaptic voltage spikes.
19
Chapter3
AnartificialspikingafferentnervebasedonMottmemristorsfor
neurorobotics
3.1 Abstract
Neuromorphic computing based on spikes offers great potential in highly efficient computing paradigms.
Recently, several hardware implementations of spiking neural networks based on traditional complemen-
tary metal-oxide semiconductor technology or memristors have been developed. However, an interface
(called an afferent nerve in biology) with the environment, which converts the analog signal from sensors
into spikes in spiking neural networks, is yet to be demonstrated. Here we propose and experimentally
demonstrate an artificial spiking afferent nerve based on highly reliable NbO
x
Mott memristors for the first
time. The spiking frequency of the afferent nerve is proportional to the stimuli intensity before encoun-
tering noxiously high stimuli and then starts to reduce the spiking frequency at an inflection point. Using
this afferent nerve, we further build a power-free spiking mechanoreceptor system with a passive piezo-
electric device as the tactile sensor. The experimental results indicate that our afferent nerve is promising
for constructing self-aware neurorobotics in the future.
20
3.2 Introduction
In the era of big data and IoT, a vast amount of sensing data, such as pictures, speeches, and videos,
needs to be processed in real-time with high energy efficiency. This poses a significant [38] [70] challenge
to the traditional computing architecture due to the von-Neumann bottleneck [99] [80] [2]. Neuromorphic
computing architecture based on spiking neural network (SNN) has been recognized as an attractive candi-
date for its promising energy efficiency and powerful computing capacity [49] [53] [12]. Recently, various
technologies have been explored to build hardware SNN, such as digital logic circuits [53] [12], comple-
mentary metal-oxide semiconductor (CMOS) analog circuits [26] [31], and emerging memristors [89] [61]
[91]. Given the physical limitations of transistors and their lack of desirable dynamics, memristors have at-
tracted special attention owing to their high integration intensity [88], low power consumption[60], analog
behavior [10] [41] [24], and diffusive dynamics [91] [85] [93] [106], etc. Accordingly, memristor-based arti-
ficial synapses [107] [5] [117], spiking neurons [52] [59] [108] [75] [118] [54], have been actively studied to
construct hardware implementations of SNN lately. However, the signals collected from the environment
are usually in the continuous and analog domain and needs to be transformed into spikes first to serve as
the inputs to SNN. Therefore, a special cell analogous to afferent nerves in biology is required to receive
signals from receptors and transmit spikes to the central nervous system and brain [86] [62]. Fortunately,
a bio-inspired afferent nerve based on an organic ring oscillator (ORO), whose output frequency matches
the action potential of the biological sensory neuron, has been reported to control the biological motor
nerves by connecting to a synapse transistor[33]. The spiking frequency of the ORO could be modulated
by the input voltage controlled by the pressure sensor. Then the output of the ORO was further used to
trigger a synapse transistor that connected with a biological efferent nerve, in which the different output
current of the synaptic transistor is converted to voltage signals to stimulate the cockroach’s leg to gener-
ate different extension force. In addition, other types of devices, including two-terminal memristors and
three-terminal transistors, have also been reported to emulate nociceptors [34] [109], mechanoreceptors
21
[20][83][113], and optical sensorimotor synapses [39], etc., to construct high-efficient artificial sensory
systems. For these systems, a high-compact artificial spiking afferent nerve (ASAN) is needed to further
transform the sensed signals into spikes. The NbO
x
memristor is a two-terminal device with a high inte-
gration intensity. It features negative differential resistance (NDR) behavior [68] [36], which can serve as
the basis of dynamic threshold switching with voltage sweeps [36] and has enabled emulation of biological
neurons [59] [108], and analog computing [35].
In this work, we report an artificial spiking afferent nerve (ASAN) based on a specifically designed
NbO
x
memristor for the first time. This NbO
x
device is fabricated in a three-dimensional (3D) structure
and with a low thermal conductivity polysilicon (poly-Si) bottom electrode to reduce the threshold current.
To construct the ASAN, a compact NbO
x
oscillator with a NbO
x
device and a resistor is built first, which
can transform analog input signals into correlated spiking frequencies. For such an ASAN, the input stimuli
are correlated with the voltage generated by receptor devices, and the oscillation frequency is related to
the spiking frequency of the neuron, which in turn depends on the intensity of the stimuli [71] [43]. This
ASAN shows a quasi-linear relationship between input intensity and spiking frequencies under proper
stimuli and tends to reduce firing frequency when noxious stimuli are provided, which faithfully emulates
the function of biological neurons [71] [43] [74]. To further demonstrate the spiking properties of the
ASAN, three types of input pulses (square, triangular, and sinusoidal) are applied, respectively. Using this
ASAN, a power-free spiking mechanoreceptor system with the piezoelectric device is further proposed and
demonstrated experimentally. Experimental results demonstrate that our ASAN has great potential for use
in neurorobotics and can be explored to build a general afferent nerve to communicate with higher-order
SNN.
22
Figure 3.1: Biologicalafferentnervevs. artificialafferentnerve. (a) Schematic of the afferent nerve
of a biological somatosensory system. Action potentials are generated in the skin and transported to the
brain for processing. Spiking frequency increases with increasing stimuli intensity and decreases under
strong stimuli due to protective inhibition. (b) The artificial spiking somatosensory system consists of a
mechanical sensor and an artificial spiking afferent nerve (ASAN) made of a resistor and a NbO
x
memris-
tor. The spiking frequency shows a similar trend to that seen in its biological counterpart, which is then
transmitted to the spiking neural processing unit for further processing to complete a complex task.
23
3.3 Results
3.3.1 Schematicofaspikingsomatosensorysystem
Figure 3.1 demonstrates the working principle of our afferent nerve and the analogy with its biological
counterpart. The bio-inspired ASAN emulates the functions of biological afferent nerves (3.1a) by collect-
ing data from somatosensory receptors and conveying this information to the cortex system. Then the
cortex system will process the afferent information and transfer it to effector by the efferent nerves to
respond to the external or internal environment [62]. Our artificial spiking somatosensory system (3.1b)
is made of a two-terminal sensor device and a compact oscillator, in which the special oscillator serves as
the ASAN and contains two passive components: a resistor and a NbO
x
memristor. In biological systems,
the firing rates of the afferent nerve increase with increasing input intensity, provided the intensity of
input stimuli exceeds the threshold of the afferent nerve [71] [43]. However, when the stimuli intensity
is excessively high, the firing rates would decrease due to the protective inhibition of the neuron cell, to
prevent the neuron from dying [74].
In our artificial somatosensory system, an analog input voltage signal is generated by the sensor device
and the NbO
x
ASAN can transform the voltage intensity into corresponding spiking frequencies. Then the
generated spikes will be transmitted to a higher-order artificial SNN for further processing. It is worth not-
ing that the spiking frequency of the ASAN is proportional to the stimuli intensity under ordinary stimuli.
