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Nano-engineered devices for display and analog computing
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Nano-engineered devices for display and analog computing
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Content
NANO-ENGINEERED DEVICES FOR DISPLAY AND ANALOG COMPUTING
by
Hao Yang
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)
May 2022
Copyright 2022 Hao Yang
ii
Dedication
To my family for your support and love.
iii
Acknowledgements
Firstly, I would like to express my sincere gratitude to my advisor Prof. Wei Wu for his mentoring,
guidance, and support over these years. His devotion to science, quest for knowledge, and curiosity
about the unknown inspire me to be a better researcher. Besides, his passion for life, modesty and
patience to people, and courage in the face of difficulty teach me to be a better person. I could not
have imagined having a better advisor for my Ph.D. study.
I would like to thank the rest members of my qualifying exam committee and dissertation
committee, Prof. Stephen B. Cronin, Prof. Aiichiro Nakano, Prof. Michelle L. Povinelli, and Prof.
Han Wang, for their kind service and support.
I would like to acknowledge all the collaborators. My sincere thanks go to Prof. Michelle L.
Povinelli and Dr. Liang Peng for the discussion on the all-dielectric metasurface project, Dr.
Haneol Lim and Prof. Jongseung Yoon for the preparation of TiO2 films, Prof. Han Wang, Prof.
Joshua Yang, and Hefei Liu for the help on memristor-related projects, Prof. Stephen B. Cronin
for the preparation of Al2O3 films, Prof. Aiichiro Nakano, Prof. Paulo Branicio, Prof. Rajiv Kalia,
and Prof. Priya Vashishta for the help on molecular dynamics simulations and corresponding
analysis, Prof. Fanxin Liu for taking the high-quality TEM and EDS images. These great
researchers provided invaluable expertise in different areas, which have greatly helped me
diversify my knowledge and broaden my vision.
I would also like to thank all our research group members. I enjoyed working in such a friendly,
encouraging, and active group. I would like to thank Dr. He Liu for teaching me nano-fabrication
skills and the support on the all-dielectric metasurface project, Dr. Yuhan Yao, Dr. Yifei Wang,
and Dr. Yuanrui Li for sharing great ideas and teaching me research methodology, Dr. Boxiang
iv
Song and Buyun Chen for the collaboration in memristor-related projects, Deming Meng, Pan Hu,
Yunxiang Wang, Tse-Hsien Ou, and Zerui Liu for discussing research projects and the kind
support in my daily life. All the works during my Ph.D. include collaboration and hardworking of
them.
I am so lucky to have some fabulous friends outside of the group, including but not limited to
Dr. Jiajun Xu, Dr. Jia Ding, Dr. Ji Liu, Dr. Lurui Zhao, Yunjie Li, Haimeng Zhang, Hongbo Wang,
and Ye Zhuo. Thank you all for being on my side all the time and making my life eventful and full
of great memories.
Last, and most importantly, I would like to thank my family. I cannot thank my parents enough
for their love, encouragement, and sacrifice. I also want to express appreciation to my girlfriend,
Wenting Zhao. She and her love, encouragement, and support help me through difficult times and
make me enjoy every day of our life. I would not have all these achievements today without them.
v
Table of Contents
Dedication ....................................................................................................................................... ii
Acknowledgements ........................................................................................................................ iii
List of Tables ............................................................................................................................... viii
List of Figures ................................................................................................................................ ix
Abstract ....................................................................................................................................... xxii
Topic 1: Switchable All-Dielectric Metasurfaces for Full-Color Reflective Display .................... 1
Chapter 1 Introduction ................................................................................................................ 2
1.1 Display Technologies for Mobile and Wearable Devices ................................................ 2
1.2 Reflective Display Based on Switchable All-Dielectric Metasurfaces ............................. 4
Chapter 2 Design of Switchable All-Dielectric Metasurfaces .................................................... 6
2.1 Architecture of Full-Color Reflective Display Based on Metasurfaces ........................... 6
2.2 Numerical Calculation and Optimization of Switchable All-Dielectric Metasurfaces ..... 8
Chapter 3 Characterization of Switchable All-Dielectric Metasurfaces ................................... 15
3.1 SEM Images and Optical Measurements of Fabricated Metasurfaces ........................... 15
3.2 Reproduction of Colors from the Tandem Switchable All-Dielectric Metasurfaces ...... 17
3.3 Large Viewing Angle, Ultrahigh Resolution Capability, and Feasibility of Hybrid Display
............................................................................................................................................... 20
Chapter 4 Effects of Roughness on the Performance of Fabricated Metasurfaces ................... 24
4.1 Roughness and Imperfection of Fabricated Metasurfaces .............................................. 24
4.2 Study of the Roughness Effect on Metasurface Performance ........................................ 25
Chapter 5 Resonant Modes Engineering to Enhance the Metasurface Performance ................ 37
Summary ................................................................................................................................... 43
Topic 2: Memristor Characteristics Engineering by Controlling the Crystallinity of Switching
Layer Materials ............................................................................................................................. 45
vi
Chapter 6 Introduction to the Memristor .................................................................................. 46
Chapter 7 Device Fabrication ................................................................................................... 48
7.1 Fabrication Process ......................................................................................................... 48
7.2 Controlling the Crystallinity of Switching Layer Material ............................................. 49
Chapter 8 Device Electrical Performance Characterization ..................................................... 54
8.1 I-V Curves and Retention Test ....................................................................................... 54
8.2 Pulse Measurements ........................................................................................................ 57
8.3 Number of Conductance States ....................................................................................... 61
Chapter 9 The Effect of the Switching Layer Material Crystallinity on Memristor Characteristics
................................................................................................................................................... 65
9.1 Comparisons Between Memristors that Adopt Different Crystalline Al2O3 .................. 65
9.2 Molecular Dynamics Simulations ................................................................................... 66
9.3 Working Mechanism Study ............................................................................................ 67
Summary ................................................................................................................................... 72
Topic 3: A Memristor-Based Hybrid Analog-Digital Computing Platform for Mobile Robotics 73
Chapter 10 Introduction ............................................................................................................ 74
10.1 Control of Mobile Robotics .......................................................................................... 74
10.2 Memristor-Based Hybrid Analog-Digital Computing Platform ................................... 75
Chapter 11 Hybrid Analog-Digital Platform Enabled by Memristor ....................................... 78
11.1 Architecture of Hybrid Analog-Digital Platform .......................................................... 78
11.2 Memristor for Hybrid Analog-Digital Platform ........................................................... 79
Chapter 12 Hardware Acceleration of Kalman Filter ............................................................... 84
12.1 Continuous-Time Analog Kalman Filter Enabled by Memristor ................................. 84
12.2 Performance of the Continuous-Time Analog Kalman Filter ....................................... 86
12.3 Kalman Gain Optimization of the Analog Kalman Filter ............................................. 88
Chapter 13 Hardware Acceleration of PD controller ................................................................ 91
13.1 Adaptive PD Controller Enabled by Memristor ........................................................... 91
vii
13.2 Performance of the Adaptive PD Controller ................................................................. 93
13.3 Damping Ratio Optimization of the Adaptive PD Controller ...................................... 94
Chapter 14 Comparison Between Different Platforms ............................................................. 99
Chapter 15 Memristor-based Analog Computing for Other Applications .............................. 102
Summary ................................................................................................................................. 108
Conclusion and Future Work ...................................................................................................... 109
References ................................................................................................................................... 110
Publications & Patents ................................................................................................................ 119
Experimental Section .................................................................................................................. 120
viii
List of Tables
Table 3.1: State of each metasurface in the demonstrations of color reproduction. ..................... 20
Table 7.1: Refractive index, crystallinity, and average grain size of Al2O3 deposited at different
temperatures. ................................................................................................................................. 50
Table 10.1: The comparison of electronically reconfigurable analog circuits using different devices.
....................................................................................................................................................... 75
Table 14.1: The comparison of speed and power efficiency on different platforms. ................... 99
Table 15.1: Solution to a QP problem from the analog circuit and the MATLAB simulation. . 104
ix
List of Figures
Figure 1.1: Parallel architecture for full-color reflective display. The theoretical maximum of
reflection efficiency is 33%, which is not favorable for reflective display. ................................... 3
Figure 1.2: Schematic illustration of the hybrid display. A hybrid display is constructed by stacking
a switchable reflective display on top of a transmissive display. ................................................... 4
Figure 2.1: Schematic illustration of the full-color reflective display. a) Tandem architecture for
full-color reflective display. Each pixel contains three color (blue, green, and red) subpixels
stacked, and the subpixels are made of hybrid all-dielectric metasurface. The theoretical maximum
of reflection efficiency can reach 100%, which is ideal for reflective display. b) Metasurface can
switch between “On” and “Off” state by introducing high-index liquid. Metasurface for blue light
is shown as an example. In “On” state, blue light from incident light is reflected. In “Off” state,
the metasurface is transparent and no light is reflected. ................................................................. 6
Figure 2.2: The ideal spectra of color metasurfaces: a) blue, b) green, c) red. ............................... 8
Figure 2.3: Schematic of the switchable all-dielectric metasurface. .............................................. 9
Figure 2.4: Calculated reflection spectra of the blue metasurface upon light incidence at different
polarizations. The spectra are identical, which indicates the metasurface is polarization
independent. .................................................................................................................................... 9
Figure 2.5: Calculated reflection spectrum of the blue metasurface at normal incidence situation.
Electrical field distributions of the blue metasurface at different wavelengths and incident angles.
....................................................................................................................................................... 10
Figure 2.6: Calculated reflection spectrum of the blue metasurface versus the lattice constant p,
hybrid pillar width w, TiO2 height ht, and SiO2 height hs (only one parameter of p, w, ht, and hs is
x
changing, given that other parameters are fixed. The fixed values are 390, 140, 180, and 300 nm
for p, w, ht, and hs, respectively). .................................................................................................. 11
Figure 2.7: Calculated reflection spectrum of the red metasurface versus the background index.
....................................................................................................................................................... 13
Figure 2.8: Calculated reflection spectra of blue, green, and red metasurfaces in “On” and “Off”
states after optimization. ............................................................................................................... 14
Figure 3.1: a) Photos of blue, green, and red metasurfaces in “On” and “Off” states (taken under
ordinary office lighting conditions with a cellphone camera), and measured color gamut of the
three metasurfaces shown in a CIE 1931 color map. b) Cross section SEM images of blue, green,
and red metasurfaces, respectively. .............................................................................................. 15
Figure 3.2: Measured reflection spectra of “On” and “Off” states of three metasurfaces,
respectively. .................................................................................................................................. 16
Figure 3.3: Reproduction of colors from the tandem switchable metasurfaces. a) Photos of the
tandem metasurfaces (the blue metasurface is at the top, the green metasurface is in the middle,
and the red metasurface is at the bottom) under different combinations of “On”/“Off” states of
each metasurfaces. The mixed colors are shown in the overlapped regions (within black dashed
rectangles). b) The corresponding measured reflection spectra of the tandem metasurfaces in (a),
respectively. .................................................................................................................................. 18
Figure 3.4: a) Calculated reflection spectrum of the blue metasurface versus the viewing angle. b)
Photos of a blue metasurface taken under different viewing angles. As shown, the color remains
blue within 60° . ............................................................................................................................. 21
xi
Figure 3.5: Photo of pixels in different sizes on a green metasurface. The black regions in the
metasurface had been etched away, and the number marked at each region represents the edge
length of the square pixel in that region. ....................................................................................... 22
Figure 3.6: Blue, green, and red metasurfaces were stacked together in their “Off” state and were
placed on top of a mobile device screen (transmissive display). The thickness of each color
metasurface with its substrate is 100 μm. The chromatic letters “USC” from the transmissive
display was seen clearly through the tandem metasurfaces. ......................................................... 23
Figure 4.1: a) Schematic of the ideal all-dielectric metasurface. The nanopillar is a rectangle with
smooth surfaces. b) Schematic of the fabricated all-dielectric metasurface. The surfaces of
nanopillar are rough. ..................................................................................................................... 24
Figure 4.2: a) Schematic of the ideal all-dielectric metasurface, which has two layers (TiO2 and
SiO2). b) Calculated reflection spectrum of the ideal all-dielectric metasurface at normal incidence.
There are two reflection peaks at 652 nm and 710nm, respectively. ............................................ 26
Figure 4.3: a) 𝐸 2distributions of the ideal all-dielectric metasurface at different wavelengths (652
or 710 nm) in different planes (YZ-plane or XZ-plane). b) Electrical field component (𝑬 ∥
or 𝑬 ⊥
)
distributions of the ideal all-dielectric metasurface at different wavelengths (652 or 710 nm) in
YZ-plane, where 𝑬 ∥
= √𝑬 𝒙 2
+ 𝑬 𝒛 2
and 𝑬 ⊥
= 𝑬 𝒚 . The 𝑬 ∥
represents the electrical field component
that is parallel to the nanopillar surface, while the 𝑬 ⊥
represents the electrical field component that
is perpendicular to the nanopillar surface. .................................................................................... 27
Figure 4.4: a) A “bump” on the interface between two materials 𝜖 1
(TiO2) and 𝜖 2
(background).
An applied electric field E will induce a dipole moment on the surface (blue/red color denotes
xii
positive/negative charge). b) Schematic of all-dielectric metasurface with a lossy shell. 5nm-thick
lossy shell is outside the TiO2 layer. ............................................................................................. 29
Figure 4.5: Calculated reflection spectrum of the all-dielectric metasurface with the lossy shell
(Figure 4.4b) at normal incidence. ................................................................................................ 30
Figure 4.6: Electrical field component (𝑬 ∥
or 𝑬 ⊥
) distributions of the all-dielectric metasurface
with the lossy shell (Figure 4.4b) at different wavelengths (652 or 710 nm) in the YZ-plane. .... 31
Figure 4.7: Calculated reflection spectra of the ideal all-dielectric metasurfaces (Figure 4.2a),
measured reflection spectra of the fabricated all-dielectric metasurfaces (Figure 3.1b and 4.1b),
and calculated reflection spectra of the all-dielectric metasurface with the lossy shell (Figure 4.4b).
All spectra are at normal incidence. Calculated reflection spectra of the all-dielectric metasurface
with the lossy shell are much closer to the measured spectra. ...................................................... 32
Figure 4.8: a) Top view SEM image of the all-dielectric metasurface. The roughness of nanopillars
can be observed clearly. b) Edge detection result of SEM image in Figure 4.8a. The average
roughness scale is 8nm (3𝜎 ). ........................................................................................................ 33
Figure 4.9: Calculated reflection spectra with different level roughness and measured reflection
spectrum of the all-dielectric metasurface at normal incidence. ................................................... 34
Figure 4.10: Resonant modes extraction from fitting measured reflection spectrum of the fabricated
all-dielectric metasurface. The three fitting peaks are at 594 nm, 653 nm, and 697 nm, respectively.
To be noticed, the second (653 nm) and third peaks (697 nm) are corresponding to the main optical
resonances. The first peak (594 nm) represents the side lobe in the shorter wavelength region. . 35
Figure 4.11: a) Resonant modes extraction for calculated reflection spectra in Figure 4.9. Higher-
level roughness has much more effect on the second peak, which is consistent with the previous
xiii
conclusion. b) The change of two fitting peaks value in reflection spectra versus the roughness
level. The two red points are experimental results, which demonstrate the effectiveness of
calculations. .................................................................................................................................. 36
Figure 5.1: a) Schematic of the all-dielectric metasurface at oblique incidence. b) Calculated
reflection spectra of the red metasurface versus the incident angle. c) The numerically calculated
color of the red metasurface versus the incident angle shown in a CIE 1931 color map. ............ 38
Figure 5.2: The numerically calculated color of the blue metasurface versus the incident angle
shown in a CIE 1931 color map. ................................................................................................... 39
Figure 5.3: |𝐸 |
2
distributions of the red metasurface (Figure 5.1a) upon 30° incidence at 580 nm
and 667 nm. The left and right field distributions correspond to the point “1” in Figure 5.1b and
the point “2” in Figure 5.1b, respectively. .................................................................................... 40
Figure 5.4: a) Schematic of the all-dielectric metasurface with an a-Si cap at oblique incidence.
The thickness of the a-Si cap is 40 nm. b) Calculated reflection spectra of the all-dielectric
metasurface with an a-Si cap versus the incident angle. c) The numerically calculated color of the
all-dielectric metasurface with an a-Si cap versus the incident angle shown in a CIE 1931 color
map. ............................................................................................................................................... 41
Figure 5.5: |𝐸 |
2
distributions of the red metasurface (Figure 5.4a) upon 30° incidence at 580 nm
and 667 nm. The left and right field distributions correspond to the point “1” in Figure 5.4b and
the point “2” in Figure 5.4b, respectively. .................................................................................... 42
Figure 7.1: Pt/Al2O3/Ta/Pt cross-point memristor. a) Fabrication process. b) Schematic of the Pt/
Al2O3/Ta/Pt cross-point memristor. c) Optical microscope image of the fabricated Pt/ Al2O3/Ta/Pt
cross-point memristor. .................................................................................................................. 49
xiv
Figure 7.2: XRD spectra of Al2O3 films at different deposition temperatures (80 ° C, 120 ° C, 160 ° C,
and 200 ° C). .................................................................................................................................. 51
Figure 7.3: a) TEM image of 80 ° C deposited Al2O3 film, which is amorphous. The SiO2 layer is
the native oxide layer on top of the Si substrate. b) TEM image of 200 ° C deposited Al2O3 film,
which is polycrystalline. The SiO2 layer is the native oxide layer on top of the Si substrate. c)
Corresponding FFT pattern of TEM image in (a) (Frequency range DC ~ 1/0.020 [1/nm]). d)
Corresponding FFT pattern of TEM image in (b) (Frequency range DC ~ 1/0.020 [1/nm]). ...... 52
Figure 7.4: a) The HAADF STEM image of 80 ° C deposited Al2O3 film. b) – e) Corresponding
EDS images of 80 ° C deposited Al2O3 film. The C layer is the protection layer for the focused ion
beam (FIB). The SiO2 layer is the native oxide layer on top of the Si substrate. ......................... 53
Figure 8.1: I-V curves (plot in log scale) from 5 by 5 μm
2
Pt/Al2O3/Ta/Pt cross-point memristors,
which use Al2O3 films deposited at different temperatures (80 ° C, 120 ° C, 160 ° C, and 200 ° C) as
the switching layer. The memristors can be set with a positive voltage sweep and then reset with a
negative voltage sweep. In the positive voltage sweep, the applied compliance currents for 80 ° C,
120 ° C, 160 ° C, and 200 ° C deposited Al2O3 memristors were 3 mA, 3 mA, 5 mA, and 5 mA,
respectively. .................................................................................................................................. 54
Figure 8.2: I-V curves (plot in linear scale, same data as Figure 8.1) from 5 by 5 μm
2
Pt/Al2O3/Ta/Pt
cross-point memristors. The memristors have good I-V linearity. ............................................... 55
Figure 8.3: 100 Cycles I-V curves (plot in linear scale) of 5 by 5 μm
2
Pt/80 ° C deposited
Al2O3/Ta/Pt cross-point memristor. .............................................................................................. 56
Figure 8.4: a) Retention test of Pt/80 ° C deposited Al2O3/Ta/Pt cross-point memristors. 20
memristors were used to test the retention. Before the test, 10 memristors were set to On state, and
xv
the other 10 memristors were set to Off states. b) Number of the unchanged (not change from On
state to Off state) Pt/80 ° C deposited Al2O3/Ta/Pt memristor in the 85 ° C retention test versus the
test time. ........................................................................................................................................ 57
Figure 8.5: a) The Pt/80 ° C deposited Al2O3/Ta/Pt memristor can be repeatedly switched between
On and Off states with 3 μs pulses (Positive pulse voltage: 2.5 V; Negative pulse voltage: −2.5 V).
Here shows the 1000 switching cycles result. b) 1000 switching cycles of the Pt/120 ° C deposited
Al2O3/Ta/Pt memristor with 3 μs pulses (Positive pulse voltage: 2.5 V; Negative pulse voltage:
−2.5 V). c) 1000 switching cycles of the Pt/160 °C deposited Al2O3/Ta/Pt memristor with 3 μs
pulses (Positive pulse voltage: 3.4 V; Negative pulse voltage: −3.0 V). d) Pulse switching of the
Pt/200 ° C deposited Al2O3/Ta/Pt memristor with 3 μs pulses (Positive pulse voltage: 6.0 V;
Negative pulse voltage: −6.0 V). This device is hard to switch with pulses (switching cycles < 10).