Once the generated voltage intensity is overly high, the spiking frequency actually starts to decrease, just
like what the biological neurons do. The quasi-linear frequency response under ordinary input intensity
can be explained as the dominant and decreasing integration time of the ASAN with increasing input in-
tensity. The frequency decrease can be explained by considering the fact that the relaxation time of the
NbO
x
memristor after firing becomes longer under a higher input intensity and eventually the oscillation
period is mainly dominated by the relaxation time. Here we discuss two reasons that lead to the increase
24
in the relaxation time: first, the increased input intensity leads to a higher total current flowing through
the memristor after firing, which requires a longer time to discharge. Second, the increased total current
induces a larger Joule heat generated in the memristor during the relaxation process, which makes the
device dwell on its on-state for a longer time [13]. Once the relaxation time becomes longer than the inte-
gration time, the firing rates begin to decrease and eventually the oscillator stops firing when the device
holds its on-state (see more details in Supplementary of [119] Fig. 6).
3.3.2 Devicecharacteristicsandmodeling
The memristor devices used in this study are based on a 3D vertical metal–insulator–metal structure
similar to those reported by us earlier [48]. The device has a titanium nitride (TiN) top electrode, a niobium
oxide (NbO
x
) switching layer, and a poly-Si bottom electrode (see Methods for the details of fabrication
processes). Here, the poly-Si bottom electrode with low thermal conductivity is specifically designed to
reduce the threshold current. The cross-section transmission electron microscopy (TEM) of the device
structure is shown in 3.2a, with the elemental mapping of the materials in the system for Ti, Nb, N, O, and
Si (from 3.2b to 3.2f).
Before the operation, a DC sweep from 0 V to 5 V was required to irreversibly precondition the low-
bias resistance of the devices from a 56 GΩ (@1 V) virgin state to a 35 MΩ (@1 V) operational regime
(Supplementary of [119] 3.1a). The forming step has previously been attributed to a soft breakdown process
that generates a channel of crystalline NbO
2
within the oxide film [36] [13] [58], which exhibits Joule-
heating-driven NDR that underlies the threshold switching behavior [68] [36] [19]. During switching,
∼ 2µ A threshold current is observed, which is much lower than devices of NbO
2
/TiN reported previously
[48] [7] (see Supplementary of [119] Fig. 1). This is attributed to the low thermal conductivity of the
poly-Si bottom electrode [7]. Fig. 3.2g, h show a closer view of the channel area, a round region of NbO
2
crystal with a diameter of∼ 8nm can be observed (3.2g). We believe the round region is a cross-section
25
Figure 3.2: NbO
x
device analysis. (a) Scanning electron micrograph cross-sectional image of the NbO
x
device. (b-f) The elemental mapping of the materials in the system for Si, O, Nb, N, and Ti, respectively. (g,
h) Zoom-in views of the channel locations. (i) The diffraction pattern extracted by Fourier transform of h.
(j) Energy dispersive spectra (EDS) of line scans of the channel. (k) Two switching cycles under triangular
waves with a 2.5 V/100µ s ramp rate.
26
of a dendrite of the NbO
2
channel and the complete crystalline NbO
2
channel might be missed during
the TEM sample cutting as the TiN top electrodes were wide (∼ 20 µ m, see Methods). Fig. 3.2h shows
a zoomed-in view of the crystal NbO
2
region in 3.2g. The clear lattice fringes and the corresponding
fast Fourier transform (FFT) image (3.2i) indicate that the nanoparticles are highly crystalline NbO
2
. The
measured angle between relative crystal faces is∼ 77
◦ , which is similar to that reported in other studies[36]
[58]. The elemental distributions along the channel (from Si towards TiN) are presented from the energy
dispersive spectra of line scans of the cell (3.2j), from which we can see that the Nb:O atoms ratio is about
2. These results suggest that a crystalline NbO
2
channel was formed during the forming process.
After the forming operation, the device could be converted from the HRS to the LRS by either a positive
or a negative voltage sweep. Fig. 3.2k shows the experimental and simulation data of the device under two
cycles of triangular voltage sweeps, exhibiting a bi-directional nonpolar switching behavior (details of the
model used for the simulation is provided in the Methods). In the resting state, the device is in the HRS,
it switches to the LRS when the absolute value of the sweep voltage surpasses a threshold voltage (V
TH
)
(3.2k, @∼ 2.05 V) and back to the HRS when the voltage absolute value is reduced below a hold voltage
value (V
H
) (3.2k, @∼ 1.53 V). To better illustrate the switching mechanism of the device, a schematic is
presented in Supplementary of [119] Fig. 2. Initially, the switching layer is in an amorphous state (a-NbO
x
;
Supplementary of [119] Fig. 2a). After forming, a crystalline NbO
2
channel is generated (Supplementary
of [119] Fig. 2b), which is similar to those reported in previous studies [60] [36] [7]. During switching
operations, either a positive or a negative voltage is applied to the TiN electrode, and the NbO
2
channel
switches to the LRS when the voltage surpasses the V
TH
(Supplementary of [119] Fig. 2c); then the channel
switches back to its HRS when the applied voltage falls below a hold voltage value (V
H
) (Supplementary
of [119] Fig. 2b).
27
Figure 3.3:Characteristicsoftheartificialspikingafferentnerve(ASAN). (a) Schematic of the ASAN.
A resistor R
c
(75 kΩ ) and a NbO
x
memristor with parallel parasitic capacitance are combined together
(R
HRS
≫ R
c
≫ R
LRS
). In real applications, the voltage on the NbO
x
top electrode serves as the output
spiking signal. The parasitic capacitor (C
parasitic
) is tested to be about 20 pF. (b) The oscillation behavior
of the ASAN. For the sake of simplicity, the current flowing through the memristor is measured as the
response. The charging time from V
H
to V
TH
is defined as the integration time and the discharging time
from V
TH
to V
H
as the relaxation time. (c) ASAN response under different input voltages. ( d) Extracted
mean value of spiking frequency vs. voltage in c. (e) Frequency response of the ASAN with triangular
stimuli pulses. (f) The quasi-linear frequency–voltage curve extracted frome.
28
3.3.3 WorkingprincipleoftheASAN
Considering the afferent nerve behavior and the characteristics of the NbO
x
Mott memristor, we
demonstrated a compact artificial spiking afferent nerve, as shown in 3.3a. The ASAN is constructed with
a fixed resistor (R
c
) and a NbO
x
memristor, which has an intrinsic parasitic capacitance. It should be noted
that the intrinsic parasitic capacitance is below one picofarad due to the nanoscale device size, rendering
it negligible in comparison with the tens of picofarads of external parasitic capacitance in the test circuits.