....................................................................................................................................................... 58
Figure 8.6: a) – d) 1000 switching cycles of four different Pt/80 ° C deposited Al2O3/Ta/Pt
memristors with 3 μs pulses (Positive pulse voltage: 2.5 V; Negative pulse voltage: −2.5 V). e) –
h) 1000 switching cycles of four different Pt/120 ° C deposited Al2O3/Ta/Pt memristors with 3 μs
pulses (Positive pulse voltage: 2.5 V; Negative pulse voltage: −2.5 V). ...................................... 61
Figure 8.7: a) Our memristor can be set to different conductance states by using different
compliance currents. Here shows the I–V curves for Pt/80 ° C deposited Al2O3/Ta/Pt memristor
with different conductances, which has 16 states (2
4
). (b) I–V curves for Pt/200 ° C deposited
Al2O3/Ta/Pt memristor with different conductances, which has 157 states (more than 2
7
). ........ 61
Figure 8.8: Through controlling the compliance currents, our memristor can be set to the target
conductance state precisely. Here shows the ten set conductance states (200μS, 400μS, 600μS,
xvi
800μS, 1000μS, 1200μS, 1400μS, 1600μS, 1800μS, and 2000μS) of Pt/200 °C deposited
Al2O3/Ta/Pt memristor. ................................................................................................................. 62
Figure 8.9: Repeatability and stability of multilevel conductance states of Pt/Al 2O3/Ta/Pt
memristors. a) - b) Two more Pt/200 ° C deposited Al2O3/Ta/Pt memristors with multilevel
conductance states. c) - d) Retention tests of Pt/80 ° C deposited Al2O3/Ta/Pt and Pt/200 ° C
deposited Al2O3/Ta/Pt memristors with multilevel conductance states, respectively. The tests were
conducted at room temperature (25 ° C). ....................................................................................... 64
Figure 9.1: a) The change of Set/Reset voltage of Pt/Al2O3/Ta/Pt memristor versus the Al2O3
deposition temperature. b) The change of the On/Off ratio of Pt/Al2O3/Ta/Pt memristor versus the
Al2O3 deposition temperature. The On/Off ratios are calculated at read voltage 0.3 V according to
the Figure 8.1. c) Resistance distribution (2% to 98%) of the Pt/Al2O3/Ta/Pt memristors that have
different Al2O3 deposition temperatures at both On and Off states in the pulse switching
measurements (Figure 8.5a, 8.5b, and 8.5c). ................................................................................ 65
Figure 9.2: a) Microstructure of amorphous Al2O3 layer generated by a melt-quench scheme. b)
Microstructures of 2 nm grain-sized Al2O3 layer generated by a Voronoi-annealing scheme. c)
Microstructures of 4 nm grain-sized Al2O3 layer generated by a Voronoi-annealing scheme. d)
Microstructures of 50 nm grain-sized Al2O3 layer generated by a Voronoi-annealing scheme. e)
Connected clusters of low-density voxels in different Al2O3 layers identified using a depth first
search method. Connected clusters in each layer are denoted by different colors for clarity. ...... 67
Figure 9.3: a) Average cross-sectional area (in the x-y plane) for each cluster of low-density voxels
versus the Al2O3 layer type. b) Average length of low-density voxels cluster versus the Al2O3 layer
type. 50 nm grain-sized Al2O3 structures with larger grain sizes contain low-density clusters of the
longest length (along the z direction). c) Density of low-density voxels cluster versus the Al2O3
xvii
layer type. Amorphous and small-grained structures have a significantly larger number density of
connected voxel clusters than larger grain-sized structures. ......................................................... 69
Figure 11.1: The memristor-based hybrid analog-digital computing platform. a) Schematic
illustration of hybrid analog-digital computing platform. b) Schematic representation of the
biological inspiration from the brain structure. In the hybrid analog-digital computing platform,
the analog component acts as the cerebellum that controls the motion of the robot, while the digital
component acts as the cerebrum running the high-level algorithms. c) Image of the mobile robotic
system (i.e., the mobile inverted pendulum) in this work. d) Image of the memristors packaged on
the chip carrier. e) Optical microscope image of the fabricated Pt/Al 2O3/Ta/Pt cross-point
memristor, the scale bar is 100 µ m. .............................................................................................. 79
Figure 11.2: a) I-V characteristics of the Pt/Al2O3/Ta/Pt memristor (plot in linear scale) from 5 by
5 μm
2
Pt/ Al2O3/Ta/Pt cross-point memristors. This memristor has excellent I-V linearity and large
On/Off ratio. The insert of Figure 10.2a shows the structure of the Pt/Al2O3/Ta/Pt cross-point
memristor. 20nm Pt was deposited as top and bottom electrodes. 8nm Ta and 8nm Al 2O3 work as
the active layer and switching layer respectively. b) The memristor can be precisely set to different
conductance states using DC sweep voltages with different compliance currents. The I–V
characteristic for Pt/Al2O3/Ta/Pt memristor with different conductance states are shown. c) The
conductance state response under potentiating pulses (red) and depressing pulses (blue). .......... 80
Figure 11.3: a) Circuit schematic diagram for pulse tuning. The bottom electrode of the memristor
is connected to the drain of the transistor to build a one transistor and one resistor (1T1R) structure.
Different voltage pulses applied on the pulse tuning circuit are Vapply, Vgate, and Vreset. The voltage
on the top electrode of the memristor (Vapply) and the reset voltage (Vreset) are used to control the
set or the reset process of the memristor. And the compliance current is controlled by the gate
xviii
voltage (Vgate). Waveforms of b) potentiating pulses and c) depressing pulses. During the
potentiating process, the memristor is only programmed by set pulses (Vset). Both reset pulses
(Vreset) and set pulses (Vset) are used in the depressing process. The conductance state of the
memristor is measured without being changed via reading pulses (Vread). ................................... 82
Figure 12.1: a) Block diagram of angle signal estimation with continuous-time analog Kalman
filter. The estimated angle signal (𝜃 𝑒𝑠𝑡 ( 𝑠 ) ) ) can be obtained after the Kalman filter with input
signals from both the gyroscope ( 𝜔 𝑒𝑠𝑡 ( 𝑠 ) ) and the accelerometer ( 𝜃 𝑚𝑒𝑎 ( 𝑠 ) )). The complex
frequency in Laplace transform is denoted S. b) Circuit schematic diagram with the device’s
parameters of the hardware implementation of the continuous-time analog Kalman filter, where
the Kalman gain (𝐾 1
) ) is implemented using a memristor. The 5V voltage is denoted VCC. c)
Photo of the continuous-time analog Kalman filter. c) Photo of the continuous-time analog Kalman
filter. .............................................................................................................................................. 85
Figure 12.2: The robotic arm for testing the continuous-time analog Kalman filter. ................... 87
Figure 12.3: Measured raw data of the angle signal (black curve) and the filtered data (red curve)
by the continuous-time analog Kalman filter. The test was performed on a rotating robotic arm
(Figure 12.2). ................................................................................................................................ 88
Figure 12.4: a) Estimated angle signal with the same Kalman gain using different sensors. To be
noticed, different gyroscopes are all from the same model (model: SMAKN ENC-03RC), as shown
in the inserted photos. b) Estimated angle signal from the same analog Kalman filter under different
temperatures. All the curves above are offset to show the comparison clearly. ........................... 89
Figure 12.5: Estimated angle signal with different Kalman gains (different conductance states of
memristor). An overlarge conductance state causes an overshoot response (blue curve), while an
xix
insufficient conductance state causes an overdamped response (black curve). The optimized
conductance state of the memristor (red curve) is chosen for the continuous-time analog Kalman
filter using the binary search method. ........................................................................................... 90
Figure 13.1: a) Schematic of the mobile inverted pendulum with the proportional–derivative (PD)
controller, which can be considered a simple damped harmonic oscillator. b) Block diagram of the
transfer function of the mobile inverted pendulum with a PD controller, where 𝜃𝑠 is the angle of
the mobile inverted pendulum, 𝑢𝑠 is the acceleration of the motion, 𝑊 ( 𝑠 ) is the disturbance of the
environment, 𝐿 is the length of the robot, and 𝑔 is the gravity of the earth. The complex frequency
in the Laplace transform is denoted S. .......................................................................................... 92
Figure 13.2: a) Circuit schematic diagram with the device’s parameters of the hardware
implementation of the adaptive PD controller, where the damping ratio (𝐾 𝑑 /𝐾 𝑝 ) is implemented
using a memristor. The acceleration of the motion (𝑢 ( 𝑡 ) ) is directly obtained from the analog PD
controller given the estimated angle (𝜃 𝑒𝑠𝑡 ( 𝑡 ) ) ) and angular velocity signals (𝜔 𝑒𝑠𝑡 ( 𝑡 ) ). The 5V
voltage is denoted VCC. b) Photo of the adaptive PD controller.................................................. 93
Figure 13.3: a) Hardware structure of the control system of the mobile inverted pendulum. b)
Experimental data of several impulse responses of the mobile inverted pendulum at different
conductance states of the memristor. The red arrow indicates the disturbance. ........................... 94
Figure 13.4: Flowchart of the random search optimization algorithm implementation on the
memristor-based hybrid analog-digital computing platform. During each learning epoch, the
control performance of certain memristor conductance states with and without small perturbation
(adding 200 Ω resistor) are tested. Then the cost function and its gradient are calculated from the
xx
angle signal data accordingly. After that, the weight of the memristor is updated towards
minimizing the cost function. ....................................................................................................... 96
Figure 13.5. Simulated (black curve) and experimental (red curve) data of the adaptive learning
process........................................................................................................................................... 97
Figure 13.6. Experimental data of impulse responses of the mobile inverted pendulum during the
adaptive learning process. ............................................................................................................. 98
Figure 14.1: a) The settling time of the mobile inverted pendulum with the hybrid platform (~ 1 s)
is much shorter than the one with the digital platform (more than 3 s). The red arrow indicates the
disturbance. b) The difference of the slope (blue dashed line) of the angle signal shows that the
mobile robotic system using the hybrid platform has a faster response than the one using the digital
platform. The red arrow indicates the disturbance...................................................................... 101
Figure 15.1: Electric circuit solving a QP. Vertical wires are variable nodes with potentials
𝑉 1
, … , 𝑉 𝑛 . Black dots represent resistors that connect vertical and horizontal wires. Horizontal wires
are cost or constraint nodes. Some of the horizontal wires are connected to the ground via a
negative resistance, a constant voltage source, and a diode for inequality. The topmost horizontal
wire is the cost circuit which is connected to a constant voltage source. ................................... 103
Figure 15.2: The circuit simulation solving a QP problem using SPICE software. ................... 104
Figure 15.3: Electric circuit solving a QP with the memristor crossbar array. ........................... 105
Figure 15.4: a) 128*64 memristor crossbar array, where the linewidth is 5 𝜇 m and the gap between
two lines is 5 𝜇 m. b) 128*64 memristor crossbar array, where the linewidth is 2 𝜇 m and the gap
between two lines is 5 𝜇 m. .......................................................................................................... 106
Figure 15.5: The circuit architecture of the memristor-based analog LP/QP solver. ................. 107
xxi
Figure 15.6: The control architecture of a general plant model using an analog optimization solver.
..................................................................................................................................................... 107
xxii
Abstract
This dissertation summarizes the three topics in my Ph.D. study. The focus is nano-engineered
devices for various applications that include display and analog computing.
The first part (Chapter 1 - 5) covers the switchable all-dielectric metasurfaces for full-color
reflective display. Our invented full-color reflective display system based on metasurfaces has a
three-layer tandem architecture and operates in an RGB additive mode. Each individual
metasurface manipulates a primary color (blue, green, or red), while it displays the color in its “On”
state and becomes transparent in its “Off” state. A hybrid display can be achieved by overlaying a
full-color reflective display on top of a transmissive display. This technology aims to solve the
drawbacks (e.g., high energy consumption and lack of readability under bright sunlight) of
conventional transmissive display in mobile and wearable device applications. In addition, this
work proposes and experimentally verifies a method to analyze the effect of roughness on
metasurface performance, which can help design more manufacturable all-dielectric metasurfaces
based on fabrication capability. Moreover, a method to enhance metasurface performance based
on resonant modes engineering is proposed and numerically verified.
The second part (Chapter 6 - 9) covers memristor characteristics engineering. Recently, the
development of memristor has attracted great interest in the semiconductor industry. Memristors
may play important roles in the future generations of electronic systems, such as bio-inspired
neuromorphic computing, analog computing, and in-memory computing. However, different
applications have different requirements for the characteristics of memristors, including the
operation voltage, the on/off ratio, and the number of conductance states. In this work, we propose
and demonstrate a method to modify the memristor characteristics specifically by controlling the
crystallinity of the switching layer material. By setting the atomic layer deposition (ALD)
xxiii
temperature, the crystallinity of deposited Al2O3 can be controlled. Using different crystalline
Al2O3 as the memristor switching layer, the characteristics of corresponding Pt/Al2O3/Ta/Pt
memristors can be modified precisely. More importantly, molecular dynamics simulations were
performed to qualitatively study how the switching layer crystallinity affects the characteristics of
memristors. This work deepens our understanding of the working mechanism of memristors and
paves the way for using memristors in a broad spectrum of applications.
The third part (Chapter 10 - 15) covers a memristor-based hybrid analog-digital computing
platform for mobile robotics. This work proposes and demonstrates a hybrid analog-digital
computing platform enabled by memristors on a mobile inverted pendulum robot. In the hybrid
computing platform, the memristor-based analog components are designed as a bio-inspired
implementation of the “cerebellum” in the robot brain, while the digital component implementing
high-level algorithms serves as the “cerebrum” of the robot brain. The memristor-based analog
component can operate independently without consuming the computing power from the digital
component. Both the Kalman filter algorithm and the control algorithm, the two main functions of
the cerebellum, are implemented and accelerated using this hybrid platform. Compared with the
mobile inverted pendulum using a conventional digital computing platform, the robot with our
hybrid computing platform not only achieves better stability and faster response, but also yields
one order of magnitude of enhancement in speed and energy efficiency. Besides, the inverted
pendulum robot can tune the conductance states of memristors adaptively using a model-free
optimization method to achieve optimal control performance. This part also introduces and
numerically demonstrates the idea of using a memristor crossbar array to build an analog LP/QP
solver.
1
Topic 1:
Switchable All-Dielectric Metasurfaces for Full-Color Reflective Display
2
Chapter 1 Introduction
1.1 Display Technologies for Mobile and Wearable Devices
The blossom of mobile and wearable devices facilitates our life and improves work efficiency.
However, the display technologies used in those devices still need to be improved dramatically.
Mobile and wearable devices mainly adopt transmissive displays. The displays consume a big
portion of energy, which requires battery recharge more frequently, and the displays are hard to
read under bright sunlight. Those are due to the inherent drawbacks of transmissive displays. First,
all light from a transmissive display is provided by an active light source that consumes energy
continuously when the display works. Besides, the display can be quite dim under direct sunlight.
Compared to transmissive display, reflective display is illuminated by ambient light. Therefore,
it does not consume energy for backlight and is readable under bright sunlight. However, two
fundamental issues limit the application of reflective display to mobile and wearable devices.
Firstly, parallel architecture is currently adopted in full-color reflective display technologies
(Figure 1.1) [1, 2]. Even in the ideal case, the optical efficiency of a parallel architecture is limited
to a poor value of 33% owing to the filling ratio of each subpixel. Secondly, when the ambient
light is insufficient, the performance of reflective display becomes poor.
3
Figure 1.1: Parallel architecture for full-color reflective display. The theoretical maximum of
reflection efficiency is 33%, which is not favorable for reflective display.
A “perfect” display for mobile and wearable devices should take the advantages of both
transmissive display and reflective display. We propose a hybrid display by stacking a full-color
reflective display on top of a transmissive display (Figure 1.2). This hybrid display can operate in
either transmissive or reflective mode. It has not only low power consumption by staying at low-
power reflective mode most of the time, but also superior display quality in both low-light and
bright sunlight environments. While there are mature transmissive display technologies, reflective
display technologies that satisfy hybrid display requirements are still unavailable. As mentioned
above, the full-color reflective display that adopts the parallel architecture has poor optical
efficiency. Additionally, none of the current color reflective displays could be switched into a
transparent state [3-7], which is critical in our proposed hybrid display.
4
Figure 1.2: Schematic illustration of the hybrid display. A hybrid display is constructed by stacking
a switchable reflective display on top of a transmissive display.
1.2 Reflective Display Based on Switchable All-Dielectric Metasurfaces
Fortunately, the breakthroughs of nanophotonics [8] and nanofabrication [9] technologies in past
decades have vigorously promoted the development of optical metasurfaces, which provide an
opportunity to get a “perfect” hybrid display. With the help of precisely designed metasurfaces,
the incident light can be effectively manipulated [10-12]. Compared to metallic metasurfaces, all-
dielectric metasurfaces have higher optical efficiency and broader bandwidth [13]. However, the
difficulty in finding high-index and low-loss dielectrics in near-IR or visible wavelength range
limited the application of all-dielectric metasurfaces to longer wavelengths. Also, when
metasurfaces are used for large size devices (e.g., flat panel display), the cost of fabrication should
be considered.
In this work, we present a switchable all-dielectric metasurface, which can be used to construct
a promising tandem-architecture full-color reflective display. The hybrid metasurface structure
5
(i.e., TiO2/SiO2) is adopted to manipulate visible light efficiently. By low-cost and high-throughput
nanoimprint lithography (NIL), blue, green, and red metasurfaces in large sizes (average area ≈ 5
cm
2
) were fabricated. The switching between “On” (highly reflective at selected wavelength) and
“Off” (transparent) states was achieved by applying high-index liquid to the metasurfaces. A high
contrast ratio of 8:1 was obtained, which is comparable to newspapers [2]. Most importantly, the
reproduction of colors besides the primary ones (blue, green, and red) from the tandem
metasurfaces was demonstrated for the first time. In addition, ultra-high resolution over 6000 ppi
was achieved with these metasurfaces. The capability of integration with a conventional
transmissive display was demonstrated successfully.
Moreover, the effects of metasurface roughness on its performance are analyzed. According to
the volume-current method, the all-dielectric metasurface roughness can be considered equivalent
to a lossy shell. Further, numerical calculations utilizing the finite difference time domain (FDTD)
method are performed to study the optical resonant modes of the all-dielectric metasurface. The
results reveal the relationship between the distributions of resonant modes and the effects of
metasurface roughness. Besides, analyses of the metasurface performance depending on the
roughness level are performed, which guides in designing metasurfaces for better
manufacturability. More importantly, a method to enhance the metasurface performance through
engineering the resonant modes is proposed. The feasibility of this method is demonstrated by an
example using a hybrid structure to improve the incident angle insensitivity of the red metasurface.
6
Chapter 2 Design of Switchable All-Dielectric Metasurfaces
2.1 Architecture of Full-Color Reflective Display Based on Metasurfaces
A qualified full-color reflective display for the hybrid display should have bright RGB colors,
color reproduction ability, switchability, polarization independence, large viewing angle, and high
resolution, all of which require serious considerations [1]. Since the parallel architecture limits the
optical efficiency inherently (Figure 1.1), tandem architecture is the key to a practical full-color
reflective display. A schematic diagram of our proposed tandem-architecture full-color reflective
display is shown in Figure 2.1a. With ideal color metasurfaces, our proposed tandem architecture
can achieve up to 100% optical efficiency, in contrast to the 33% maximum possible efficiency of
the parallel architecture (Figure 1.1).
Figure 2.1: Schematic illustration of the full-color reflective display. a) Tandem architecture for
full-color reflective display. Each pixel contains three color (blue, green, and red) subpixels
stacked, and the subpixels are made of hybrid all-dielectric metasurface. The theoretical maximum
of reflection efficiency can reach 100%, which is ideal for reflective display. b) Metasurface can
switch between “On” and “Off” state by introducing high-index liquid. Metasurface for blue light
7
is shown as an example. In “On” state, blue light from incident light is reflected. In “Off” state,
the metasurface is transparent and no light is reflected.
This tandem-architecture display operates in an RGB additive mode, and each pixel consists
of three stacked subpixels. Each subpixel is made of a hybrid metasurface. The metasurface
manipulates a primary color (blue, green, or red), while it displays the color in its “On” state and
becomes transparent in its “Off” state (Figure 2.1b). More importantly, each metasurface can freely
transmit the light that is handled by the metasurface(s) beneath it, which means that different colors
can be reproduced through corresponding combinations of the states (“On” or “Off”) in individual
metasurfaces.
For the tandem metasurfaces, the shape of reflection spectrum from each individual
metasurface is crucial. In “Off” state, the metasurface should become transparent to have
reflectance close to zero within all visible light range. The situation of “On” state is more
complicated. Although a broad bandwidth reflection spectrum could provide high brightness, it
reduces the color saturation simultaneously [14]. Hence, the reflection bandwidth of each
metasurface is deliberately limited to 100 nm for achieving high saturation and high brightness
simultaneously (Figure 2.2). Moreover, this design covers most of the visible spectrum without
overlap, which maximizes optical efficiency and prevents interference among tandem
metasurfaces.
8
Figure 2.2: The ideal spectra of color metasurfaces: a) blue, b) green, c) red.
2.2 Numerical Calculation and Optimization of Switchable All-Dielectric
Metasurfaces
The high-contrast all-dielectric metasurface is adopted in this work because it has highly tunable
optical responses [15-20]. Figure 2.3 illustrates the schematic of a high-contrast all-dielectric
metasurface, which consists of a hybrid nanopillar array with lattice constant p and pillar width w
on a SiO2 substrate. The hybrid nanopillar comprises a top TiO2 layer with height ht and a bottom
SiO2 layer with height hs. It has square and rectangular cross sections in horizontal and vertical
directions, respectively.
9
Figure 2.3: Schematic of the switchable all-dielectric metasurface.
To achieve high effective refractive index contrast, TiO2 is used to fabricate the metasurface,
which has the highest refractive index with almost no loss in the visible range [21]. In addition,
the hybrid nanopillar design further increases the effective index contrast [22]. Since the nanopillar
array is symmetric in x and y directions with the same lattice constant p, the optical response of
the metasurface is polarization independent (Figure 2.4).
Figure 2.4: Calculated reflection spectra of the blue metasurface upon light incidence at different
polarizations. The spectra are identical, which indicates the metasurface is polarization
independent.
10
Figure 2.5 shows the numerically calculated reflection spectrum of the blue metasurface at
normal incidence and the electrical field distributions of this metasurface at different wavelengths
and incident angles. By comparing the electrical field distributions, we can find that the two peaks
(445 and 487 nm) in the reflection spectrum represent different resonant modes.
Figure 2.5: Calculated reflection spectrum of the blue metasurface at normal incidence situation.
Electrical field distributions of the blue metasurface at different wavelengths and incident angles.
Taking the blue metasurface as an example, Figure 2.6 shows the effect of metasurface
parameters (p, w, ht, hs) on the metasurface reflection spectrum. The positions of these two
resonant modes, the resonance intensity, and the full width at half maximum (FWHM) can all be
11
engineered by choosing the proper parameters. By adjusting the metasurface parameters (p, w, ht,
hs) precisely, we can set these two resonant modes at proper positions, which realizes the
selectively high efficiency (≈ 80%) and broad bandwidth (≈ 100 nm) reflection (as shown in the
reflection spectrum of Figure 2.5) [23-25]. The reflection spectrum of the blue metasurface after
parameter optimization matched the expected ideal reflection spectrum (Figure 2.2) very well.
Figure 2.6: Calculated reflection spectrum of the blue metasurface versus the lattice constant p,
hybrid pillar width w, TiO2 height ht, and SiO2 height hs (only one parameter of p, w, ht, and hs is
changing, given that other parameters are fixed. The fixed values are 390, 140, 180, and 300 nm
for p, w, ht, and hs, respectively).
12
To be noticed, the high reflective index contrast of the metasurface resulted in localized optical
resonances instead of guided-mode resonances. In this case, such a type of metasurface is less
sensitive to the incident angle. As shown in the electrical field distribution of 20° incidence at 445
nm (Figure 2.5), strong optical resonance still existed at oblique incidence situation. The incident
angle insensitivity indicates a large viewing angle, which is critical for display application.
The optical resonant modes of high-contrast all-dielectric metasurface are quite sensitive to the
refractive index contrast between metasurface and its background [23-25], so the switch of
metasurface between “On” and “Off” states can be easily realized by modifying the index of
background [17]. The background index change was achieved by filling liquid with desired index
to the metasurfaces (Figure 2.1b). In principle, electro-wetting can accomplish the precise
manipulation of the liquid with a 2 μs response time [26, 27]. Using the red metasurface as an
example, Figure 2.7 shows the calculated reflection spectra of the red metasurface versus the
background index. The reflectance of the red metasurface is very weak when the background index
is above 1.4. The situations are similar for blue and green color metasurfaces.
13
Figure 2.7: Calculated reflection spectrum of the red metasurface versus the background index.
Figure 2.8 shows the numerically calculated reflection spectra of the blue, green, and red
metasurfaces in “On” and “Off” states after optimization (in experiments, the changing of
background index was realized by applying liquid with the desired index to the metasurface).
These reflection spectra in both “On” and “Off” states of those metasurfaces indicate that they
have bright RGB colors, switchability, and color reproduction capability. Together with the
properties of polarization independence and large viewing angle mentioned above, our proposed
high-contrast all-dielectric metasurfaces satisfy all the requirements for a qualified full-color
reflective display.
14
Figure 2.8: Calculated reflection spectra of blue, green, and red metasurfaces in “On” and “Off”
states after optimization.
15
Chapter 3 Characterization of Switchable All-Dielectric
Metasurfaces
3.1 SEM Images and Optical Measurements of Fabricated Metasurfaces
After finishing the design of blue, green, and red metasurfaces, corresponding large area (average
area ≈ 5 cm
2
) metasurfaces were fabricated via NIL [28-30] (details can be found in Experimental
Section). Photos of these metasurfaces and the corresponding SEM images are shown in Figure
3.1a and Figure 3.1b, respectively. The photos were taken under ordinary office lighting conditions
without any special illumination.
Figure 3.1: a) Photos of blue, green, and red metasurfaces in “On” and “Off” states (taken under
ordinary office lighting conditions with a cellphone camera), and measured color gamut of the
three metasurfaces shown in a CIE 1931 color map. b) Cross section SEM images of blue, green,
and red metasurfaces, respectively.
16
The measured reflection spectra of metasurfaces in “On” and “Off” states are shown in Figure
3.2, in which a high contrast ratio (8:1) was demonstrated for all three color metasurfaces. Bright
blue, green, and red colors could be observed from these metasurfaces in “On” state, and the colors
remained uniform over the entire metasurfaces except the defect regions. The “On” state reflection
spectra show that the peak reflectance is 82% at a wavelength of 450 nm, 79% at 528 nm, and 80%
at 650 nm for the blue, green, and red metasurfaces, respectively. The corresponding bandwidths
(FWHM) are 71, 88, and 93 nm. In the “Off” state, high-index liquid (refractive index of 1.8, Ade
Advanced Optics) was injected onto the metasurfaces. The black background was revealed because
these metasurfaces became transparent. The visual contrast between “On” and “Off” states is
evident, which demonstrates the feasibility of switching metasurfaces via high-index liquid
injection.
Figure 3.2: Measured reflection spectra of “On” and “Off” states of three metasurfaces,
respectively.
A close examination of the experimental data reveals a slight difference between numerically
calculated and experimentally measured reflection spectra of all three metasurfaces. As mentioned
17
above, there are two peaks in each numerically calculated spectrum corresponding to two different
localized resonant modes in high-contrast grating (Figure 3.2) [25]. However, only one peak is
observed in each measured spectrum. The reason is that the numerical calculations assumed perfect
nanopillar edge and surface smoothness, while the real surfaces and edges of nanopillars were not
ideally smooth after fabrication. Details are introduced in Chapter 4.
The corresponding gamut of these color metasurfaces is also shown in Figure 3.1a. In principle,
the tandem metasurfaces can reproduce all colors inside the color triangle, which verifies their
feasibility for the construction of full-color reflective display. The switch operation demonstrated
in Figure 3.1a is binary. Furthermore, any intermediate reflectance between “On” and “Off” states
can be achieved by controlling the coverage percentage of the liquid within individual pixels.
3.2 Reproduction of Colors from the Tandem Switchable All-Dielectric
Metasurfaces
The metasurfaces that we fabricated are designed for a tandem-architecture full-color reflective
display operating in an RGB additive mode. As shown in Figure 3.2, the reflection spectra of color
metasurfaces in “On” state almost have no overlap, and these metasurfaces are highly transparent
for all visible light in “Off” state. Therefore, if these color metasurfaces are stacked into tandem
metasurfaces, each color metasurface can operate independently. The upper-layer metasurfaces
behave as a transparent film to the under-layer ones. These tandem metasurfaces can realize the
reproduction of various colors. For example, if only one metasurface is in its “On” state with the
other two in their “Off” states, the stack will display the primary color of the metasurface in “On”
state. When more than one metasurfaces are in their “On” states, a mixed color will be generated.
18
In this work, eight different cases were demonstrated, and the tandem metasurfaces behaved
exactly as expected. Both primary and mixed colors were obtained successfully. Figure 3.3a and
Figure 3.3b show the photos and the corresponding measured spectra of the tandem metasurfaces,
respectively. The photos were taken under ordinary office lighting conditions without any special
illuminations, and the color metasurfaces were stacked in the order of blue, green, and red from
top to bottom.
Figure 3.3: Reproduction of colors from the tandem switchable metasurfaces. a) Photos of the
tandem metasurfaces (the blue metasurface is at the top, the green metasurface is in the middle,
19
and the red metasurface is at the bottom) under different combinations of “On”/“Off” states of
each metasurfaces. The mixed colors are shown in the overlapped regions (within black dashed
rectangles). b) The corresponding measured reflection spectra of the tandem metasurfaces in (a),
respectively.
In the purple color demonstration from Figure 3.3a, as an example, the green metasurface was
in contact with the high-index liquid, which switched the green metasurface to “Off” state.
Meanwhile, the blue and red metasurfaces stayed in “On” state. Therefore, blue and red light were
reflected from the top and bottom metasurfaces, while the green light was not reflected because
the middle green metasurface was in its “Off” state. The mixing of reflected blue and red light
generated a purple color, as shown clearly in the overlapped region (black dashed rectangular
region). That manifests the effectiveness of color reproduction from the tandem metasurfaces.
In total, eight colors (black, blue, green, red, yellow, cyan, purple, and white) were obtained
from the tandem metasurfaces, which correspond to all the eight binary combinations of these
metasurface. The “On” or “Off” state of each metasurface in these eight color demonstrations are
listed in Table 3.1. To our knowledge, this is the first time that tandem metasurfaces are
demonstrated, which paves the way for a practical full-color reflective display using tandem-
architecture. With one step further, the tandem metasurfaces can reproduce all colors inside the
color triangle (Figure 3.1a) by using electro-wetting [26, 27] to control the coverage percentage of
the liquid within individual pixels.
20
Reproduced Color
Blue Metasurface
State
Green Metasurface
State
Red Metasurface
State
Black Off Off Off
Blue On Off Off
Green Off On Off
Red Off Off On
Yellow Off On On
Cyan On On Off
Purple On Off On
White On On On
Table 3.1: State of each metasurface in the demonstrations of color reproduction
Two observations are remarkable in the color reproduction demonstration results. First, when
three metasurfaces are all in “On” state, an average white state reflectance close to 80% is obtained,
which is better than the value of 60% from newspapers [2]. Second, the white and black states of
the tandem metasurfaces have a contrast of roughly 8:1, which is comparable to newspapers [2].
3.3 Large Viewing Angle, Ultrahigh Resolution Capability, and Feasibility of
Hybrid Display
High incident-angle sensitivity is a major challenge for many structural color devices wherein the
reflection spectra change with the light incident angle [1, 20, 31]. Fortunately, the high-contrast
all-dielectric metasurface adopted in this work has incident-angle insensitivity, which therefore
enables a large viewing angle. For example, the numerically calculated reflection spectrum of the
21
blue metasurface at different viewing angles is shown in Figure 3.4a. It is noteworthy that the main
peaks remain within the wavelength range of 400–500 nm at a viewing angle up to 60° , which
indicates that the generated color of the metasurface remains almost constant as the viewing angle
changes. Figure 3.4b shows the photos of a blue metasurface taken at different viewing angles
without any special limitation. The color of the metasurface fades a little at a larger angle but
remains bluish even at 60° , which is consistent with our numerical simulations (Figure 3.4a).
Figure 3.4: a) Calculated reflection spectrum of the blue metasurface versus the viewing angle. b)
Photos of a blue metasurface taken under different viewing angles. As shown, the color remains
blue within 60° .
Resolution is also an important specification for a display [20, 32]. As mentioned above, the
optical resonances of our metasurfaces are localized, which indicates that these metasurfaces can
have strong enough optical resonances without a large number of unit cells. In other words, these
metasurfaces have ultrahigh resolutions. This conclusion is also supported by previously reported
high-resolution metasurfaces [32-34]. Using the green metasurface as an example, the photo of
pixels in different sizes on the green metasurface is shown in Figure 3.5. As can be seen, pixels of
22
different sizes (ranging from 125 × 125 to 4 × 4 μm) uniformly generate a bright and pure green
color. The smallest pixel (4 × 4 μm) corresponds to a resolution as high as 6350 pixels per inch
(ppi), which is far beyond the human eye perception limit [35].
Figure 3.5: Photo of pixels in different sizes on a green metasurface. The black regions in the
metasurface had been etched away, and the number marked at each region represents the edge
length of the square pixel in that region.
The concept of our proposed hybrid display (Figure 1.2) was demonstrated. As shown in Figure
3.6, all the tandem metasurfaces were set in “Off” state and placed on top of a mobile device screen.
The chromatic letters “USC” from the mobile device can be seen clearly through these tandem
metasurfaces, which demonstrated the feasibility of our proposed revolutionary hybrid display.
23
Figure 3.6: Blue, green, and red metasurfaces were stacked together in their “Off” state and were
placed on top of a mobile device screen (transmissive display). The thickness of each color
metasurface with its substrate is 100 μm. The chromatic letters “USC” from the transmissive
display was seen clearly through the tandem metasurfaces.
24
Chapter 4 Effects of Roughness on the Performance of Fabricated
Metasurfaces
4.1 Roughness and Imperfection of Fabricated Metasurfaces
Due to the imperfection in the fabrication process, the roughness of all-dielectric metasurfaces is
inevitable. As shown in Figure 3.1b, there are some “bumps” on the nanopillar surface, which
makes the surface rough. Figure 4.1 shows the schematic of an ideal all-dielectric metasurface and
the schematic of the fabricated all-dielectric metasurface. Each nanopillar of the ideal all-dielectric
metasurface (Figure 4.1a) is a rectangle with smooth surfaces. However, the nanopillars in the
fabricated all-dielectric metasurfaces (Figure 3.1b and 4.1b) are frustum with random roughness.
Figure 4.1: a) Schematic of the ideal all-dielectric metasurface. The nanopillar is a rectangle with
smooth surfaces. b) Schematic of the fabricated all-dielectric metasurface. The surfaces of
nanopillar are rough.
Figure 2.8 (calculated reflection spectra) and Figure 3.2 (measured reflection spectra) show
that the roughness or imperfection of the all-dielectric metasurface has a large effect on its
performance. For each metasurface, there are two reflection peaks in the calculated reflection
25
spectrum (Figure 2.8) when the ideal metasurface structure (Figure 4.1a) is used for numerical
calculations. However, only one peak is observed in the measured reflection spectrum (Figure 3.2).
These data were obtained from the fabricated metasurfaces (Figure 3.1b and Figure 4.1b). It is
especially noticeable that all three all-dielectric metasurfaces lose the reflection peak at longer
wavelengths. This indicates that the effects of metasurface roughness are not even. Since the two
reflection peaks represent different optical resonant modes, the metasurface roughness should have
different effects on different optical resonant modes.
4.2 Study of the Roughness Effect on Metasurface Performance
To study how the roughness of the metasurface affects its performance, the red metasurface is
taken as an example. Figure 4.2a and 4.2b show the schematic of the all-dielectric red metasurface
and corresponding calculated reflection spectrum in a normal incidence, respectively. To be
noticed, the nanopillar in the ideal all-dielectric metasurface is adjusted from rectangle (Figure
4.1a) to frustum (Figure 4.2a) to fit the shape of fabricated metasurfaces (Figure 3.1b) better.
Comparing Figure 2.8 and 4.2b, we can find that this slight change of nanopillar shape doesn’t
affect the corresponding reflection spectrum largely. This indicates that the random roughness on
the nanopillar surface (Figure 4.1b) is the dominant reason for the spectrum change.
26
Figure 4.2: a) Schematic of the ideal all-dielectric metasurface, which has two layers (TiO2 and
SiO2). b) Calculated reflection spectrum of the ideal all-dielectric metasurface at normal incidence.
There are two reflection peaks at 652 nm and 710nm, respectively.
There are two reflection peaks in the calculated spectrum (Figure 4.2b) at 652 and 710 nm. As
mentioned above, the peak at the longer wavelength (710 nm) is absent in the measured spectrum
(Figure 3.2). Figure 4.3 shows the |𝐸 |
2
distributions of the ideal all-dielectric metasurface at
different wavelengths (652 or 710 nm) in different planes (YZ-plane or XZ-plane). Both the YZ-
plane and XZ-plane go through the nanopillar center. Due to the symmetry of our all-dielectric
metasurface, the reflection spectrum is independent of polarization at normal incidence [36]. To
show the resonant modes clearly, the incident light is set to propagate along the -z axis and is y-
polarized in Figure 4.3.
27
Figure 4.3: a) |𝐸 |
2
distributions of the ideal all-dielectric metasurface at different wavelengths (652
or 710 nm) in different planes (YZ-plane or XZ-plane). b) Electrical field component (𝑬 ∥
or 𝑬 ⊥
)
distributions of the ideal all-dielectric metasurface at different wavelengths (652 or 710 nm) in
YZ-plane, where 𝑬 ∥
= √𝑬 𝒙 2
+ 𝑬 𝒛 2
and 𝑬 ⊥
= 𝑬 𝒚 . The 𝑬 ∥
represents the electrical field component
that is parallel to the nanopillar surface, while the 𝑬 ⊥
represents the electrical field component that
is perpendicular to the nanopillar surface.
The metasurface roughness can be regarded as “bumps” on the metasurface sidewalls.
Intuitively, these “bumps” should have different effects on 𝑬 ∥
and 𝑬 ⊥
because the distributions of
𝑬 ∥
and 𝑬 ⊥
differ. In addition, the 𝑬 ∥
is oscillating along these “bumps”, so 𝑬 ∥
receives larger
28
scattering or absorption from these “bumps” compared to 𝑬 ⊥
. Also, Figure 4.3 shows that the
electrical fields are mainly distributed in the TiO2 layer. The refractive index of TiO2 (around 2.6)
is much higher than that of SiO2 (around 1.5) [17, 18, 21]. As a result, the roughness of the TiO2
layer has a larger effect on metasurface performance. In the following discussion, only the
roughness of the TiO2 layer will be considered.
As mentioned above, the FDTD method is adopted to do the numerical calculations in this
work. In the numerical calculation, a periodic boundary condition is applied. If the structure
imperfection is added to the unit cell directly to simulate the roughness, this will make the
roughness part of the unit cell and hence periodic. The periodic features and random features
scatter light very differently, so we cannot directly put the roughness feature in the unit cell to
study the effects of surface roughness. Hence, a thin lossy layer is added to the nanopillar surface
to mimic the surface roughness equivalently. Here, the volume-current method is adopted [37].
TiO2 and the background (n=1) have a high refractive index contrast, so the TiO2 bump is in a
high-index-contrast boundary with small volume △ V and a shift in the dielectric constant △ ϵ.
The electric field will induce a dipole moment in the bump by inducing charge density △ ρ, as
shown in Figure 4.4a. This induced dipole moment can be expressed as
𝒑 = △ V ( 𝛼 ∥
𝑬 ∥
+ 𝛾 ⊥
𝑫 ⊥
) (4.1)
where 𝛼 ∥
and 𝛾 ⊥
are polarizability tensors, 𝑬 ∥
and 𝑫 ⊥
are the surface parallel and
perpendicular components. Polarizability tensors 𝛼 ∥
and 𝛾 ⊥
are determined by the shape of the
bump.
29
Figure 4.4: a) A “bump” on the interface between two materials 𝜖 1
(TiO2) and 𝜖 2
(background).