The C
parasitic
in the figure indicates the total parasitic capacitance. One node of the R
c
serves as the input
node and another node connects with the top electrode of the NbO
x
memristor, with the bottom electrode
grounded. The R
c
used here is 75 kΩ , which is much smaller than the HRS value (R
HRS
) and much larger
than the LRS value (R
LRS
) of the NbO
x
memristor (R
HRS
≫ R
c
≫ R
LRS
).
When a voltage is applied to the input node, the parasitic capacitor charges through the charging loop
first because R
HRS
C
parasitic
≫ R
c
C
parasitic
[118]. Once the voltage on the capacitor surpasses V
TH
, the
memristor device switches to its LRS due to the Joule-heating-driven NDR mechanism (V
2
/R
HRS
× ∆ t
) and then the capacitor discharges through the discharging loop [118]. Due to the fact that the R
LRS
is
much smaller than the R
c
(R
LRS
C
parasitic
≪ R
c
C
parasitic
), eventually the discharging process dominates
over the charging process and the net charge on the capacitor decreases.
When the voltage on the capacitor falls below V
H
, the Joule heating is not sufficient to hold the metallic
state of NbO
2
anymore, the device returns back to its HRS, and the capacitor begins charging again. Under
a continuous input, the memristor keeps switching between HRS and LRS, and an oscillation behavior can
be observed, as shown in 3.3b. The current flowing through the memristor is measured. Here, for easy
understanding, we define the charging time from V
H
to V
TH
as the integration time and the discharging
time from V
TH
to V
H
as the relaxation time. It should be noted that the endurance of the threshold switch
is of critical importance for practical application, so we tested the endurance by successfully running the
ASAN for∼ 106 s at a period of <1µ s.
29
After that, the device can also work normally, yielding an endurance value >1012. (see Supplementary
of [119] Fig. 3). To estimate the relationship between input intensity and output frequency, different
voltages were applied on the input node (3.3c). When the input voltage surpasses 2 V, the memristor starts
switching and the oscillation frequency increases with increasing input voltage. Fig. 3.3d shows the direct
relationship between oscillation frequency and input voltage, each data point is the mean value under
a certain voltage calculated from 3.3c. We can see the clear increment of the oscillation frequency with
increasing voltage.
High energy efficiency is known as critical merit of biological systems. Recently, artificial synapses
have been reported with a∼ pJ level energy consumption per spike [110] [9] and even∼ fJ with specifi-
cally designed devices based on organic materials [102] [101]. To verify the feasibility of our ASAN for
constructing a high-efficient artificial SNN machine, we further calculated the energy consumption of the
ASAN (see Supplementary of [119] Fig.4). Energy consumption for each spike was determined by dividing
the total energy consumption by the spike numbers within a period of time, in which the total energy
consumption is power integration. The minimal energy consumption as low as∼ 38pJ per spike event was
achieved. We believe the energy consumption could be further reduced by using a NbO
x
device with a
lower threshold voltage, a smaller V
H
–V
TH
window, and a testing circuit with a smaller parasitic capaci-
tance [60] [46].
To further demonstrate the frequency evolution under continuously increased voltage, a triangular
pulse (from 1.9 V to 2.5 V) with a 1 V/ms ramp was taken as the input stimuli signal, as shown in 3.3e.
The third panel shows the corresponding frequency evolution. The oscillation frequency increases with
increasing voltages and decreases with decreasing voltages. Fig. 3.3f is the frequency–voltage relationship
curve extracted from 3.3e. It can be concluded that the ASAN can also properly work in a triangular pulse.
With our memristor model, we have also demonstrated the frequency response in simulations, a similar
30
Figure 3.4: artificialspikingafferentnerve(ASAN)withanexternalcapacitor (a) Schematic of the
ASAN with an external parallel capacitor (4.7 nF). (b) Frequency response with different input voltages. ( c)
The frequency–voltage curve with two stages: the excitatory spiking stage under low input voltages and
the protective inhibition stage under high voltages. (d-f) The frequency response with a sinusoidal signal
as input. (d, f) The input signals only with a positive voltage, protective inhibition can be observed in f
which has a higher amplitude. (e) An input sinusoidal signal without bias, where the oscillation behavior
can be obtained upon applications of both positive and negative voltage.
relationship between input intensity and spiking frequency has been observed (see Supplementary of [119]
Fig. 5).
3.3.4 TheASANwithanexternalcapacitor
To demonstrate the oscillation behavior of the ASAN under analog input sensing signal, for conve-
nience, an external parallel 4.7 nF capacitor was used (the parallel parasitic capacitance in 3.3a is∼ 20
pF during the testing process, with which the resulting resistor-capacitor time constant is not easy to be
operated to complete our following artificial mechanoreceptor system), as shown in 3.4a.
Here, the voltage on the capacitor was measured as the output signal. Fig. 3.4b shows the experimental
results of the ASAN with a parallel capacitor (more experimental data are presented in Supplementary
31
of [119] Fig. 6). It should be noted that the output oscillation frequency under different input voltages
was tested separately using a peripheral oscilloscope. At the beginning of each input signal, an obvious
integration process of the capacitor can be observed. Then the incremental input voltages were applied
successively, the output voltage oscillates between V
TH
and V
H
.
The frequency–voltage curve is shown in 3.4c. When the input voltage increases from 2.6 V to 4.8
V, the oscillation frequency shows a quasi-linear increment. Then the spiking frequencies decrease with
further increasing input voltage and eventually stops oscillating at 6.2 V due to the fact that the memris-
tor starts to hold its on-state. The behavior of increasing frequency with increasing input intensity has
been systematically demonstrated in previous literature [46] [16], whereas the frequency decrease with
further increasing input intensity has not been specifically reported yet. The quasi-linear increment of
frequency under ordinary input intensity can be explained as the dominant and decreasing integration
time of the ASAN with increasing the input intensity (spike period = integration time + relaxation time
)(see Supplementary of [119] Fig. 7a, b).
Furthermore, owing to the increasing input intensity, the total current flowing through the memristor
is increased within the relaxation process (see 3.3c and simulation results in Supplementary of [119] Fig. 8),
which requires a longer time to discharge. In addition, the increasing current flow through the memristor
leads to more Joule heat in the memristor during the relaxation process, which makes the device dwell
on its on-state for a longer time. Consequently, the relaxation time of the ASAN increases and eventually
dominates the oscillation period (see Supplementary of [119] Fig. 7d). Thus, the spiking period time of
the ASAN decreases first and then increases, and correspondingly the frequency increases first and then
decreases. It should be noted that the ASAN stops firing continuously under a higher voltage owning to
the voltage divided on the NbO
x
device is always larger than its holding voltage after the first-fire event.
The voltage on the device could generate sufficient Joule heat to hold the device in its “on-state” (see
Supplementary of [119] Fig. 9). This frequency response is similar to the biological afferent nerve whose
32
spiking rates increase with an increase in the intensity of harmless stimuli, but decreases and eventually
stops firing under excessively strong stimuli due to the intrinsic protective-inhibition mechanism that
serves to keep the system balanced and prevent neurons from dying [74].