An applied electric field E will induce a dipole moment on the surface (blue/red color denotes
positive/negative charge). b) Schematic of all-dielectric metasurface with a lossy shell. 5nm-thick
lossy shell is outside the TiO2 layer.
The oscillation of the induced dipole will cause energy loss [38]. The total time-average power
radiated by a harmonically oscillating electric dipole is
𝑃 =
𝜇 0
𝜔 4
𝑝 2
12𝜋𝑐
(4.2)
where ω is the angular frequency, p is the dipole moment, 𝜇 0
is the permeability in the vacuum
and c is the light speed in the vacuum.
Since the material is linear and isotropic, 𝑫 ⊥
= 𝜀 𝑬 ⊥
, where 𝜀 is the material permittivity. 𝛼 ∥
and 𝛾 ⊥
are diagonal. Substitute Equation (4.1) into Equation (4.2):
𝑃 =
𝜇 0
𝜔 4
△V
2
( 𝛼 ∥
𝛼 ∥
𝑬 ∥
2
+𝛾 ⊥
𝛾 ⊥
𝑫 ⊥
2
)
12𝜋𝑐
=
𝜇 0
𝜔 4
△V
2
12𝜋𝑐
( 𝛼 ∥
𝛼 ∥
𝑬 ∥
2
+ 𝛾 ⊥
𝛾 ⊥
𝜖 2
𝑬 ⊥
2
) (4.3)
Equation (4.3) shows that the parallel and perpendicular components of the electrical field (𝑬 ∥
and 𝑬 ⊥
) are scattered differently by the bumps (roughness); therefore, they have different
contributions to energy loss. In other words, the bumps have different effects on parallel and
30
perpendicular components (𝑬 ∥
and 𝑬 ⊥
). Considering that the radiation loss due to the roughness
or the material loss on the surface have the same effect on the optical resonant modes [39], the
metasurface roughness effect can be equivalent to a lossy shell added to the nanopillar (Figure
4.4b). The index of the lossy shell is 𝑛 𝑙𝑜𝑠𝑠𝑦 𝑠 ℎ𝑒𝑙𝑙 = 𝑛 + 𝑖𝑘 , where n is the refractive index of TiO2,
and k is the absorption constant. Since roughness has different effects on parallel and perpendicular
components, 𝑘 = (
𝑘 𝑥𝑥
0 0
0 𝑘 𝑦𝑦
0
0 0 𝑘 𝑧𝑧
). By adjusting the values of 𝑘 𝑥𝑥
, 𝑘 𝑦𝑦
and 𝑘 𝑧𝑧
, the effect of
roughness on the nanopillar sidewalls can be simulated equivalently.
Figure 4.5 shows the calculated reflection spectrum of the all-dielectric metasurface with the
lossy shell (Figure 4.4b) at normal incidence. It is noticeable that the peak at the longer wavelength
(710 nm) receives much larger effects from the lossy shell, which fits the experimental results
quite well.
Figure 4.5: Calculated reflection spectrum of the all-dielectric metasurface with the lossy shell
(Figure 4.4b) at normal incidence.
31
Figure 4.6 shows the distributions of the electrical field component (𝑬 ∥
or 𝑬 ⊥
) of the all-
dielectric metasurface with the lossy shell (Figure 4.4b) at different wavelengths (652 or 710 nm)
in the YZ-plane. To be noticed, the color scale bar in Figure 4.6 is the same as the one in Figure
4.3b. Compared with Figure 4.3b, the distributions of the resonant modes barely change. However,
the resonance intensity at 710 nm decreases a lot, which is in accord with Figure 4.5.
Figure 4.6: Electrical field component (𝑬 ∥
or 𝑬 ⊥
) distributions of the all-dielectric metasurface
with the lossy shell (Figure 4.4b) at different wavelengths (652 or 710 nm) in the YZ-plane.
Figure 4.7 shows the calculated reflection spectra of the ideal all-dielectric metasurfaces
(Figure 4.2), measured reflection spectra of the fabricated all-dielectric metasurfaces (Figure 3.1b
and Figure 4.1b), and calculated reflection spectra of the all-dielectric metasurface with the lossy
shell (Figure 4.4b). These spectra indicate that the numerical calculations with the lossy shell fit
the experimental results much better, which demonstrates the validity of our assumption and
derivation.
32
Figure 4.7: Calculated reflection spectra of the ideal all-dielectric metasurfaces (Figure 4.2a),
measured reflection spectra of the fabricated all-dielectric metasurfaces (Figure 3.1b and 4.1b),
and calculated reflection spectra of the all-dielectric metasurface with the lossy shell (Figure 4.4b).
All spectra are at normal incidence. Calculated reflection spectra of the all-dielectric metasurface
with the lossy shell are much closer to the measured spectra.
In the above discussion, our proposed volume-current method has established a way to
simulate the effects of random roughness equivalently. By comparing the experimental spectra and
numerically calculated spectra, the equivalent loss (i.e., 𝑘 𝑥𝑥
, 𝑘 𝑦𝑦
and 𝑘 𝑧𝑧
) of the lossy shell
corresponding to the as-fabricated roughness level can be extracted. Based on those, the effects of
different level roughness on metasurfaces performance can be predicted. Assumes that the average
roughness scale is ∆𝐿 , the bump volume is proportional to ∆𝐿 3
. Figure 3.1b shows that the
nanopillar sidewall is fully occupied by “bumps” (roughness). In this case, in the unit area of the
nanopillar surface, the total “bump” volume should be proportional to ∆𝐿 . Using equation (4.3),
the radiated power should be proportional to ∆𝐿 2
, in other words,
33
𝑃 ∝ ∆𝐿 2
(4.4)
The metasurface roughness is mainly determined by fabrication techniques, our fabricated all-
dielectric metasurfaces (Figure 3.1b) all have the same level of roughness. Using the fabricated
red metasurface as the example, Figure 4.8 shows the top view SEM image of fabricated all-
dielectric metasurface and corresponding edge detection result (More images can be found in
Supporting Information Figure S1). From the edge detection result, the average roughness (3𝜎 )
scale can be calculated, which is 8 nm.
Figure 4.8: a) Top view SEM image of the all-dielectric metasurface. The roughness of nanopillars
can be observed clearly. b) Edge detection result of SEM image in Figure 4.8a. The average
roughness scale is 8nm (3𝜎 ).
Using our proposed lossy shell method and Equation (4.4), the effects of different level
roughness on metasurface performance are calculated numerically (Figure 4.9).
34
Figure 4.9: Calculated reflection spectra with different level roughness and measured reflection
spectrum of the all-dielectric metasurface at normal incidence.
Through fitting reflection spectrum, the effects of different level roughness on different
resonant modes can be revealed. Figure 4.10 shows the resonant modes extraction using the
measured spectrum of the fabricated red metasurface as an example.
35
Figure 4.10: Resonant modes extraction from fitting measured reflection spectrum of the fabricated
all-dielectric metasurface. The three fitting peaks are at 594 nm, 653 nm, and 697 nm, respectively.
To be noticed, the second (653 nm) and third peaks (697 nm) are corresponding to the main optical
resonances. The first peak (594 nm) represents the side lobe in the shorter wavelength region.
Figure 4.11a and 4.11b show the resonant modes extraction results for Figure 4.9 and the
change of two peaks value in reflection spectra versus the change of roughness level, respectively.
Higher-level roughness has much more effect on the resonant mode at the second main optical
resonance, which is consistent with the above results (Figure 4.3 and Figure 4.6). These analyses
explain the effect of different roughness levels on all-dielectric metasurface performance, which
could guide in designing more practical metasurfaces by taking into consideration of the
nanofabrication capability.
36
Figure 4.11: a) Resonant modes extraction for calculated reflection spectra in Figure 4.9. Higher-
level roughness has much more effect on the second peak, which is consistent with the previous
conclusion. b) The change of two fitting peaks value in reflection spectra versus the roughness
level. The two red points are experimental results, which demonstrate the effectiveness of
calculations.
37
Chapter 5 Resonant Modes Engineering to Enhance the Metasurface
Performance
Our experimental and theoretical data indicate that the surface roughness has different effects on
different resonant modes according to the field distribution of each resonant mode. This causes the
absence of the peak at longer wavelengths in all three spectra of Figure 3.2. Inspired by this, we
propose a method to engineer the resonant modes by adding high-loss material in certain locations.
Through precious design, we can keep the desired resonant modes while weakening the unwanted
resonant modes simultaneously.
As introduced in chapter 3.3, the high contrast hybrid structure (TiO2/SiO2) of our all-dielectric
metasurfaces increases the incident angle insensitivity. The performance of the blue metasurface
has a viewing angle of up to 60° . However, the performances of the green and red metasurfaces
are not as good as the performance of blue metasurface. Using the red metasurface as the example,
Figure 5.1a and 5.1b show the schematic of the red metasurface at oblique incidence and the
calculated reflection spectra of the red metasurface versus the incident angle, respectively. Figure
5.1c shows the calculated color of the red metasurface versus the incident angle. It can be observed
that the reflected light color changes from red to pink gradually with the increasing incident angle
from 0° to 39° . This phenomenon has two causes. First, side lobes less than 600 nm (unwanted
resonant modes, for example, point 1 in Figure 5.1b) appear in the reflection spectra with the
increase in the incident angle. Second, the reflection intensity of the light between 600 and 700
nm (desired resonant modes, for example, point 2 in Figure 5.1b) decreases with the increase in
the incident angle.
38
Figure 5.1: a) Schematic of the all-dielectric metasurface at oblique incidence. b) Calculated
reflection spectra of the red metasurface versus the incident angle. c) The numerically calculated
color of the red metasurface versus the incident angle shown in a CIE 1931 color map.
The calculated reflection spectra of the blue metasurface (Figure 3.4a) has similar changes with
the calculated reflection spectra of the blue metasurface (Figure 5.1b). However, the reflected color
of the blue metasurface has no noticeable change when the incident angle changes, as shown in
Figure 3.4a. Figure 5.2 shows the calculated color of the blue metasurface versus the incident
angle, which fits the experiment observation (Figure 3.4a) well. This is because the wavelengths
of the side lobes that appear in the reflection spectra of blue metasurface with the increase in the
incident angle are smaller than 400 nm. In other words, these side lobes cannot be seen by human
eyes. As a result, the reflected color of the blue metasurface will not have a big change.
39
Figure 5.2: The numerically calculated color of the blue metasurface versus the incident angle
shown in a CIE 1931 color map.
Previously, several methods (e.g., plasmonic systems) have been demonstrated to improve the
incident angle insensitivity [40-43]. However, these methods cannot be used to improve the
performance of all-dielectric metasurfaces. Fortunately, the intensities and distributions of the
desired resonant modes and unwanted modes (Figure 5.1b) are different, as shown in Figure 5.3,
respectively. It is noteworthy that the incident light is set as y-polarized here to provide clear
distributions of resonant modes. If the incident light is set as x-polarized, the results are very
similar.
40
Figure 5.3: |𝐸 |
2
distributions of the red metasurface (Figure 5.1a) upon 30° incidence at 580 nm
and 667 nm. The left and right field distributions correspond to the point “1” in Figure 5.1b and
the point “2” in Figure 5.1b, respectively.
The unwanted resonant modes are mainly distributed at the top part of the TiO2 layer, while
the desired resonant modes are mainly distributed at lower positions. Amorphous Si (a-Si) is a
high-index and high-loss material, and its absorption to short wavelength light is stronger than its
absorption to longer wavelength light. Hence, a method based on engineering resonant modes was
proposed (Figure 5.4a). A 40 nm a-Si cap is added to each nanopillar to contrast a hybrid
nanopillar. The unwanted resonant modes overlap with the a-Si cap, while the location of desired
resonant modes is far from the a-Si cap. Also, the unwanted resonant modes have shorter
wavelengths compared to the desired resonant modes. As a result, this method can weaken the
unwanted resonant modes without significantly affecting desired resonant modes.
41
Figure 5.4: a) Schematic of the all-dielectric metasurface with an a-Si cap at oblique incidence.
The thickness of the a-Si cap is 40 nm. b) Calculated reflection spectra of the all-dielectric
metasurface with an a-Si cap versus the incident angle. c) The numerically calculated color of the
all-dielectric metasurface with an a-Si cap versus the incident angle shown in a CIE 1931 color
map.
Figure 5.4b shows the calculated reflection spectra of the all-dielectric metasurface with an a-
Si cap versus the incident angle, and Figure 5.4c shows the reflected color of the all-dielectric
metasurface with an a-Si cap versus the incident angle. It can be observed that the side lobes
decrease in the reflection spectra. In addition, the reflection in the red light range (600 ~ 700 nm)
also increases. This is because the a-Si is also a high-index material. Although a-Si is highly lossy,
its high index property (around 4.0) [18] can confine the incident light effectively and enhance the
optical resonance.
The right field distributions in Figure 5.5 show the intensities and distributions of the desired
resonant modes and unwanted modes have huge differences after adding the a-Si cap. It is
noticeable that the unwanted resonant modes almost disintegrate, while the desired resonant modes
still have high intensities. Hence, the change in the reflected light color of the metasurface in Figure
42
5.4c becomes much smaller compared to Figure 5.1c. All these performance enhancements
demonstrate the feasibility and validity of improving all-dielectric metasurface performance
through engineering resonant modes.
Figure 5.5: |𝐸 |
2
distributions of the red metasurface (Figure 5.4a) upon 30° incidence at 580 nm
and 667 nm. The left and right field distributions correspond to the point “1” in Figure 5.4b and
the point “2” in Figure 5.4b, respectively.
43
Summary
This work proposes and demonstrates switchable all-dielectric metasurfaces for tandem-
architecture full-color reflective display as well as the concept of a hybrid display consisting of a
reflective top display and a transmissive bottom display. By low-cost and high-throughput NIL,
large-area (average area ≈ 5 cm
2
) blue, green, and red metasurfaces were designed, fabricated, and
studied. These metasurfaces can be switched between “On” (highly reflective at selected
wavelength) and “Off” (transparent) states by the injection of high-index liquid, which can be
further integrated with electro-wetting to achieve full modulation. Bright colors, high contrast
ratio, large viewing angle, and ultrahigh resolution (over 6000 ppi) were obtained from these
metasurfaces. Most importantly, color reproduction from tandem metasurfaces and the concept of
a hybrid display were demonstrated successfully.
This work also proposes and experimentally verifies a method to analyze the effect of
roughness on metasurface performance. Using the volume-current method, the metasurface
roughness can be equivalent to a lossy shell outside the nanopillar. Based on the FDTD method,
different resonant modes are also studied. It is demonstrated that the different effects of
metasurface roughness on different resonant modes are due to the different resonance distributions.
Further, the effects of different level roughness on metasurface performance are predicted. This
can help design more manufacturable all-dielectric metasurfaces based on fabrication capability.
Moreover, a method to enhance metasurface performance based on resonant modes engineering is
proposed. High-index and high-loss dielectric material (a-Si) can be put to an appropriate position
to weaken unwanted resonant modes without affecting desired resonant modes. An example of
improving the incident angle insensitivity of the red metasurface demonstrates the feasibility of
this method.
44
We anticipate that, with the combination of switchable all-dielectric metasurfaces, electro-
wetting technique, and sealing technique, switchable full-color reflective display and revolutionary
hybrid display can greatly boost the user experience of mobile and wearable devices.
45
Topic 2:
Memristor Characteristics Engineering by Controlling
the Crystallinity of Switching Layer Materials
46
Chapter 6 Introduction to the Memristor
A memristor is a non-volatile electronic memory device that was first theorized by Leon Ong Chua
in 1971[44]. The resistance of the memristor can be programmed (resistor function) and
subsequently remains stored (memory function). Unlike other memories that exist today in modern
electronics, memristors are stable and remember their state even if the device loses power. It was
almost 40 years later that the first practical device was fabricated [45]. This was in 2008, when a
group at HP Research Labs realized that switching of the resistance between a conducting and less
conducting state in metal-oxide thin-film devices was showing Leon Chua's memristor behavior.
Since then, the memristor [46-49] has attracted great interest in the semiconductor industry.
Significant progress has been made in the development of memristors, including its integration
with the Si CMOS circuit [50, 51], switching cycles up to 10
12
[52], switching speed down to 100
ps [53], and retention time up to a few years [54]. So far, most efforts are targeting bio-inspired
neuromorphic computing applications [55-57]. Many emerging applications can greatly benefit
from memristors [56, 58]. For example, by using memristors as the reconfiguration bits in a field
programmable gate array (FPGA), the FPGA is expected to achieve a 5.18× area saving, a 2.28 ×
speedup, and a 1.63× power saving [59]. Also, memristors can be used for in-memory computing
systems, which eliminate the von Neumann bottleneck by performing computation directly within
the memory [60]. Moreover, memristors can be used to improve the speed of the computing
platform, since the computation speed of the memristor-based analog component is much faster
than that of the digital component [61]. Besides, the number of analog-to-digital converters (ADCs)
and digital-to-analog converters (DACs) decreases in the entire computing platform, which
increases the power efficiency of the platform [61].
47
However, there are still many critical challenges to be resolved before using memristors in
those applications. Different applications have different requirements for the characteristics of
memristors, including the operation voltage, the on/off ratio, and the number of conductance states
[62-64]. Therefore, significant effort is still needed to tailor the existing memristor technologies
for specific applications. The traditional method to engineer memristor characteristics is by
selecting appropriate material stack and film thicknesses for both the switching and contact layers
[65], which cannot satisfy all needed requirements.
In this work, we report a method to modify the memristor characteristics specifically by
controlling the crystallinity of switching layer material. Al2O3 was used in our Pt/Al2O3/Ta/Pt
cross-point memristors as the switching layer material. By controlling the atomic layer deposition
(ALD) temperature, the crystallinity of Al2O3 changed from amorphous to polycrystalline, which
affected the memristor performance directly. Through choosing an appropriate Al2O3 deposition
temperature, the Pt/Al2O3/Ta/Pt memristors can have great characteristics, such as good I-V
linearity, high On/Off ratio (around 10
8
), low pulse operation voltage (2.5 V), and multilevel
conductance states (157 states). The mechanism of modifying memristor characteristics by
controlling switching layer crystallinity was also studied.
48
Chapter 7 Device Fabrication
7.1 Fabrication Process
The fabrication process of the Pt/Al2O3/Ta/Pt cross-point memristor is shown in Figure 7.1a. A Si
wafer that has 150 nm thermally grown SiO2 on top was used as the substrate. First, the bottom
electrodes were patterned using ultraviolet photolithography. Then, a 2 nm Ti (adhesion layer) and
a 20 nm Pt (bottom electrode metal) were deposited by the electron-beam evaporator, followed by
a lift-off process. Next, an 8 nm Al2O3 blanket layer was deposited by ALD as the memristor
switching layer. The reason that ALD was chosen to deposit the switching layer material is that
the ALD temperature can be set precisely (80 ° C, 120 ° C, 160 ° C, or 200 ° C) to control the
crystallinity of deposited Al2O3 [66, 67]. The details are introduced in the next section. Finally, an
8 nm thick Ta and a 20 nm thick Pt top electrode were defined by a second photolithography,
evaporation, and lift-off process to get the Pt/Al2O3/Ta/Pt cross-point memristor. Figure. 7.1b
shows the schematic of the Pt/Al2O3/Ta/Pt cross-point memristor, which has a four layers structure.
The optical microscope image of the fabricated Pt/Al2O3/Ta/Pt cross-point memristor is shown in
Figure 7.1c.
49
Figure 7.1: Pt/Al2O3/Ta/Pt cross-point memristor. a) Fabrication process. b) Schematic of the Pt/
Al2O3/Ta/Pt cross-point memristor. c) Optical microscope image of the fabricated Pt/ Al2O3/Ta/Pt
cross-point memristor.
7.2 Controlling the Crystallinity of Switching Layer Material
ALD is a chemical vapor deposition technique based on successive, separated, and self-terminating
gas-solid reactions of typically two gaseous reactants [66]. Like other thin film deposition
techniques, the ALD temperature affects the crystallinity of deposited material [66, 67]. The
50
deposited material undergoes a transition from amorphous to polycrystalline at a characteristic
temperature. Al2O3 can be deposited by ALD using water (H2O) and trimethylaluminum (TMA)
as precursors. To compare the crystallinity of Al2O3 films at different deposition temperatures, 200
cycles of Al2O3 (around 16 nm) were deposited on the Si substrate at four different temperatures
(80 ° C, 120 ° C, 160 ° C, and 200 ° C), separately.