In nature, signals are usually transmitted in an analog form and the generated signals from sensors are
continuous [79]. To mimic such signals, sinusoidal signals with or without DC bias were applied on the
input node, as shown in 3.4d, e. The input sinusoidal signal with DC bias (makes the input signal only with
positive voltage) was applied first (3.4d). The output spiking frequency is presented in the third panel. We
can see that the frequency-time curve also exhibited a sinusoidal form. The spiking behavior generated by
a sinusoidal input signal without DC bias (with both positive and negative voltage) is given in 3.4e. The
ASAN can be successfully operated, and the corresponding frequency displays the same evolutionary trend
as the case with only positive input voltage. Fig. 3.4f shows the output spiking behavior under a strong
input voltage. The protective inhibition of neuron cells is observed and could recover to the excitable state
whenever the input voltage becomes normal. We note that the stop spiking voltage in 3.4f is about 5.9
V, which is slightly smaller than that in 3.4c (6.2V). This difference results from the V
H
variability of the
NbO
x
device. The V
H
at the moment of testing 3.4f (1.62 V) is lower than that in 3.4c (1.71 V); thus, a lower
stop spiking voltage in 3.4f is observed.
Besides, to extend the application of our ASAN, we employed a 47nF capacitor to test its spiking be-
havior and achieved a lower frequency range from 0 Hz to 1100 Hz, which matches the human nervous
system (from 1 Hz to 1000 Hz) (see Supplementary of [119] Fig. 10). These results demonstrated that our
afferent nerve could work with analog signals and has a great potential to be used in various environments,
even suitable for the human-machine interface.
33
Figure 3.5:Illustrationoftheartificialspikingmechanoreceptorsystem(ASMS) (a) Schematic of the
ASMS. A piezoelectric device is used as the tactile sensor and connected with the artificial spiking afferent
nerve. The voltage generated by the piezoelectric device serves as the input signal. (b) The experimental
data of the ASMS. (c-f) A closer view of b, the protective inhibition behavior can be observed inc. (g) The
frequency response of the ASMS under different pressure intensities.
34
3.3.5 Power-freeartificialspikingmechanoreceptorsystem
Mechanoreceptors are primary sensory structures for detecting mechanical stimuli (e.g., pressure,
touch, stretching, and vibration) and for sending the generated responses to the brain by afferent nerves
for further processing to generate an appropriate response to the external and internal environments.
Under harmless stimuli, mechanoreceptors can encode mechanical deformation into proportional spiking
frequency [83] but tend to stop firing under noxious stimuli due to the protective inhibition mechanism
[74].
With a piezoelectric device connecting to the ASAN, we demonstrated an artificial spiking mechanore-
ceptor system (ASMS) (3.5a). When the pressure was applied to a piezoelectric device, a positive voltage
was generated on the top electrode and a negative voltage was generated when pressure was lifted [114]
[22]. The positive and negative voltages are a result of the deformation of atomic structures [22]. It should
be noted that the input voltage signal of our artificial mechanoreceptor is generated by the piezoelectric
device, so the system does not need an external power source. The piezoelectric device started to generate
a voltage at the beginning of the time when the pressure was applied and then up to a peak value depend-
ing on the pressure intensity, and then the voltage decreased due to the leaky nature of the charge [22]. An
opposite voltage was generated when the finger was lifted and then the charge leaked (see Supplementary
of [119] Fig. 11).
Fig. 3.5b shows the experimental results of the artificial mechanoreceptor system. When a force is
applied to the piezoelectric device, a sinusoid-like voltage signal was generated and then this signal was
transformed into spiking signals by the ASAN. It can be seen that the ASAN exhibits the same spiking
behavior as it did when an analog input voltage from an external power source was applied to it. When the
force is high, a high peak voltage is generated, which makes the ASAN stop spiking (protective inhibition),
as shown in 3.5c (a closer view of 3.5b). Fig. 3.5d–f shows the zoom-in of the other time slot of 3.5b. The
dynamic frequency response can be clearly observed, which has the same trend as the generated voltage.
35
To illustrate the frequency response of our ASMS under different pressure, we apply different forces of
varying intensities on the piezoelectric device, as shown in 3.5g. When the pressure force on the piezoelec-
tric device is small, the generated voltage is insufficient to drive the memristor, then no dynamic spiking
behavior can be obtained. Once the applied pressure force is sufficiently large, the voltage generated by the
piezoelectric device can drive the memristor to switch. The peak frequency of the afferent nerve increases
with increasing the pressure force; more experimental data under other pressure intensities are presented
in Supplementary of [119] Fig. 12.
These results demonstrate that a power-free artificial mechanoreceptor has been successfully imple-
mented experimentally and the afferent nerve can be used for transforming analog sense signals into
dynamic spiking frequencies. These results suggest that our afferent nerve has a great potential to be used
in spiking neurorobotics.
3.4 Discussion
Neuromorphic machines consisting of spiking neurons and synapses could provide a more efficient
approach to performing complex tasks than traditional hardware. An ASAN combined with sensors is
critical for interacting with the environment, which converts the analog signal in the environment into
spiking signals that could be further processed by the neuromorphic machine. The ASAN using CMOS
ring oscillators shows the analog information could be converted into spiking signals [33] [83], in which
the spiking frequency is dominated by the inverter delay. Given the physical limitations of transistors and
their lack of desirable dynamics, oscillators with memristors become a more promising candidate, owing
to their high integration intensity, low power consumption, inherent dynamics, etc. However, previous
works merely focus on the emulation of dynamic cortex neurons or operations for classifications [91]
[59] [108] [16]. The interface between the neuromorphic machine and the environment is also a critical
component to construct a self-aware machine.
36
In summary, we have proposed and experimentally demonstrated an ASAN based on specially engi-
neered NbO
x
Mott memristors. The ASAN can transform analog signals into dynamic oscillation frequen-
cies. The frequency has a quasi-linear relationship to the input voltage within a certain range of the input
signal intensity and tends to stop spiking under noxious input intensity, closely resembling a biological
neuron. The dynamic spiking behavior under various input signals, such as rectangular, triangular, and
sinusoidal pulses, was studied systematically.
We further integrated the ASAN into a piezoelectric device to construct an ASMS without any external
power source. The ASMS can respond to the pressure signal and transform the pressure intensity into a
corresponding spiking frequency. The ASAN can be readily extended to process sensory signals from
other sensors, such as smell, taste, sight, hearing, temperature, magnetic field, and humidity. In addition
to constructing the diversiform sense systems, our nerve cell is also suitable for applications in spiking
neurons owning to its leaky integration and fire characteristics or coupled oscillator neural network owing
to its input-intensity-dependent oscillation behavior [16] [69]. The nerve can thus be further used to
construct complex neural networks to process central information and fabricate a highly efficient spiking
neurorobotics system.