The refractive indexes of these four Al2O3 films were measured by an ellipsometer. With the
increase in deposition temperature, the Al2O3 refractive index is increased, as shown in Table 7.1.
These data indicate that the Al2O3 deposited at higher temperature is denser.
Al2O3 Deposition
Temperature
Refractive Index
(λ=532nm)
Crystallinity Average Grain Size
80 ° C 1.630 Amorphous N/A
120 ° C 1.647 Amorphous N/A
160 ° C 1.652 Polycrystalline ~ 150.5 nm
200 ° C 1.656 Polycrystalline ~ 207.0 nm
Table 7.1: Refractive index, crystallinity, and average grain size of Al2O3 deposited at different
temperatures.
The corresponding X-ray diffraction (XRD) spectra of Al2O3 films at these four different
deposition temperatures are shown in Figure 7.2. The Al2O3 films deposited at 80 ° C and 120 ° C
do not have characteristic peaks in the XRD spectra, while the Al2O3 films deposited at 160 ° C and
200 ° C have clear characteristic peaks in the XRD spectra. These indicate that the Al 2O3 films
51
deposited at 80 ° C and 120 ° C are amorphous, while the Al2O3 films deposited at 160 ° C and 200
° C are polycrystalline.
Figure 7.2: XRD spectra of Al2O3 films at different deposition temperatures (80 ° C, 120 ° C, 160 ° C,
and 200 ° C).
According to the Scherrer equation 𝜏 =
𝐾𝜆
𝛽𝑐𝑜𝑠𝜃 (where 𝜏 is the average grain size, 𝐾 is a
dimensionless shape factor, 𝜆 is the X-ray wavelength, 𝛽 is the line broadening at half the
maximum intensity, and 𝜃 is the Bragg angle), the estimated average grain size of polycrystalline
Al2O3 can be calculated, as shown in Table 7.1. The average grain size of polycrystalline Al2O3 is
also increased with the increase in the deposition temperature (Table 7.1), which is consistent with
the change in refractive index.
52
Figure 7.3 shows the TEM images of Al2O3 films deposited at 80 ° C and 200 ° C and the
corresponding FFT patterns. The results indicate that the Al2O3 film deposited at 80 ° C is
amorphous, while the Al2O3 film deposited at 200 ° C is polycrystalline. This direct evidence
demonstrates that the deposited Al2O3 film has the transition from amorphous to polycrystalline
with increasing deposition temperature.
Figure 7.3: a) TEM image of 80 ° C deposited Al2O3 film, which is amorphous. The SiO2 layer is
the native oxide layer on top of the Si substrate. b) TEM image of 200 °C deposited Al2O3 film,
which is polycrystalline. The SiO2 layer is the native oxide layer on top of the Si substrate. c)
Corresponding FFT pattern of TEM image in (a) (Frequency range DC ~ 1/0.020 [1/nm]). d)
Corresponding FFT pattern of TEM image in (b) (Frequency range DC ~ 1/0.020 [1/nm]).
53
Figure 7.4 shows the High-angle Annular Dark-field (HAADF) STEM and Energy Dispersive
X-Ray Spectroscopy (EDS) images of 80 °C deposited Al2O3 film. Above all, the crystallinity of
the deposited Al2O3 can be controlled through the ALD temperature.
Figure 7.4: a) The HAADF STEM image of 80 °C deposited Al2O3 film. b) – e) Corresponding
EDS images of 80 °C deposited Al2O3 film. The C layer is the protection layer for the focused ion
beam (FIB). The SiO2 layer is the native oxide layer on top of the Si substrate.
54
Chapter 8 Device Electrical Performance Characterization
8.1 I-V Curves and Retention Test
Figure 8.1 shows the typical bipolar resistive switching I–V curves of the 5 by 5 μm
2
Pt/Al2O3/Ta/Pt cross-point memristors, which use Al2O3 films deposited at different temperatures
(80 ° C, 120 ° C, 160 ° C, and 200 ° C) as the switching layer. The memristors can be switched from
the Off state (high resistance state) to the On state (low resistance state) after positive voltages
(Vset) are applied [45, 68, 69]. By sweeping negative bias (Vreset), the memristors can be switched
from the On state to the Off state, which is defined as the reset process. As shown in Figure 8.1,
the Set and Reset voltage of Pt/Al2O3/Ta/Pt memristor are increased with the increase in Al2O3
deposition temperature. The physics behind it is discussed in Chapter 9.
Figure 8.1: I-V curves (plot in log scale) from 5 by 5 μm
2
Pt/Al2O3/Ta/Pt cross-point memristors,
which use Al2O3 films deposited at different temperatures (80 ° C, 120 ° C, 160 ° C, and 200 ° C) as
the switching layer. The memristors can be set with a positive voltage sweep and then reset with a
negative voltage sweep. In the positive voltage sweep, the applied compliance currents for 80 ° C,
55
120 ° C, 160 ° C, and 200 ° C deposited Al2O3 memristors were 3 mA, 3 mA, 5 mA, and 5 mA,
respectively.
Figure 8.2 shows the linear plot of resistive switching I–V curves of the Pt/Al2O3/Ta/Pt
memristors using Al2O3 deposited at different temperatures, which demonstrates that our
memristors have good I-V linearity [70].
Figure 8.2: I-V curves (plot in linear scale, same data as Figure 8.1) from 5 by 5 μm
2
Pt/Al2O3/Ta/Pt
cross-point memristors. The memristors have good I-V linearity.
Figure 8.3 shows the I-V curve of multiple switching cycles of Pt/Al2O3/Ta/Pt memristor,
which demonstrates the robustness and stability of our memristors.
56
Figure 8.3: 100 Cycles I-V curves (plot in linear scale) of 5 by 5 μm
2
Pt/80 °C deposited
Al2O3/Ta/Pt cross-point memristor.
Using the Pt/80 ° C deposited Al2O3/Ta/Pt cross-point memristor as the example, the retention
characteristic of our memristors was investigated (Figure 8.4). The result indicates that the
memristors are highly stable in each state without degradation over 90h at the elevated temperature
(85 ° C). After 90h, the memristors in the On state started to change to the Off state.
57
Figure 8.4: a) Retention test of Pt/80 ° C deposited Al2O3/Ta/Pt cross-point memristors. 20
memristors were used to test the retention. Before the test, 10 memristors were set to On state, and
the other 10 memristors were set to Off states. b) Number of the unchanged (not change from On
state to Off state) Pt/80 ° C deposited Al2O3/Ta/Pt memristor in the 85 ° C retention test versus the
test time.
8.2 Pulse Measurements
The pulse switching measurements of the Pt/Al2O3/Ta/Pt memristors that use Al2O3 at different
deposition temperatures (80 ° C, 120 ° C, 160 ° C, and 200 ° C) are depicted in Figure 8.5. The length
of the pulse is 3 μs. To compare the difference of Pt/Al2O3/Ta/Pt memristors using Al2O3 deposited
at different temperatures, 1000 switching cycles were done for Pt/80 ° C deposited Al2O3/Ta/Pt
memristor, Pt/120 ° C deposited Al2O3/Ta/Pt memristor, and Pt/160 ° C deposited Al2O3/Ta/Pt.
58
Figure 8.5: a) The Pt/80 ° C deposited Al2O3/Ta/Pt memristor can be repeatedly switched between
On and Off states with 3 μs pulses (Positive pulse voltage: 2.5 V; Negative pulse voltage: −2.5 V).
Here shows the 1000 switching cycles result. b) 1000 switching cycles of the Pt/120 ° C deposited
Al2O3/Ta/Pt memristor with 3 μs pulses (Positive pulse voltage: 2.5 V; Negative pulse voltage:
−2.5 V). c) 1000 switching cycles of the Pt/160 °C deposited Al2O3/Ta/Pt memristor with 3 μs
pulses (Positive pulse voltage: 3.4 V; Negative pulse voltage: −3.0 V). d) Pulse switching of the
Pt/200 ° C deposited Al2O3/Ta/Pt memristor with 3 μs pulses (Positive pulse voltage: 6.0 V;
Negative pulse voltage: −6.0 V). This device is hard to switch with pulses (switching cycles < 10).
It is noticeable that the used pulse voltage was not very high (±2.5 V for 80 ° C deposited
Al2O3 and 120 ° C deposited Al2O3 memristor, +3.4 V and -3.0 V for 120 ° C deposited Al2O3
59
memristor, and ±6.0 V for 200 ° C deposited Al2O3 memristor). This is because the memristors
were not switched off totally in the pulse switching measurements. This can be demonstrated by
observing the On/Off ratio (< 10
4
) in the pulse switching measurements. The On/Off ratio in the
pulse switching measurements is much smaller than the On/Off ratio in the I-V curves (Figure
8.1). In addition, for Pt/200 ° C deposited Al2O3/Ta/Pt memristor, though ±6 V pulses were used,
the memristor was still hard to switch. As a result, the results of only several switching cycles (<
10) are shown in Figure 8.5d. It is noteworthy that the pulse switching results of different
memristors are very different, like resistance distribution (variation). The details and the reason
behind the differences in pulse switching results are also discussed in Chapter 9.
More pulse switching data of Pt/Al2O3/Ta/Pt memristor from different devices can be found in
Figure 8.6, which demonstrates the device-to-device variation of our memristors is very small.
60
61
Figure 8.6: a) – d) 1000 switching cycles of four different Pt/80 ° C deposited Al2O3/Ta/Pt
memristors with 3 μs pulses (Positive pulse voltage: 2.5 V; Negative pulse voltage: −2.5 V). e) –
h) 1000 switching cycles of four different Pt/120 ° C deposited Al2O3/Ta/Pt memristors with 3 μs
pulses (Positive pulse voltage: 2.5 V; Negative pulse voltage: −2.5 V).
8.3 Number of Conductance States
The number of conductance states is critical to memristors, which is an important feature for bio-
inspired neuromorphic computing [70-72]. Figure 8.7 shows the I–V curves for Pt/80 ° C deposited
Al2O3/Ta/Pt memristor and Pt/200 ° C deposited Al2O3/Ta/Pt memristor with different conductance
states, respectively. The Pt/80 ° C deposited Al2O3/Ta/Pt memristor can provide conductance
ranging from 70 to 350 μS, and the Pt/200 °C deposited Al2O3/Ta/Pt memristor can provide
conductance ranging from 70 to 2900 μS. Moreover, Figure. 8.7 also indicates that our memristors
have good I-V linearity.
Figure 8.7: a) Our memristor can be set to different conductance states by using different
compliance currents. Here shows the I–V curves for Pt/80 ° C deposited Al2O3/Ta/Pt memristor
62
with different conductances, which has 16 states (2
4
). (b) I–V curves for Pt/200 ° C deposited
Al2O3/Ta/Pt memristor with different conductances, which has 157 states (more than 2
7
).
Through controlling the compliance currents, the memristor can be set to the target state
preciously, as shown in Figure 8.8. The standard deviation of setting the memristor to an exact
conductance state is 9 μS. As a result, the Pt/80 °C deposited Al2O3/Ta/Pt memristor (Figure 8.7a)
can provide 16 states (2
4
). The Pt/200 ° C deposited Al2O3/Ta/Pt memristor (Figure 8.7b) can
provide 157 states (more than 2
7
), which is much better than the Pt/80 ° C deposited Al2O3/Ta/Pt
memristor. The reason behind these results is discussed in Chapter 9. Also, the feedback of the
memristor programming can help set each memristor to the target state, which ensures the
repeatability of the conduction state programing.
Figure 8.8: Through controlling the compliance currents, our memristor can be set to the target
conductance state precisely. Here shows the ten set conductance states (200μS, 400μS, 600μS,
63
800μS, 1000μS, 1200μS, 1400μS, 1600μS, 1800μS, and 2000μS) of Pt/200 °C deposited
Al2O3/Ta/Pt memristor.
Figure 8.9a and 8.9b show that the multilevel conductance states of two more Pt/200 ° C
deposited Al2O3/Ta/Pt memristors, which indicate that the different memristors can provide a
similar conductance range. As mentioned above, the memristor can be set to the target state
preciously by controlling the compliance currents. Also, the memristor can be set to the desired
target state using the programming feedback (Details can be found in Chapter 11.2). In other
words, the memristor can be set using a series of pulses, while the pulse voltage can be adjusted
flexibly according to the current conductance of the memristor. All of these demonstrate the
repeatability of the multilevel states of our memristors.
64
Figure 8.9: Repeatability and stability of multilevel conductance states of Pt/Al2O3/Ta/Pt
memristors. a) - b) Two more Pt/200 ° C deposited Al2O3/Ta/Pt memristors with multilevel
conductance states. c) - d) Retention tests of Pt/80 ° C deposited Al2O3/Ta/Pt and Pt/200 °C
deposited Al2O3/Ta/Pt memristors with multilevel conductance states, respectively. The tests were
conducted at room temperature (25 ° C).
Figure 8.9c and 8.9d show the retention test of our memristors with different conductance
states. Since this test is time-consuming, 10 hours retention tests were conducted. The retention of
our memristors is much longer than 10 hours (as shown in Figure 8.4). These results demonstrate
the stability of our memristors.
65
Chapter 9 The Effect of the Switching Layer Material Crystallinity
on Memristor Characteristics
9.1 Comparisons Between Memristors that Adopt Different Crystalline Al2O3
As introduced in chapter 8.3, the Pt/200 ° C deposited Al2O3/Ta/Pt memristor can provide many
more conductance states than the Pt/80 ° C deposited Al2O3/Ta/Pt memristor can. Moreover, as
shown in Figure 9.1a and 9.1b, the Set/Reset voltage and On/Off ratio of Pt/Al2O3/Ta/Pt
memristors are increased with the increase in Al2O3 deposition temperature. Figure 9.1c shows the
resistance distribution of the Pt/Al2O3/Ta/Pt memristors that have different Al2O3 deposition
temperatures at both On and Off states in the pulse switching measurements. It is noticeable that
the variations of different memristors are different, and the Pt/120 ° C deposited Al2O3/Ta/Pt
memristor has the lowest variation. All of these demonstrate that the Al2O3 deposition temperature
directly affects the characteristics of Pt/Al2O3/Ta/Pt memristor. In other words, the characteristics
of Pt/Al2O3/Ta/Pt memristor can be modified specifically by controlling the crystallinity of the
switching layer material (Al2O3).
Figure 9.1: a) The change of Set/Reset voltage of Pt/Al2O3/Ta/Pt memristor versus the Al2O3
deposition temperature. b) The change of the On/Off ratio of Pt/Al2O3/Ta/Pt memristor versus the
66
Al2O3 deposition temperature. The On/Off ratios are calculated at reading voltage 0.3 V according
to Figure 8.1. c) Resistance distribution (2% to 98%) of the Pt/Al2O3/Ta/Pt memristors that have
different Al2O3 deposition temperatures at both On and Off states in the pulse switching
measurements (Figure 8.5a, 8.5b, and 8.5c).
9.2 Molecular Dynamics Simulations
Chapter 7.2 introduces that different crystalline Al2O3 has different grain size. To understand the
effect of switching layer material (Al2O3) crystallinity on the memristor characteristics at the
atomic level, multi-million-atom molecular dynamics (MD) simulations of the active Al2O3 layer
with different grain sizes were performed.
As shown in Table 7.1, the estimated average grain size of the polycrystalline Al2O3 deposited
at 160 ° C and 200 ° C is ~150.5 nm and ~207.0 nm, respectively. Due to the simulation resource
limitation, it is hard to do MD simulations for polycrystalline Al2O3 films that have these grain
sizes. Since we just want to study the effect of crystallinity qualitatively, we change the simulation
cell to Al2O3 layers that are amorphous and with grain sizes at 2 nm, 4 nm, and 50 nm were studied
numerically. They were chosen to present Al2O3 films that are amorphous, in transition between
amorphous and polycrystalline and polycrystalline. Figure 9.2 shows the constructed amorphous
Al2O3 layer using a melt-quench scheme [73], and the constructed microstructures of Al2O3 layers
at grain sizes of 2 nm, 4 nm, and 50 nm using a Voronoi-annealing scheme [74-76]. The details of
MD simulations can be found in Experimental Section.
67
Figure 9.2: a) Microstructure of amorphous Al2O3 layer generated by a melt-quench scheme. b)
Microstructures of 2 nm grain-sized Al2O3 layer generated by a Voronoi-annealing scheme. c)
Microstructures of 4 nm grain-sized Al2O3 layer generated by a Voronoi-annealing scheme. d)
Microstructures of 50 nm grain-sized Al2O3 layer generated by a Voronoi-annealing scheme. e)
Connected clusters of low-density voxels in different Al2O3 layers identified using a depth first
search method. Connected clusters in each layer are denoted by different colors for clarity.
9.3 Working Mechanism Study
68
The characteristics of Pt/Al2O3/Ta/Pt memristors are determined by the energetics of formation
and dissolution of conductive filaments [54, 77, 78]. Besides, the grain boundaries of the Al2O3
layer and regions of low local atomic density in the Al2O3 layer constitute potential pathways for
the formation of conductive filaments in the Pt/Al2O3/Ta/Pt memristors [79-84]. As a result, the
characteristics of Pt/Al2O3/Ta/Pt memristors can be estimated by quantifying the dimension and
connectivity of grain boundaries and regions of low local atomic density in the Al 2O3 layer. To
quantify this, a connected component analysis (using depth first search) of low-density voxels was
performed [85] (details can be found in Experimental Section).
Here, the low-density voxels are the 3Å ⨉ 3Å ⨉ 3Å regions containing no Al or O atoms. The
connected component analysis identifies all possible pathways for the conductive filaments. Figure
9.2e shows the results of the connected component analysis on different (amorphous, 2 nm grain-
sized, 4 nm grain-sized, and 50 nm grain-sized) Al2O3 layers highlighting the structure and
connectivity of local low-density voxels. The connected component analysis results indicate that
the amorphous Al2O3 layer has a uniform distribution of small clusters of connected low-density
voxels. In contrast, clusters of connected low-density voxels in other (2 nm grain-sized, 4 nm
grain-sized, and 50 nm grain-sized) Al2O3 layers are more heterogeneously distributed and exist
exclusively at the grain boundaries.
Figure 9.2e also shows that non-amorphous Al2O3 layers can only form filament through those
low-density clusters on grain boundary. This indicates that the characteristics of Pt/Al2O3/Ta/Pt
memristors using non-amorphous Al2O3 layers are mainly determined by the grain boundaries of
the Al2O3 layer while not the regions of low local atomic density in the Al2O3 layer. For
Pt/Al2O3/Ta/Pt memristors have non-amorphous Al2O3 layers, their characteristics are mainly
69
determined by the regions of low local atomic density in the Al2O3 layer. This is because the
amorphous Al2O3 layers do not have grain boundaries.
It is reasonable to expect that the number of conductance states will be proportional to the
cross-sectional area (in the x-y plane) of connected clusters of low-density voxels. This is because
the larger cross-sectional area of connected clusters of low-density voxels means more possible
diameters of conductive filament in memristors. Different conduction filament diameters
correspond to different conductance states. Figure 9.3a shows the change in cross-sectional area
(in the x-y plane) of connected clusters of low-density voxels versus the type of Al2O3 layer. The
cross-sectional area of connected clusters increases from an amorphous to a polycrystalline Al2O3
layer, and further monotonically increases with grain size. This behavior is consistent with the
experimental observation of the number of resistance states of Pt/80 ° C deposited Al2O3/Ta/Pt
memristor and Pt/200 ° C deposited Al2O3/Ta/Pt memristor (Figure 8.7).
Figure 9.3: a) Average cross-sectional area (in the x-y plane) for each cluster of low-density voxels
versus the Al2O3 layer type. b) Average length of low-density voxels cluster versus the Al2O3 layer
type. 50 nm grain-sized Al2O3 structures with larger grain sizes contain low-density clusters of the
longest length (along the z direction). c) Density of low-density voxels cluster versus the Al2O3
70
layer type. Amorphous and small-grained structures have a significantly larger number density of
connected voxel clusters than larger grain-sized structures.