3.5 ExperimentalSection
Device fabrication: First, one SiO
2
(150 nm)/Si(60 nm)/SiO
2
(150 nm) multi-layers were deposited by
PVD and PECVD, respectively. Patterning and only one-step etching were applied to form the bottom
electrode (poly-Si) with a smooth sidewall profile. Then the NbO
x
switching layer (∼ 25 nm) and TiN
top electrode (∼ 40 nm) were deposited on the sidewalk sequentially by magnetron sputtering at room
temperature, followed by a lift-off process to form top electrodes. The area of the memristor cell is defined
by the thickness of the bottom electrode Si (60 nm) and the width of the literal top electrode (TiN) width
(20µ m).
37
Measurement method: In the electrical experiment, the electrical characteristics of a single NbO
x
device and the experimental results in Fig. 3.3 are performed on an Agilent B1500A. During the test with
an external parallel capacitor (Fig. 3.4), a Keysight 81160A pulse generator is used as the power source
to generate input signals and a Keysight InfiniiVision MSO-X 3104T oscilloscope is performed to measure
the input signal and output spikes. The artificial mechanoreceptor system, in which the tactile sensor
is implemented using the off-the-shelf piezoelectric device, and a Keysight InfiniiVision MSO-X 3104T
oscilloscope are used to measure the generated input and output signals (Fig. 3.5).
LTspicedevicemodel: In this study, we used a biphasic memristor model proposed in ref. [60]. In this
model, there are four assumptions: (a) cylindrical symmetry, (b) constant temperature within the metallic
core fixed at the transition temperature, (c) ambient temperature at the exterior of the channel, and (d) two-
dimensional heat flow along the radial direction. The total device resistance is described by a function of
phase fraction (Eq. 3.1):
R
ch
(u)=
ρ ins
L
πr
2
ch
[1+(
ρ ins
ρ met
− 1)u
2
]
− 1
(3.1)
whereR
ch
is the channel resistance,ρ ins
andρ met
are metallic and insulating phase electrical resistivity,
respectively,r
ch
is the conduction channel radius, Lis the channel lengthu =r
met
/r
ch
is the metallic phase
fraction expressed in radial coordinates. The dynamical state evolution relation with timet is presented
as Eq. 3.2:
du
dt
=(
d∆ H
du
)
− 1
(R
ch
(u)i
2
− Γ th
(u)∆ T) (3.2)
In Eq. 3.2, the∆ H andΓ th
are the system enthalpy and thermal conductance of the insulating shell,
respectively, and∆ T is the heating temperature; they could be presented as Eqs. 3.3 and 3.4:
38
∆ H =πLr
2
ch
[c
p
∆ T
u
2
− 1
2lnu
+∆ h
tr
u
2
] (3.3)
Γ th
(u)=2πLγ (ln
1
u
)
− 1
(3.4)
The variation of the enthalpy concerningu is thus as the Eq. 3.5
d∆ H
du
=πLr
2
ch
[c
p
∆ T
1− u
2
+2u
2
lnu
2u(lnu)
2
+2∆ h
tr
u] (3.5)
According to the above five equations, we programmed an LTspice model and carried out the simula-
tion.
39
Chapter4
EarlyPreventionofHeartAttacksUsingMemristor-BasedMachine
LearningandSurfaceEnhancedRamanSpectroscopywithCollapsible
Nanofinger
4.1 Abstract
Heart attacks remain a leading cause of death worldwide, and early intervention is crucial for im-
proving patient outcomes. However, current heart-attack detection systems are often slow (> 15min) and
imprecise, leading to delays in treatment and a higher risk of mortality. In this study, we propose a novel
approach to the early detection and prevention of heart attacks using memristor-based machine learn-
ing and plasmon-enhanced Raman spectroscopy with collapsible nanofinger. Our system offers a simple,
low-cost, and rapid detection time of only 10 seconds, providing accurate warnings of silent heart-attack
attempts ahead of actual attacks. By utilizing a memristor-based array for classification, we can harness
the unique properties of memristors, including simultaneously improved speed and energy efficiency, to
40
achieve high precision and accuracy above 90%, potentially in portable devices. Our demonstrations sug-
gest that memristor-based machine learning has the potential to revolutionize heart attack detection and
prevention, offering a promising new avenue for improving patient outcomes.
4.2 Introduction
Heart attacks have a high lethal rate, with over 30.3 million US adults threatened by acute myocardial
infarction (AMI) and one in four deaths in the US due to heart attacks. Despite considerable effort and re-
sources directed towards prevention and treatment,≈ 659 000 people in the US die from AMI yearly [50].
The electrocardiogram (ECG), echocardiogram, and blood tests represent the current dominant diagnostic
techniques. The electrocardiogram measures the heart’s electrical activity, while the echocardiogram em-
ploys ultrasound to produce images of the heart in motion, identifying damaged areas. Because abnormal
signals or images indicate an unhealthy heart, these diagnostic techniques are limited to detecting the
presence or onset of a heart attack and are unsuitable for early diagnosis[40]. Moreover, these diagnos-
tic techniques are characterized by being laborious and time-consuming, and the accuracy of detecting
AMI hinges entirely on the expertise of the physicians performing the tests. As AMI causes sudden heart
stoppage without warning, early intervention is the only way to prevent mortality and morbidity. Thus,
life-saving treatments need an ultra-fast, low-cost, high-sensitivity, and widely deployable early warning
platform with high accuracy. A more cost-effective alternative is identifying acute myocardial infarction
(AMI) biomarkers in the bloodstream. Before the onset of AMI, specific proteins and enzymes such as tro-
ponin and brain natriuretic peptide (BNP) gradually leak into the bloodstream and can be detected through
blood tests[115]. The potential of blood tests as a preventive measure against heart attacks is noteworthy.
Nevertheless, there are some drawbacks to overcome. The current blood tests require a minimum of 15
minutes to separate serum from the blood, isolate target proteins, and collect data to generate results. They
41
have low sensitivity, making them supplementary tests only [21]. As such, rapid and accurate identification
of biomarkers in the blood is a promising approach to address the aforementioned challenges.
Raman spectroscopy, which relies on the inelastic scattering of photons, allows the label-free detection
of molecules like biomarkers, which is the focus of an early prevention approach. However, spontaneous
Raman scattering is inherently weak and challenging to detect. Researchers have demonstrated that pairs
of plasmonic nanostructures formed by sub-nanometer metal nanoparticles can achieve ultra-strong elec-
tromagnetic (EM) fields. The critical goal is precisely controlling the gap size between adjacent metal
structures[90]. The increasing prevalence of cutting-edge nanofabrication methods has led to the creation
of a high-aspect-ratio nanofinger structure that delivers ultra-high electromagnetic signal enhancement,
enabling highly sensitive detection of molecules across a wide range of applications[103]. The nanofin-
ger, a distinctive nanostructure generated via the process of nanoimprint lithography (NIL), yields over
10
11
-fold surface-enhanced Raman spectroscopy (SERS) enhancement, which arises from the precise ma-
nipulation of the gap size[23]. Applying SERS amplifies the intensity of Raman signals by employing metal
nanostructures. SERS allows for the intrinsic fingerprint identification of molecules attached to the surface
of nanostructures with exceptional sensitivity, which is a promising method for preventing heart attacks.
Another challenge is to accurately isolate the BNP signal from the background of the Raman signal.
Because of the complex components in the serum, there is too much noise in the Raman signal, making
it difficult to distinguish between healthy individuals and patients by the existing systems or well-trained
personnel. Neural networks are highly effective in medical classification tasks, particularly in areas such
as disease diagnosis and medical image analysis. Some of the key benefits of using neural networks for
medical classification include improved accuracy, faster diagnosis, reduced errors, etc. Neural networks
can be trained on large amounts of data to identify even subtle patterns or correlations that human analysts
may miss. Therefore, the use of neural networks in medical classification has the potential to improve
diagnosis accuracy, speed up treatment, reduce errors, and enable more personalized care.
42
Memristors have gained attention recently due to their potential use in neuromorphic computing and
neural network acceleration[25]. Memristors can store information more compactly than a traditional
computer since it has multiple conductance states[63]. Using memristors in neural networks can lead to
significant improvements in energy efficiency and speed of computation. Traditional computing archi-
tectures rely on transferring data between a central processing unit (CPU) and memory, which can be a
time-consuming and energy-intensive process. On the other hand, memristors can be integrated into the
neural network itself, reducing the need for data transfer and improving energy efficiency. Overall, using
memristors in neural networks has the potential to create more efficient and adaptable computing systems
that can better mimic the brain’s functionality.
In this study, we have developed an innovative and high-speed early warning platform for heart at-
tacks, as illustrated in Fig. 4.1. Our approach involves the utilization of collapsed nanofinger to capture
and greatly amplify (10
11
fold) the biomarkers associated with heart attacks, resulting in Raman signals
that serve as unique biomarker fingerprints. By employing a 2-layer Neural Network based on an analog
memristor array, we effectively analyze the mixed Raman signals and achieve remarkable accuracy in heart
attack identification. The hardware system we have implemented demonstrates a prediction accuracy of
over 90%, surpassing the performance of well-trained medical personnel. This indicates that most heart
attacks can be identified in advance without waiting 15 mins to separate serum from the blood, enabling
timely intervention. By significantly reducing the rescue time required to less than 10s, our heart attack
early warning system holds the potential to save numerous lives. The outcomes of our work serve as a
noteworthy demonstration of the efficacy of early prevention in mitigating the impact of heart attacks.
4.3 EarlyPreventionSystem
To demonstrate the efficacy of our heart attack prevention system, we developed a nanofinger platform
specifically designed to enhance Raman signals during serum measurements. Additionally, we fabricated
43
Figure 4.1: Schematic of the proposed Early Prevention System, which is comprised of Nanofinger Platform,
Memristor Crossbar identification, and Early Intervention
a One Transistor One Memristor (1T1R) crossbar array, which served as the training platform for a 2-
layer neural network. This integrated system enables accurate prediction of potential heart attacks. The
system provides timely information to attending physicians by detecting biomarkers, such as BNP. In cases
where early intervention is deemed necessary, appropriate measures can be promptly initiated, resulting in
improved patient outcomes and reduced risks associated with heart attacks. The schematic of the proposed
system can be seen in Fig. 4.1.
4.3.1 BiomarkersandReceptors
Natriuretic peptides, particularly BNP and NT-proBNP, are widely recognized as the primary biomark-
ers for heart attacks[84]. BNP has demonstrated significant clinical utility in diagnosing heart failure and
heart failure exacerbation[6]. The American College of Cardiology Foundation acknowledges BNPs as the
most valuable and reliable biomarkers for heart attack warnings[81][30]. Hence, in this experiment, BNP
was selected as the biomarker for AMI, and the corresponding receptors were affixed to the nanofinger,
creating a targeted capture platform for BNP molecules.
4.3.2 HumanSerumSampling
Serum samples were collected from both healthy individuals and patients who either experienced pre-
heart attack symptoms or were threatened by heart-attack attempts. The study involved the participa-
tion of numerous volunteers, including patients with heart disease, from the No.10 People’s Hospital of
44
Shanghai, China. The serum collection took place on different days and at various times. Whenever a pa-
tient experienced discomfort, serum samples were promptly obtained. Simultaneously, the patient’s heart
rhythms were monitored using ECGs, and blood tests were conducted as a reference for the attending
physician to assess the likelihood of a heart attack. In cases where a heart attack was confirmed, immedi-
ate medical intervention was initiated to rescue the patient. The serum sample collected immediately prior
to the heart attack was labeled as "Patient No. XX before the onset of a heart attack," and this labeling only
took place after a confirmed heart attack occurred subsequent to the sample collection.
Our research focused on a specific subset of patients withacute myocardial infarction (AMI). The se-
lection criteria ensured that the participants met specific qualifications. Firstly, only hospitalized patients
were eligible to participate, as it allowed for continuous monitoring and timely serum collection upon ex-
periencing discomfort. Secondly, the hospitalized patients’ willingness to participate in the research was
essential, and their involvement required approval from both the ethical and clinical committees. Thirdly,
we aimed to include participants from diverse age groups, each consisting of an equal number of males
and females, ensuring representative demographics. Additionally, it is essential to note that the serum
collected from patients was labeled as "Patient No. XX before the onset of a heart attack" only when a con-
firmed heart attack occurred after the collection. This labeled serum was then utilized for further analysis
using the memristor-based neural network system.
After a stringent screening process, we obtained qualified serum samples from a total of nine patients
who participated in our research. These samples were collected before the onset of a heart attack. Four of
these patients were female, and the remaining were male. They were distributed across three age groups:
18-35 years (one male and one female), 36-55 years (two males and two females), and 56-80 years (two
males and one female). The collection of serum samples was conducted on different days and at various
times, allowing for a diverse set of samples. Additionally, we followed the same procedure, rules, and
45
Figure 4.2: Left: A transmission electron microscopy (TEM) image and scanning electron microscopy (SEM)
image of the nanogap after the nanofinger collapsed. Right: The numerical simulation of the electric-field
enhancement of a collapsed nanofinger.
requirements to obtain serum samples from nine healthy individuals for comparison. All experiments in-
volving human serum samples were conducted with the approval of the Shanghai No.10 Hospital Ethics
Committee in China, with the approval letter number SHSY-IEC-4.1/21-81/08. This research received sup-
port from the Chinese Association for Clinical Research, with accreditation number ChiCTR2100050983.
Before participation, consent was obtained from each patient involved in the study.