Figure 9.3b and 9.3c indicate that a large grain-sized Al2O3 layer has fewer, but longer low-
density clusters, while amorphous and small-grained Al2O3 layers contain a larger number of non-
percolating clusters of smaller lengths. As mentioned above, the characteristics of Pt/Al2O3/Ta/Pt
memristors are determined by the energetics of the formation and dissolution of conductive
filaments. Both grain boundaries and regions of low local atomic density in the Al2O3 layer
constitute potential pathways for the formation of conductive filaments in the Pt/Al2O3/Ta/Pt
memristors. Also, only amorphous Al2O3 layers have uniform distributions of small clusters of
connected low-density voxels for filament formation, while non-amorphous Al2O3 layers can only
form filament through those low-density clusters on grain boundary. That is why amorphous Al2O3
layers have the lowest programming voltage.
Figure 9.3b and 9.3c also indicate that the larger grain-sized Al2O3 layer has fewer, but longer
low-density clusters for filament formation. The longer the cluster, the larger the programming
voltage is needed. Those results are consistent with experiment results (Figure 8.1, 8.2, 9.1a, and
9.1b). Moreover, as shown in Figure 8.5d, it is hard to switch the Pt/200 ° C deposited Al2O3/Ta/Pt
memristor using pulse. This is because the Pt/200 ° C deposited Al2O3/Ta/Pt memristor needs the
highest programming voltage. The larger energy is dumped on the memristor when it is switched
on, the more stress on the memristor. Therefore, the Pt/200 ° C deposited Al 2O3/Ta/Pt memristor
has the worst endurance. To be emphasized, those memristors are not damaged, they only need to
be either reformed or using different pulse parameters. Besides, the increase of conductive
pathways (proportional to the density of low-density clusters) in the Al2O3 layer will reduce the
71
variation in the electrical measurements of memristors. This is because a larger number of
conductive pathways can decrease the effects of abnormal switching. If the density of low-density
clusters in the Al2O3 layer is higher, the corresponding Pt/Al2O3/Ta/Pt memristor will have a lower
variation. This also fits the experimental results well (Figure 8.5 and 9.1c).
72
Summary
This work proposes and demonstrates a method to modify the memristor characteristics
specifically by controlling the crystallinity of the switching layer material. By setting the ALD
temperature, the crystallinity of deposited Al2O3 can be controlled. Using different crystalline
Al2O3 as the memristor switching layer, the characteristics of corresponding Pt/Al 2O3/Ta/Pt cross
point memristors can be engineered. When memristors are used as switches, the switching layer
deposited at the highest “amorphous” temperature is preferred. When memristors are used to
implement synapse form neuromorphic computing, the switching layer deposited at a higher
temperature, and hence polycrystalline film with larger grain size, is preferred. Good
characteristics like high IV linearity, high On/Off ratio (around 10
8
), low pulse operation voltage
(2.5 V), and multilevel conductance states (157 states) were obtained from our modified
Pt/Al2O3/Ta/Pt memristors. More importantly, molecular dynamics simulations were performed to
qualitatively study how the switching layer crystallinity affects the characteristics of memristors.
Through modifying the characteristics of memristors preciously, memristors can be used for a
broad spectrum of applications.
73
Topic 3:
A Memristor-Based Hybrid Analog-Digital Computing Platform for Mobile Robotics
74
Chapter 10 Introduction
10.1 Control of Mobile Robotics
Presently, the most advanced mobile robotic system in the world has only 114 degrees of freedom
(DOFs) [86], which is much less than that in the human body (650 skeletal muscles) [87]. This is
the reason that state-of-art robots cannot move as naturally as humans can. As a result, more DOFs
are necessary for the next generation of mobile robotic systems. Nevertheless, requirements for
computing power increase commensurate with the complexity of mobile robotic systems.
Improvements in computing power efficiency are diminishing over time as performance gains due
to complementary metal-oxide-semiconductor (CMOS) scaling nears its end [88, 89]. The growing
demand for computing power and the saturation of Moore’s law limit the development of mobile
robotic systems with more functions and higher degrees of freedom (DOFs).
The control of the human body is enabled by the highly sophisticated ultralow-power
computational capability of the human brain. The human brain [90] consists of the cerebrum, the
cerebellum, and the brainstem. The cerebrum is a major part of the brain in charge of vision,
hearing, and thinking, while the cerebellum plays an important role in motion control. Through
this cooperation of the cerebrum and the cerebellum, the human brain can conduct multiple tasks
simultaneously with extremely low power consumption.
Inspired by the structure of the human brain, the ideal solution to break the bottleneck of
increasing the DOFs in robots is a hybrid analog-digital computation platform. This platform could
bring higher speed and power efficiency for mobile robotics, in which the digital component runs
the high-level algorithm, while the analog component is responsible for sensor fusion and motion
control. 40 years ago, a similar approach was proposed [91, 92]. Unfortunately, this approach has
never been adopted widely, due to technological limitations (lack of electronically reconfigurable
75
devices and silicon integrated circuits (IC) compatible analog devices to implement such systems
efficiently).
10.2 Memristor-Based Hybrid Analog-Digital Computing Platform
As introduced in Chapter 6, memristor-related technologies are vastly developing in recent years.
With memristors, it is now possible to implement an efficient hybrid analog-digital computing
platform for mobile robotics. The memristor is a two-terminal IC compatible analog device, which
can be programmed precisely to different conductance states (Chapter 8.3). The tunable
conductance states of the memristor enable the computation in-memory architecture, which is
considered a promising candidate to address the von Neumann bottleneck. The memristor is ideal
for analog computing as it offers excellent scalability, a broad range of IV linearity, and non-
volatility. In addition, space-saving and cost-effectiveness make memristor a greater candidate to
develop electronically reconfigurable analog circuits than other analog computing devices [93]
(Table 10.1).
Configurable
Circuits
Number of
devices
IV
Characteristic
Circuit Area Control Circuit
Switched
Capacitor
Multiple Linear Large Need
Switched
Resistor
Multiple Nonlinear Large Need
Transistor Single Linear Small Need
Memristor Single Linear Small Need
Table 10.1: The comparison of electronically reconfigurable analog circuits using different devices.
76
A mobile robot, as a real-time control system, can benefit substantially from the memristor-
based hybrid computing platform with higher speed and power efficiency. Both the sensor fusion
algorithm and motion control algorithm can be expressed as linear equations, which can be
performed by analog circuits with memristors. The digital platform, however, consumes more time
and energy since it needs to store and compute the information separately. Moreover, the
memristor-based analog component can operate independently without using the computing
resources from the digital component. This parallel computing architecture is essential for further
increasing the DOFs of mobile robotic systems.
In this work, we demonstrate a one DOF low-latency self-adaptive mobile robotic system using
our proposed memristor-based hybrid analog-digital computing platform. The sensor fusion
algorithm (a single Kalman filter) and the motion control algorithm, a single proportional–
derivative (PD) controller, are implemented using a customized analog circuit with two memristors
to control the motion of the robot. The computation cycle time of the hybrid platform is minimized
to 6 µ s, which includes the time of reading the processed analog signal (4 µ s) and the time of the
data transfer to the digital motor driver (2 µ s).
Since the Kalman filter and motion control are both implemented on the analog component,
the signal can be directly read and processed from sensors to the motion controller without
quantization error. There is no need for analog-to-digital converters (ADCs) and digital-to-analog
converters (DACs), thus substantially reducing the power, space, and cost while improving the
performance of the computing platform. Also, the separation of the Kalman filter algorithm and
the motion control algorithm from the high-level algorithms reduces the computation load of the
digital component, which increases the performance of the computing platform further. We show
that the mobile robotic system using a hybrid computing platform with higher speed-energy
77
efficiency performs better (shorter settling time, faster response, and better stability) than the same
robot with the traditional digital platform. Moreover, the idea of using a memristor crossbar array
to build an analog LP/QP solver is introduced and demonstrated numerically.
78
Chapter 11 Hybrid Analog-Digital Platform Enabled by Memristor
11.1 Architecture of Hybrid Analog-Digital Platform
A mobile inverted pendulum [94] is chosen to demonstrate our memristor-based analog-digital
hybrid platform. It is a mobile robotic system with many applications [95]. However, the high
latency and large power consumption in the conventional digital platform limit the performance
of the mobile inverted pendulum [96]. Our proposed hybrid analog-digital computing platform can
address the above challenges.
Figure 11.1a and 11.1b show our proposed hybrid analog-digital computing platform. The
digital component implements high-level algorithms (e.g., perception algorithm and decision-
making algorithm), which serve as the “cerebrum” of the robot brain. Meanwhile, memristor-based
analog components implement sensing and motion control algorithms, which act as the
“cerebellum” of the robot brain. More specifically, a continuous-time Kalman filter using a
memristor-based analog component was implemented, and it is responsible for the sensor fusion
(Figure 11.1a). The motion control function (Figure 11.1a) is realized by a proportional–derivative
controller [94] utilizing the memristor-based analog component. The home-built mobile inverted
pendulum, the memristor packaged on the chip carrier, and the optical microscope image of the
Pt/Al2O3/Ta/Pt cross-point memristor are shown in Figure 11.1c, 11.1d, and 11.1e, respectively.
79
Figure 11.1: The memristor-based hybrid analog-digital computing platform. a) Schematic
illustration of hybrid analog-digital computing platform. b) Schematic representation of the
biological inspiration from the brain structure. In the hybrid analog-digital computing platform,
the analog component acts as the cerebellum that controls the motion of the robot, while the digital
component acts as the cerebrum running the high-level algorithms. c) Image of the mobile robotic
system (i.e., the mobile inverted pendulum) in this work. d) Image of the memristors packaged on
the chip carrier. e) Optical microscope image of the fabricated Pt/Al2O3/Ta/Pt cross-point
memristor, the scale bar is 100 µ m.
11.2 Memristor for Hybrid Analog-Digital Platform
80
Pt/Al2O3/Ta/Pt memristors were used for our proposed hybrid analog-digital computing platform
[97]. The typical IV curve (Figure 10.2a) of our memristor demonstrates an excellent IV linearity,
which is ideal for analog computing. The insert of Figure 11.2a shows the four-layer structure of
the Pt/Al2O3/Ta/Pt memristor. This device can be tuned to multiple conductance states using both
DC voltage sweep (Figure 11.2b) and voltage pulses (Figure 11.2c) with different compliance
currents.
Figure 11.2: a) I-V characteristics of the Pt/Al2O3/Ta/Pt memristor (plot in linear scale) from 5 by
5 μm
2
Pt/ Al2O3/Ta/Pt cross-point memristors. This memristor has excellent I-V linearity and a
large On/Off ratio. The insert of Figure 10.2a shows the structure of the Pt/Al2O3/Ta/Pt cross-point
memristor. 20nm Pt was deposited as top and bottom electrodes. 8nm Ta and 8nm Al2O3 work as
the active layer and switching layer respectively. b) The memristor can be precisely set to different
conductance states using DC sweep voltages with different compliance currents. The I–V
characteristic for Pt/Al2O3/Ta/Pt memristor with different conductance states are shown. c) The
conductance state response under potentiating pulses (red) and depressing pulses (blue).
81
When the conductance state of the memristor is tuned, the compliance current is controlled
using the serial transistor (R6015KNX, Rohm Semiconductor®) with different voltages applied
(Figure 11.3a). Voltage pulses (Figure 11.2c) can tune the conductance state of the memristor
much faster than the DC voltage sweep (Figure 11.2b). As shown in Figure 11.2c, we design a
tuning method that uses potentiating pulses and depressing pulses to control the state of the
memristor robustly and precisely. Both potentiating pulses and depressing pulses are generated by
our customized tuning circuit. The pulse width in our customized digital tuning circuit is 10 ms.
During the potentiating process (Figure 11.3b), the pulses voltage applied on the top electrode
of the memristor ranges from 400 mV to 2200 mV with increments of 200mV. While under the
same amount of applied voltage, the gate voltage of the transistor changes from 4150 mV to 4350
mV with increments of 50 mV to gradually increase the conductance of the memristor. In this way,
a large range of tuning current can be obtained, and thus the number of states of memristor can be
maximized. After that, 100mV read voltage is applied to the memristor to measure its conductance
without disturbing it.
In each depression epoch (Figure 11.3c), the 2000mV reset voltage is used to reset the device
first. Then the device is set again using a similar protocol in the potentiating process but with the
opposite sequence. Therefore, instead of moving in one direction during the potentiating process,
the ion moves back and forth inside the switching layer in each depression epoch [98]. Therefore,
the depressing process (Figure 11.2c blue points) behaves differently from the potentiating process
(Figure 11.2c red points). However, since the conductance states of the memristor are selected
using feedback detection with high accuracy, the non-linear second half of the pulse tuning
behavior will not affect the performance of the robotic system.
82
Figure 11.3: a) Circuit schematic diagram for pulse tuning. The bottom electrode of the memristor
is connected to the drain of the transistor to build a one transistor and one resistor (1T1R) structure.
Different voltage pulses applied on the pulse tuning circuit are Vapply, Vgate, and Vreset. The voltage
on the top electrode of the memristor (Vapply) and the reset voltage (Vreset) are used to control the
set or the reset process of the memristor. And the compliance current is controlled by the gate
voltage (Vgate). Waveforms of b) potentiating pulses and c) depressing pulses. During the
potentiating process, the memristor is only programmed by set pulses (Vset). Both reset pulses
(Vreset) and set pulses (Vset) are used in the depressing process. The conductance state of the
memristor is measured without being changed via reading pulses (Vread).
83
Moreover, as introduced in Chapter 8, small device-to-device variation (Figure 8.6, 8.9a, and
8.9b) and long retention time (Figure 8.9d) are demonstrated in Pt/Al2O3/Ta/Pt memristors. These
characteristics guarantee the reliability of the device, thus the hybrid analog-digital platform. More
details about our memristors can be found in Chapters 6 to 9.
84
Chapter 12 Hardware Acceleration of Kalman Filter
12.1 Continuous-Time Analog Kalman Filter Enabled by Memristor
Precisely detecting the angle of the system is necessary for controlling a mobile inverted pendulum
successfully. In the mobile inverted pendulum (Figure 11.1c), an accelerometer and a gyroscope
are typically used to detect the angle and angular velocity signals of the mobile inverted pendulum,
respectively. The accelerometer measures the angle of the system by measuring the acceleration
along the vertical axis. However, the white noise in the sensor measured signal is inevitable, which
causes instability in the mobile inverted pendulum.
The Kalman filter [99-102] is the most commonly used method to perform signal preprocessing
and to filter the white noise. Traditionally, the analog signal is detected by the sensor and converted
to the digital signal via ADCs, and then transported to the digital processor through a
communication bus. After that, the signal is processed using a discrete-time Kalman filter on the
digital platform. All the above procedures consume a substantial amount of power and cause high
latency [103].
To solve this problem, a memristor-based analog circuit is prototyped to realize the continuous-
time Kalman filter, as shown in Figure 12.1. In the continuous-time analog Kalman filter, the
measured signal is processed physically without conversion to the digital domain, thereby
minimizing both the latency and the quantization error. Therefore, the Kalman filter can be
accelerated notably using hardware.
85
Figure 12.1: a) Block diagram of angle signal estimation with continuous-time analog Kalman
filter. The estimated angle signal (𝜃 𝑒𝑠𝑡 ( 𝑠 ) ) can be obtained after the Kalman filter with input
signals from both the gyroscope ( 𝜔 𝑒𝑠𝑡 ( 𝑠 ) ) and the accelerometer ( 𝜃 𝑚𝑒𝑎 ( 𝑠 ) ). The complex
frequency in Laplace transform is denoted S. b) Circuit schematic diagram with the device’s
parameters of the hardware implementation of the continuous-time analog Kalman filter, where
the Kalman gain (𝐾 1
) is implemented using a memristor. The 5V voltage is denoted VCC. c) Photo
of the continuous-time analog Kalman filter. c) Photo of the continuous-time analog Kalman filter.
In the continuous-time Kalman filter [99, 104], the system model and measure model of the
angle measurement can be defined as
[
𝜃 ̇ ( 𝑡 )
𝑏𝑖𝑎𝑠 ̇ ( 𝑡 )
] = [
0 −1
0 0
] [
𝜃 ( 𝑡 )
𝑏𝑖𝑎𝑠 ( 𝑡 )
] + [
1
0
] 𝜔 𝑚𝑒𝑎 ( 𝑡 )+ 𝑤 ( 𝑡 ) (12.1)
𝜃 𝑚𝑒𝑎 ( 𝑡 )= [
1 0
] [
𝜃 ( 𝑡 )
𝑏𝑖𝑎𝑠 ( 𝑡 )
] + 𝑣 ( 𝑡 ) (12.2)
where 𝜃 ( 𝑡 ) is the ideal angle of the system, 𝑏𝑖𝑎𝑠 ( 𝑡 ) is the bias error of the angular velocity,
𝜔 𝑚𝑒𝑎 ( 𝑡 ) is the measurement of the angular velocity, 𝑤 ( 𝑡 ) is the white noise of the system model,
𝜃 𝑚𝑒𝑎 ( 𝑡 ) is the measurement signal of the accelerometer, and 𝑣 ( 𝑡 ) is the white noise of the
measurement model. In addition, 𝑤 ( 𝑡 ) and 𝑣 ( 𝑡 ) are mutually uncorrelated.
Using Equation (12.1) and (12.2), the estimate update equation can be expressed as
86
[
𝜃 ̇ 𝑒𝑠𝑡 ( 𝑡 )
𝑏𝑖𝑎𝑠 ̇ 𝑒𝑠𝑡 ( 𝑡 )
] = [
0 −1
0 0
] [
𝜃 𝑒𝑠𝑡 ( 𝑡 )
𝑏𝑖𝑎𝑠 𝑒𝑠𝑡 ( 𝑡 )
] + [
1
0
] 𝜔 𝑚𝑒𝑎 ( 𝑡 )+ [
𝐾 1
𝐾 2
] [𝜃 𝑚𝑒𝑎 ( 𝑡 )− 𝜃 𝑒𝑠𝑡 ( 𝑡 ) ] (12.3)
where the vector [𝐾 1
𝐾 2
]
𝑇 is the Kalman gain [99] of the estimate update equation. Equation
(12.3) can be simplified further. Based on the readout signal of the sensor where the white noise
is negligible, it is reasonable to assume that the bias error from the gyroscope is a constant, and
thus the Kalman gain 𝐾 2
of the estimated bias is expected to be 0. In addition, the 𝑏𝑖𝑎𝑠 𝑒𝑠𝑡 ( 𝑡 ) can
be measured directly from the voltage output of the gyroscope and then the angular velocity can
be reconstructed, as shown in Equation (12.4)
𝜔 𝑒𝑠𝑡 ( 𝑡 )= 𝜔 𝑚𝑒𝑎 ( 𝑡 )− 𝑏𝑖𝑎𝑠 𝑒𝑠𝑡 ( 𝑡 ) (12.4)
After the above simplifications, Equation (12.3) can be expressed as
𝜃 ̇ 𝑒𝑠𝑡 ( 𝑡 )= 𝜔 𝑒𝑠𝑡 ( 𝑡 )+ 𝐾 1
[𝜃 𝑚𝑒𝑎 ( 𝑡 )− 𝜃 𝑒𝑠𝑡 ( 𝑡 ) ] (12.5)
It has been proved that the Kalman gain will converge to a constant after several iterations [99].
Since the Kalman gain is implemented using a memristor, the memristor only needs to be
programmed once when the environment changes dramatically. More importantly, the non-volatile
nature of the memristor ensures that the Kalman gain 𝐾 1
is still reserved even though the mobile
robotic system is shut off. The transfer function block diagram (Figure 12.1a) shows Equation
(12.5) in the frequency domain. Figure 12.1b and 12.1c show the circuit schematic diagram with
the device’s parameters and the photo of the continuous-time analog Kalman filter, respectively.
12.2 Performance of the Continuous-Time Analog Kalman Filter
87
To test and optimize the continuous-time analog Kalman filter, a robotic arm is built, which
can swing between 45° and 135° horizontally (Figure 12.2). The sensor is mounted on the robotic
arm to measure various angles.
Figure 12.2: The robotic arm for testing the continuous-time analog Kalman filter.
The black curve in Figure 12.3a shows that the raw measured angle signal is very noisy. Since
the noise can cause instability in the mobile inverted pendulum, the raw measured signal cannot
be directly used to compute the motion control signal. For comparison, the signal filtered by our
continuous-time analog Kalman filter (Figure 12.3a red curve) eliminates the noise and
reconstructs the ideal signal, which demonstrates the feasibility of our proposed analog Kalman
filter.
88
Figure 12.3: Measured raw data of the angle signal (black curve) and the filtered data (red curve)
by the continuous-time analog Kalman filter. The test was performed on a rotating robotic arm
(Figure 12.2).
Compared with the discrete-time Kalman filter implemented on the digital platform, the
continuous-time analog Kalman filter substantially accelerates the sensor fusion process and
reduces the computing load of the digital component. The details are introduced in Chapter 14.
12.3 Kalman Gain Optimization of the Analog Kalman Filter
As mentioned above, the Kalman gain is determined by the conductance of the memristor.
Therefore, the dynamic response of the Kalman filter circuit depends on the memristor
conductance state. An excessively large-conductance state can cause an overshoot in the filter
response, while a small conductance can lead to overdamping. The response of the Kalman filter
89
circuit is also affected by sensors and the environment. For example, even with the same model
(details can be found in Experimental Section) and the same Kalman gain, different gyroscopes
may cause different filter responses (Figure 12.4a). The overshoot and overdamping can also occur
when the temperature changes (Figure 12.4b).
Figure 12.4: a) Estimated angle signal with the same Kalman gain using different sensors. To be
noticed, different gyroscopes are all from the same model (model: SMAKN ENC-03RC), as shown
in the inserted photos. b) Estimated angle signal from the same analog Kalman filter under different
temperatures. All the curves above are offset to show the comparison clearly.
Therefore, to achieve the best performance of the Kalman filter, the conductance of the
memristor needs to be optimized before using it in the robot. A binary search method is adopted
in this process. In the first step, this method chooses two conductance values (a high value and a
low value) in the memristor to generate both the overshoot and overdamped responses,
respectively. Then the conductance value will be re-programmed to a new value between the two
initial values. If there is an overdamped initial response in the circuit, the search interval for the
90
subsequent conductance value can be narrowed down to the upper half of the range between the
initial values, otherwise, it can be narrowed to the lower half of this range. The performance of the
Kalman filter can be optimized within 8 iterations using this method since the total number of
states of the memristor is around 7 bits. Once the optimal conductance state (Figure 12.5 red curve)
of the memristor is chosen, there should be no overshoot (Figure 12.5 blue curve) or overdamped
(Figure 12.5 black curve) response in the filtered signal.
Figure 12.5: Estimated angle signal with different Kalman gains (different conductance states of
memristor). An overlarge conductance state causes an overshoot response (blue curve), while an
insufficient conductance state causes an overdamped response (black curve). The optimized
conductance state of the memristor (red curve) is chosen for the continuous-time analog Kalman
filter using the binary search method.
91
Chapter 13 Hardware Acceleration of PD controller
13.1 Adaptive PD Controller Enabled by Memristor
Except for filtering the measured angle signal, the controller is also important for successfully
balancing the mobile inverted pendulum. Controlling a mobile inverted pendulum is not an easy
task since the nonlinearity of the dynamical system is inevitable and difficult to analyze. Generally,
this nonlinearity of the mobile inverted pendulum mainly comes from the high latency due to the
long cycle time of the computation. Many nonlinear controllers have been proposed to mitigate
the nonlinear effect, such as neural network controllers and fuzzy logic controllers [105-107].
However, these controllers have not reduced the cycle time. The nonlinearity of the system still
exists thus limiting the upper bound of the robotic system performance. In this work, we proposed
and demonstrated an adaptive PD controller based on memristors, which notably reduces the
computation cycle time, thus fundamentally solving the nonlinearity problem.
The dynamic model of an ideal mobile inverted pendulum is very similar to the cart-pole
scenario [108]. The body of the inverted pendulum is free to rotate due to the gravitational force.
To balance the body of the inverted pendulum, the inertial force generated by the acceleration of
the inverted pendulum needs to be equal to the force because of the gravity. The linear dynamic
model can be roughly defined as
𝐿 𝑑 2
𝜃 ( 𝑡 )
𝑑 𝑡 2
= 𝑔𝜃 ( 𝑡 )− 𝑢 ( 𝑡 )+ 𝐿𝑤 ( 𝑡 ) (13.1)
where 𝑢 ( 𝑡 ) is the acceleration of the motion, 𝑤 ( 𝑡 ) is the disturbance of the environment, and
𝐿 is the length of the robot. Since the time constant of the motor is much larger than the cycle time,
the torque of the motor (i.e., acceleration of motion) can be considered as being proportional to
the voltage applied on the motor. Therefore, the function of the controller is to create the proper
92
movement of the robot to balance itself. According to previous research [94, 109], the 𝑢 ( 𝑡 ) is
defined as
𝑢 ( 𝑡 )= 𝐾 𝑝 𝜃 ( 𝑡 )+ 𝐾 𝑑 𝑑𝜃 ( 𝑡 )
𝑑𝑡
(13.2)
where 𝐾 𝑝 is the proportional term and 𝐾 𝑑 is the derivative term of the controller. By combining
Equation (13.1) and (13.2), the mobile inverted pendulum can be considered as a damped harmonic
oscillator, which can be modeled as
𝑑 2
𝜃 ( 𝑡 )
𝑑 𝑡 2
+
𝐾 𝑑 𝐿 𝑑𝜃 ( 𝑡 )
𝑑𝑡
+
𝐾 𝑝 −𝑔 𝐿 𝜃 ( 𝑡 )= 𝑤 ( 𝑡 ) (13.3)
The schematic representation and the block diagram of the mobile inverted pendulum with the
PD controller are shown in Figure 13.1a and 13.1b, respectively.
Figure 13.1: a) Schematic of the mobile inverted pendulum with the proportional–derivative (PD)
controller, which can be considered a simple damped harmonic oscillator. b) Block diagram of the
transfer function of the mobile inverted pendulum with a PD controller, where 𝜃 ( 𝑠 ) is the angle
of the mobile inverted pendulum, 𝑢 ( 𝑠 ) is the acceleration of the motion, 𝑊 ( 𝑠 ) is the disturbance
93
of the environment, 𝐿 is the length of the robot, and 𝑔 is the gravity of the earth. The complex
frequency in the Laplace transform is denoted S.
In the PD controller, the 𝐾 𝑝 and 𝐾 𝑑 can be considered as the spring constant of an elastic spring
and the damping coefficient of a damper, respectively. In this work, a single memristor is used to
implement the damping ratio 𝐾 𝑑 /𝐾 𝑝 of the controller. Figure 13.2a and 13.2b show the circuit
schematic diagram with the device’s parameters and the photo of our PD controller, respectively.
The damping ratio is determined by the conductance state of the memristor.
Figure 13.2: a) Circuit schematic diagram with the device’s parameters of the hardware
implementation of the adaptive PD controller, where the damping ratio (𝐾 𝑑 /𝐾 𝑝 ) is implemented
using a memristor. The acceleration of the motion (𝑢 ( 𝑡 ) ) is directly obtained from the analog PD
controller given the estimated angle (𝜃 𝑒𝑠𝑡 ( 𝑡 ) ) and angular velocity signals (𝜔 𝑒𝑠𝑡 ( 𝑡 ) ). The 5V
voltage is denoted VCC. b) Photo of the adaptive PD controller.
13.2 Performance of the Adaptive PD Controller
94
Figure 13.3a provides an overview of the hardware structure of the control system of the mobile
inverted pendulum. The impulse responses (Figure 13.3b) of the mobile inverted pendulum are
measured in the experiment. The result indicates that as the conductance value of the memristor
(damping ratio) increases, the oscillation of the mobile inverted pendulum decreases as expected.
Figure 13.3: a) Hardware structure of the control system of the mobile inverted pendulum. b)
Experimental data of several impulse responses of the mobile inverted pendulum at different
conductance states of the memristor. The red arrow indicates the disturbance.
13.3 Damping Ratio Optimization of the Adaptive PD Controller
The conductance state of the memristor (damping ratio) needs to be optimized for the mobile
inverted pendulum in different scenarios. In other words, the mobile inverted pendulum is expected
to work in different unknown situations, where the motion acceleration 𝑢 ( 𝑡 ) , depending on both
the interaction with the environment and the load on the robot, will be unpredictable. Therefore,
the parameters must be optimized in different cases. The random search algorithm is adopted in
the robot [110]. This is a model-free method, which can optimize the parameters of the system
95
without knowing the exact physical model of the robot. This optimization problem can be
expressed as
𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝐸 𝑒 𝑡 ,𝜔 [∑ 𝐶 𝑡 ( 𝑥 𝑡 , 𝑢 𝑡 )
𝑇 𝑡 =1
] (13.4)
𝑠 . 𝑡 . 𝑥 𝑡 +1
= 𝑓 𝑡 ( 𝑥 𝑡 , 𝑢 𝑡 , 𝑒 𝑡 ) and 𝑢 𝑡 = 𝜋 ( 𝜏 𝑡 , 𝐾 + 𝜔 )
where the cost function used to describe the system vibration can be written as
𝐶 ( 𝐾 )= ∑ ( 𝜃 𝐾 ( 𝑡 )− 𝜃 0
)
2 𝑛 𝑡 =0
(13.5)
where 𝜃 0
is 0 in the system. However, it is impossible to get all the physical parameters
accurately in reality, thus the traditional optimization method using gradient descent cannot be
applied. To know the tuning direction of parameters, the gradient 𝐺 ( 𝜔 , 𝐾 ) of the cost function
𝐶 ( 𝐾 ) is tested from the system.
𝐺 ( 𝜔 , 𝐾 )=
1
𝑚 ∑
𝐶 ( 𝐾 +𝜎 𝜔 𝑖 ) −𝐶 ( 𝐾 −𝜎 𝜔 𝑖 )
2𝜎 𝜔 𝑖 𝑚 𝑖 =1
(13.6)
The flowchart in Figure 13.4 schematically illustrates the adaptive learning process. During
each learning epoch, the control performance of the certain memristor conductance value both with
and without introducing a small perturbation (adding a 200 Ω resistor in serial) are tested. Then
the cost function can be calculated, and thus determines the direction of optimization.
96
Figure 13.4: Flowchart of the random search optimization algorithm implementation on the
memristor-based hybrid analog-digital computing platform. During each learning epoch, the
control performance of certain memristor conductance states with and without small perturbation
(adding 200 Ω resistor) are tested. Then the cost function and its gradient are calculated from the
angle signal data accordingly. After that, the weight of the memristor is updated towards
minimizing the cost function.
97
Figure 13.5 shows that the cost function converges after 15 learning epochs in both the
simulated and experimental situations, which indicates the feasibility of our optimization method.
Here, the Runge–Kutta method [111] is used to simulate the dynamic model of the mobile inverted
pendulum with nonlinearity, including both the latency and the finite acceleration effect.
Figure 13.5. Simulated (black curve) and experimental (red curve) data of the adaptive learning
process.
Figure 13.6 shows the impulse responses of the mobile inverted pendulum during the adaptive
learning process. During each learning epoch, both the control performance of each memristor
conductance value with (red curve) and without (black curve) small perturbation (adding a 200 Ω
resistor in serial) are tested. These results indicate that the cost function of the mobile robotic
system quickly converges, which is consistent with Figure 13.5.
98
Figure 13.6. Experimental data of impulse responses of the mobile inverted pendulum during the
adaptive learning process.
99
Chapter 14 Comparison Between Different Platforms
Table 14.1 shows the comparison between different platforms. Based on the up-to-date
information that we are aware of, we present a systematic study on the latency and power
consumption of the memristor-based hybrid analog-digital system, NXP MK60N512VLQ100
microcontroller-based system (the comparison system that we built) and Xlinx Zynq UltrScale+
FPGA based system (the best performance we found in the literature [112]). The performance is
benchmarked by one computing cycle of the computing platform while the robot is operating. To
make the comparison straightforward and fair, the latency and energy consumption are directly
measured from the systems. The result of the FPGA-based system is reported from previous
literature. (Details of comparison can be found in Experimental Section).
Platform
Hybrid
Analog-
digital
platform
NXP
MK60N512VLQ
with MPU6050
(using DMP)
NXP
MK60N512VLQ0
with MPU6050
(not using DMP)
Xlinx Zynq
UltrScale+
MPSoC
One
computing
cycle
Sensor
Reading
Analog
Component:
0.25 µ J
Digital
Component:
2.68 µ J
4 µ s
6793.1 µ J
9503 µ s
2145 µ J
2934 µ s
172.3 µ J
Kalman
Filter
62.8 µ J
86 µ s
PD
Controller
8.6 µ J
12 µ s
8.77 µ J
12 µ s
3.9 µ J
Data
Transfer
to PWM
1.47 µ J
2 µ s
1.43 µ J
2 µ s
1.46 µ J
2 µ s
Total
4.4 µ J
6 µ s
6803.13 µ J
9517 µ s
2218.03 µ J
3034 µ s
176.2 µ J
100 µ s
Normalization
1×
1×
1546×
1586×
504×
506×
40×
16.6×
Table 14.1: The comparison of speed and power efficiency on different platforms.
100
The memristor-based hybrid platform yields much better performance in speed and energy
efficiency compared with the traditional digital platforms. Therefore, the control performance of
the mobile inverted pendulum is substantially improved using the hybrid platform with much lower
latency. As indicated in Figure 14.1a, the settling time of the mobile inverted pendulum with our
hybrid analog-digital computing platform is about 1s. Using the traditional digital platform, the
mobile inverted pendulum is still not perfectly stabilized even after more than 3s. In addition, the
mobile inverted pendulum using our hybrid platform has a much faster response (Figure 14.1b)
than the one using a traditional digital platform. These results demonstrate that the mobile inverted
pendulum using our hybrid computing platform can achieve much better control performance.
101
Figure 14.1: a) The settling time of the mobile inverted pendulum with the hybrid platform (~ 1 s)
is much shorter than the one with the digital platform (more than 3 s). The red arrow indicates the
disturbance. b) The difference of the slope (blue dashed line) of the angle signal shows that the
mobile robotic system using the hybrid platform has a faster response than the one using the digital
platform. The red arrow indicates the disturbance.
102
Chapter 15 Memristor-based Analog Computing for Other
Applications
The nano-engineered devices can also benefit many other applications. For example, we can use
memristors to build analog circuits, which can solve linear programming (LP) and quadratic
programming (QP) problems. LP/QP problems aim to minimize or maximize an objective function
(linear or quadratic) subject to bounds, linear equality, and inequality constraints. The general form
of LP is shown in Equation (15.1a), (15.1b), and (15.1c):
min
𝑉 =[𝑉 1
,…,𝑉 𝑛 ]
𝑇 𝑐 𝑇 𝑉 (15.1a)
𝑠 . 𝑡 . 𝐴 𝑒𝑞
𝑉 = 𝑏 𝑒𝑞
(15.1b)
𝐴 𝑖 𝑛 𝑒𝑞
𝑉 ≤ 𝑏 𝑖𝑛𝑒𝑞 (15.1c)
where [𝑉 1
, … , 𝑉 𝑛 ] are the optimization variables, 𝐴 𝑖𝑛𝑒𝑞 and 𝐴 𝑒𝑞
are matrices, and 𝑐 , 𝑏 𝑒𝑞
, and
𝑏 𝑖𝑛𝑒𝑞 are column vectors. Equation (15.1a), (15.1b), and (15.1c) represent linear objective function,
linear equality constraints, and inequality constraints, respectively.
The general form of QP is shown in Equation (15.2):
min
𝑉 =[𝑉 1
,…,𝑉 𝑛 ]
𝑇 1
2
𝑉 𝑇 𝑄𝑉 + 𝑑 𝑇 𝑉 (15.2a)
𝑠 . 𝑡 . 𝐴 𝑒𝑞
𝑉 = 𝑏 𝑒𝑞
(15.2b)
𝐴 𝑖𝑛𝑒𝑞 𝑉 ≤ 𝑏 𝑖𝑛𝑒𝑞 (15.2c)
where [𝑉 1
, … , 𝑉 𝑛 ] are the optimization variables, 𝑄 , 𝐴 𝑖𝑛𝑒𝑞 , and 𝐴 𝑒𝑞
are matrices, and 𝑑 , 𝑏 𝑒𝑞
,
and 𝑏 𝑖𝑛𝑒𝑞 are column vectors. Equation (15.2a), (15.2b), and (15.2c) represent quadratic objective
function, linear equality constraints, and inequality constraints, respectively.
103
LP and QP have wide applications in legged robotics [113] and autonomous driving [114].
Previous work reported that an analog circuit-based optimization solver can solve a QP problem
with the power consumption of 4.32 mW within 50 ns [115]. The general idea is that the QP
problem can be converted to an analog circuit that uses resistors, voltage sources, and diodes. After
setting the correct parameters of devices in the circuit, the solution to the QP problem can be get
by reading the voltages on columns of the analog circuit. The schematic is shown in Figure 15.1.
Figure 15.1: Electric circuit solving a QP. Vertical wires are variable nodes with potentials
𝑉 1
, … , 𝑉 𝑛 . Black dots represent resistors that connect vertical and horizontal wires. Horizontal wires
are cost or constraint nodes. Some of the horizontal wires are connected to the ground via a
negative resistance, a constant voltage source, and a diode for inequality. The topmost horizontal
wire is the cost circuit which is connected to a constant voltage source.
A specific QP problem is chosen to demonstrate the feasibility of this idea, as shown below:
min
𝑥 =[𝑥 1
, 𝑥 2
]
𝑇 1
2
𝑥 𝑇 𝐻𝑥 + 𝑓 𝑇 𝑥
104
𝑠 . 𝑡 . 𝑥 1
+ 2𝑥 2
≤ −6
𝑤 ℎ𝑒𝑟𝑒 𝐻 = [
6 −1
−1 1
] 𝑎𝑛𝑑 𝑓 = [
0
0
]
The corresponding analog circuit to solve the above QP problem is shown in Figure 15.3.
Figure 15.2: The circuit simulation solving a QP problem using SPICE software.
The result from the analog circuit is very close (error rate around 0.67%) to the result from the
MATLAB simulation, as shown in Table 15.1.
Solver Result
Analog Circuit 𝑥 = [−0.6165, −2.6717]
MATLAB 𝑥 = [−0.6207, −2.6897]
Table 15.1: Solution to a QP problem from the analog circuit and the MATLAB simulation.
105
However, this proposed idea lacks practical meaning. This is because the analog circuit can
only solve one specific LP/QP problem if we use resistors, diodes, and voltage sources to build it.
To solve this issue, we can introduce memristors into the analog circuit. The schematic is shown
in Figure 15.3. Our proposed architecture has three advantages. First, the introduction of
memristors enables weight changing of the network. Second, the memristor is easy to be scaled up
to a high dimensional array. Third, the computation speed of this circuit will be very fast, which
is mainly limited by RC delay.
Figure 15.3: Electric circuit solving a QP with the memristor crossbar array.
Using a similar fabrication process in Chapter 7.1, two memristor crossbar arrays with different
parameters were fabricated, as shown in Figure 15.4. These memristor crossbar arrays are the most
important part of our proposed analog LP/QP solver (Figure 15.3).
106
Figure 15.4: a) 128*64 memristor crossbar array, where the linewidth is 5 𝜇 m and the gap between
two lines is 5 𝜇 m. b) 128*64 memristor crossbar array, where the linewidth is 2 𝜇 m and the gap
between two lines is 5 𝜇 m.
There are still many works that need to do in this project. As shown in Figure 15.5, the
corresponding tuning circuit, control circuit, reading circuit, and optimization circuit should be
designed and tested.
107
Figure 15.5: The circuit architecture of the memristor-based analog LP/QP solver.
Our proposed analog LP/QP solver could revolutionize the field of computation, control, and
robotics. For example, it can be used to solve a real-time model predictive problem on a robot
platform, as shown in Figure 15.6.
Figure 15.6: The control architecture of a general plant model using an analog optimization solver.
108
Summary
In this work, a mobile inverted pendulum robot with a hybrid analog-digital computing platform
using memristors is successfully demonstrated. All the circuit components are built using
conventional electronics devices except for the memristors. The reconfigurability of the
memristors enables the mobile robot to adapt to the environment through analog computing. The
memristor-based analog components are designed as a bio-inspired implementation of the
“cerebellum” in the robot brain, while the digital component implementing high-level algorithms
serves as the “cerebrum” of the robot brain. The memristor-based analog component can operate
independently without consuming the computing power from the digital component.
Through this cooperation of the “cerebrum” and the “cerebellum”, the robot can conduct
multiple tasks simultaneously with much shorter latency and lower power consumption. The
sensor fusion and the motion control algorithms are implemented on our hybrid analog-digital
computing platform. Most importantly, the hybrid platform shows more than one order of
magnitude enhancement of speed and energy efficiency over traditional digital platforms. With the
enhancement in performance, our hybrid computing platform has the potential to improve the
robustness and the performance of mobile robotic systems with higher DOFs.