4.3.3 Nanofinger
As mentioned earlier, the nanofinger technology can capture biomarkers and enhance the Raman sig-
nal. The left section of Fig. 4.1 presents the schematic representation of the nanofinger system. Within
this illustration, twelve nanofinger clusters are depicted, with each cluster consisting of four individual
nanofingers, forming hotspots for enhanced detection. Additionally, the figure demonstrates the nanofin-
ger cluster in two states: one without any captured BNP and another with BNP captured. The nanofinger
cluster with receptors is highlighted in green, while the nanofinger cluster with both receptors and cap-
tured BNP is highlighted in red.
4.3.3.1 NanofingerFabricationandCharacteristics
The nanofinger platform, as depicted in Fig. 4.1, was fabricated using a previously reported method[72].
The fabrication process involved techniques such as nanoimprint lithography (NIL), reactive-ion etching
46
(RIE), evaporation deposition, and atomic layer deposition (ALD). The precise control provided by ALD en-
abled the accurate definition of the gap size between the metallic particles, ensuring atomic precision[73].
The nanofinger structure comprised flexible polymer pillars with a height of 300 nm and metal particles
coated with a dielectric layer, resulting in a high-aspect ratio design.
4.3.3.2 NanofingerWorkingMechanism
The working mechanism of the nanofinger platform involved the collapsing of adjacent fingers in
forming a sandwich structure (finger/antibody/finger) driven by capillary force. This occurred after soak-
ing the nanofingers in an antibody solution followed by air drying[57]. The antibodies were connected
to the surface of the gold nanoparticles through covalent bonds facilitated by thiols[97]. The receptors
attached to the nanofingers had the capability to detect target biomarkers amidst the numerous complex
components present in the blood. Furthermore, the captured target biomarkers were immobilized in the
gap between the nanofingers, which offered the maximum enhancement of the electromagnetic (EM) field
due to the gap-plasmon resonance created by the closely spaced nanofingers. This design achieved high
selectivity through a simple surface treatment. Subsequently, the enhanced Raman signals were collected
from the captured BNP.
4.3.3.3 NanofingerEnhancementRatio
The spot size of our 785 nm laser was approximately 1.9 µ m, covering 25 nanofinger clusters, each
composed of four nanofingers[47]. When four nanofingers collapsed together, they created 100 hotspots.
Although BNP was not guaranteed to be trapped in every hotspot, the signals obtained were averages from
100 hotspots. Statistically, there was a sufficient probability for BNP to be captured in one or more hotspots,
enabling easy collection of enhanced Raman signals. Furthermore, the BNP antigen is readily bound to
47
Figure 4.3: Raman signals of serum from healthy and patient individuals were collected using the nanofin-
ger platform.
the BNP antibodies attached to the metallic particles, further enhancing the Raman signals through the
hotspots.
With atomic precision in gap thickness, a significant enhancement factor of approximately 10
11
was
achieved, which is adequate for detecting a single molecule[45]. Various parameters, including the gap
materials, gap distance, and background refractive index, influence the enhancement factor. In this study,
proteins were employed as the gap materials, which resulted in a larger gap size. As a result, the enhance-
ment factor with proteins was approximately2× 10
8
, smaller than in previous studies due to the increased
gap size[45]. Fig. 4.2 illustrates the numerical simulation of the electric-field enhancement in a collapsed
nanofinger.
Fig. 4.2 also showcases a TEM image of the nanogap after the nanofinger collapse, providing visual
insight into the structure. Additionally, Fig. 4.2 presents a scanning electron microscopy (SEM) image of
the nanofinger following collapse, offering a detailed view of the nanofinger configuration.
48
4.3.4 RamanResults
Human serum was directly applied to functionalized nanofingers without preprocessing. BNP anti-
bodies on the nanofingers captured and immobilized BNP antigens on the nanofingers. Metal particles
attached to the nanofinger surfaces carried antibodies specific to heart attack biomarkers, achieving ultra-
high selectivity. Raman signals of the serum were collected for predictive analysis using a neural network.
Raman measurements used a Renishaw inVia Raman microscope with 785 nm laser excitation. A 50x
standard objective in spot focus mode recorded Raman signals from 500 to 2500 cm
− 1
, comprising 1800
data points.
Due to the serum’s complex composition, there were significant spectral variations between measure-
ments of each sample. Multiple measurements were conducted for each sample to obtain comprehensive
information.
A total of 530 Raman spectra were collected, with 144 from healthy individuals and 386 from patients.
Four representative spectra are shown in Fig. 4.3. Due to serum complexity, the noise was present in the
Raman signals, making visual identification of heart attacks challenging. A student trained to identify
the signals achieved only 73.85% accuracy. To address this, a neural network was used to analyze the
Raman signals and uncover intricate data structures[67]. Employing a machine learning algorithm reduced
subjective judgment and minimized misdiagnosis probability[14].
Serums from healthy individuals lacked the BNP biomarker, while patients’ serums contained the
biomarker. SERS techniques enabled rapid detection of target molecules, even at the single-molecule level,
using functionalized nanofingers. This allowed for detecting trace amounts of biomarkers released during
heart attacks, facilitating early warning of AMI.
49
Figure 4.4: Scanning Electron Microscope of the 1T1R device inside a crossbar array (Scale Bar 20µ m)
Figure 4.5: Photograph of a probe card in contact with an operational 128 × 64 1T1R array (scale bar 500
µ m)
4.3.5 HardwareComputingAccelerationwithMemristorArrays
Memristors were utilized to build the neural network in this study due to their favorable characteris-
tics[10]. In our system, the memristor array was constructed by integrating drift memristors with tran-
sistor arrays manufactured through back-end-of-the-line processes. Each Pd/HfO
2
/Ta memristor[28] was
connected to an n-type enhancement-mode transistor in a 1T1R configuration. The 1T1R array functioned
as a fully connected memristor crossbar when all the transistors were turned on. Fig. 4.4 presents a Scan-
ning Electron Microscope image of a 1T1R device. Further fabrication details can be found in the provided
report[41]. The transistor arrays, fabricated with minimized wire resistance in a commercial laboratory,
were integrated with in-house fabricated memristor arrays using photolithography, thin-film deposition,
and liftoff techniques. Fig. 4.6 showcases our 1T1R system for running neural networks, while Fig. 4.5
displays an image of the memristor array with 388 probes.
50
Figure 4.6: The Comprehensive Architecture of the 1T1R Measurement System for Neural Network Clas-
sification
4.3.5.1 ComputingAcceleration
One Transistor One Memristor (1T1R) array enables dot-product calculation through a physical multi-
plication process called vector and matrix multiplication (VMM)[41]. This acceleration technique expedites
the feed-forward process of neural networks and reduces training and inference time consumption [82].
Details regarding the system’s performance and energy efficiency can be found in the provided report[41].
By performing the physical multiplication of a 128-dimensional vector and a 128 × 64 matrix through a
single current read process on the column wires, our system achieves a readout time of less than 10ns,
resulting in a computational throughput of 1.64 tera-operations per second (TOPS).