The nano-engineered memristor can also be used for many other applications like the analog
LP/QP solver. In this dissertation, the memristor crossbar was fabricated and the feasibility of this
idea was demonstrated numerically. There are still some works that need to do, for example, the
design and testing of the corresponding tuning circuit, control circuit, read circuit, and optimization
circuit.
109
Conclusion and Future Work
In this dissertation, all aspects of my Ph.D. work were summarized and covered with technological
details. Devices for various applications including display and analog computing are designed,
fabricated, and optimized. The performances of these nano-engineered devices meet or even
exceed our expectations.
First, my work on switchable all-dielectric metasurfaces for full-color reflective display was
reported, including the design of the display and metasurfaces, optimizations of metasurfaces,
characterizations of metasurfaces, analysis of fabrication imperfection, and a method to enhance
the performance of metasurfaces.
Second, we reported a method that can tune the memristor characteristics precisely by
controlling the crystallinity of the switching layer material. The corresponding fabrication process,
electrical characterizations, and the working mechanism of this method were introduced in detail.
Third, using the engineered memristors, we proposed and demonstrated a hybrid analog-digital
computing platform, which can be used for mobile robotics. It was shown that the mobile robotic
system using our hybrid computing platform with higher speed-energy efficiency performs better
(shorter settling time, faster response, and better stability) than the same robot with the traditional
digital platform.
In the last chapter of my dissertation, the idea of using memristors to build an analog LP/QP
solver was reported. However, there are still some works to do before implementing this solver.
My lab mates (Buyun Chen, Zerui Liu, Sushmit Hossain) are currently working on it. We anticipate
that the memristor-based analog LP/QP solver can be implemented soon and be used for a broad
spectrum of applications in the future, such as the Internet of Things and legged robotics.
110
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International Conference on ReConFigurable Computing and FPGAs (ReConFig) 1-8
(2018).
[113] R. Grandia, F. Farshidian, R. Ranftl, and M. Hutter, "Feedback mpc for torque-controlled
legged robots," 2019 IEEE/RSJ International Conference on Intelligent Robots and
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[114] H. Wang, B. Liu, X. Ping, and Q. An, "Path tracking control for autonomous vehicles based
on an improved MPC," IEEE Access 7(161064-161073 (2019).
[115] S. Vichik, Quadratic and linear optimization with analog circuits, University of California,
Berkeley (2015).
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source FPGA for a self-balancing robot," Electronics 8(2), 198 (2019).
[117] V. Šetka, R. Čečil, and M. Schlegel, "Triple inverted pendulum system implementation
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[118] S. Seok, A. Wang, M. Y. M. Chuah, et al., "Design principles for energy-efficient legged
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[119] S. Sarathy, M. M. Hibah, S. Anusooya, and S. Kalaivani, "Implementation of efficient self
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119
Publications & Patents
1. Buyun Chen
†
, Hao Yang
†
, Boxiang Song, Deming Meng, Xiaodong Yan, Yuanrui Li,
Yunxiang Wang, Pan Hu, Tse-Hsien Ou, Mark Barnell, Qing Wu, Han Wang, Wei Wu. A
Memristor-based Hybrid Analog-digital Computing Platform for Mobile Robotics. Science
Robotics, 5.47 (2020). († equal contribution)
2. Hao Yang, He Liu, Boxiang Song, Yuanrui Li, Deming Meng, Buyun Chen, Pan Hu,
Yunxiang Wang, Tse-Hsien Ou, Michelle L Povinelli, Wei Wu. Effects of Roughness and
Resonant-mode Engineering in All-dielectric Metasurfaces. Nanophotonics, 9(6), 1401-1410
(2020).
3. Hao Yang, Buyun Chen, Boxiang Song, Deming Meng, Subodh Tiwari, Aravind
Krishnamoorthy, Xiaodong Yan, Zerui Liu, Yunxiang Wang, Pan Hu, Tse-Hsien Ou, Paulo
Branicio, Rajiv Kalia, Aiichiro Nakano, Priya Vashishta, Fanxin Liu, Han Wang, Wei Wu.
Memristive Device Characteristics Engineering by Controlling the Crystallinity of Switching
Layer Materials. ACS Applied Electronic Materials, 2(6), 1529-1537 (2020).
4. He Liu
†
, Hao Yang
†
, Yuanrui Li, Boxiang Song, Yifei Wang, Zerui Liu, Liang Peng, Haneol
Lim, Jongseung Yoon, Wei Wu. Switchable All‐dielectric Metasurfaces for Full‐color
Reflective Display. Advanced Optical Materials, 7(8), 1801639 (2019). († equal contribution)
5. Hefei Liu, Tong Wu, Xiaodong Yan, Jiangbin Wu, Nan Wang, Zhonghao Du, Hao Yang,
Buyun Chen, Zhihan Zhang, Fanxin Liu, Wei Wu, Jing Guo, Han Wang. A Tantalum Disulfide
Charge-Density-Wave Stochastic Artificial Neuron for Emulating Neural Statistical Properties.
Nano Letters, 21(8), 3465–3472 (2021).
6. Boxiang Song, Zhihao Jiang, Zerui Liu, Yunxiang Wang, Fanxin Liu, Stephen B Cronin, Hao
Yang, Deming Meng, Buyun Chen, Pan Hu, Adam M Schwartzberg, Stefano Cabrini, Stephan
Haas, Wei Wu. Probing the Mechanisms of Strong Fluorescence Enhancement in Plasmonic
Nanogaps with Sub-nanometer Precision. ACS Nano, 14(11), 14769-14778 (2020).
7. Deming Meng, Yifei Wang, Hao Yang, Buyun Chen, Pan Hu, Boxiang Song, Yunxiang Wang,
Zerui Liu, Tse-Hsien Ou, Ximing Zheng, Yichen Gong, Wei Wu. Optical Metrology of
Characterizing Wetting States. Journal of Vacuum Science & Technology B, 39(6), 064001
(2021).
8. Wei Wu, Tse-Hsien Ou, Yunxiang Wang, Hao Yang. Design of Metasurfaces for High-
Efficient IR Photodetectors. U.S. Patent, S/N: 17/333,847, pending.
9. Wei Wu, Tse-Hsien Ou, Hao Yang, Yunxiang Wang. Inverse Design of Angle Sensitive
Metasurfaces for Light Field Imaging. U.S. Patent, S/N: 17/334,196, pending.
120
Experimental Section
1. Switchable All-Dielectric Metasurfaces for Full-color Reflective Display
Numerical Calculation: In this work, all the numerical analysis was performed by finite
difference time domain method with commercial software (FDTD Solutions, Lumerical Inc.). The
numerical calculations were performed under periodic or Bloch boundary conditions. In Figure
2.5, 2.6, 2.7, 2.8, 3.4a, 4.2, 4.5, 4.7, 4.9, 5.1, 5.2, and 5.4, the input light source was set as
collimated and unpolarized, with wavelengths ranging from 400 to 800 nm. In Figures 4.3, 4.6,
5.3, and 5.5, the input light source was set as collimated and y-polarized, with the wavelength
ranging from 400 to 800 nm. The values of kxx, kyy, and kzz for each band metasurface in Figure 4.9
are determined by fitting the measured spectra with the numerically calculated spectra.
Device Fabrication: The metasurfaces were fabricated via NIL and the following series of
processes. TiO2 was first deposited onto a clean SiO2 substrate by sputtering. Then, the patterns
on the nanoimprint mold were transferred to the TiO2 surface using NIL followed by reactive ion
etching, metal deposition, and lift-off process. Finally, TiO2 and SiO2 were etched by reactive ion
etching to get the metasurface. The metasurface nanoimprint molds were also obtained from a
series of processes. First, 1D Si gratings were fabricated via interference lithography. Then, the
linewidth of the 1D gratings was tuned to desired values by angled evaporation. After that, two
steps of NIL were carried out to obtain the metasurface molds with the linewidth-tuned 1D molds.
Optical Characterization: The photos of the metasurfaces were taken with a cellphone camera,
under ordinary office lighting conditions. The reflection spectra were measured with an Ocean
121
Optics USB4000 spectrometer. The high-index liquid used to switch the metasurfaces was Ade
Advanced Optics refractive index liquid for gem refractometer.
2. Memristor Characteristics Engineering by Controlling the Crystallinity of
Switching Layer Materials
Device Fabrication: As shown in Figure 7.1a, first, a layer of 150 nm SiO2 film was grown onto
a 3-inch Si wafer ( ⟨100 ⟩) by thermal oxidation in a furnace (Thermco Products Corporation,
MB71). Next, a lift-off layer (Shipley Microposit LOL 2000, 3000 rpm spin coating for 60 s and
baking at 170 ° C for 10 min) and photoresist layer (AZ MiR 701, 3000 rpm spin coating for 40 s
and baking at 90 ° C for 1 min) was deposited onto the substrate. UV light exposure was performed
at 54.3 mJ/cm
2
with a custom-designed photomask. Afterward, post bake was performed at 110
° C for 1 min, and the substrate was immersed into the developer solution (AZ 300 MIF Developer)
for 1 min. Then, 2 nm Ti (adhesion layer) and 20 nm Pt (bottom electrode metal) were vertically
deposited onto the substrate by e-beam evaporation (Temescal BJD 1800 E-Beam Evaporator)
with a deposition rate of 0.3 Å/s. Next, a lift-off process was performed by immersing the substrate
into an acetone solution with ultrasound vibration and spraying the substrate with the acetone
solution. The substrate then was immersed into the developer solution (AZ 300 MIF Developer)
for 90 s to remove the residual lift-off layer. The patterns after the lift-off process consist of bottom
electrodes. The samples were then covered with an 8nm Al2O3 blanket layer using a plasma
enhanced ALD process (Oxford PlasmaPro 100). The ALD temperature can be set precisely to
control the crystallinity of deposited Al2O3. Finally, an 8 nm thick Ta and a 20 nm thick Pt top
122
electrode were defined using a second photolithography, evaporation, and lift-off process using
the same recipes to get the Pt/Al2O3/Ta/Pt cross point memristor.
Measurement and Characterization: The refractive index of Al2O3 deposited at different
temperature was measured by ellipsometry (Spectroscopic Ellipsometers, J.A. Woollam Co., Inc.).
The high-resolution TEM images were acquired in a transmission electron microscope (Model:
FEI Titan Themis G2 with spherical aberration and 4 detectors) operated at 200keV. The cross-
section samples were prepared with dual beam FIB (Model: FEI Helios 450S). The optical
microscope image was taken with a Nikon Eclipse LV150N microscope. DC electrical
characterizations, retention tests, pulse measurements, and multilevel conductance states
measurements were all carried out with the Keithley 4200 semiconductor characterization system.
The DC sweep rate is approximately 1 V/s. For the pulse measurements, the devices were
programmed to On or Off states and the resistance was read at 1 V, 2 𝜇𝑠 pulse between switching
events. The retention tests at 85 ° C were performed on a hot plate in the nitrogen environment.
Molecular Dynamics Simulation: An amorphous Al2O3 layer was prepared by the melt-quench
scheme,[73] i.e., by cooling the melt. Starting from a crystalline -Al2O3, the system was gradually
heated until a very well thermalized, high temperature liquid at 3,000 K was obtained. From this
liquid, the system was gradually cooled to 300 K in a total of 50 ps, and was thermalized for 700
ps.
The nanocrystalline -Al2O3 layers were generated using the Voronoi tessellation method [74-
76]. Three layers were generated with a 2, 4, and 50 nm average grain size. The 2 nm and 4 nm
123
grain size layers are three-dimensional nanostructures with grain distributed in a 40 x 40 x 8 nm
periodic cell. The 50 nm grain size layer is a two-dimensional nanostructure with columnar grains
distributed in a 200 x 200 x 4 nm cell. The centers for the tessellations are randomly distributed
points within the sample, with points closer than 0.4d removed to avoid producing grains with very
large aspect ratios. Once the grain microstructure was obtained, the atomic positions were chosen
by randomly assigning a crystallographic orientation to each grain and then placing atoms on sites
of the appropriately oriented -Al2O3 lattice. Periodic boundary conditions were applied in all
three directions. The -Al2O3 nanocrystals were annealed to eliminate low or high-density regions
near the GB and triple junctions. Annealing was also used to relax the GB structure and residual
stresses. The annealing process was done by increasing the temperature of the sample to 2000 K
for 20 ps. Samples were further relaxed at 100 K and P = 0 GPa for a further 20 ps.
Depth first search (DFS) is an algorithm to traverse the tree or graph [85]. DFS was employed
to identify all possible Ta diffusion pathways in the Al2O3 layer. Since the diffusion of Ta in
alumina can occur only through the low-density regions, a graph of the low-density region was
created to be used in the DFS search, using the following steps. After thermalization using, the
molecular dynamics system was divided into voxels of size 27Å
3
. Each voxel with no Aluminum
or Oxygen atoms is called an empty voxel and treated as a node on the graph. Further, if the nearest
voxel of each is empty, an edge between both nodes will be created. DFS was performed on the
graph to identify all the connected paths in graphs. Each path found by DFS Empty voxels will
allow the transfer of Ta in the Al2O3 layer.
124
3. A Memristor-Based Hybrid Analog-Digital Computing Platform for Mobile
Robotics
Device Characterization: Both DC electrical characterizations and multilevel conductance states
measurement were all carried out with a Keithley 4200 semiconductor characterization system.
The system can be programmed to meet the requirements of different experiments. During the
measurement, the top and bottom electrodes were directly connected to the probes. A microscope
can help correctly align the device to a certain position. The voltage sweep mode has multiple
sweeping functions with high precision measurement, which offers accurate measurement of the
electrical property of the device. In addition, the module can be programmed to measure multiple
times automatically. By controlling the compliance currents from 20 μA to 200 μA, the memristor
can be set precisely to the target state.
Robotic System Set-up: The mobile inverted pendulum was built on a custom-designed
mechanical platform. For the mobile inverted pendulum using our memristor-based hybrid analog-
digital computing platform, an accelerometer (model: NXP MMA7361) and a gyroscope (model:
SMAKN ENC-03RC) were used to detect the angle and angular velocity signals of the robot. Then
the signals were processed physically using memristor-based analog circuits (the details of the
circuits are discussed in the previous sections). The mainboard and the motor control module were
also custom designed on two printed circuit boards, respectively.
Comparison between Different Platforms:
125
Hybrid analog-digital system: Since the robotic system doesn’t need to be initialized very
frequently, the tuning circuit will not be used when the robot is operating. Therefore, only the time
and energy cost of the hybrid computing platform are considered. In the hybrid platform, the
latency is dominated by the digital process, including the time of reading the processed analog
signal (4 µ s) and the time of the data transfer to the digital motor driver (2 µ s). The power
consumption is measured experimentally. To be noticed, the memristor-based analog component
consumes 0.25 µ J in each computation cycle. The main power consumption in our system is
dominated by the digital component, which is 4.15 µ J.
Digital computing system: The digital computing platform is based on the NXP
MK60N512VLQ100 microcontroller with 100 MHz ARM Cortex-M4 core combined with DSP,
the same microcontroller that we used as the digital component in the hybrid platform. The motion
sensor is a widely used digital Six-Axis (Gyro + Accelerometer) MEMS device, the InvenSense
MPU-6050 with the digital motion processor (DMP). The angle signal can be either processed
with DMP or processed using the microcontroller. Both cases are listed in Table 14.1. Both the
computing cycle time and the energy cost are measured directly from the system.
FPGA-based system: Recently, the FPGA has been widely used in robotics applications for its
high performance. Many researchers have demonstrated the mobile inverted pendulum using an
FPGA-based platform [116-119]. Here we chose the best performance system from the literature
that we are aware of. The cycle time and power consumption of both PD controller and Kalman
filter are reported by the previous research work [112]. This system is based on the Xilinx PYNQ-
Z1 (XC7Z020-1CLG400C FPGA) with a dual-core ARM Cortex-A9 processor. The power
consumption of the PD controller and Kalman filter are 0.039W and 1.723W respectively. The
real-time system runs at the cycle time of 0.1ms.
126
Summary of the comparison: Table 14.1 summarizes the time cost and energy consumption of
the memristor-based hybrid analog-digital system, NXP MK60N512VLQ100 microcontroller-
based system, and Xlinx Zynq UltrScale+ FPGA based system. The comparison shows that the
hybrid computing platform has much better speed and power efficiency than digital systems. The
computation is performed using the hybrid platform with nearly no latency due to the nature of
analog circuits. A digital system, however, needs time to process and transfer the data after the
sensor reading. Therefore, even though the FPGA-based system can be customized to process the
signal with the shortest amount of time, it still creates more latency and power consumption than
an analog processing circuit.
Abstract (if available)
Abstract
This dissertation summarizes the three topics in my Ph.D. study. The focus is nano-engineered devices for various applications that include display and analog computing. ❧ The first part (Chapter 1 - 5) covers the switchable all-dielectric metasurfaces for full-color reflective display. Our invented full-color reflective display system based on metasurfaces has a three-layer tandem architecture and operates in an RGB additive mode. Each individual metasurface manipulates a primary color (blue, green, or red), while it displays the color in its “On” state and becomes transparent in its “Off” state. A hybrid display can be achieved by overlaying a full-color reflective display on top of a transmissive display. This technology aims to solve the drawbacks (e.g., high energy consumption and lack of readability under bright sunlight) of conventional transmissive display in mobile and wearable device applications. In addition, this work proposes and experimentally verifies a method to analyze the effect of roughness on metasurface performance, which can help design more manufacturable all-dielectric metasurfaces based on fabrication capability. Moreover, a method to enhance metasurface performance based on resonant modes engineering is proposed and numerically verified. ❧ The second part (Chapter 6 - 9) covers memristor characteristics engineering. Recently, the development of memristor has attracted great interest in the semiconductor industry. Memristors may play important roles in the future generations of electronic systems, such as bio-inspired neuromorphic computing, analog computing, and in-memory computing. However, different applications have different requirements for the characteristics of memristors, including the operation voltage, the on/off ratio, and the number of conductance states. In this work, we propose and demonstrate a method to modify the memristor characteristics specifically by controlling the crystallinity of the switching layer material. By setting the atomic layer deposition (ALD) temperature, the crystallinity of deposited Al2O3 can be controlled. Using different crystalline Al2O3 as the memristor switching layer, the characteristics of corresponding Pt/Al2O3/Ta/Pt memristors can be modified precisely. More importantly, molecular dynamics simulations were performed to qualitatively study how the switching layer crystallinity affects the characteristics of memristors. This work deepens our understanding of the working mechanism of memristors and paves the way for using memristors in a broad spectrum of applications. ❧ The third part (Chapter 10 - 15) covers a memristor-based hybrid analog-digital computing platform for mobile robotics. This work proposes and demonstrates a hybrid analog-digital computing platform enabled by memristors on a mobile inverted pendulum robot. In the hybrid computing platform, the memristor-based analog components are designed as a bio-inspired implementation of the “cerebellum” in the robot brain, while the digital component implementing high-level algorithms serves as the “cerebrum” of the robot brain. The memristor-based analog component can operate independently without consuming the computing power from the digital component. Both the Kalman filter algorithm and the control algorithm, the two main functions of the cerebellum, are implemented and accelerated using this hybrid platform. Compared with the mobile inverted pendulum using a conventional digital computing platform, the robot with our hybrid computing platform not only achieves better stability and faster response, but also yields one order of magnitude of enhancement in speed and energy efficiency. Besides, the inverted pendulum robot can tune the conductance states of memristors adaptively using a model-free optimization method to achieve optimal control performance. This part also introduces and numerically demonstrates the idea of using a memristor crossbar array to build an analog LP/QP solver.
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Asset Metadata
Creator
Yang, Hao
(author)
Core Title
Nano-engineered devices for display and analog computing
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Degree Conferral Date
2022-05
Publication Date
02/22/2022
Defense Date
12/21/2021
Publisher
University of Southern California
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Tag
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committee chair
), Cronin, Stephen Burke (
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), Nakano, Aiichiro (
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Tags
all-dielectric metasurfaces
atomic layer deposition
crystallinity
hardware acceleration
high-contrast gratings
hybrid analog-digital computing
hybrid metasurfaces
Kalmen filter
linear/quadratic programming
memristor
nanoimprint lithography
PD controller
reflective displays, roughness, resonant-mode engineering