4.3.6 NeuralNetworkClassificationandPrediction
As previously mentioned, the accuracy achieved by the student (73.85%) was inadequate compared to
what can be achieved with a neural network.
In this study, we employed a fully connected neural network to analyze the mixed Raman signals,
significantly improving the accuracy of heart-attack identification. However, we faced three primary chal-
lenges during the process. Firstly, the signals were highly noisy, posing difficulties in extracting meaningful
51
features for training the neural network. Secondly, our dataset consisted of only a few hundred signals,
necessitating the development of a neural network that could effectively utilize limited data. Lastly, each
signal had a high dimensionality, leading to computational complexities and limitations in prediction per-
formance.
4.3.6.1 PrincipalComponentAnalysis(PCA)
The Raman signals obtained from human serum possess a high dimensionality, comprising 1800 di-
mensions and numerous features. Moreover, these signals often suffer from significant noise due to the
complex composition of serum, making data analysis challenging. We employed Principal Component
Analysis (PCA) as a feature extraction technique to overcome these challenges. By utilizing PCA, we ex-
tracted the most important principal components that capture the essential features of the spectral data.
This dimensionality reduction step, reducing the dimensions from 1800 to 2, preserved crucial information
while enhancing the signal-to-noise ratio of the Raman spectra. The resulting well-labeled, dimension-
reduced Raman signals served as the training dataset for our neural network. For this purpose, we utilized
a widely recognized supervised Machine Learning algorithm, namely the neural network.
To construct the neural network, we randomly divided the dataset into training and test sets. Roughly
80% of the spectra from each group (healthy and patients) were randomly selected as the training set, while
the remaining 20% were reserved as the test data for evaluating the neural network’s performance using
a Memristor array.
Our proposed neural network architecture consists of two layers: an input layer and a hidden layer.
The input layer serves as the entry point for the network, receiving two specific inputs representing the
initial data or features. The hidden layer comprises 50 nodes and plays a critical role in processing and
transforming the input data. Each node in the hidden layer receives inputs from the input layer and per-
forms a weighted sum, followed by an activation function that introduces non-linearity into the network’s
52
Figure 4.7: Accuracy Evolution of the Memristor Neural Network during Training. The accuracy gradually
increases over the course of training, showcasing the network’s learning capabilities.
computations. This layer acts as a powerful feature extractor, allowing the network to learn complex re-
lationships and patterns within the data. The final output layer consists of two nodes that directly receive
inputs from the hidden layer nodes. The network is trained using a suitable optimization algorithm and
a chosen loss function, minimizing the discrepancy between predicted outputs and actual outputs. In this
work, we have thoroughly evaluated the performance of our neural network architecture in addressing
the specific problem at hand.
To execute this neural network on our memristor-based vector-matrix multiplication (VMM) machine,
we transformed the weight matrix into a conductance map of the memristor array, where the conductance
values ranged from 0uS to 1mS. The dimension-reduced Raman signal data were converted to voltages
within the range of 0 to 0.2V. We provided a list of voltages to the crossbar on the row lines, and the resulting
current was collected through the columns of the crossbar, following Kirchhoff’s current summation law
By tuning the conductance of the memristor array, we adjusted the weights of each layer in the neural
network. Additionally, through the backpropagation process, the accuracy of the neural network on the
memristor array gradually improved with increasing training samples. We achieved over 90% accuracy in
predicting acute myocardial infarction (AMI), as shown in Fig. 4.7.
53
4.4 Conclusion
We have developed a cutting-edge heart-attack warning system by combining a SERS-based platform
with a collapsible nanofinger and a memristor-based neural network. This innovative system offers heart
attack warnings in a short time and with high accuracy and can overcome the challenges of rescuing
patients suffering from heart disease. While we have started with a relatively small sample size in our
proof of principle demonstrations, we continue to collect data on patients threatened by heart attacks to
enhance this prediction system’s accuracy further. With this system, we envision saving millions of lives
when applied on a large scale in the future. Moreover, we believe that this method can be extended beyond
heart attack prevention to help monitor other diseases, providing a breakthrough in healthcare.
54
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Abstract (if available)
Abstract
This thesis comprises three works that utilize emerging semiconductor devices, specifically memristors, to address three key challenges in the era of big data. These advancements have the potential to accelerate data processing and other applications.
In Chapter 2, we focus on modeling various types of memristors. Our objective is to facilitate the simulation of memristor applications without the need for physical fabrication. We investigate the underlying mechanisms of several memristors and propose a set of formulas that can accurately emulate three typical types of memristors. Additionally, we demonstrate the application of this model in the construction of a circuit capable of emulating Spike-Timing-Dependent Plasticity (STDP) learning.
Chapter 3 presents the design and proposal of an artificial receptor based on a NbO2 memristor. This receptor serves as an interface, analogous to an afferent nerve in biology, that converts analog signals from sensors into spikes within spiking neural networks. The spiking frequency of the afferent nerve is proportional to the stimulus intensity until it encounters noxiously high stimuli, at which point the spiking frequency begins to decrease at an inflection point. Leveraging this afferent nerve, we further develop a power-free spiking mechanoreceptor system that utilizes a passive piezoelectric device as a tactile sensor. Experimental results indicate the promising potential of our afferent nerve in constructing self-aware neurorobotics in the future.
In Chapter 4, we propose a novel approach to early detection and prevention of heart attacks, employing memristor-based machine learning and plasmon-enhanced Raman spectroscopy with collapsible nanofingers. Our system offers a simple, low-cost, and rapid detection time of only 10 seconds, providing accurate warnings of silent heart-attack attempts prior to actual attacks. By utilizing a memristor-based array for classification, we can leverage the unique properties of memristors, such as improved speed and energy efficiency, to achieve high precision and accuracy above 90%, potentially even in portable devices. Our demonstrations suggest that memristor-based machine learning has the potential to revolutionize heart attack detection and prevention, opening up a promising new avenue for improving patient outcomes.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Zhuo, Ye
(author)
Core Title
Memristor for parallel and analog data processing in the era of big data
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Degree Conferral Date
2023-08
Publication Date
08/14/2023
Defense Date
08/07/2023
Publisher
University of Southern California. Libraries
(digital)
Tag
big data,CMOS,memristor,Modeling,neural networks,neuromorphic computing,OAI-PMH Harvest
Language
English
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Electronically uploaded by the author
(provenance)
Advisor
Yang, Jianhua Joshua (
committee chair
)
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yezhuo@usc.edu;ustc12zy@gmail.com
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https://doi.org/10.25549/usctheses-oUC113298049
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UC113298049
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etd-ZhuoYe-12219.pdf (filename)
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etd-ZhuoYe-12219
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Dissertation
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Zhuo, Ye
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texts
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20230814-usctheses-batch-1084
(batch),
University of Southern California
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University of Southern California Dissertations and Theses
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Tags
big data
CMOS
memristor
neural networks
neuromorphic computing